Device awareness methods and apparatuses
By generating Gray complement pairs (GCPs) of various lengths, the interference problem between multiple devices in the integrated communication and sensing system is solved, thereby improving sensing accuracy and system performance.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HUAWEI TECH CO LTD
- Filing Date
- 2022-01-14
- Publication Date
- 2026-05-19
AI Technical Summary
In the integrated communication and sensing system of the sixth-generation mobile communication system, existing technologies are unable to effectively reduce interference between multiple sensing devices, thus affecting the accuracy of sensing.
It provides Gray complement pairs (GCPs) of various lengths, generates 40 GCPs to meet the needs of multiple devices sensing simultaneously, and reduces interference between devices through low aperiodic cross-correlation.
It improves perception accuracy, effectively reduces interference between multiple sensing devices, and enhances the system's perception performance.
Smart Images
Figure CN116489672B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of communications, and more particularly to device sensing methods and apparatus. Background Technology
[0002] Joint communication and sensing (JCS) is a key technology for sixth-generation (6G) mobile communication systems. A JCS system comprises two parts: a communication system and a sensing system. Both systems reuse the same system architecture, hardware, and spectrum resources, while simultaneously mitigating interference between them through time-division or frequency-division multiplexing.
[0003] In the JCS system, the sensing system works in the same way as radar. It senses targets by sending sensing signals and receiving the echoes reflected from the targets. It decodes information such as the target's distance by performing correlation calculations between the sent sensing signals and the echo signals.
[0004] To ensure the accuracy of the sensing results, the sensing signal needs to have good aperiodic autocorrelation characteristics. To achieve this, in practical applications, sensing signals are generally generated based on sensing sequences with good aperiodic autocorrelation properties. Therefore, it is necessary to design the sensing sequence to achieve accurate sensing. Summary of the Invention
[0005] This application provides a device sensing method and apparatus that can provide various Gray complement pairs (GCPs) of different lengths to increase the capacity of GCPs and meet the needs of simultaneous sensing by multiple devices.
[0006] Firstly, a sensing method is provided. This method can be executed by a sensing device, a component of the sensing device such as a processor, chip, or chip system, or a logic module or software capable of implementing all or part of the functions of the sensing device. The method includes: the sensing device sending a sensing signal, receiving an echo signal of the sensing signal, and processing the echo signal. The sensing signal is generated based on a GCP of length N, where N is greater than or equal to 32.
[0007] When N equals 128, the parameters used to generate the GCP can be any of the following sets:
[0008] x π =[0,1,2,3,4,5,6], c=[1,0,0,0,0,0,0], d1=0, d2=0; or
[0009] x π =[0,1,2,3,4,5,6], c=[1,0,0,0,0,0,1], d1=0, d2=0; or
[0010] x π =[0,1,2,4,3,6,5], c=[0,1,1,0,1,0,0], d1=0, d2=0; or
[0011] x π =[0,1,2,4,3,6,5], c=[0,1,1,0,1,1,0], d1=0, d2=0; or
[0012] x π =[0,1,2,4,5,3,6], c=[0,0,1,0,1,0,0], d1=0, d2=1; or
[0013] x π =[0,1,2,4,5,3,6], c=[0,0,1,0,1,0,1], d1=0, d2=1; or
[0014] x π = [0,1,2,4,5,3,6], c = [1,0,1,0,1,0,0], d1 = 0, d2 = 1; or
[0015] x π =[0,1,2,4,5,3,6], c=[1,0,1,0,1,0,1], d1=0, d2=1; or
[0016] x π = [0,1,2,3,4,5,6], c = [1,0,0,0,0,0,0], d1 = 0, d2 = 1; or
[0017] x π = [0,1,2,3,4,5,6], c = [1,0,0,0,0,0,1], d1 = 0, d2 = 1; or
[0018] x π =[0,1,2,4,3,6,5], c=[0,1,1,0,1,0,0], d1=0, d2=1; or
[0019] x π =[0,1,2,4,3,6,5], c=[0,1,1,0,1,1,0], d1=0, d2=1; or
[0020] x π =[0,1,2,4,5,3,6], c=[0,0,1,0,1,0,0], d1=0, d2=0; or
[0021] x π=[0,1,2,4,5,3,6], c=[0,0,1,0,1,0,1], d1=0, d2=0; or
[0022] x π = [0,1,2,4,5,3,6], c = [1,0,1,0,1,0,0], d1 = 0, d2 = 0; or
[0023] x π =[0,1,2,4,5,3,6], c=[1,0,1,0,1,0,1], d1=0, d2=0; or
[0024] x π = [0,1,2,3,4,5,6], c = [0,0,0,0,0,0,0], d1 = 0, d2 = 0; or
[0025] x π = [0,1,2,3,4,5,6], c = [0,0,0,0,0,0,1], d1 = 0, d2 = 0; or
[0026] x π =[0,1,2,3,4,5,6], c=[0,0,0,0,0,0,0], d1=0, d2=1; or
[0027] x π =[0,1,2,3,4,5,6], c=[0,0,0,0,0,0,1], d1=0, d2=1; or
[0028] x π =[0,1,2,3,4,6,5], c=[0,1,0,0,1,0,0], d1=0, d2=0; or
[0029] x π =[0,1,2,3,4,6,5], c=[0,1,0,0,1,1,0], d1=0, d2=0; or
[0030] x π = [0,1,2,3,4,6,5], c = [0,1,0,0,1,0,0], d1 = 0, d2 = 1; or
[0031] x π =[0,1,2,3,4,6,5], c=[0,1,0,0,1,1,0], d1=0, d2=1; or
[0032] x π =[0,1,2,3,4,6,5], c=[1,1,1,0,1,0,1], d1=0, d2=0; or
[0033] x π =[0,1,2,3,4,6,5], c=[1,1,1,0,1,1,1], d1=0, d2=0; or
[0034] x π = [0,1,2,3,4,6,5], c = [1,1,1,0,1,0,1], d1 = 0, d2 = 1; or
[0035] x π =[0,1,2,3,4,6,5], c=[1,1,1,0,1,1,1], d1=0, d2=1; or
[0036] x π =[0,1,2,4,3,5,6], c=[1,1,0,1,1,1,0], d1=0, d2=0; or
[0037] x π =[0,1,2,4,3,5,6], c=[1,1,0,1,1,1,1], d1=0, d2=0; or
[0038] x π =[0,1,2,4,3,5,6], c=[1,1,0,1,1,1,0], d1=0, d2=1; or
[0039] x π =[0,1,2,4,3,5,6], c=[1,1,0,1,1,1,1], d1=0, d2=1; or
[0040] x π =[0,1,2,4,6,3,5], c=[0,0,1,1,0,0,0], d1=0, d2=0; or
[0041] x π =[0,1,2,4,6,3,5], c=[0,0,1,1,0,1,0], d1=0, d2=0; or
[0042] x π =[0,1,2,4,6,3,5], c=[0,0,1,1,0,0,0], d1=0, d2=1; or
[0043] x π =[0,1,2,4,6,3,5], c=[0,0,1,1,0,1,0], d1=0, d2=1; or
[0044] x π= [0,1,2,4,6,3,5], c = [1,0,1,1,0,0,0], d1 = 0, d2 = 0; or
[0045] x π =[0,1,2,4,6,3,5], c=[1,0,1,1,0,1,0], d1=0, d2=0; or
[0046] x π = [0,1,2,4,6,3,5], c = [1,0,1,1,0,0,0], d1 = 0, d2 = 0; or
[0047] x π =[0,1,2,4,6,3,5], c=[1,0,1,1,0,1,0], d1=0, d2=0.
[0048] Based on this scheme, this application can provide GCPs of various lengths. At a length of 128, 40 sets of GCP generation parameters are provided to generate 40 pairs of GCPs, thus providing a large number of GCPs that can be used for simultaneous sensing by multiple sensing devices. Furthermore, the aperiodic cross-correlation between these 40 pairs of GCPs is low, effectively reducing interference between devices when multiple sensing devices are sensing simultaneously, thereby improving sensing accuracy.
[0049] In some possible designs, when N equals 64, the parameters used to generate the GCP can be any of the following sets:
[0050] x π =[0,1,2,3,4,5], c=[0,0,0,0,0,0], d1=0, d2=1; or
[0051] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,1], d1 = 0, d2 = 1; or
[0052] x π = [0,2,4,3,1,5], c = [1,0,0,0,0,0], d1 = 0, d2 = 1; or
[0053] x π = [0,2,4,3,1,5], c = [1,0,0,0,0,1], d1 = 0, d2 = 1; or
[0054] x π =[0,3,5,2,1,4], c=[0,0,1,1,0,1], d1=0, d2=0; or
[0055] x π=[0,3,5,2,1,4], c=[0,0,1,1,1,1], d1=0, d2=0; or
[0056] x π = [0,1,3,2,4,5], c = [1,0,1,1,1,0], d1 = 0, d2 = 1; or
[0057] x π = [0,1,3,2,4,5], c = [1,0,1,1,1,1], d1 = 0, d2 = 1; or
[0058] x π =[0,2,1,3,5,4], c=[0,0,1,0,0,0], d1=0, d2=1; or
[0059] x π =[0,2,1,3,5,4], c=[0,0,1,0,1,0], d1=0, d2=1; or
[0060] x π =[0,3,2,1,5,4], c=[0,0,0,1,0,0], d1=0, d2=0; or
[0061] x π =[0,3,2,1,5,4], c=[0,0,0,1,1,0], d1=0, d2=0; or
[0062] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,0], d1 = 0, d2 = 0; or
[0063] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,1], d1 = 0, d2 = 0; or
[0064] x π = [0,1,2,3,5,4], c = [1,0,0,1,0,0], d1 = 0, d2 = 0; or
[0065] x π = [0,1,2,3,5,4], c = [1,0,0,1,1,0], d1 = 0, d2 = 0; or
[0066] x π = [0,1,2,3,5,4], c = [1,1,0,1,0,1], d1 = 0, d2 = 1; or
[0067] x π= [0,1,2,3,5,4], c = [1,1,0,1,1,1], d1 = 0, d2 = 1; or
[0068] x π = [0,1,2,4,3,5], c = [0,1,0,0,1,0], d1 = 0, d2 = 0; or
[0069] x π = [0,1,2,4,3,5], c = [0,1,0,0,1,1], d1 = 0, d2 = 0; or
[0070] x π =[0,1,3,2,5,4], c=[1,1,0,1,0,0], d1=0, d2=0; or
[0071] x π =[0,1,3,2,5,4], c=[1,1,0,1,1,0], d1=0, d2=0; or
[0072] x π = [0,1,3,4,2,5], c = [0,1,0,1,0,0], d1 = 0, d2 = 1; or
[0073] x π = [0,1,3,4,2,5], c = [0,1,0,1,0,1], d1 = 0, d2 = 1; or
[0074] x π =[0,1,3,5,2,4], c=[0,1,1,0,0,0], d1=0, d2=1; or
[0075] x π =[0,1,3,5,2,4], c=[0,1,1,0,1,0], d1=0, d2=1; or
[0076] x π =[0,2,1,3,4,5], c=[0,0,1,1,0,0], d1=0, d2=0; or
[0077] x π = [0,2,1,3,4,5], c = [0,0,1,1,0,1], d1 = 0, d2 = 0; or
[0078] x π =[0,2,1,4,3,5], c=[0,1,0,0,0,0], d1=0, d2=0; or
[0079] x π=[0,2,1,4,3,5], c=[0,1,0,0,0,1], d1=0, d2=0; or
[0080] x π =[0,2,3,1,4,5], c=[0,1,1,0,1,0], d1=0, d2=1; or
[0081] x π = [0,2,3,1,4,5], c = [0,1,1,0,1,1], d1 = 0, d2 = 1; or
[0082] x π =[0,2,3,1,4,5], c=[1,1,0,0,0,0], d1=0, d2=1; or
[0083] x π = [0,2,3,1,4,5], c = [1,1,0,0,0,1], d1 = 0, d2 = 1; or
[0084] x π = [0,2,3,4,5,1], c = [1,0,0,1,1,0], d1 = 0, d2 = 0; or
[0085] x π =[0,2,3,4,5,1], c=[1,1,0,1,1,0], d1=0, d2=0; or
[0086] x π =[0,3,1,4,5,2], c=[0,1,0,1,1,0], d1=0, d2=0; or
[0087] x π =[0,3,1,4,5,2], c=[0,1,1,1,1,0], d1=0, d2=0; or
[0088] x π =[1,0,2,3,4,5], c=[0,1,0,0,0,0], d1=0, d2=1; or
[0089] x π =[1,0,2,3,4,5], c=[0,1,0,0,0,1], d1=0, d2=1.
[0090] In some possible designs, when N equals 32, the parameters used to generate the GCP can be any of the following sets:
[0091] x π = [0,1,3,2,4], c = [1,0,0,0,0], d1 = 0, d2 = 0; or
[0092] x π = [0,1,3,2,4], c = [1,0,0,0,1], d1 = 0, d2 = 0; or
[0093] x π =[0,2,1,3,4], c=[0,1,0,1,0], d1=0, d2=1; or
[0094] x π =[0,2,1,3,4], c=[0,1,0,1,1], d1=0, d2=1; or
[0095] x π =[2,1,3,0,4], c=[1,1,1,1,0], d1=0, d2=1; or
[0096] x π =[2,1,3,0,4], c=[1,1,1,1,1], d1=0, d2=1; or
[0097] x π =[0,1,3,2,4], c=[0,0,1,0,0], d1=0, d2=0; or
[0098] x π =[0,1,3,2,4], c=[0,0,1,0,1], d1=0, d2=0; or
[0099] x π =[0,1,3,2,4], c=[0,0,1,1,0], d1=0, d2=1; or
[0100] x π =[0,1,3,2,4], c=[0,0,1,1,1], d1=0, d2=1; or
[0101] x π = [0,1,3,2,4], c = [1,0,0,1,0], d1 = 0, d2 = 1; or
[0102] x π = [0,1,3,2,4], c = [1,0,0,1,1], d1 = 0, d2 = 1; or
[0103] x π =[0,2,1,3,4], c=[0,0,0,0,0], d1=0, d2=0; or
[0104] x π=[0,2,1,3,4], c=[0,0,0,0,1], d1=0, d2=0; or
[0105] x π =[1,2,0,3,4], c=[0,0,1,1,0], d1=0, d2=1; or
[0106] x π =[1,2,0,3,4], c=[0,0,1,1,1], d1=0, d2=1; or
[0107] x π =[0,3,2,1,4], c=[1,1,1,1,0], d1=0, d2=0; or
[0108] x π =[0,3,2,1,4], c=[1,1,1,1,1], d1=0, d2=0; or
[0109] x π =[1,0,2,3,4], c=[0,0,0,0,0], d1=0, d2=1; or
[0110] x π =[1,0,2,3,4], c=[0,0,0,0,1], d1=0, d2=1; or
[0111] x π =[1,3,0,2,4], c=[0,1,0,1,0], d1=0, d2=1; or
[0112] x π =[1,3,0,2,4], c=[0,1,0,1,1], d1=0, d2=1; or
[0113] x π =[1,3,0,2,4], c=[1,1,1,1,0], d1=0, d2=0; or
[0114] x π =[1,3,0,2,4], c=[1,1,1,1,1], d1=0, d2=0; or
[0115] x π =[2,0,3,1,4], c=[0,0,0,0,0], d1=0, d2=0; or
[0116] x π =[2,0,3,1,4], c=[0,0,0,0,1], d1=0, d2=0; or
[0117] xπ =[2,1,0,3,4], c=[1,1,1,1,0], d1=0, d2=0; or
[0118] x π =[2,1,0,3,4], c=[1,1,1,1,1], d1=0, d2=0; or
[0119] x π =[3,0,1,2,4], c=[0,1,0,0,0], d1=0, d2=0; or
[0120] x π =[3,0,1,2,4], c=[0,1,0,0,1], d1=0, d2=0; or
[0121] x π =[3,2,0,1,4], c=[0,0,1,0,0], d1=0, d2=0; or
[0122] x π =[3,2,0,1,4], c=[0,0,1,0,1], d1=0, d2=0.
[0123] In some possible designs, when N equals 256, the parameters used to generate the GCP can be any of the following sets:
[0124] x π = [0,1,2,3,4,5,6,7], c = [0,0,0,0,0,0,0,0], d1 = 0, d2 = 0; or
[0125] x π =[0,1,2,3,4,5,6,7], c=[0,0,0,0,0,0,0,1], d1=0, d2=0; or
[0126] x π =[0,1,2,3,5,4,7,6], c=[1,1,0,0,0,0,0,0], d1=0, d2=0; or
[0127] x π =[0,1,2,3,5,4,7,6], c=[1,1,0,0,0,0,1,0], d1=0, d2=0; or
[0128] x π =[0,1,2,3,6,4,5,7], c=[1,1,1,0,1,0,1,0], d1=0, d2=1; or
[0129] x π=[0,1,2,3,6,4,5,7], c=[1,1,1,0,1,0,1,1], d1=0, d2=1; or
[0130] x π =[0,1,2,4,6,5,3,7], c=[0,0,0,0,0,1,0,0], d1=0, d2=1; or
[0131] x π =[0,1,2,4,6,5,3,7], c=[0,0,0,0,0,1,0,1], d1=0, d2=1; or
[0132] x π =[0,1,2,3,4,5,6,7], c=[0,1,1,0,0,1,1,0], d1=0, d2=0; or
[0133] x π =[0,1,2,3,4,5,6,7], c=[0,1,1,0,0,1,1,1], d1=0, d2=0; or
[0134] x π = [0,1,2,3,4,6,5,7], c = [0,1,0,1,0,0,1,0], d1 = 0, d2 = 1; or
[0135] x π =[0,1,2,3,4,6,5,7], c=[0,1,0,1,0,0,1,1], d1=0, d2=1; or
[0136] x π = [0,1,2,3,5,4,7,6], c = [1,1,0,0,0,0,0,0], d1 = 0, d2 = 1; or
[0137] x π = [0,1,2,3,5,4,7,6], c = [1,1,0,0,0,0,1,0], d1 = 0, d2 = 1; or
[0138] x π =[0,1,2,4,6,5,3,7], c=[1,0,0,1,1,1,1,0], d1=0, d2=0; or
[0139] x π =[0,1,2,4,6,5,3,7], c=[1,0,0,1,1,1,1,1], d1=0, d2=0; or
[0140] x π= [0,1,2,3,4,5,6,7], c = [0,1,1,0,0,1,1,0], d1 = 0, d2 = 1; or
[0141] x π = [0,1,2,3,4,5,6,7], c = [0,1,1,0,0,1,1,1], d1 = 0, d2 = 1; or
[0142] x π =[0,1,2,3,4,6,5,7], c=[0,1,0,1,0,0,1,0], d1=0, d2=0; or
[0143] x π =[0,1,2,3,4,6,5,7], c=[0,1,0,1,0,0,1,1], d1=0, d2=0; or
[0144] x π =[0,1,2,3,6,4,5,7], c=[1,1,1,0,1,0,1,0], d1=0, d2=0; or
[0145] x π = [0,1,2,3,6,4,5,7], c = [1,1,1,0,1,0,1,1], d1 = 0, d2 = 0; or
[0146] x π =[0,1,2,4,6,5,3,7], c=[1,0,0,1,1,1,1,0], d1=0, d2=1; or
[0147] x π =[0,1,2,4,6,5,3,7], c=[1,0,0,1,1,1,1,1], d1=0, d2=1; or
[0148] x π =[0,1,2,3,4,6,5,7], c=[1,0,1,1,1,0,0,0], d1=0, d2=0; or
[0149] x π =[0,1,2,3,4,6,5,7], c=[1,0,1,1,1,0,0,1], d1=0, d2=0; or
[0150] x π =[0,1,2,3,4,6,5,7], c=[1,0,1,1,1,0,0,0], d1=0, d2=1; or
[0151] x π=[0,1,2,3,4,6,5,7], c=[1,0,1,1,1,0,0,1], d1=0, d2=1; or
[0152] x π =[0,1,2,3,5,4,6,7], c=[0,0,1,1,1,1,1,0], d1=0, d2=1; or
[0153] x π =[0,1,2,3,5,4,6,7], c=[0,0,1,1,1,1,1,1], d1=0, d2=1; or
[0154] x π =[0,1,2,4,6,5,3,7], c=[0,0,0,0,0,1,0,0], d1=0, d2=0; or
[0155] x π =[0,1,2,4,6,5,3,7], c=[0,0,0,0,0,1,0,1], d1=0, d2=0; or
[0156] x π = [0,1,2,3,4,5,6,7], c = [0,0,0,0,0,0,0,0], d1 = 0, d2 = 1; or
[0157] x π =[0,1,2,3,4,5,6,7], c=[0,0,0,0,0,0,0,1], d1=0, d2=1; or
[0158] x π = [0,1,2,3,4,5,6,7], c = [1,0,0,0,1,0,1,0], d1 = 0, d2 = 0; or
[0159] x π = [0,1,2,3,4,5,6,7], c = [1,0,0,0,1,0,1,1], d1 = 0, d2 = 0; or
[0160] x π = [0,1,2,3,4,5,6,7], c = [1,0,0,0,1,0,1,0], d1 = 0, d2 = 1; or
[0161] x π =[0,1,2,3,4,5,6,7], c=[1,0,0,0,1,0,1,1], d1=0, d2=1; or
[0162] x π=[0,1,2,3,5,4,6,7], c=[0,0,1,1,1,1,1,0], d1=0, d2=0; or
[0163] x π =[0,1,2,3,5,4,6,7], c=[0,0,1,1,1,1,1,1], d1=0, d2=0.
[0164] In some possible designs, when N equals 512, the parameters used to generate the GCP can be any of the following sets:
[0165] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,0,0,0,0,0,0,0], d1 = 0, d2 = 0; or
[0166] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,0,0,0,0,0,0,1], d1 = 0, d2 = 0; or
[0167] x π = [0,1,2,3,4,5,6,7,8], c = [1,0,1,0,1,0,0,1,0], d1 = 0, d2 = 1; or
[0168] x π =[0,1,2,3,4,5,6,7,8], c=[1,0,1,0,1,0,0,1,1], d1=0, d2=1; or
[0169] x π = [0,1,2,3,4,5,6,7,8], c = [1,1,0,1,0,1,0,1,0], d1 = 0, d2 = 0; or
[0170] x π =[0,1,2,3,4,5,6,7,8], c=[1,1,0,1,0,1,0,1,1], d1=0, d2=0; or
[0171] x π = [0,1,2,3,4,5,7,6,8], c = [0,0,1,1,1,0,0,1,0], d1 = 0, d2 = 1; or
[0172] x π =[0,1,2,3,4,5,7,6,8], c=[0,0,1,1,1,0,0,1,1], d1=0, d2=1; or
[0173] x π= [0,1,2,3,4,5,6,7,8], c = [0,0,1,0,0,0,1,1,0], d1 = 0, d2 = 0; or
[0174] x π =[0,1,2,3,4,5,6,7,8], c=[0,0,1,0,0,0,1,1,1], d1=0, d2=0; or
[0175] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,1,0,0,0,1,1,0], d1 = 0, d2 = 1; or
[0176] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,1,0,0,0,1,1,1], d1 = 0, d2 = 1; or
[0177] x π = [0,1,2,3,4,5,6,8,7], c = [1,1,1,1,0,0,0,0,0], d1 = 0, d2 = 0; or
[0178] x π = [0,1,2,3,4,5,6,8,7], c = [1,1,1,1,0,0,0,1,0], d1 = 0, d2 = 0; or
[0179] x π = [0,1,2,3,4,5,6,8,7], c = [1,1,1,1,0,0,0,1,0], d1 = 0, d2 = 1; or
[0180] x π = [0,1,2,3,4,5,6,8,7], c = [1,1,1,1,0,0,0,1,0], d1 = 0, d2 = 1; or
[0181] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,0,0,0,0,0,0,0], d1 = 0, d2 = 1; or
[0182] x π = [0,1,2,3,4,5,6,7,8], c = [0,0,0,0,0,0,0,0,1], d1 = 0, d2 = 1; or
[0183] x π = [0,1,2,3,4,5,6,7,8], c = [1,0,1,0,1,0,0,1,0], d1 = 0, d2 = 0; or
[0184] x π = [0,1,2,3,4,5,6,7,8], c = [1,0,1,0,1,0,0,1,1], d1 = 0, d2 = 0; or
[0185] x π = [0,1,2,3,4,5,6,7,8], c = [1,1,0,1,0,1,0,1,0], d1 = 0, d2 = 1; or
[0186] x π = [0,1,2,3,4,5,6,7,8], c = [1,1,0,1,0,1,0,1,1], d1 = 0, d2 = 1; or
[0187] x π =[0,1,2,3,4,5,7,6,8], c=[0,0,1,1,1,0,0,1,0], d1=0, d2=0; or
[0188] x π = [0,1,2,3,4,5,7,6,8], c = [0,0,1,1,1,0,0,1,1], d1 = 0, d2 = 0; or
[0189] x π = [0,1,2,3,4,5,6,7,8], c = [0,1,0,0,0,1,1,0,0], d1 = 0, d2 = 0; or
[0190] x π =[0,1,2,3,4,5,6,7,8], c=[0,1,0,0,0,1,1,0,1], d1=0, d2=0; or
[0191] x π = [0,1,2,3,4,5,6,7,8], c = [0,1,0,0,0,1,1,0,0], d1 = 0, d2 = 1; or
[0192] x π =[0,1,2,3,4,5,6,7,8], c=[0,1,0,0,0,1,1,0,1], d1=0, d2=1; or
[0193] x π = [0,1,2,3,4,5,7,6,8], c = [1,0,0,1,1,1,0,0,0], d1 = 0, d2 = 0; or
[0194] x π=[0,1,2,3,4,5,7,6,8], c=[1,0,0,1,1,1,0,0,1], d1=0, d2=0; or
[0195] x π =[0,1,2,3,4,5,7,6,8], c=[1,0,0,1,1,1,0,0,0], d1=0, d2=1; or
[0196] x π =[0,1,2,3,4,5,7,6,8], c=[1,0,0,1,1,1,0,0,1], d1=0, d2=1; or
[0197] x π = [0,1,2,3,4,5,6,7,8], c = [1,0,0,0,1,0,1,0,0], d1 = 0, d2 = 0; or
[0198] x π = [0,1,2,3,4,5,6,7,8], c = [1,0,0,0,1,0,1,0,1], d1 = 0, d2 = 0; or
[0199] x π =[0,1,2,3,4,5,6,7,8], c=[1,0,0,0,1,0,1,0,0], d1=0, d2=1; or
[0200] x π =[0,1,2,3,4,5,6,7,8], c=[1,0,0,0,1,0,1,0,1], d1=0, d2=1; or
[0201] x π =[0,1,2,3,4,5,7,8,6], c=[0,1,1,0,0,1,0,1,0], d1=0, d2=0; or
[0202] x π =[0,1,2,3,4,5,7,8,6], c=[0,1,1,0,0,1,1,1,0], d1=0, d2=0; or
[0203] x π =[0,1,2,3,4,5,7,8,6], c=[0,1,1,0,0,1,0,1,0], d1=0, d2=1; or
[0204] x π =[0,1,2,3,4,5,7,8,6], c=[0,1,1,0,0,1,1,1,0], d1=0, d2=1.
[0205] In some possible designs, when N equals 1024, the parameters used to generate the GCP can be any of the following sets:
[0206] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,0,0,0,0,0,0,0], d1=0, d2=0; or
[0207] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,0,0,0,0,0,0,1], d1=0, d2=0; or
[0208] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,1,1,0,0,1,0,0], d1=0, d2=0; or
[0209] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,1,1,0,0,1,0,1], d1=0, d2=0; or
[0210] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,1,0,1,0,0,1,0], d1=0, d2=1; or
[0211] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,1,0,1,0,0,1,1], d1=0, d2=1; or
[0212] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,0,1,0,1,0,0,0], d1=0, d2=0; or
[0213] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,0,1,0,1,0,0,1], d1=0, d2=0; or
[0214] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,0,0,0,0,0,0,0], d1=0, d2=1; or
[0215] x π= [0,1,2,3,4,5,6,7,8,9], c = [0,0,0,0,0,0,0,0,0,1], d1 = 0, d2 = 1; or
[0216] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,1,1,0,0,1,0,0], d1=0, d2=1; or
[0217] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,1,1,0,0,1,0,1], d1=0, d2=1; or
[0218] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,1,0,1,0,0,1,0], d1=0, d2=0; or
[0219] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,1,0,1,0,0,1,1], d1=0, d2=0; or
[0220] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,0,1,0,1,0,0,0], d1=0, d2=1; or
[0221] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,0,1,0,1,0,0,1], d1=0, d2=1; or
[0222] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,1,0,0,0,1,0,1,0], d1=0, d2=0; or
[0223] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,1,0,0,0,1,0,1,1], d1=0, d2=0; or
[0224] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,1,0,0,0,1,0,1,0], d1=0, d2=1; or
[0225] x π= [0,1,2,3,4,5,6,7,8,9], c = [0,0,1,0,0,0,1,0,1,1], d1 = 0, d2 = 1; or
[0226] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,1,0,0,0,0,1,0], d1=0, d2=0; or
[0227] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,1,0,0,0,0,1,1], d1=0, d2=0; or
[0228] x π = [0,1,2,3,4,5,6,7,8,9], c = [1,0,0,1,0,0,0,0,1,0], d1 = 0, d2 = 1; or
[0229] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,0,1,0,0,0,0,1,1], d1=0, d2=1; or
[0230] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,1,0,0,0,1,1,0], d1=0, d2=0; or
[0231] x π = [0,1,2,3,4,5,6,7,8,9], c = [0,0,0,1,0,0,0,1,1,1], d1 = 0, d2 = 0; or
[0232] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,1,0,0,0,1,1,0], d1=0, d2=1; or
[0233] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,0,0,1,0,0,0,1,1,1], d1=0, d2=1; or
[0234] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,0,0,1,1,0,0,0], d1=0, d2=0; or
[0235] x π= [0,1,2,3,4,5,6,7,8,9], c = [0,1,0,0,0,1,1,0,0,1], d1 = 0, d2 = 0; or
[0236] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,0,0,1,1,0,0,0], d1=0, d2=1; or
[0237] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,0,0,0,1,1,0,0,1], d1=0, d2=1; or
[0238] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,0,0,1,1,1,0,0], d1=0, d2=0; or
[0239] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,0,0,1,1,1,0,1], d1=0, d2=0; or
[0240] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,0,0,1,1,1,0,0], d1=0, d2=1; or
[0241] x π =[0,1,2,3,4,5,6,7,8,9], c=[0,1,1,0,0,1,1,1,0,1], d1=0, d2=1; or
[0242] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,1,0,0,1,0,0,0,0], d1=0, d2=0; or
[0243] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,1,0,0,1,0,0,0,1], d1=0, d2=0; or
[0244] x π =[0,1,2,3,4,5,6,7,8,9], c=[1,0,1,0,0,1,0,0,0,0], d1=0, d2=1; or
[0245] x π=[0,1,2,3,4,5,6,7,8,9], c=[1,0,1,0,0,1,0,0,0,1], d1=0, d2=1.
[0246] In some possible designs, the aforementioned GCP is generated through a generalized Boolean function mapping.
[0247] In some possible designs, one of the sequences in the aforementioned GCP is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2 m =N.
[0248] In some possible designs, N equals 160, 320, 640, or 832. The GCP is the direct product of the first and second GCPs, with the length of the first GCP being N1 and the length of the second GCP being N2, where N1 × N2 = N. One sequence in the first GCP is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2 l =N1; the second GCP is any one of the following:
[0249] x1=1,1,-1,1,-1,1,-1,-1,1,1;
[0250] y1=1,1,-1,1,1,1,1,1,-1,-1;
[0251] or,
[0252] x2=1,1,1,1,1,-1,1,-1,-1,1;
[0253] y2=1,1,-1,-1,1,1,1,-1,1,-1;
[0254] or,
[0255] x3=1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1;
[0256] y3=1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,1,-1,1,1,-1;
[0257] or,
[0258] x4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1;
[0259] y4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1.
[0260] In some possible designs, when N equals 160, the parameters used to generate the GCP are any of the following sets:
[0261] x π = [0,2,1,3], c = [0,0,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0262] x π = [0,2,1,3], c = [0,0,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0263] x π =[2,1,0,3], c=[0,0,0,0], d1=0, d2=0, second GCP=(x2,y2); or
[0264] x π =[2,1,0,3], c=[0,0,0,1], d1=0, d2=0, second GCP=(x2,y2); or
[0265] x π = [0,1,2], c = [0,0,0], d1 = 0, d2 = 1, second GCP = (x3, y3); or
[0266] x π = [0,1,2], c = [0,0,1], d1 = 0, d2 = 1, second GCP = (x3, y3); or
[0267] x π = [0,1,2,3], c = [0,1,0,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0268] x π = [0,1,2,3], c = [0,1,0,1], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0269] x π= [0,1,2,3], c = [0,1,1,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0270] x π = [0,1,2,3], c = [0,1,1,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0271] x π = [0,2,1,3], c = [0,0,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0272] x π = [0,2,1,3], c = [0,0,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0273] x π =[1,0,2,3], c=[1,1,0,0], d1=0, d2=1, second GCP=(x1,y1); or
[0274] x π = [1,0,2,3], c = [1,1,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0275] x π = [1,0,2,3], c = [1,1,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0276] x π = [1,0,2,3], c = [1,1,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0277] x π = [1,2,0,3], c = [1,1,0,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0278] x π =[1,2,0,3], c=[1,1,0,1], d1=0, d2=0, second GCP=(x2,y2); or
[0279] x π = [1,2,0,3], c = [1,1,1,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0280] x π=[1,2,0,3], c=[1,1,1,1], d1=0, d2=0, second GCP=(x1,y1).
[0281] In some possible designs, when N equals 320, the parameters used to generate the GCP are any of the following sets:
[0282] x π = [0,1,2,3,4], c = [0,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0283] x π = [0,1,2,3,4], c = [0,0,0,0,1], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0284] x π = [0,1,2,3,4], c = [0,0,0,1,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0285] x π = [0,1,2,3,4], c = [0,0,0,1,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0286] x π = [0,1,2,3,4], c = [0,0,1,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0287] x π = [0,1,2,3,4], c = [0,0,1,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0288] x π = [0,1,2,3,4], c = [0,0,1,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0289] x π = [0,1,2,3,4], c = [0,0,1,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0290] x π = [0,1,3,2,4], c = [1,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0291] x π= [0,1,3,2,4], c = [1,0,0,0,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0292] x π = [0,1,3,2,4], c = [1,0,0,1,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0293] x π = [0,1,3,2,4], c = [1,0,0,1,1], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0294] x π = [0,1,3,4,2], c = [1,1,0,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0295] x π = [0,1,3,4,2], c = [1,1,1,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0296] x π = [0,1,3,4,2], c = [1,1,0,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0297] x π = [0,1,3,4,2], c = [1,1,1,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0298] x π = [0,2,4,3,1], c = [0,0,0,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0299] x π = [0,2,4,3,1], c = [0,1,0,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0300] x π = [0,2,4,3,1], c = [0,0,0,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0301] x π = [0,2,4,3,1], c = [0,1,0,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2).
[0302] In some possible designs, when N equals 640, the parameters used to generate the GCP are any of the following sets:
[0303] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0304] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,1], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0305] x π = [0,1,2,4,3,5], c = [1,0,0,0,0,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0306] x π = [0,1,2,4,3,5], c = [1,0,0,0,0,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0307] x π = [0,1,3,4,2,5], c = [1,0,1,1,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0308] x π = [0,1,3,4,2,5], c = [1,0,1,1,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0309] x π = [0,2,4,3,1,5], c = [0,0,0,1,1,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0310] x π = [0,2,4,3,1,5], c = [0,0,0,1,1,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0311] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,0], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0312] x π = [0,1,2,3,4,5], c = [0,0,0,0,0,1], d1 = 0, d2 = 1, second GCP = (x1, y1); or
[0313] x π = [0,1,2,3,4,5], c = [0,0,0,0,1,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0314] x π = [0,1,2,3,4,5], c = [0,0,0,0,1,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0315] x π = [0,1,2,3,4,5], c = [0,0,0,0,1,0], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0316] x π = [0,1,2,3,4,5], c = [0,0,0,0,1,1], d1 = 0, d2 = 1, second GCP = (x2, y2); or
[0317] x π = [0,1,2,4,3,5], c = [1,0,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0318] x π = [0,1,2,4,3,5], c = [1,0,0,0,0,1], d1 = 0, d2 = 0, second GCP = (x2, y2); or
[0319] x π = [0,1,2,4,3,5], c = [1,0,0,0,1,0], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0320] x π = [0,1,2,4,3,5], c = [1,0,0,0,1,1], d1 = 0, d2 = 0, second GCP = (x1, y1); or
[0321] x π = [0,1,2,3,4], c = [0,0,0,0,0], d1 = 0, d2 = 1, second GCP = (x3, y3); or
[0322] x π = [0,1,2,3,4], c = [0,0,0,0,1], d1 = 0, d2 = 1, second GCP = (x3, y3).
[0323] In some possible designs, when N equals 832, the parameters used to generate the GCP can be any of the following sets:
[0324] x π = [0,1,2,3,4], c = [0,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0325] x π = [0,1,2,3,4], c = [0,0,0,0,1], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0326] x π = [0,3,1,2,4], c = [1,0,1,0,0], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0327] x π = [0,3,1,2,4], c = [1,0,1,0,1], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0328] x π = [0,1,3,2,4], c = [1,0,0,1,0], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0329] x π = [0,1,3,2,4], c = [1,0,0,1,1], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0330] x π =[2,0,1,4,3], c=[0,1,0,0,0], d1=0, d2=0, second GCP=(x4,y4); or
[0331] x π =[2,0,1,4,3], c=[0,1,0,1,0], d1=0, d2=0, second GCP=(x4,y4); or
[0332] x π = [1,0,3,2,4], c = [0,0,0,0,0], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0333] x π =[1,0,3,2,4], c=[0,0,0,0,1], d1=0, d2=0, second GCP=(x4,y4); or
[0334] x π=[2,0,1,3,4], c=[0,1,0,1,0], d1=0, d2=1, second GCP=(x4,y4); or
[0335] x π =[2,0,1,3,4], c=[0,1,0,1,1], d1=0, d2=1, second GCP=(x4,y4); or
[0336] x π = [0,1,2,3,4], c = [0,0,1,0,0], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0337] x π = [0,1,2,3,4], c = [0,0,1,0,1], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0338] x π = [0,1,3,2,4], c = [1,0,0,0,0], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0339] x π = [0,1,3,2,4], c = [1,0,0,0,1], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0340] x π =[1,0,2,3,4], c=[0,1,1,0,0], d1=0, d2=0, second GCP=(x4,y4); or
[0341] x π = [1,0,2,3,4], c = [0,1,1,0,1], d1 = 0, d2 = 0, second GCP = (x4, y4); or
[0342] x π = [1,3,2,0,4], c = [0,0,1,1,0], d1 = 0, d2 = 1, second GCP = (x4, y4); or
[0343] x π = [1,3,2,0,4], c = [0,0,1,1,1], d1 = 0, d2 = 1, second GCP = (x4, y4).
[0344] Based on the various possible designs described above, this application provides GCPs of multiple lengths, with a large number of GCPs for each length, enabling simultaneous sensing by a large number of sensing devices. Furthermore, the aperiodic cross-correlation between multiple pairs of GCPs of each length is low, effectively reducing interference between devices when multiple sensing devices are sensing simultaneously, thereby improving sensing accuracy.
[0345] Secondly, a sensing method is provided. This method can be executed by a sensing device, a component of the sensing device such as a processor, chip, or chip system, or a logic module or software capable of implementing all or part of the functions of the sensing device. The method includes: the sensing device sending a sensing signal, receiving an echo signal of the sensing signal, and processing the echo signal based on the sensing signal. The sensing signal is generated based on a Gray complement pair (GCP) of length N, where N is greater than or equal to 32. When N equals 128, the GCP is any one of the following pairs:
[0346] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1, 1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1, -1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0347] y=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1, 1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1 ,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1;
[0348] or,
[0349] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1 ,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1 ,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0350] y=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,- 1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,- 1,1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0351] or,
[0352] x=1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1, 1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1 ,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1;
[0353] y=1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1, -1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1 ,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1,1;
[0354] or,
[0355] x=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1 ,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1 ,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1;
[0356] y=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1, -1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,- 1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1;
[0357] or,
[0358] x=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1, 1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1 ,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0359] y=-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1, -1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1 ,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0360] or,
[0361] x=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1 ,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1 ,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1;
[0362] y=-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1 ,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,- 1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0363] or,
[0364] x=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,- 1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1 ,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1;
[0365] y=-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,- 1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1, -1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0366] or,
[0367] x=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1, -1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1 ,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1;
[0368] y=-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1, -1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1 ,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,1;
[0369] or,
[0370] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1, 1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1, -1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0371] y=-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1 ,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1 ,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1;
[0372] or,
[0373] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1 ,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1 ,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0374] y=-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1, 1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,- 1,-1,-1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0375] or,
[0376] x=1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1, 1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1 ,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1;
[0377] y=-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1 ,-1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1 ,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,-1,1,-1,-1;
[0378] or,
[0379] x=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1 ,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1 ,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1;
[0380] y=-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1, 1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,1,1 ,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,1;
[0381] or,
[0382] x=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1, 1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1 ,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0383] y=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,- 1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1 ,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1;
[0384] or,
[0385] x=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1 ,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1 ,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1;
[0386] y=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1, -1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1 ,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1;
[0387] or,
[0388] x=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,- 1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1 ,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1;
[0389] y=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1, 1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1 ,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0390] or,
[0391] x=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1, -1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1 ,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1;
[0392] y=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1 ,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1 ,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,-1;
[0393] or,
[0394] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1, 1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1 ,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1;
[0395] y=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1, 1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,-1, -1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0396] or,
[0397] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,- 1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,- 1,1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0398] y=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1 ,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1 ,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0399] or,
[0400] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1, 1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1 ,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1;
[0401] y=-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1 ,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1, -1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1;
[0402] or,
[0403] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,- 1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,- 1,1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0404] y=-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1, -1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1 ,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,1,1,-1,-1,-1,-1,-1;
[0405] or,
[0406] x=1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,- 1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,- 1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0407] y=1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1, -1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1 ,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0408] or,
[0409] x=1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1, -1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1 ,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0410] y=1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1 ,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1, -1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0411] or,
[0412] x=1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,- 1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,- 1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0413] y=-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,1,-1, 1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,1,1 ,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,1,1,1,1,1;
[0414] or,
[0415] x=1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1, -1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1 ,1,1,-1,1,-1,1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0416] y=-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1, -1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,- 1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0417] or,
[0418] x=1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1 ,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1, 1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0419] y=1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1, -1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1 ,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0420] or,
[0421] x=1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,- 1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1 ,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1;
[0422] y=1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1, 1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,- 1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0423] or,
[0424] x=1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1 ,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1, 1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0425] y=-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,- 1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1 ,-1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0426] or,
[0427] x=1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,- 1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1 ,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1;
[0428] y=-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,- 1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1, 1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1;
[0429] or,
[0430] x=1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1 ,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1 ,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0431] y=1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,- 1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1 ,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0432] or,
[0433] x=1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,- 1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1 ,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1;
[0434] y=1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1, 1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1 ,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,1,1,1,-1,1,1,1,-1,1,-1,1,-1,-1;
[0435] or,
[0436] x=1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1 ,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1 ,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0437] y=-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1, 1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1, -1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1;
[0438] or,
[0439] x=1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,- 1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1 ,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1;
[0440] y=-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1, 1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1 ,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,1;
[0441] or,
[0442] x=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1, 1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1 ,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0443] y=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1, 1,1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1 ,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,1,-1,-1,-1;
[0444] or,
[0445] x=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1 ,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1 ,1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1;
[0446] y=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1, -1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1 ,1,1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1;
[0447] or,
[0448] x=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1, 1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1 ,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0449] y=-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1, -1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,1 ,1,1,1,1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0450] or,
[0451] x=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1 ,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1 ,1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1;
[0452] y=-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,-1 ,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1 ,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0453] or,
[0454] x=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1, 1,1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1 ,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,1,-1,-1,-1;
[0455] y=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1, 1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1 ,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0456] or,
[0457] x=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1, -1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1 ,1,1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1;
[0458] y=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1 ,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1 ,1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1;
[0459] or,
[0460] x=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1, 1,1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1 ,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,-1,1,-1,-1,-1;
[0461] y=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1, 1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1 ,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1;
[0462] or,
[0463] x=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1, -1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1 ,1,1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1;
[0464] y=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1 ,-1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1 ,1,1,-1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,1,-1,-1,1,1,1,1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1.
[0465] Based on this scheme, this application can provide GCPs of various lengths. With a length of 128, 40 pairs of GCPs are provided, enabling a large number of GCPs to be used for simultaneous sensing by multiple sensing devices. Furthermore, the aperiodic cross-correlation among these 40 pairs of GCPs is low, effectively reducing interference between devices when multiple sensing devices are sensing simultaneously, thereby improving sensing accuracy.
[0466] In some possible designs, when N equals 64, GCP is any of the following pairs:
[0467] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1 ,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1;
[0468] y=-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1, -1,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1;
[0469] or,
[0470] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1, -1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1;
[0471] y=-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1 ,1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1;
[0472] or,
[0473] x=1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,1,-1,1,-1,1,- 1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,1;
[0474] y=-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,1, -1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,1;
[0475] or,
[0476] x=1,-1,1,-1,1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,- 1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1;
[0477] y=-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,1,1,1,1,1,- 1,1,-1,1,-1,1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1;
[0478] or,
[0479] x=1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1, -1,1,-1,1,-1,1,1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1;
[0480] y=1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1,1,1, -1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,1,-1;
[0481] or,
[0482] x=1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,-1 ,1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,1,1,1,-1,1,-1;
[0483] y=1,-1,-1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1,-1,1,1,1,1,-1,1,-1,1,- 1,1,1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1;
[0484] or,
[0485] x=1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1, -1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1;
[0486] y=-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1 ,1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1;
[0487] or,
[0488] x=1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1 ,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1;
[0489] y=-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,- 1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1;
[0490] or,
[0491] x=1,1,1,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,-1, -1,1,1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1;
[0492] y=-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1 ,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1;
[0493] or,
[0494] x=1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,1 ,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1;
[0495] y=-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1, -1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1;
[0496] or,
[0497] x=1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1, -1,1,1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1;
[0498] y=1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,- 1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1;
[0499] or,
[0500] x=1,1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,1 ,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1;
[0501] y=1,1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,- 1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1;
[0502] or,
[0503] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1 ,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1;
[0504] y=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,- 1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1;
[0505] or,
[0506] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1, -1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1;
[0507] y=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,- 1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1;
[0508] or,
[0509] x=1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,- 1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1;
[0510] y=1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1, -1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,1,-1,1,1;
[0511] or,
[0512] x=1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,- 1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1;
[0513] y=1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1 ,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1;
[0514] or,
[0515] x=1,-1,1,1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1,- 1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1;
[0516] y=-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1 ,1,-1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,1,1,1,-1;
[0517] or,
[0518] x=1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1 ,1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1;
[0519] y=-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,1, -1,-1,1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,-1,1;
[0520] or,
[0521] x=1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,1 ,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1;
[0522] y=1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,- 1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1;
[0523] or,
[0524] x=1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1, -1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1;
[0525] y=1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,- 1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1;
[0526] or,
[0527] x=1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1,- 1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1;
[0528] y=1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1 ,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,1,1,1,-1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1;
[0529] or,
[0530] x=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1, -1,-1,-1,1,-1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1;
[0531] y=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,1,-1,-1, -1,1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,-1,1,1,1;
[0532] or,
[0533] x=1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1 ,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1;
[0534] y=-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1, -1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1;
[0535] or,
[0536] x=1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1, -1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1;
[0537] y=-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,1 ,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1;
[0538] or,
[0539] x=1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,-1,1 ,1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1;
[0540] y=-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1, -1,1,1,1,1,1,-1,1,-1,-1,1,1,-1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,-1,1,1,-1,1,1,-1,-1;
[0541] or,
[0542] x=1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,1,-1,-1,-1,-1, -1,1,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1;
[0543] y=-1,-1,1,1,-1,1,1,-1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,1 ,1,-1,-1,1,-1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1;
[0544] or,
[0545] x=1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1 ,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1;
[0546] y=1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,1,- 1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1;
[0547] or,
[0548] x=1,-1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1, -1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1;
[0549] y=1,-1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,- 1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1;
[0550] or,
[0551] x=1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,1 ,1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,1;
[0552] y=1,1,1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,1,-1,- 1,-1,-1,-1,-1,1,1,-1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,-1,1,-1;
[0553] or,
[0554] x=1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1,1,1 ,-1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1;
[0555] y=1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,1 ,1,-1,1,-1,1,-1,-1,1,1,1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,1,1,1;
[0556] or,
[0557] x=1,1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1 ,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0558] y=-1,-1,1,-1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1 ,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0559] or,
[0560] x=1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,1,1 ,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1;
[0561] y=-1,1,1,1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1 ,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1;
[0562] or,
[0563] x=1,1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,- 1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1;
[0564] y=-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,- 1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1;
[0565] or,
[0566] x=1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,- 1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0567] y=-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1, -1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1;
[0568] or,
[0569] x=1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1 ,1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1;
[0570] y=1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1 ,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1;
[0571] or,
[0572] x=1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,- 1,-1,1,-1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1;
[0573] y=1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,1 ,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1;
[0574] or,
[0575] x=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,-1,1,-1, -1,1,1,-1,1,1,1,-1,1,1,-1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,1,-1,1,1;
[0576] y=1,1,-1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,-1,-1,-1,1,-1, -1,-1,-1,1,-1,-1,-1,1,-1,-1,1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,1,-1,1,1,-1,1,-1,-1;
[0577] or,
[0578] x=1,1,-1,1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,1 ,1,1,1,-1,1,1,1,-1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,1,1,1,1,-1,1,-1,1,1,-1,1,-1,-1;
[0579] y=1,1,-1,1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,-1,1,1,-1,1,1,1,-1,1,1,- 1,-1,1,-1,-1,-1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,-1,1,1;
[0580] or,
[0581] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1 ,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1;
[0582] y=-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1 ,1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1;
[0583] or,
[0584] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,1 ,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1;
[0585] y=-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1, -1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1.
[0586] In some possible designs, when N equals 32, GCP can be any of the following pairs:
[0587] x=1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1,-1;
[0588] y=1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1;
[0589] or,
[0590] x=1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,1
[0591] y=1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1;
[0592] or,
[0593] x=1,1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0594] y=-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0595] or,
[0596] x=1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1;
[0597] y=-1,1,1,1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1;
[0598] or,
[0599] x=1,1,-1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,-1,1,-1,1,1,-1,1,-1,1,-1,-1,1,1,-1,-1,1;
[0600] y=-1,-1,1,1,-1,-1,1,1,1,1,1,1,-1,-1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,1,-1,-1,1;
[0601] or,
[0602] x=1,-1,-1,1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,-1,-1,-1,1,1,1,1,1,1,-1,-1,1,1,-1,-1;
[0603] y=-1,1,1,-1,-1,1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,1,1,1,1,1,1,-1,-1,1,1,1,1,-1,-1;
[0604] or,
[0605] x=1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,-1,-1,1,1,1,-1,1,-1;
[0606] y=1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,1;
[0607] or,
[0608] x=1,-1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,1,1,-1,1,1,1,1;
[0609] y=1,-1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,-1,-1,-1;
[0610] or,
[0611] x=1,1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1;
[0612] y=-1,-1,1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1;
[0613] or,
[0614] x=1,-1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1;
[0615] y=-1,1,1,-1,1,1,1,1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1;
[0616] or,
[0617] x=1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1;
[0618] y=-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1;
[0619] or,
[0620] x=1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1;
[0621] y=-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1;
[0622] or,
[0623] x=1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1;
[0624] y=1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1;
[0625] or,
[0626] x=1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,1,-1,1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1;
[0627] y=1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,1;
[0628] or,
[0629] x=1,1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,1,1,-1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1;
[0630] y=-1,-1,1,-1,1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1;
[0631] or,
[0632] x=1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,1,1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1;
[0633] y=-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1;
[0634] or,
[0635] x=1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,1;
[0636] y=1,1,-1,-1,-1,-1,-1,-1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,-1,-1,1,1,-1,1,-1,1,-1,1,1,-1;
[0637] or,
[0638] x=1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,1,-1,-1,1,1,1,1,1,1,1,-1,-1;
[0639] y=1,-1,-1,1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,-1,-1,-1,-1,-1,-1,1,1;
[0640] or,
[0641] x=1,1,1,-1,1,1,-1,1,1,1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,-1,1;
[0642] y=-1,-1,-1,1,-1,-1,1,-1,1,1,1,-1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1,-1,-1,-1,1,1,1,-1,1;
[0643] or,
[0644] x=1,-1,1,1,1,-1,-1,-1,1,-1,1,1,1,-1,-1,-1,1,-1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,-1,-1;
[0645] y=-1,1,-1,-1,-1,1,1,1,1,-1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,1,-1,-1,1,-1,-1,-1;
[0646] or,
[0647] x=1,1,-1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,-1,-1,1,1,1,-1,-1,1;
[0648] y=-1,-1,1,1,-1,1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,1,1,1,-1,-1,1;
[0649] or,
[0650] x=1,-1,-1,1,1,1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,1,-1,1,1,-1,-1;
[0651] y=-1,1,1,-1,-1,-1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,1,1,1,1,-1,1,1,-1,1,1,-1,-1;
[0652] or,
[0653] x=1,1,-1,-1,-1,1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,1,1,-1,-1,1,-1,-1,1;
[0654] y=1,1,-1,-1,-1,1,1,-1,1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,1,1,-1,1,1,-1;
[0655] or,
[0656] x=1,-1,-1,1,-1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,1,-1,-1,-1,-1,1,-1,-1,1,1,1,-1,-1;
[0657] y=1,-1,-1,1,-1,-1,1,1,1,-1,1,-1,-1,-1,-1,-1,-1,1,-1,1,-1,-1,-1,-1,-1,1,1,-1,-1,-1,1,1;
[0658] or,
[0659] x=1,1,1,1,1,1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,1,-1,-1,1,-1,1;
[0660] y=1,1,1,1,-1,-1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,1,-1;
[0661] or,
[0662] x=1,-1,1,-1,1,-1,1,-1,1,1,-1,-1,1,1,-1,-1,1,-1,-1,1,-1,1,1,-1,1,1,1,1,-1,-1,-1,-1;
[0663] y=1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,1,1,-1,-1,1,1,1,1,1,1,1,1,1;
[0664] or,
[0665] x=1,1,-1,1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1;
[0666] y=1,1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,1,1,1,-1;
[0667] or,
[0668] x=1,-1,-1,-1,-1,1,1,1,-1,1,1,1,-1,1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,-1,1,-1,-1;
[0669] y=1,-1,-1,-1,1,-1,-1,-1,-1,1,1,1,1,-1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,-1,1,-1,-1,1,-1,1,1;
[0670] or,
[0671] x=1,1,1,1,1,-1,1,-1,-1,-1,-1,-1,1,-1,1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,-1,1,1,-1;
[0672] y=1,1,-1,-1,1,-1,-1,1,-1,-1,1,1,1,-1,-1,1,1,1,1,1,1,-1,1,-1,1,1,1,1,-1,1,-1,1;
[0673] or,
[0674] x=1,-1,1,-1,1,1,1,1,-1,1,-1,1,1,1,1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-1,1,-1,-1,1,1;
[0675] y=1,-1,-1,1,1,1,-1,-1,-1,1,1,-1,1,1,-1,-1,1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,-1,-1,-1;
[0676] or,
[0677] x=1,1,1,1,-1,-1,1,1,1,-1,1,-1,-1,1,1,-1,1,1,1,1,1,1,-1,-1,-1,1,-1,1,-1,1,1,-1;
[0678] y=1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,-1,1,-1,1,1,1,-1,-1,1,1,1,1,-1,1,1,-1,-1,1,-1,1;
[0679] or,
[0680] x=1,-1,1,-1,-1,1,1,-1,1,1,1,1,-1,-1,1,1,1,-1,1,-1,1,-1,-1,1,-1,-1,-1,-1,-1,-1,1,1;
[0681] y=1,-1,-1,1,-1,1,-1,1,1,1,-1,-1,-1,-1,-1,-1,1,-1,-1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1,-1.
[0682] Based on the various possible designs described above, this application provides GCPs of multiple lengths, with a large number of GCPs for each length, enabling simultaneous sensing by a large number of sensing devices. Furthermore, the aperiodic cross-correlation between multiple pairs of GCPs of each length is low, effectively reducing interference between devices when multiple sensing devices are sensing simultaneously, thereby improving sensing accuracy.
[0683] In conjunction with the first or second aspect, in some possible designs, the characteristic is that the sensing signal is a single-carrier signal or a multi-carrier signal. Based on this possible design, the sensing signal being a single-carrier signal or a multi-carrier signal can be adapted to various communication scenarios, enabling the solution of this application to be widely used.
[0684] In combination with the first or second aspect, in some possible designs, when the sensing signal is a multi-carrier signal, the difference between the length N of the GCP and the target value is less than a threshold. The target value is determined by the subcarrier spacing, sensing bandwidth, and resource element RE mapping method.
[0685] Combining the first or second aspect, in some possible designs, the RE mapping method is to map one element of the GCP for every M REs; the target value, subcarrier spacing, sensing bandwidth, and M satisfy the following formula:
[0686]
[0687] Where SCS is the subcarrier spacing and W is the sensing bandwidth. This indicates rounding down to the nearest integer.
[0688] Based on this possible design, the length of the GCP can be adapted to the sensing bandwidth, thereby increasing the actual bandwidth occupied by the GCP. In sensing and ranging scenarios, since the ranging resolution is proportional to the bandwidth occupied by the GCP, the ranging resolution can be improved.
[0689] In conjunction with the first or second aspect, some possible designs involve processing based on the echo signal, including: sensing the distance to a target object based on the echo signal. The target object is the object whose echo signal is generated by reflecting the sensing signal.
[0690] In conjunction with the first or second aspect, in some possible designs, the distance to the target object is sensed based on the echo signal, including: performing an aperiodic autocorrelation operation on the GCP used to generate the sensing signal and the GCP corresponding to the echo signal, determining the signal propagation delay between the sensing device and the target object based on the result of the aperiodic autocorrelation operation, and then determining the distance to the target object based on the signal propagation delay.
[0691] Thirdly, a communication device is provided for implementing the various methods described above. This communication device can be a sensing device as described in the first or second aspect, or a device included in the sensing device, such as a chip. The communication device includes modules, units, or means corresponding to the methods described above, which can be implemented in hardware, software, or by hardware executing corresponding software. The hardware or software includes one or more modules or units corresponding to the functions described above.
[0692] In some possible designs, the communication device may include a transceiver module and a processing module. The transceiver module, also referred to as a transceiver unit, is used to implement the transmission and / or reception functions in any of the above aspects and their possible implementations. The transceiver module may consist of transceiver circuits, transceivers, transceivers, or communication interfaces. The processing module can be used to implement the processing functions in any of the above aspects and their possible implementations.
[0693] In some possible designs, the transceiver module includes a sending module and a receiving module, which are used to implement the sending and receiving functions in any of the above aspects and any possible implementation methods.
[0694] Fourthly, a communication device is provided, comprising: a processor and a memory; the memory is used to store computer instructions, which, when executed by the processor, cause the communication device to perform the method described in any of the preceding aspects. The communication device may be a sensing device as described in the first or second aspect, or a device included in the sensing device, such as a chip.
[0695] Fifthly, a communication device is provided, comprising: a processor and a communication interface; the communication interface being used to communicate with a module outside the communication device; the processor being used to execute computer programs or instructions to cause the communication device to perform the method described in any of the preceding aspects. The communication device may be a sensing device as described in the first or second aspect, or a device included in the aforementioned sensing device, such as a chip.
[0696] A sixth aspect provides a communication device, comprising: an interface circuit and a processor, wherein the interface circuit is a code / data read / write interface circuit, the interface circuit being used to receive computer execution instructions (the computer execution instructions are stored in memory, and may be read directly from memory, or may be transmitted through other devices) and transmit them to the processor; the processor is used to execute the computer execution instructions to cause the communication device to perform the method described in any of the preceding aspects. The communication device may be a sensing device as described in the first or second aspect, or a device included in the aforementioned sensing device, such as a chip.
[0697] A seventh aspect provides a communication device, comprising: at least one processor; the processor being configured to execute a computer program or instructions to cause the communication device to perform the method described in any of the preceding aspects. The communication device may be a sensing device as described in the first or second aspect, or a device included in the sensing device, such as a chip.
[0698] In some possible designs, the communication device includes a memory for storing necessary program instructions and data. This memory may be coupled to the processor, or it may be independent of the processor.
[0699] In some possible designs, the communication device can be a chip or a chip system. When the device is a chip system, it can be composed of chips or may include chips and other discrete components.
[0700] Eighthly, a computer-readable storage medium is provided that stores instructions which, when executed on a communication device, cause the communication device to perform the method described in any of the preceding aspects.
[0701] Ninthly, a computer program product containing instructions is provided, which, when run on a communication device, enables the communication device to perform the method described in any of the preceding aspects.
[0702] It is understood that when the communication device provided by any of the third to ninth aspects is a chip, the aforementioned sending action / function can be understood as output information, and the aforementioned receiving action / function can be understood as input information.
[0703] The technical effects of any of the design methods in aspects three through nine can be found in the technical effects of different design methods in aspects one or two above, and will not be repeated here. Attached Figure Description
[0704] Figure 1 A schematic diagram illustrating a communication scenario provided in an embodiment of this application;
[0705] Figure 2 A schematic diagram illustrating another communication scenario provided in an embodiment of this application;
[0706] Figure 3a This application provides a schematic diagram of a perception system in a smart home scenario.
[0707] Figure 3b This application provides a schematic diagram of perception in a vehicle-to-everything (V2X) scenario.
[0708] Figure 4 This is a schematic diagram of the structure of a communication device provided in an embodiment of this application;
[0709] Figure 5 A flowchart illustrating a sensing method provided in an embodiment of this application;
[0710] Figure 6 A waveform diagram of a single carrier provided for an embodiment of this application;
[0711] Figure 7 A schematic diagram illustrating the generation process of a multi-carrier waveform provided in an embodiment of this application;
[0712] Figure 8 A schematic diagram illustrating resource allocation as provided in an embodiment of this application;
[0713] Figure 9 A flowchart illustrating another sensing method provided in an embodiment of this application;
[0714] Figure 10 This is a schematic diagram of the structure of a sensing device provided in an embodiment of this application. Detailed Implementation
[0715] In the description of this application, unless otherwise stated, " / " indicates that the objects before and after are in an "or" relationship. For example, A / B can mean A or B. "And / or" in this application is merely a description of the relationship between the related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. A and B can be singular or plural.
[0716] In the description of this application, unless otherwise stated, "multiple" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of single or multiple items. For example, at least one of a, b, or c can mean: a, b, c, a and b, a and c, b and c, or a and b and c, where a, b, and c can be single or multiple.
[0717] Furthermore, to facilitate a clear description of the technical solutions in the embodiments of this application, the terms "first" and "second" are used in the embodiments of this application to distinguish identical or similar items with substantially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and the terms "first" and "second" are not necessarily different.
[0718] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner to facilitate understanding.
[0719] It is understood that the term "embodiment" used throughout the specification means that a specific feature, structure, or characteristic related to an embodiment is included in at least one embodiment of this application. Therefore, various embodiments throughout the specification do not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. It is understood that in the various embodiments of this application, the sequence number of each process does not imply the order of execution; the execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.
[0720] It is understood that some optional features in the embodiments of this application can be implemented independently in certain scenarios without relying on other features, such as the current solution on which they are based, to solve the corresponding technical problems and achieve the corresponding effects. Alternatively, they can be combined with other features as needed in certain scenarios. Accordingly, the apparatus given in the embodiments of this application can also implement these features or functions, which will not be elaborated here.
[0721] In this application, unless otherwise specified, the same or similar parts between the various embodiments can be referred to each other. In the various embodiments of this application, unless otherwise specified or logically conflicting, the terminology and / or descriptions between different embodiments are consistent and can be mutually referenced. Technical features in different embodiments are combined according to their inherent logical relationships to form new embodiments. The following descriptions of the embodiments of this application do not constitute a limitation on the scope of protection of this application.
[0722] To facilitate understanding of the technical solutions of the embodiments of this application, the relevant technologies of this application are first briefly described by way of example as follows.
[0723] 1) Correlation operation: Correlation operation refers to multiplying corresponding elements of two sequences and then adding them together. For example, the correlation operation between sequences a = [a1, a2, a3] and b = [b1, b2, b3] is: a1 × b1 + a2 × b2 + a3 × b3.
[0724] 2) Autocorrelation: If two sequences are identical, then the correlation operation between them is called autocorrelation.
[0725] 3) Cross-correlation: If two sequences are different, then the correlation operation between them is called cross-correlation.
[0726] 4) Aperiodic autocorrelation: When calculating the autocorrelation of sequences, the correlation value of overlapping elements in two sequences is calculated through the relative displacement between the sequences. If the sequence length is L, then the relative displacement between the sequences may have 2L-1 possible cases: -L+1, -L+2, ..., -1, 0, 1, ..., L-2, L-1. Therefore, the aperiodic autocorrelation calculation has a total of 2L-1 possible results.
[0727] For example, for the sequence [1,2,3], when the relative displacement between sequences is -2, the following situation applies:
[0728] 1, 2, 3
[0729] 1, 2, 3
[0730] At this point, the aperiodic autocorrelation result is 1×3=3.
[0731] When the relative displacement between sequences is -1, the following situation applies:
[0732] 1, 2, 3
[0733] 1, 2, 3
[0734] At this point, the aperiodic autocorrelation result is 1×2+2×3=8. Similarly, when the relative shifts between sequences are -2, -1, 0, 1, 2, the aperiodic autocorrelation results are 3, 8, 14, 8, 3 respectively.
[0735] 5) Aperiodic cross-correlation: When calculating the cross-correlation of sequences, the correlation value of overlapping elements in two sequences is calculated by the relative shift between the sequences.
[0736] 6) Perfect aperiodic autocorrelation: If the aperiodic autocorrelation result of a sequence is zero at every shift except 0, then the sequence has perfect aperiodic autocorrelation. If the values at shifts other than 0 are not zero, but are very small compared to the peak value at 0, then the sequence has good aperiodic autocorrelation.
[0737] 7) Perfect aperiodic cross-correlation: If the aperiodic cross-correlation result of two sequences is 0 at all shifts, then the two sequences have perfect aperiodic cross-correlation, or they are said to be orthogonal to each other. If the aperiodic cross-correlation result of two sequences remains small at all shifts, then the two sequences have good aperiodic cross-correlation.
[0738] 8) Golay complementary pair (GCP):
[0739] GCP, also known as Gray complement sequence or GCP sequence, is defined as follows: A pair of sequences x and y of code length N are considered a GCP if the sum of their aperiodic autocorrelation function (AACF) is zero everywhere except at the zero shift. Specifically, for the sequence x = [x[0], x[1], ..., x[N-1]], its AACF is defined as:
[0740]
[0741] For example, for sequences x = [1,1,1,-1] and t = [1,1,-1,1], since the AACF of sequence x is C x [k] = [-1, 0, 1, 4, 1, 0, -1], k = -3, -2, ..., 3, and the AACF of sequence y is C. y [k] = [1,0,-1,4,-1,0,1], k = -3,-2,..,3, since C x [k]+C y [k] = [0,0,0,8,0,0,0], therefore sequences x and y are a pair of GCPs.
[0742] Furthermore, for two pairs of GCP sequences (x1, y1) and (x2, y2), their aperiodic cross-correlation function (ACCF) is defined as:
[0743]
[0744] if If the values are all zero at all displacements, then (x1,y1) and (x2,y2) are called orthogonal GCP sequences.
[0745] GCPs can be used as sensing sequences in sensing systems. However, since current fifth-generation (5G) mobile communication systems do not yet have sensing capabilities, current new radio (NR) standards have not specified or used GCPs. The Wi-Fi 802.11ad / ay standard specifies three pairs of binary GCPs with lengths of 32, 64, and 128, as shown in Tables 1, 2, and 3 below.
[0746] Table 1
[0747]
[0748] Table 2
[0749]
[0750] Table 3
[0751]
[0752] However, since Wi-Fi and 5G or 6G are different communication systems, and the GCPs specified in the 802.11ad / ay standard are limited in length and cannot flexibly adapt to the multi-carrier waveforms of 5G or 6G, they are difficult to apply directly. Therefore, this application provides a sensing method for providing multiple GCPs of various lengths to increase GCP capacity and meet the needs of simultaneous sensing by multiple devices.
[0753] The technical solutions of this application embodiment can be used in various communication systems, including 3GPP communication systems such as 5G or 6G mobile communication systems, vehicle-to-everything (V2X) systems, device-to-device (D2D) communication systems, machine-to-machine (M2M) communication systems, Internet of Things (IoT) systems, and other next-generation communication systems. The communication system can also be a non-3GPP communication system, such as Wi-Fi or other wireless local area network (WLAN) systems; there is no limitation.
[0754] The technical solutions of this application embodiment can be applied to various communication scenarios, such as one or more of the following communication scenarios: smart home, D2D, V2X, and IoT communication scenarios.
[0755] The communication systems and scenarios applicable to this application mentioned above are merely illustrative examples, and are not limited to these examples. This will be explained uniformly here and will not be repeated below.
[0756] See Figure 1 This application provides a communication scenario. In this scenario, a sensing device sends a sensing signal. After the sensing signal is reflected by a target object, the sensing device can receive the echo signal of the sensing signal, thereby enabling the sensing device to sense the target object. Figure 1 The scenario described is merely an example and is not actually limited to the interaction between a sensing device and a target object. Optionally, a sensing device can interact with multiple target objects, or multiple sensing devices can interact with the same target object.
[0757] See Figure 2 This is another communication scenario provided by the embodiments of this application. In this scenario, multiple sensing devices each send sensing signals. After each sensing signal is reflected by the same or different target objects, the sensing devices can receive the echo signals of the sensing signals, thereby enabling multiple sensing devices to sense the target objects independently.
[0758] Optionally, the sensing device in this application can be a terminal device or a network device. A terminal device can be a device with wireless transceiver capabilities. A network device is a device that connects a terminal device to a wireless network.
[0759] The network equipment can be a next-generation node B (gNodeB or gNB) in a 5G or 6G system; or a transmission reception point (TRP); or a base station in a future public land mobile network (PLMN). This application does not specifically limit the specific type of equipment.
[0760] Terminal equipment can also be referred to as user equipment (UE), terminal, access terminal, user unit, user station, mobile station (MS), remote station, remote terminal, mobile terminal (MT), user terminal, wireless communication equipment, user agent, or user device, etc. Terminal equipment can be, for example, a wireless terminal in IoT, V2X, D2D, M2M, 5G network, 6G network, or a future PLMN. Terminal equipment can be deployed on land, including indoors or outdoors, handheld or vehicle-mounted; it can also be deployed on water (such as on ships); and it can also be deployed in the air (such as on airplanes, balloons, and satellites).
[0761] For example, terminal devices can be drones, IoT devices (e.g., sensors, electricity meters, water meters, etc.), V2X devices, stations (STs) in wireless local area networks (WLANs), cellular phones, cordless phones, session initiation protocol (SIP) phones, wireless local loop (WLL) stations, personal digital assistant (PDA) devices, handheld devices with wireless communication capabilities, computing devices or other processing devices connected to a wireless modem, in-vehicle devices, wearable devices (also known as wearable smart devices), tablets or computers with wireless transceiver capabilities, virtual reality (VR) terminals, terminals in industrial control, terminals in self-driving, terminals in remote medical care, terminals in smart grids, terminals in transportation safety, and terminals in smart cities. Terminals in cities, terminals in smart homes, vehicle terminals, vehicles with vehicle-to-vehicle (V2V) communication capabilities, intelligent connected vehicles, drones with drone-to-drone (UAV-to-UAV (U2U)) communication capabilities, etc.
[0762] For example, in a smart home scenario, such as Figure 3a As shown, sensing devices can be various smart appliances in the home, such as smart TVs and smart speakers. When it is necessary to track a person's trajectory, each terminal in the home can send sensing signals to detect the person, thereby enhancing the accuracy of trajectory tracking. Alternatively, in a V2X scenario, such as... Figure 3b As shown, the sensing device can be an in-vehicle terminal, which can send sensing signals and receive the echo signals of the sensing signals reflected by the target object to sense the surrounding road conditions, etc.
[0763] The related functions of the sensing device involved in this application can be implemented by one device, or by multiple devices, or by one or more functional modules within one device, or by one or more chips, or by a system on a chip (SOC) or chip system. A chip system can be composed of chips or include chips and other discrete devices. The embodiments of this application do not specifically limit this.
[0764] It is understood that the above functions can be network elements in hardware devices, software functions running on dedicated hardware, a combination of hardware and software, or virtualization functions instantiated on a platform (e.g., a cloud platform).
[0765] For example, the relevant functions of the sensing device involved in this application can be achieved through... Figure 4 This is achieved through the communication device 400. Figure 4 The diagram shown is a structural schematic of a communication device 400 provided in an embodiment of this application. The communication device 400 includes one or more processors 401 and at least one communication interface. Figure 4 (This is merely an example illustration of a communication interface 404 and a processor 401. Optionally, it may also include a communication line 402 and a memory 403.)
[0766] The processor 401 may be a general-purpose central processing unit (CPU), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits used to control the execution of the program of the present application.
[0767] In a specific implementation, as one example, processor 401 may include one or more CPUs, for example... Figure 4 CPU0 and CPU1 in the CPU.
[0768] In a specific implementation, as one embodiment, the communication device 400 may include multiple processors. Each of these processors may be a single-core processor or a multi-core processor. The processors here may include, but are not limited to, at least one of the following: a central processing unit (CPU), a microprocessor, a digital signal processor (DSP), a microcontroller unit (MCU), or an artificial intelligence processor, and other computing devices that run software. Each computing device may include one or more cores for executing software instructions to perform calculations or processing.
[0769] Communication line 402 can be used for communication between different components included in communication device 400.
[0770] The communication interface 404 can be a transceiver module used to communicate with other devices or communication networks, such as Ethernet, wireless access networks (RAN), and wireless local area networks (WLAN). For example, the transceiver module can be a transceiver or similar device. Optionally, the communication interface 404 can also be a transceiver circuit located within the processor 401, used to implement the processor's signal input and signal output.
[0771] Memory 403 can be a device with storage function. For example, it can be read-only memory (ROM) or other types of static storage devices capable of storing static information and instructions; random access memory (RAM) or other types of dynamic storage devices capable of storing information and instructions; electrically erasable programmable read-only memory (EEPROM); compact disc read-only memory (CD-ROM) or other optical disc storage; optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.); magnetic disk storage media or other magnetic storage devices; or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to these. Memory can exist independently and be connected to the processor via communication line 402. Memory can also be integrated with the processor.
[0772] The memory 403 stores computer execution instructions for implementing the scheme of this application, and its execution is controlled by the processor 401. The processor 401 executes the computer execution instructions stored in the memory 403 to implement the method provided in the embodiments of this application.
[0773] Alternatively, in this embodiment, the processor 401 may execute the processing-related functions of the method provided in the following embodiments of this application, and the communication interface 404 may be responsible for communicating with other devices or communication networks. This embodiment does not specifically limit this.
[0774] Optionally, the computer execution instructions in the embodiments of this application may also be referred to as application code, and the embodiments of this application do not specifically limit this.
[0775] In a specific implementation, as one embodiment, the communication device 400 may further include an output device 405 and an input device 406. The output device 405 communicates with the processor 401 and can display information in various ways. For example, the output device 405 may be a liquid crystal display (LCD), a light-emitting diode (LED) display device, a cathode ray tube (CRT) display device, or a projector, etc. The input device 406 communicates with the processor 401 and can receive user input in various ways. For example, the input device 406 may be a mouse, keyboard, touchscreen device, or sensing device, etc.
[0776] It should be noted that, Figure 4 The structural composition shown does not constitute a limitation on the communication device, except... Figure 4 In addition to the components shown, the communication device may include more or fewer components than illustrated, or combine certain components, or have different component arrangements. The illustrated components may be implemented in hardware, software, or a combination of software and hardware.
[0777] The method provided in the embodiments of this application will now be described in detail with reference to the accompanying drawings. In the embodiments of this application, the executing entity may perform some or all of the steps in the embodiments of this application. These steps or operations are merely examples, and the embodiments of this application may also perform other operations or variations thereof. Furthermore, the steps may be performed in different orders as presented in the embodiments of this application, and it is not necessary to perform all the operations in the embodiments of this application.
[0778] In this application, the sensing signal is generated by a GCP of length N. For ease of understanding, the GCP provided in this application will be introduced first before introducing the sensing method provided in this application.
[0779] Specifically, this application defines 32 pairs of binary GCPs with a length of 32, 40 pairs of binary GCPs with a length of 64, 40 pairs of binary GCPs with a length of 128, 40 pairs of binary GCPs with a length of 256, 40 pairs of binary GCPs with a length of 512, 40 pairs of binary GCPs with a length of 1024, 20 pairs of binary GCPs with a length of 160, 20 pairs of binary GCPs with a length of 320, 20 pairs of binary GCPs with a length of 640, and 20 pairs of binary GCPs with a length of 832.
[0780] In this application, both sequences in each pair of GCPs possess perfect aperiodic autocorrelation. Furthermore, for each pair of GCPs, there exists another pair of GCPs of the same length that are orthogonal to it.
[0781] In other words, the length N of the GCP defined in this application can be equal to 32, 64, 128, 256, 512, 1024, 160, 320, 640, or 832. The GCPs of each length are described below.
[0782] In some embodiments, when N equals 32, the 32 pairs of binary GCPs defined in this application are shown in Table 4 below.
[0783] Table 4
[0784]
[0785]
[0786]
[0787]
[0788] It should be noted that the GCP serial numbers in Table 4 are merely exemplary representations. In actual implementations, GCP serial numbers can also be represented in other ways, such as starting from 0. Furthermore, the order of the GCPs shown in Table 4 is also only an exemplary representation. The 32 pairs of GCPs can also be arranged in other orders, which this application does not specifically limit.
[0789] Optionally, the 32 pairs of GCPs shown in Table 4 can be divided into 16 groups, each group consisting of two adjacent pairs of GCPs. That is, the first group includes GCPs numbered 1 and 2, the second group includes GCPs numbered 3 and 4, ..., the fifteenth group includes GCPs numbered 29 and 30, and the sixteenth group includes GCPs numbered 31 and 32. The two pairs of GCPs in each group are orthogonal to each other.
[0790] Optionally, the 32 pairs of GCPs shown in Table 4 have lower aperiodic cross-correlation peak values, or in other words, better aperiodic cross-correlation properties. Furthermore, the six pairs of GCPs numbered 1-6 have even lower aperiodic cross-correlation peak values and can be preferentially used when the number of devices requiring simultaneous sensing is less than or equal to six. These six pairs of GCPs numbered 1-6 can be referred to as preferred GCPs.
[0791] In some embodiments, when N equals 64, the 40 pairs of binary GCPs defined in this application are shown in Table 5 below.
[0792] Table 5
[0793]
[0794]
[0795]
[0796]
[0797]
[0798]
[0799] It should be noted that the GCP serial numbers and the order of GCPs in Table 5 are only illustrative representations. Please refer to the relevant explanations in Table 4, which will not be repeated here.
[0800] Optionally, the 40 pairs of GCPs shown in Table 5 can be divided into 20 groups, each group consisting of two adjacent pairs of GCPs. That is, the first group includes GCPs numbered 1 and 2, the second group includes GCPs numbered 3 and 4, ..., the nineteenth group includes GCPs numbered 37 and 38, and the twentieth group includes GCPs numbered 39 and 40. The two pairs of GCPs in each group are orthogonal to each other.
[0801] Optionally, the 40 pairs of GCPs shown in Table 5 exhibit low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Further, the six pairs of GCPs numbered 1-6 exhibit even lower aperiodic cross-correlation peak values. Additionally, the six pairs of GCPs numbered 7-12 also exhibit lower aperiodic cross-correlation peak values. When the number of devices requiring simultaneous sensing is less than or equal to six, the six pairs of GCPs numbered 1-6 or the six pairs of GCPs numbered 7-12 can be preferentially used. The six pairs of GCPs numbered 1-6 or the six pairs of GCPs numbered 7-12 can be referred to as preferred GCPs.
[0802] In some embodiments, when N equals 128, the 40 pairs of binary GCPs defined in this application are shown in Table 6 below.
[0803] Table 6
[0804]
[0805]
[0806]
[0807]
[0808]
[0809]
[0810]
[0811]
[0812]
[0813]
[0814]
[0815] It should be noted that the GCP serial numbers and the order of GCPs in Table 6 are merely illustrative representations. Please refer to the relevant explanations in Table 4, which will not be repeated here.
[0816] Optionally, the 40 pairs of GCPs shown in Table 6 can be divided into 20 groups, each group consisting of two adjacent pairs of GCPs. That is, the first group includes GCPs numbered 1 and 2, the second group includes GCPs numbered 3 and 4, ..., the nineteenth group includes GCPs numbered 37 and 38, and the twentieth group includes GCPs numbered 39 and 40. The two pairs of GCPs in each group are orthogonal to each other.
[0817] Optionally, the 40 pairs of GCPs shown in Table 6 exhibit low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Further, the 8 pairs of GCPs numbered 1-8 exhibit even lower aperiodic cross-correlation peak values. Additionally, the 8 pairs of GCPs numbered 9-16 also exhibit lower aperiodic cross-correlation peak values. When the number of devices requiring simultaneous sensing is less than or equal to 8, the 8 pairs of GCPs numbered 1-8 or 8 pairs of GCPs numbered 9-16 can be preferentially used. The 8 pairs of GCPs numbered 1-8 or 8 pairs of GCPs numbered 9-16 can be referred to as preferred GCPs.
[0818] The above describes the GCPs of lengths 32, 64, and 128 as defined in this application. The generation methods and parameters for each length of GCP are described below.
[0819] When N equals 32, 64, 128, 256, 512, or 1024, the GCP is generated through a generalized Boolean function mapping. That is, a sequence in the GCP is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2 m =N.
[0820] Where, x π This represents a permutation of the indices [0, 1, ..., m-1] of x. For example, if x π=[0,1,2] means that the subscripts of x are arranged as 0, 1, 2, and correspondingly, the elements in x are arranged as x[0], x[1], x[2]. At this time, x π [0] maps to x[0], x π [1] Map x[1], x π [2] Map x[2]. Or, if x π =[1,0,2], indicating that the subscripts of x are arranged as 1, 0, 2, and correspondingly, the elements in x are arranged as x[1], x[0], x[2]. At this time, x π [0]Map x[1], x π [1] Map x[0], x π [2]Map x[2].
[0821] Where c = [c[0], c[1], ..., c[m-1]], c[k] ∈ {0, 1}. When the input x = (x[0], x[1], ..., x[m-1]) traverses from (0, 0, ..., 0) and (0, 0, ..., 1) to (1, 1, ..., 1), the functions a(x) = f(x) + d1 and b(x) = f(x) + x π The output of [0]+d2 corresponds to the binary sequence (-1). a(x) and (-1) b(x) That is, the length is 2 m The GCP. d1,d2∈{0,1}.
[0822] For example, suppose m = 3, x π = [0,1,2], c = [0,0,0], d1 = 0, d2 = 0, then:
[0823] f(x) = x π [0]x π [1]+x π [1]x π [2]+c[0]x[0]+c[1]x[1]+c[2]x[2]
[0824] = x[0]x[1]+x[1]x[2]
[0825] Therefore, a(x) = f(x), b(x) = f(x) + x[0]. When the input (x[0], x[1], x[2]) iterates from (0,0,0) and (0,0,1) to (1,1,1), (-1) a(x) The outputs are [1,1,1,-1,1,1,-1,1], (-1) b(x) The outputs are [1,1,1,-1,-1,-1,-1,1,-1] in sequence, and their outputs form a pair of lengths 2. 3=8 GCP. Wherein, (x[0],x[1],x[2]) traversing from (0,0,0) and (0,0,1) to (1,1,1) means: when x[0],x[1],x[2] take 0, 0, 0 respectively, we get a value of f(x). Substituting this value of f(x) into a(x) = f(x) and b(x) = f(x) + x[0] respectively, we get an element in the sequence. Then let x[0],x[1],x[2] take 0, 0, 1 respectively, and get an element in the sequence according to the above formula. And so on, until x[0],x[1],x[2] take 1, 1, 1 respectively, we get the last element in the sequence.
[0826] Based on the above analysis, when generating a GCP using a generalized Boolean function mapping, it is necessary to define x. π There are four generation parameters: c, d1, and d2.
[0827] In some embodiments, when N equals 32, the 32 sets of parameters defined in this application for generating GCP are shown in Table 7 below.
[0828] Table 7
[0829]
[0830]
[0831] In Table 7, each row shows x π c, d1, and d2 are a set of parameters. Using the 32 sets of parameters shown in Table 7 and the generalized Boolean function mapping method described above, 32 pairs of GCPs shown in Table 4 can be generated. Specifically, the i-th set of parameters shown in Table 7 generates the i-th pair of GCPs shown in Table 4, where i is a positive integer from 1 to 32. It should be noted that the 32 pairs of GCPs shown in Table 4 can also be generated using other methods, such as sequential recursion. This application does not specifically limit the generation method of the GCPs shown in Table 4.
[0832] In some embodiments, when N equals 64, the 40 sets of parameters defined in this application for generating GCP are shown in Table 8 below.
[0833] Table 8
[0834]
[0835]
[0836] Using the 40 sets of parameters shown in Table 8 and the generalized Boolean function mapping method described above, the 40 pairs of GCPs shown in Table 5 can be generated. Specifically, the i-th set of parameters shown in Table 8 generates the i-th pair of GCPs in Table 5, where i is a positive integer from 1 to 40. It should be noted that the 40 pairs of GCPs shown in Table 5 can also be generated using other methods, such as sequential recursion. This application does not specifically limit the generation method of the GCPs shown in Table 5.
[0837] In some embodiments, when N equals 128, the 40 sets of parameters defined in this application for generating GCP are shown in Table 9 below.
[0838] Table 9
[0839]
[0840]
[0841] Using the 40 sets of parameters shown in Table 9 and the generalized Boolean function mapping method described above, the 40 pairs of GCPs shown in Table 6 can be generated. Specifically, the i-th set of parameters shown in Table 9 generates the i-th pair of GCPs in Table 6, where i is a positive integer from 1 to 40. It should be noted that the 40 pairs of GCPs shown in Table 6 can also be generated using other methods, such as sequential recursion. This application does not specifically limit the generation method of the GCPs shown in Table 6.
[0842] In some embodiments, when N equals 256, the 40 sets of parameters defined in this application for generating GCP are shown in Table 10 below.
[0843] Table 10
[0844]
[0845]
[0846] Using the 40 sets of parameters shown in Table 10 and the generalized Boolean function mapping method described above, 40 pairs of GCPs can be generated. Each set of parameters can be used to generate a unique pair of GCPs.
[0847] Optionally, the 40 sets of parameters shown in Table 10 can be divided into 20 sets. Each set includes two adjacent sets of parameters; that is, the first set includes the sets of parameters numbered 1 and 2, the second set includes the sets of parameters numbered 3 and 4, and so on. The nineteenth set includes the sets of parameters numbered 37 and 38, and the twentieth set includes the sets of parameters numbered 39 and 40. The two pairs of GCPs generated by the two sets of parameters in each set are orthogonal to each other.
[0848] Optionally, the 40 pairs of GCPs generated by the 40 sets of parameters shown in Table 10 have low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Further, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 1-8 have even lower aperiodic cross-correlation peak values. Additionally, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 9-16 also have lower aperiodic cross-correlation peak values. When the number of devices requiring simultaneous sensing is less than or equal to 8, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 1-8 or 8 pairs of GCPs generated by the 8 sets of parameters numbered 9-16 can be preferentially used. The 8 sets of parameters numbered 1-8 or 8 sets of parameters numbered 9-16 can be referred to as preferred parameters.
[0849] In some embodiments, when N equals 512, the 40 sets of parameters defined in this application for generating GCP are shown in Table 11 below.
[0850] Table 11
[0851]
[0852]
[0853] Using the 40 sets of parameters shown in Table 11 and the generalized Boolean function mapping method described above, 40 pairs of GCPs can be generated. Each set of parameters can be used to generate a unique pair of GCPs.
[0854] Optionally, the 40 sets of parameters shown in Table 11 can be divided into 20 sets, each set including two adjacent sets of parameters, wherein the two pairs of GCPs generated by the two sets of parameters in each set are orthogonal to each other. Refer to the relevant explanation in Table 10, which will not be repeated here.
[0855] Optionally, the 40 pairs of GCPs generated by the 40 sets of parameters shown in Table 11 exhibit low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Furthermore, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 1-8 exhibit even lower aperiodic cross-correlation peak values. Additionally, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 9-16 also exhibit lower aperiodic cross-correlation peak values. Refer to the relevant explanations in Table 10; they will not be repeated here.
[0856] In some embodiments, when N equals 1024, the 40 sets of parameters defined in this application for generating GCP are shown in Table 12 below.
[0857] Table 12
[0858]
[0859]
[0860] Using the 40 sets of parameters shown in Table 12 and the generalized Boolean function mapping method described above, 40 pairs of GCPs can be generated. Each set of parameters can be used to generate a unique pair of GCPs.
[0861] Optionally, the 40 sets of parameters shown in Table 12 can be divided into 20 sets, each set including two adjacent sets of parameters, wherein the two pairs of GCPs generated by the two sets of parameters in each set are orthogonal to each other. Refer to the relevant explanation in Table 10, which will not be repeated here.
[0862] Optionally, the 40 pairs of GCPs generated by the 40 sets of parameters shown in Table 12 exhibit low aperiodic cross-correlation peaks, or in other words, good aperiodic cross-correlation properties. Furthermore, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 1-8 exhibit even lower aperiodic cross-correlation peaks. Additionally, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 9-16 also exhibit lower aperiodic cross-correlation peaks. Refer to the relevant explanations in Table 10; they will not be repeated here.
[0863] The generation methods and parameters of GCPs when N equals 32, 64, 128, 256, 512, and 1024 have been explained above. The generation methods and parameters of GCPs when N equals 160, 320, 640, or 832 will be introduced below.
[0864] When N equals 160, 320, 640, or 832, GCP is the direct product of the first GCP and the second GCP, the length of the first GCP is N1, the length of the second GCP is N2, and N1 × N2 = N.
[0865] For example, suppose the first GCP is denoted as (a, b) and the second GCP is denoted as (c, d). The sequence (e, f) generated by the direct product of the two is a GCP of length N1N2, which can be represented as:
[0866]
[0867]
[0868] in, Describes the inverse sequence of sequence c. Describes the inverse sequence of sequence d. It represents the Kronecker product.
[0869] Optionally, one of the sequences in the first GCP is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2l =N1, please refer to the relevant explanations mentioned above, and will not be repeated here.
[0870] Optionally, the second GCP can be any of the following:
[0871] x1=1,1,-1,1,-1,1,-1,-1,1,1;
[0872] y1=1,1,-1,1,1,1,1,1,-1,-1.
[0873] or,
[0874] x2=1,1,1,1,1,-1,1,-1,-1,1;
[0875] y2=1,1,-1,-1,1,1,1,-1,1,-1.
[0876] or,
[0877] x3=1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1;
[0878] y3=1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,1,-1,1,1,-1.
[0879] or,
[0880] x4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1;
[0881] y4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1.
[0882] In this application, the second GCP can also be referred to as the base sequence. That is, the description "second GCP" in this application can be replaced with the base sequence, and this application does not make any specific limitation on it.
[0883] In some embodiments, when N equals 160, the 20 sets of parameters defined in this application for generating GCP are shown in Table 13 below.
[0884] Table 13
[0885]
[0886]
[0887] In Table 13, each row shows x π c, d1, d2, and the second GCP form a set of parameters. π c, d1, and d2 are used to generate the first GCP. A GCP can then be generated from the first and second GCPs using the direct product of the sequences described above. Each set of parameters can be used to generate a unique pair of GCPs.
[0888] From Table 13, we can see that a GCP of length 160 can be generated by a first GCP of length 16 and a second GCP of length 10, i.e., N1 = 16, N2 = 10, and the second GCP is (x1, y1) or (x2, y2). Alternatively, it can be generated by a first GCP of length 8 and a second GCP of length 20, i.e., N1 = 8, N2 = 20, and the second GCP is (x3, y3).
[0889] Optionally, the 20 sets of parameters shown in Table 13 can be divided into 10 sets, each set including two adjacent sets of parameters. That is, the first set includes two sets of parameters numbered 1 and 2, the second set includes two sets of parameters numbered 3 and 4, ..., the ninth set includes two sets of parameters numbered 17 and 18, and the tenth set includes two sets of parameters numbered 19 and 20. The two pairs of GCPs generated by the two sets of parameters in each set are orthogonal to each other.
[0890] Optionally, the 20 pairs of GCPs generated by the 20 sets of parameters shown in Table 13 have low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Further, the 6 pairs of GCPs generated by the 6 sets of parameters numbered 1-6 have even lower aperiodic cross-correlation peak values. When the number of devices requiring simultaneous sensing is less than or equal to 6, the 6 pairs of GCPs generated by the 6 sets of parameters numbered 1-6 can be preferentially used. The 6 sets of parameters numbered 1-6 can be referred to as the preferred parameters.
[0891] In some embodiments, when N equals 320, the 20 sets of parameters defined in this application for generating GCP are shown in Table 14 below.
[0892] Table 14
[0893]
[0894]
[0895] Each set of parameters in Table 14 can be used to generate a unique pair of GCPs. Refer to Table 13 for further details; they will not be repeated here.
[0896] As shown in Table 14, a GCP of length 320 can be generated by a first GCP of length 32 and a second GCP of length 10, i.e., N1 = 32, N2 = 10, and the second GCP is (x1, y1) or (x2, y2).
[0897] Optionally, the 20 sets of parameters shown in Table 13 can be divided into 10 sets, with the two sets of parameters in each set generating two pairs of orthogonal GCPs. Refer to the relevant explanation in Table 13; it will not be repeated here.
[0898] Optionally, the 20 pairs of GCPs generated by the 20 sets of parameters shown in Table 14 have low aperiodic cross-correlation peak values, or in other words, good aperiodic cross-correlation properties. Further, the 4 pairs of GCPs generated by the 4 sets of parameters numbered 1-4 have even lower aperiodic cross-correlation peak values. Additionally, the 4 pairs of GCPs generated by the 4 sets of parameters numbered 5-8 also have even lower aperiodic cross-correlation peak values. When the number of devices requiring simultaneous sensing is less than or equal to 4, the 4 pairs of GCPs generated by the 4 sets of parameters numbered 1-4 can be used preferentially, or the 4 pairs of GCPs generated by the 4 sets of parameters numbered 5-8 can be used preferentially.
[0899] In some embodiments, when N equals 640, the 20 sets of parameters defined in this application for generating GCP are shown in Table 15 below.
[0900] Table 15
[0901]
[0902]
[0903] Each set of parameters in Table 15 can be used to generate a unique pair of GCPs. Refer to Table 13 for further details; they will not be repeated here.
[0904] From Table 15, we can see that a GCP of length 640 can be generated by a first GCP of length 64 and a second GCP of length 10, i.e., N1 = 64, N2 = 10, and the second GCP is (x1, y1) or (x2, y2). Alternatively, it can be generated by a first GCP of length 32 and a second GCP of length 20, i.e., N1 = 32, N2 = 20, and the second GCP is (x3, y3).
[0905] Optionally, the 20 sets of parameters shown in Table 15 can be divided into 10 sets, with the two sets of parameters in each set generating two pairs of orthogonal GCPs. Refer to the relevant explanation in Table 13; it will not be repeated here.
[0906] Optionally, the 20 pairs of GCPs generated by the 20 sets of parameters shown in Table 15 exhibit low aperiodic cross-correlation peaks, or in other words, good aperiodic cross-correlation properties. Furthermore, the 8 pairs of GCPs generated by the 8 sets of parameters numbered 1-8 exhibit even lower aperiodic cross-correlation peaks. Refer to the relevant explanations in Table 13; they will not be repeated here.
[0907] In some embodiments, when N equals 832, the 20 sets of parameters defined in this application for generating GCP are shown in Table 16 below.
[0908] Table 16
[0909]
[0910]
[0911] Each set of parameters in Table 16 can be used to generate a unique pair of GCPs. See Table 13 for further details; they will not be repeated here.
[0912] As shown in Table 16, a GCP of length 832 can be generated by a first GCP of length 32 and a second GCP of length 26, i.e., N1 = 32, N2 = 26, and the second GCP is (x4, y4).
[0913] Optionally, the 20 sets of parameters shown in Table 16 can be divided into 10 sets, with the two sets of parameters in each set generating two pairs of orthogonal GCPs. Refer to the relevant explanation in Table 13; it will not be repeated here.
[0914] Optionally, the 20 pairs of GCPs generated by the 20 sets of parameters shown in Table 16 have low peak values of aperiodic cross-correlation, or in other words, good aperiodic cross-correlation properties. Furthermore, the 4 pairs of GCPs generated by the 4 sets of parameters numbered 1-4 or 5-8 have even lower peak values of aperiodic cross-correlation. Refer to the relevant explanations in Table 14; they will not be repeated here.
[0915] Based on this, this application provides GCPs of various lengths, with a large number of GCPs for each length, enabling simultaneous sensing by multiple sensing devices. Furthermore, the aperiodic cross-correlation between multiple pairs of GCPs of each length is low, effectively reducing interference between devices when multiple sensing devices are sensing simultaneously, thereby improving sensing accuracy.
[0916] The above provides a description of the various lengths of GCPs provided in this application. Although the embodiments of this application define multiple lengths of GCPs separately, it does not limit the specific technical solution to supporting all GCPs defined in this application. Supporting at least one defined length of GCP is sufficient, such as GCPs with lengths of 32, 64, 128, 256, 512, 1024, 160, 320, 640 and / or 832.
[0917] The sensing method provided in this application is described below. For example... Figure 5 The diagram shown is a flowchart of a sensing method provided in this application, which includes:
[0918] S501, The sensing device sends a sensing signal.
[0919] The sensing signal is generated based on a GCP of length N, or in other words, the sensing signal is generated according to a GCP of length N, or the sensing signal is used to carry a GCP of length N. N is equal to one of 32, 64, 128, 256, 512, 1024, 160, 320, 640, or 832.
[0920] Optionally, the parameters used to generate the GCP are a set of parameters included in Tables 7 to 16. Alternatively, when N equals 32, 64, or 128, the GCP is a pair of GCPs defined in Tables 4 to 6.
[0921] Optionally, the sensing device supports GCPs generated from at least one set of parameters in at least one of the tables from Tables 7 to 16. As one possible implementation, the sensing device can store at least one set of parameters from at least one of the tables from Tables 7 to 16. Before step S501, the sensing device can select a set of parameters to generate a GCP, and then generate a sensing signal based on the generated GCP.
[0922] As another possible implementation, the sensing device can store GCPs generated from at least one set of parameters in at least one of the tables from Tables 7 to 16; that is, the sensing device stores GCPs. Before step S501, the sensing device can select a pair of GCPs and generate a sensing signal based on the GCPs.
[0923] Optionally, the parameters or stored GCPs used to generate GCPs stored in the sensing device may be configured at the factory; or they may be pre-configured by the management node or the user. This application does not specifically limit this.
[0924] Optionally, the sensing signal can be a single-carrier signal or a multi-carrier signal. In other words, the sensing signal can be a single-carrier waveform or a multi-carrier waveform. For example, a single-carrier waveform can be a single-carrier pulse waveform. A multi-carrier waveform can be a cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) waveform or a discrete fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM) waveform. Of course, other forms of single-carrier or multi-carrier waveforms are also possible, and this application does not specifically limit this.
[0925] Optionally, the sensing device can transmit sensing signals in an omnidirectional or directional manner. As one possible implementation, when the sensing device lacks prior knowledge of the target's location, it can transmit sensing signals uniformly throughout the entire space using an omnidirectional method. For example, in a smart home scenario, when tracking a person's trajectory, the sensing devices in the home lack prior knowledge of the person's location and can transmit sensing signals omnidirectionally to detect information such as the person's distance and location.
[0926] As another possible implementation, when the sensing device has prior knowledge of the target's location, it can send a sensing signal in a specific direction. For example, in an in-vehicle sensing scenario, when triggering a drowsy alarm for the driver, the sensing device can have prior knowledge of the driver's location (e.g., the driver's seat) and send a sensing signal to that location.
[0927] S502, The sensing device receives the echo signal of the sensing signal.
[0928] Optionally, after the sensing device begins to send sensing signals, the receiving antenna begins to receive echo signals in an omnidirectional or directional manner.
[0929] Optionally, the receiving method of the receiving antenna is matched with the transmission method of the sensing signal. For example, when the sensing device transmits the sensing signal in an omnidirectional manner, the echo signal is received in an omnidirectional manner in step S502; when the sensing device transmits the sensing signal in a directional manner, the echo signal is received in a directional manner in step S502.
[0930] Optionally, the same antenna can be reused for transmitting and receiving, meaning the sensing device can operate in full-duplex mode.
[0931] S503, The sensing device processes the echo signal.
[0932] Optionally, the processing of the sensing device based on the echo signal may include: the sensing device sensing based on the echo signal, for example, sensing the distance of the target object based on the echo signal, i.e., determining the distance between the sensing device and the target object.
[0933] Optionally, after receiving the echo signal, the sensing device can decode it to obtain the GCP corresponding to the echo signal. For example, when the sensing signal is a single-carrier signal, the sensing device can decode it based on the phase information of the echo signal to obtain the GCP corresponding to the echo signal. The GCP corresponding to the sensing signal can be understood as the GCP carried by the sensing signal.
[0934] After obtaining the GCP corresponding to the echo signal, the sensing device can perform an aperiodic autocorrelation operation on the GCP used to generate the sensing signal (denoted as GCP#1) and the GCP corresponding to the echo signal (denoted as GCP#2) in step S501. Based on the result of the aperiodic autocorrelation operation, the signal propagation delay between the sensing device and the target object is determined. For example, the signal propagation delay can be determined based on the displacement corresponding to the maximum correlation peak. Then, the distance between the target object and the sensing device is determined based on this signal propagation delay. Assuming the displacement corresponding to the maximum correlation peak is l, then the delay is lT. c The distance between the target object and the sensing device is clT c / 2, where c is the speed of light. When the perceived signal is a single-carrier waveform, T c T represents the duration of a narrow pulse; when the sensed signal is a multi-carrier waveform, T c This indicates the duration of the sampling point after time-domain sampling of a multi-carrier signal.
[0935] Optionally, the maximum correlation peak mentioned above is the maximum value of the aperiodic autocorrelation function. Since GCP#1 has good aperiodic autocorrelation, the maximum correlation peak in the aperiodic autocorrelation operation is usually at the zero displacement, i.e., when GCP#1 and GCP#2 are perfectly aligned. Because the echo signal has a delay compared to the sensing signal, GCP#1 needs to be shifted by the corresponding delay time to ensure alignment during the aperiodic autocorrelation operation. Therefore, the time delay can be determined by judging the displacement of GCP#1, and thus the distance between the target object and the sensing device can be determined.
[0936] In some embodiments, when the sensing device supports multiple pairs of GCPs generated from multiple sets of parameters in at least one of the tables in Tables 7 to 16, a pair of GCPs can be selected from the multiple pairs of GCPs to generate a sensing signal before step S501 described above. The selection of GCPs can be performed at a higher level, where "higher level" refers to the layer above the physical layer.
[0937] As one possible implementation, when there is a central management node in the sensing scenario and there are multiple sensing devices with the same sensing bandwidth in the sensing scenario, the central management node can assign GCPs corresponding to different parameter groups in the same table in Tables 7 to 16 to each sensing device, so that the aperiodic cross-correlation peak value of the GCP used by each sensing device is lower, thereby reducing the interference between different sensing devices.
[0938] For example, in a smart home scenario, when it is necessary to track a person's trajectory, multiple sensing devices (such as various smart home appliances or mobile phones) are usually required to sense simultaneously to increase the accuracy of trajectory tracking. In this case, the wireless access point or edge cloud server in the home can act as a central management node, assigning different GCPs of the same length to multiple sensing devices to reduce interference.
[0939] Optionally, sensing bandwidth can be understood as the maximum bandwidth that a sensing signal can occupy. The specific sensing bandwidth can be defined by the protocol. Different sensing devices with the same sensing bandwidth typically use different GCPs of the same length.
[0940] As another possible implementation, in a sensing scenario where there is no central management node but different sensing devices with the same sensing bandwidth can communicate with each other, each sensing device can coordinate through communication before sensing to ensure that each sensing device selects different GCPs with the same length.
[0941] For example, in a V2X scenario, before performing sensing, the vehicle-mounted terminal can indicate the selected GCP (Global Policy Contact) to surrounding devices via the communication network. Upon receiving this indication, surrounding devices can select other GCPs to reduce interference if they need to perform sensing. For instance, the vehicle-mounted terminal can indicate its selected GCP to surrounding devices via broadcast or multicast.
[0942] As another possible implementation, in a sensing scenario where there is no central management node and different sensing devices cannot communicate with each other, the sensing device can listen for sensing processes performed by other devices within its operating frequency band before sensing. If such processes exist, the GCP used by the sensing process can be determined through relevant calculations. When performing subsequent sensing processes, the sensing device can then select other GCPs of the same length to reduce interference.
[0943] Optionally, when the sensed signal is a multi-carrier signal, the length N of the GCP selected by the sensing device can be adapted to the sensing bandwidth. For example, the difference between the GCP length N and the target value is less than a threshold. That is, the GCP length N should be as close as possible to the target value. This target value is determined by the subcarrier spacing, the sensing bandwidth, and the resource element (RE) mapping method.
[0944] For example, when the RE mapping method is to map one element of the GCP for every M REs, the target value, subcarrier spacing, and M satisfy the following formula:
[0945]
[0946] Where SCS is the subcarrier spacing and W is the sensing bandwidth. This indicates rounding down to the nearest integer.
[0947] For example, when the multi-carrier waveform is a CP-OFDM waveform or a DFT-s-OFDM waveform, the sensing bandwidth and subcarrier spacing determine the number of subcarriers in that waveform. Taking a sensing bandwidth of 400 MHz as an example, when the subcarrier spacing is 240 kHz, the sensing bandwidth includes... Subcarriers.
[0948] If 1RE mapping is chosen, meaning each RE maps one element and M equals 1, then 1666 subcarriers can carry a GCP of length 1666. However, if a GCP of length N equals 32 is selected for transmission on subcarriers 0-31, or a GCP of length N equals 64 is selected for transmission on subcarriers 0-63, with the remaining subcarriers padded with 0s, then over 90% of the subcarriers are not utilized, resulting in wasted bandwidth. Furthermore, if the sensing process is used to measure the distance between the sensing device and the target object, the ranging resolution is proportional to the bandwidth occupied by the GCP, and GCPs of length 32 or 64 occupy very little bandwidth, significantly reducing the ranging resolution. Therefore, if 1RE mapping is chosen, the GCP length can be 1024 to best suit the sensing bandwidth.
[0949] If we choose 2RE mapping, where every two REs map one element, M equals 2, and the target value equals... At this point, a GCP of length 832 can be selected. When mapping an element to every two REs, mapping can be performed every other subcarrier, with 0s padded in between subcarriers. For example, if the first element is mapped on subcarrier 0, 0s are padded on subcarrier 1; if the second element is mapped on subcarrier 2, 0s are padded on subcarrier 3, and so on.
[0950] Optionally, after selecting a pair of GCPs, the sensing device can generate a sensing signal based on those GCPs. As one possible implementation, when the sensing signal is a single-carrier waveform, the sensing device can generate a single-carrier waveform using phase modulation based on the GCPs.
[0951] For example, taking a single-carrier pulse waveform as an example, such as Figure 6As shown, the sensing device transmits narrow pulses of different phases using phase modulation based on a selected GCP. Each narrow pulse corresponds to an element in a sequence (x sequence or y sequence) within the GCP. For example, when the element in the sequence is 1, the sensing device transmits a positive narrow pulse; when the element in the sequence is -1, the sensing device transmits a negative narrow pulse. Assuming the sensing bandwidth of the sensing device is W, then the duration of the narrow pulse is T. c = 1 / W. Therefore, for a GCP of length N, one sequence (x sequence or y sequence) is represented by a wide pulse consisting of N narrow pulses, the duration of which is NT. c In generating sensing signals, the elements in the sequence can also be called code elements.
[0952] Understandably, the GCP includes a wide pulse for each of the x and y sequences. For example, Figure 6 The second wide pulse in the sequence represents the x sequence, and the third wide pulse represents the y sequence.
[0953] Furthermore, the sensing device can repeatedly use the x and y sequences included in the GCP to generate wide pulses, thereby constructing a sensing signal with a single-carrier pulse waveform. The pulse repetition interval (PRI) of each wide pulse is... Figure 6 The middle part is represented by T.
[0954] As another possible implementation, when the sensed signal is a multi-carrier waveform, taking the DFT-s-OFDM waveform as an example, the process by which the sensing device generates the multi-carrier waveform according to the GCP can be as follows: Figure 7 As shown.
[0955] See Figure 7 The sensing device performs a discrete Fourier transform (DFT) on the x-sequence or y-sequence to be transmitted, then performs subcarrier mapping according to the RE mapping rule, then performs an inverse fast Fourier transform (IFFT) on the mapped RE, and finally inserts a fixed-length cyclic prefix (CP) to obtain the sensing signal.
[0956] Optionally, in a joint communication and sensing (JCS) system, the communication system may also use DFT-s-OFDM waveforms. Therefore, to reduce interference between the sensing and communication systems, resource reuse is typically performed in a time-division or frequency-division manner. In this application, time-division multiplexing can be used, meaning that at the same time domain location, only sensing signals from the sensing system or communication signals from the communication system are transmitted, and the signal transmitted at that time domain location occupies the entire bandwidth configured in the frequency domain. Based on this method, the sensing signal can occupy the entire configured bandwidth, which, compared to frequency-division multiplexing, increases the bandwidth occupied by the sensing signal, thereby improving the ranging resolution of the sensing system.
[0957] For example, such as Figure 8 As shown, each rectangle can represent a DFT-s-OFDM symbol (i.e., a time-domain resource). Horizontally filled rectangles represent DFT-s-OFDM symbols used in the sensing system (also called sensing resources), and vertically filled rectangles represent DFT-s-OFDM symbols used in the communication system (also called communication resources). Each DFT-s-OFDM symbol used in the sensing system can transmit a sequence from a GCP. Therefore, based on... Figure 8 As shown in the resource allocation, the sensing device can transmit one sequence in the GCP on the first DFT-s-OFDM symbol used by the sensing system, and another sequence in the GCP on the second DFT-s-OFDM symbol used by the sensing system.
[0958] Optionally, when using time-division multiplexing for resource reuse, the specific multiplexing method or resource allocation method can be implemented by the transport layer or network layer protocol. For example, multiple consecutive DFT-s-OFDM symbols can be used for the sensing system, while other symbols are used for the communication system; or, the multiple DFT-s-OFDM symbols allocated to the sensing system can be non-consecutive, for example... Figure 8 As shown. This application does not specify any particular limitation on the reuse method.
[0959] It should be noted that this application does not limit the multicarrier waveform to a DFT-s-OFDM waveform. When the multicarrier waveform is in other forms, the implementation of the DFT-s-OFDM waveform provided in this application can be referred to.
[0960] Figure 5 The illustrated embodiment uses a sensing device to sense information through self-transmission and self-reception. In some embodiments, this can be achieved by... Figure 5 The illustrated embodiments can be appropriately modified to construct new methods for sensing between different devices. For example, such as... Figure 9 As shown, the method may include:
[0961] S901, The first device generates a sensing signal.
[0962] The generation method of the sensing signal and the selection of GCP can be found in [reference needed]. Figure 5 The relevant descriptions in the illustrated embodiments will not be repeated here.
[0963] S902, the first device sends a sensing signal to the second device. Correspondingly, the second device receives the signal.
[0964] It is understood that after the sensing signal is transmitted through the channel, the signal received by the second device is not the sensing signal itself sent by the first device. In this application, the signal received by the second device is referred to as the received signal, which is the signal after the sensing signal is transmitted through the channel.
[0965] S903, The second device processes the received signal.
[0966] Optionally, the second device can sense the distance between itself and the first device based on the received signal. For example, the second device can perform an aperiodic autocorrelation operation on the GCP used to generate the sensing signal and the GCP corresponding to the received signal, and then determine the distance between itself and the first device based on the result of the autocorrelation operation. For specific implementation details, please refer to the relevant description in step S503, which will not be repeated here.
[0967] Optionally, before step S903, the first device may instruct the second device to perform a periodic autocorrelation calculation for generating the sensing signal.
[0968] Optional, in Figure 9 In the illustrated embodiment, the first device can generate and send a sensing signal based on a request from the second device. For example, when the second device needs to obtain the distance between itself and the first device, it can send a request message to the first device to request the first device to send a sensing signal so that the second device can perform sensing.
[0969] Alternatively, the first device can actively send a sensing signal to the second device. In this scenario, the second device can send the processing result (e.g., the distance between the first and second devices) to the first device after step S903.
[0970] The above explanation primarily uses the GCP provided in this application for sensing as an example. It is understood that the GCP provided in this application can also be applied to other processes without limitation.
[0971] It is understood that the methods and / or steps implemented by the sensing device in the above embodiments can also be implemented by components (e.g., processors, chips, chip systems, circuits, logic modules, or software such as chips or circuits) that can be used in the sensing device.
[0972] The above primarily describes the solutions provided in this application from the perspective of the device. Accordingly, this application also provides a communication device for implementing the various methods described above. This communication device can be a sensing device in the above method embodiments, a device containing the aforementioned sensing device, or a component that can be used with a sensing device.
[0973] It is understood that, in order to achieve the aforementioned functions, the communication device includes hardware structures and / or software modules corresponding to the execution of each function. Those skilled in the art should readily recognize that, based on the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein, this application can be implemented in hardware or a combination of hardware and computer software. Whether a function is executed in hardware or by computer software driving hardware depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0974] This application embodiment can divide the communication device into functional modules according to the above method embodiment. For example, each function can be divided into a separate functional module, or two or more functions can be integrated into one processing module. The integrated module can be implemented in hardware or as a software functional module. It should be noted that the module division in this application embodiment is illustrative and only represents one logical functional division. In actual implementation, there may be other division methods.
[0975] In one implementation scenario, taking a communication device as the sensing device in the above method embodiment as an example. Figure 10 A schematic diagram of a sensing device 100 is shown. The sensing device 100 includes a processing module 1001 and a transceiver module 1002.
[0976] In some embodiments, the sensing device 100 may further include a storage module. Figure 10 (Not shown in the image) is used to store program instructions and data.
[0977] In some embodiments, the transceiver module 1002, also referred to as a transceiver unit, is used to implement sending and / or receiving functions. The transceiver module 1002 may consist of a transceiver circuit, a transceiver, a transceiver unit, or a communication interface.
[0978] In some embodiments, the transceiver module 1002 may include a receiving module and a sending module, respectively used to perform the receiving and sending steps performed by the sensing device in the above method embodiments, and / or other processes used to support the technology described herein; the processing module 1001 may be used to perform the processing steps (e.g., determining, acquiring, generating, etc.) performed by the sensing device in the above method embodiments, and / or other processes used to support the technology described herein.
[0979] The transceiver module 1002 is used to transmit the sensing signal; the transceiver module 1002 is also used to receive the echo signal of the sensing signal; the processing module 1001 is used to process the echo signal. The sensing signal is generated based on a GCP of length N, where N is greater than or equal to 32.
[0980] When N equals 32, 64, 128, 256, 512, or 1024, one of the sequences in the GCP used to generate the sensing signal is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2 m =N.
[0981] When N equals 160, 320, 640, or 832, the GCP used to generate the sensing signal is the direct product of the first GCP and the second GCP. The length of the first GCP is N1, and the length of the second GCP is N2, where N1 × N2 = N. One sequence in the first GCP is (-1). a(x) The other sequence is (-1). b(x) , a(x)=f(x)+d1, b(x)=f(x)+x π [0]+d2, 2 l =N1. The second GCP is any one of the following:
[0982] x1=1,1,-1,1,-1,1,-1,-1,1,1;
[0983] y1=1,1,-1,1,1,1,1,1,-1,-1;
[0984] or,
[0985] x2=1,1,1,1,1,-1,1,-1,-1,1;
[0986] y2=1,1,-1,-1,1,1,1,-1,1,-1;
[0987] or,
[0988] x3=1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1;
[0989] y3=1,1,1,1,-1,1,1,1,1,1,-1,-1,-1,1,-1,1,-1,1,1,-1;
[0990] or,
[0991] x4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,-1,1,-1,1,1,1,-1,-1,1,1,1;
[0992] y4=1,1,1,1,-1,1,1,-1,-1,1,-1,1,1,1,1,1,-1,1,-1,-1,-1,1,1,-1,-1,-1.
[0993] Optionally, the sensing signal can be a single-carrier signal or a multi-carrier signal. When the sensing signal is a multi-carrier signal, the difference between the length N of the GCP and the target value is less than a threshold. The target value is determined by the subcarrier spacing, sensing bandwidth, and resource element (RE) mapping method.
[0994] Optionally, the RE mapping method maps one element of the GCP for every M REs; the target value, subcarrier spacing, sensing bandwidth, and M satisfy the following formula:
[0995]
[0996] Where SCS is the subcarrier spacing and W is the sensing bandwidth. This indicates rounding down to the nearest integer.
[0997] Optionally, the processing module 1001 is used to process the echo signal, including: the processing module 1001 is used to sense the distance of the target object based on the echo signal. The target object is the object whose echo signal is generated by reflecting the sensing signal.
[0998] Optionally, the processing module 1001 is used to sense the distance of the target object based on the echo signal, including: the processing module 1001 is used to perform an aperiodic autocorrelation operation on the GCP that generates the sensing signal and the GCP corresponding to the echo signal; the processing module 1001 is also used to determine the signal propagation delay between the sensing device and the target object based on the result of the aperiodic autocorrelation operation; the processing module 1001 is also used to determine the distance of the target object based on the signal propagation delay.
[0999] All relevant content of each step involved in the above method embodiments can be referenced from the functional description of the corresponding functional module, and will not be repeated here.
[1000] In this application, the sensing device 100 is presented in an integrated manner, divided into various functional modules. Here, "module" may refer to an application-specific integrated circuit (ASIC), a circuit, a processor and memory that executes one or more software or firmware programs, integrated logic circuits, and / or other devices that can provide the above functions.
[1001] As one possible product form, those skilled in the art will conceive that the sensing device 100 can adopt... Figure 4 The communication device 400 shown is in the form of [example device].
[1002] As an example, Figure 10 The function / implementation process of the processing module 1001 can be achieved through... Figure 4 The processor 401 in the communication device 400 shown calls computer execution instructions stored in the memory 403 to implement the communication. Figure 10 The function / implementation process of the transceiver module 1002 can be obtained through Figure 4 This is achieved through the communication interface 404 in the communication device 400 shown.
[1003] As another possible product form, the sensing device described in the embodiments of this application can also be implemented using the following: one or more field programmable gate arrays (FPGAs), programmable logic devices (PLDs), controllers, state machines, gate logic, discrete hardware components, any other suitable circuits, or any combination of circuits capable of performing the various functions described throughout this application.
[1004] In some embodiments, when Figure 10 When the sensing device 100 is a chip or chip system, the function / implementation process of the transceiver module 1002 can be implemented through the input / output interface (or communication interface) of the chip or chip system, and the function / implementation process of the processing module 1001 can be implemented through the processor (or processing circuit) of the chip or chip system.
[1005] Since the sensing device 100 provided in this embodiment can execute the above method, the technical effects it can achieve can be referred to the above method embodiment, and will not be repeated here.
[1006] In some embodiments, this application also provides a communication device, which includes a processor for implementing the methods in any of the above method embodiments.
[1007] As one possible implementation, the communication device also includes a memory. This memory stores necessary program instructions and data, and the processor can call the program code stored in the memory to instruct the communication device to execute the methods in any of the above method embodiments. Of course, the memory may also be absent from the communication device.
[1008] As another possible implementation, the communication device also includes an interface circuit, which is a code / data read / write interface circuit, used to receive computer execution instructions (which are stored in memory and may be read directly from memory or may be transmitted through other devices) and transmit them to the processor.
[1009] As another possible implementation, the communication device also includes a communication interface for communicating with modules outside the communication device.
[1010] It is understood that the communication device can be a chip or a chip system. When the communication device is a chip system, it can be composed of chips or may include chips and other discrete devices. This application does not specifically limit this.
[1011] This application also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a computer, implements the functions of any of the above-described method embodiments.
[1012] This application also provides a computer program product that, when executed by a computer, implements the functions of any of the above method embodiments.
[1013] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.
[1014] It is understood that the systems, apparatuses, and methods described in this application can also be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be through some interfaces; indirect couplings or communication connections between devices or units may be electrical, mechanical, or other forms.
[1015] The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. The components shown as units may or may not be physical units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.
[1016] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.
[1017] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented using software programs, implementation can be, in whole or in part, in the form of a computer program product. This computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device containing one or more servers, data centers, etc., that can be integrated with the medium. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)). In this embodiment, the computer may include the aforementioned apparatus.
[1018] Although this application has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the accompanying drawings, disclosure, and appended claims, will understand and implement other variations of the disclosed embodiments in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.
[1019] Although this application has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made thereto without departing from the spirit and scope of this application. Accordingly, this specification and drawings are merely exemplary illustrations of this application as defined by the appended claims, and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of this application. Clearly, those skilled in the art can make various alterations and modifications to this application without departing from the spirit and scope of this application. Thus, if such modifications and modifications of this application fall within the scope of the claims of this application and their equivalents, this application is also intended to include such modifications and modifications.
Claims
1. A device sensing method, characterized in that, The method includes: A sensing signal is transmitted, which is generated based on a Gray complement pair GCP of length N, where N is greater than or equal to 32. When the sensing signal is a multi-carrier signal, the difference between the length N of the GCP and the target value is less than a threshold. The target value is determined by the subcarrier spacing, sensing bandwidth, and resource element (RE) mapping method. Receive the echo signal of the sensed signal; Process the echo signal accordingly; When N equals 128, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5,6], [1,0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6], [1,0,0,0,0,0,1], 0, 0; or [0,1,2,4,3,6,5], [0,1,1,0,1,0,0], 0, 0; or [0,1,2,4,3,6,5], [0,1,1,0,1,1,0], 0, 0; or [0,1,2,4,5,3,6], [0,0,1,0,1,0,0], 0, 1; or [0,1,2,4,5,3,6], [0,0,1,0,1,0,1], 0, 1; or [0,1,2,4,5,3,6], [1,0,1,0,1,0,0], 0, 1; or [0,1,2,4,5,3,6], [1,0,1,0,1,0,1], 0, 1; or [0,1,2,3,4,5,6], [1,0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6], [1,0,0,0,0,0,1], 0, 1; or [0,1,2,4,3,6,5], [0,1,1,0,1,0,0], 0, 1; or [0,1,2,4,3,6,5], [0,1,1,0,1,1,0], 0, 1; or [0,1,2,4,5,3,6], [0,0,1,0,1,0,0], 0, 0; or [0,1,2,4,5,3,6], [0,0,1,0,1,0,1], 0, 0; or [0,1,2,4,5,3,6], [1,0,1,0,1,0,0], 0, 0; or [0,1,2,4,5,3,6], [1,0,1,0,1,0,1], 0, 0; or [0,1,2,3,4,5,6], [0,0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6], [0,0,0,0,0,0,1], 0, 0; or [0,1,2,3,4,5,6], [0,0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6], [0,0,0,0,0,0,1], 0, 1; or [0,1,2,3,4,6,5], [0,1,0,0,1,0,0], 0, 0; or [0,1,2,3,4,6,5], [0,1,0,0,1,1,0], 0, 0; or [0,1,2,3,4,6,5], [0,1,0,0,1,0,0], 0, 1; or [0,1,2,3,4,6,5], [0,1,0,0,1,1,0], 0, 1; or [0,1,2,3,4,6,5], [1,1,1,0,1,0,1], 0, 0; or [0,1,2,3,4,6,5], [1,1,1,0,1,1,1], 0, 0; or [0,1,2,3,4,6,5], [1,1,1,0,1,0,1], 0, 1; or [0,1,2,3,4,6,5], [1,1,1,0,1,1,1], 0, 1; or [0,1,2,4,3,5,6], [1,1,0,1,1,1,0], 0, 0; or [0,1,2,4,3,5,6], [1,1,0,1,1,1,1], 0, 0; or [0,1,2,4,3,5,6], [1,1,0,1,1,1,0], 0, 1; or [0,1,2,4,3,5,6], [1,1,0,1,1,1,1], 0, 1; or [0,1,2,4,6,3,5], [0,0,1,1,0,0,0], 0, 0; or [0,1,2,4,6,3,5], [0,0,1,1,0,1,0], 0, 0; or [0,1,2,4,6,3,5], [0,0,1,1,0,0,0], 0, 1; or [0,1,2,4,6,3,5], [0,0,1,1,0,1,0], 0, 1; or [0,1,2,4,6,3,5], [1,0,1,1,0,0,0], 0, 0; or [0,1,2,4,6,3,5], [1,0,1,1,0,1,0], 0, 0; or [0,1,2,4,6,3,5], [1,0,1,1,0,0,0], 0, 0; or [0,1,2,4,6,3,5]， [1,0,1,1,0,1,0]， 0， 0。 2. The method according to claim 1, characterized in that, When N equals 64, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5], [0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5], [0,0,0,0,0,1], 0, 1; or [0,2,4,3,1,5], [1,0,0,0,0,0], 0, 1; or [0,2,4,3,1,5], [1,0,0,0,0,1], 0, 1; or [0,3,5,2,1,4], [0,0,1,1,0,1], 0, 0; or [0,3,5,2,1,4], [0,0,1,1,1,1], 0, 0; or [0,1,3,2,4,5], [1,0,1,1,1,0], 0, 1; or [0,1,3,2,4,5], [1,0,1,1,1,1], 0, 1; or [0,2,1,3,5,4], [0,0,1,0,0,0], 0, 1; or [0,2,1,3,5,4], [0,0,1,0,1,0], 0, 1; or [0,3,2,1,5,4], [0,0,0,1,0,0], 0, 0; or [0,3,2,1,5,4], [0,0,0,1,1,0], 0, 0; or [0,1,2,3,4,5], [0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5], [0,0,0,0,0,1], 0, 0; or [0,1,2,3,5,4], [1,0,0,1,0,0], 0, 0; or [0,1,2,3,5,4], [1,0,0,1,1,0], 0, 0; or [0,1,2,3,5,4], [1,1,0,1,0,1], 0, 1; or [0,1,2,3,5,4], [1,1,0,1,1,1], 0, 1; or [0,1,2,4,3,5], [0,1,0,0,1,0], 0, 0; or [0,1,2,4,3,5], [0,1,0,0,1,1], 0, 0; or [0,1,3,2,5,4], [1,1,0,1,0,0], 0, 0; or [0,1,3,2,5,4], [1,1,0,1,1,0], 0, 0; or [0,1,3,4,2,5], [0,1,0,1,0,0], 0, 1; or [0,1,3,4,2,5], [0,1,0,1,0,1], 0, 1; or [0,1,3,5,2,4], [0,1,1,0,0,0], 0, 1; or [0,1,3,5,2,4], [0,1,1,0,1,0], 0, 1; or [0,2,1,3,4,5], [0,0,1,1,0,0], 0, 0; or [0,2,1,3,4,5], [0,0,1,1,0,1], 0, 0; or [0,2,1,4,3,5], [0,1,0,0,0,0], 0, 0; or [0,2,1,4,3,5], [0,1,0,0,0,1], 0, 0; or [0,2,3,1,4,5], [0,1,1,0,1,0], 0, 1; or [0,2,3,1,4,5], [0,1,1,0,1,1], 0, 1; or [0,2,3,1,4,5], [1,1,0,0,0,0], 0, 1; or [0,2,3,1,4,5], [1,1,0,0,0,1], 0, 1; or [0,2,3,4,5,1], [1,0,0,1,1,0], 0, 0; or [0,2,3,4,5,1], [1,1,0,1,1,0], 0, 0; or [0,3,1,4,5,2], [0,1,0,1,1,0], 0, 0; or [0,3,1,4,5,2], [0,1,1,1,1,0], 0, 0; or [1,0,2,3,4,5], [0,1,0,0,0,0], 0, 1; or [1,0,2,3,4,5]， [0,1,0,0,0,1]， 0， 1。 3. The method according to claim 1 or 2, characterized in that, When N equals 32, the parameters used to generate the GCP are any one of the following sets: [0,1,3,2,4], [1,0,0,0,0], 0, 0; or [0,1,3,2,4], [1,0,0,0,1], 0, 0; or [0,2,1,3,4], [0,1,0,1,0], 0, 1; or [0,2,1,3,4], [0,1,0,1,1], 0, 1; or [2,1,3,0,4], [1,1,1,1,0], 0, 1; or [2,1,3,0,4], [1,1,1,1,1], 0, 1; or [0,1,3,2,4], [0,0,1,0,0], 0, 0; or [0,1,3,2,4], [0,0,1,0,1], 0, 0; or [0,1,3,2,4], [0,0,1,1,0], 0, 1; or [0,1,3,2,4], [0,0,1,1,1], 0, 1; or [0,1,3,2,4], [1,0,0,1,0], 0, 1; or [0,1,3,2,4], [1,0,0,1,1], 0, 1; or [0,2,1,3,4], [0,0,0,0,0], 0, 0; or [0,2,1,3,4], [0,0,0,0,1], 0, 0; or [1,2,0,3,4], [0,0,1,1,0], 0, 1; or [1,2,0,3,4], [0,0,1,1,1], 0, 1; or [0,3,2,1,4], [1,1,1,1,0], 0, 0; or [0,3,2,1,4], [1,1,1,1,1], 0, 0; or [1,0,2,3,4], [0,0,0,0,0], 0, 1; or [1,0,2,3,4], [0,0,0,0,1], 0, 1; or [1,3,0,2,4], [0,1,0,1,0], 0, 1; or [1,3,0,2,4], [0,1,0,1,1], 0, 1; or [1,3,0,2,4], [1,1,1,1,0], 0, 0; or [1,3,0,2,4], [1,1,1,1,1], 0, 0; or [2,0,3,1,4], [0,0,0,0,0], 0, 0; or [2,0,3,1,4], [0,0,0,0,1], 0, 0; or [2,1,0,3,4], [1,1,1,1,0], 0, 0; or [2,1,0,3,4], [1,1,1,1,1], 0, 0; or [3,0,1,2,4], [0,1,0,0,0], 0, 0; or [3,0,1,2,4], [0,1,0,0,1], 0, 0; or [3,2,0,1,4], [0,0,1,0,0], 0, 0; or [3,2,0,1,4]， [0,0,1,0,1]， 0， 0。 4. The method according to any one of claims 1-3, characterized in that, When N equals 256, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5,6,7], [0,0,0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7], [0,0,0,0,0,0,0,1], 0, 0; or [0,1,2,3,5,4,7,6], [1,1,0,0,0,0,0,0], 0, 0; or [0,1,2,3,5,4,7,6], [1,1,0,0,0,0,1,0], 0, 0; or [0,1,2,3,6,4,5,7], [1,1,1,0,1,0,1,0], 0, 1; or [0,1,2,3,6,4,5,7], [1,1,1,0,1,0,1,1], 0, 1; or [0,1,2,4,6,5,3,7], [0,0,0,0,0,1,0,0], 0, 1; or [0,1,2,4,6,5,3,7], [0,0,0,0,0,1,0,1], 0, 1; or [0,1,2,3,4,5,6,7], [0,1,1,0,0,1,1,0], 0, 0; or [0,1,2,3,4,5,6,7], [0,1,1,0,0,1,1,1], 0, 0; or [0,1,2,3,4,6,5,7], [0,1,0,1,0,0,1,0], 0, 1; or [0,1,2,3,4,6,5,7], [0,1,0,1,0,0,1,1], 0, 1; or [0,1,2,3,5,4,7,6], [1,1,0,0,0,0,0,0], 0, 1; or [0,1,2,3,5,4,7,6], [1,1,0,0,0,0,1,0], 0, 1; or [0,1,2,4,6,5,3,7], [1,0,0,1,1,1,1,0], 0, 0; or [0,1,2,4,6,5,3,7], [1,0,0,1,1,1,1,1], 0, 0; or [0,1,2,3,4,5,6,7], [0,1,1,0,0,1,1,0], 0, 1; or [0,1,2,3,4,5,6,7], [0,1,1,0,0,1,1,1], 0, 1; or [0,1,2,3,4,6,5,7], [0,1,0,1,0,0,1,0], 0, 0; or [0,1,2,3,4,6,5,7], [0,1,0,1,0,0,1,1], 0, 0; or [0,1,2,3,6,4,5,7], [1,1,1,0,1,0,1,0], 0, 0; or [0,1,2,3,6,4,5,7], [1,1,1,0,1,0,1,1], 0, 0; or [0,1,2,4,6,5,3,7], [1,0,0,1,1,1,1,0], 0, 1; or [0,1,2,4,6,5,3,7], [1,0,0,1,1,1,1,1], 0, 1; or [0,1,2,3,4,6,5,7], [1,0,1,1,1,0,0,0], 0, 0; or [0,1,2,3,4,6,5,7], [1,0,1,1,1,0,0,1], 0, 0; or [0,1,2,3,4,6,5,7], [1,0,1,1,1,0,0,0], 0, 1; or [0,1,2,3,4,6,5,7], [1,0,1,1,1,0,0,1], 0, 1; or [0,1,2,3,5,4,6,7], [0,0,1,1,1,1,1,0], 0, 1; or [0,1,2,3,5,4,6,7], [0,0,1,1,1,1,1,1], 0, 1; or [0,1,2,4,6,5,3,7], [0,0,0,0,0,1,0,0], 0, 0; or [0,1,2,4,6,5,3,7], [0,0,0,0,0,1,0,1], 0, 0; or [0,1,2,3,4,5,6,7], [0,0,0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7], [0,0,0,0,0,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7], [1,0,0,0,1,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7], [1,0,0,0,1,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7], [1,0,0,0,1,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7], [1,0,0,0,1,0,1,1], 0, 1; or [0,1,2,3,5,4,6,7], [0,0,1,1,1,1,1,0], 0, 0; or [0,1,2,3,5,4,6,7]， [0,0,1,1,1,1,1,1]， 0， 0。 5. The method according to any one of claims 1-4, characterized in that, When N equals 512, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5,6,7,8], [0,0,0,0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [0,0,0,0,0,0,0,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8], [1,0,1,0,1,0,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8] [1,0,1,0,1,0,0,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8], [1,1,0,1,0,1,0,1,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [1,1,0,1,0,1,0,1,1], 0, 0; or [0,1,2,3,4,5,7,6,8], [0,0,1,1,1,0,0,1,0], 0, 1; or [0,1,2,3,4,5,7,6,8] [0,0,1,1,1,0,0,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8], [0,0,1,0,0,0,1,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [0,0,1,0,0,0,1,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8], [0,0,1,0,0,0,1,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [0,0,1,0,0,0,1,1,1], 0, 1; or [0,1,2,3,4,5,6,8,7], [1,1,1,1,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6,8,7], [1,1,1,1,0,0,0,1,0], 0, 0; or [0,1,2,3,4,5,6,8,7], [1,1,1,1,0,0,0,1,0], 0, 1; or [0,1,2,3,4,5,6,8,7], [1,1,1,1,0,0,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [0,0,0,0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [0,0,0,0,0,0,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8], [1,0,1,0,1,0,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [1,0,1,0,1,0,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8], [1,1,0,1,0,1,0,1,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [1,1,0,1,0,1,0,1,1], 0, 1; or [0,1,2,3,4,5,7,6,8], [0,0,1,1,1,0,0,1,0], 0, 0; or [0,1,2,3,4,5,7,6,8], [0,0,1,1,1,0,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8] [0,1,0,0,0,1,1,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [0,1,0,0,0,1,1,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8], [0,1,0,0,0,1,1,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [0,1,0,0,0,1,1,0,1], 0, 1; or [0,1,2,3,4,5,7,6,8], [1,0,0,1,1,1,0,0,0], 0, 0; or [0,1,2,3,4,5,7,6,8], [1,0,0,1,1,1,0,0,1], 0, 0; or [0,1,2,3,4,5,7,6,8], [1,0,0,1,1,1,0,0,0], 0, 1; or [0,1,2,3,4,5,7,6,8], [1,0,0,1,1,1,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8], [1,0,0,0,1,0,1,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8], [1,0,0,0,1,0,1,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8] [1,0,0,0,1,0,1,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8], [1,0,0,0,1,0,1,0,1], 0, 1; or [0,1,2,3,4,5,7,8,6], [0,1,1,0,0,1,0,1,0], 0, 0; or [0,1,2,3,4,5,7,8,6], [0,1,1,0,0,1,1,1,0], 0, 0; or [0,1,2,3,4,5,7,8,6], [0,1,1,0,0,1,0,1,0], 0, 1; or [0,1,2,3,4,5,7,8,6]， [0,1,1,0,0,1,1,1,0]， 0， 1。 6. The method according to any one of claims 1-5, characterized in that, When N equals 1024, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5,6,7,8,9], [0,0,0,0,0,0,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,0,0,0,0,0,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,1,1,0,0,1,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,1,1,0,0,1,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,1,0,1,0,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,1,0,1,0,0,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,0,1,0,1,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,0,1,0,1,0,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,0,0,0,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,0,0,0,0,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,1,1,0,0,1,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,1,1,0,0,1,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,1,0,1,0,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,1,0,1,0,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,0,1,0,1,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,0,1,0,1,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,0,1,0,0,0,1,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,1,0,0,0,1,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,1,0,0,0,1,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,0,1,0,0,0,1,0,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,1,0,0,0,0,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,1,0,0,0,0,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,1,0,0,0,0,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [1,0,0,1,0,0,0,0,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,1,0,0,0,1,1,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,1,0,0,0,1,1,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,1,0,0,0,1,1,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,0,0,1,0,0,0,1,1,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,0,0,1,1,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,0,0,1,1,0,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,0,0,1,1,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,0,0,0,1,1,0,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,0,0,1,1,1,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,0,0,1,1,1,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,0,0,1,1,1,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [0,1,1,0,0,1,1,1,0,1], 0, 1; or [0,1,2,3,4,5,6,7,8,9], [1,0,1,0,0,1,0,0,0,0], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,1,0,0,1,0,0,0,1], 0, 0; or [0,1,2,3,4,5,6,7,8,9], [1,0,1,0,0,1,0,0,0,0], 0, 1; or [0,1,2,3,4,5,6,7,8,9]， [1,0,1,0,0,1,0,0,0,1]， 0， 1。 7. The method according to any one of claims 1-6, characterized in that, The GCP is generated through a generalized Boolean function mapping.
8. The method according to claim 7, characterized in that, One of the sequences in the GCP is Another sequence is , , , .
9. The method according to any one of claims 1-8, characterized in that, The N is equal to 160, 320, 640, or 832, and the GCP is based on the first GCP. Second GCP It is determined that the length of the first GCP is The length of the second GCP is , The GCP satisfy: in, Represents a sequence The reverse sequence, Represents a sequence The reverse sequence, Indicates the Kronecker product; One of the sequences in the first GCP is Another sequence is , , , ; When N equals 160, 320, or 640, the second GCP is any one of the following: 1, 1, -1, 1, -1, 1, -1, -1, 1, 1； 1, 1, -1, 1, 1, 1, 1, 1, -1, -1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1； 1, 1, -1, -1, 1, 1, 1, -1, 1, -1； or, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1； 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1； When N equals 832, the second GCP is: 1, 1, 1, 1, -1, 1, 1, -1,-1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1,1,-1,-1,1,1,1； 1, 1, 1, 1, -1, 1, 1, -1,-1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1,1, 1, -1, -1, -1。 10. The method according to claim 9, characterized in that, When N equals 160, the parameters used to generate the GCP are any one of the following sets: [0,2,1,3], [0,0,0,0], 0, 1, the second GCP = ( );or [0,2,1,3], [0,0,0,1], 0, 1, the second GCP = ( );or [2,1,0,3], [0,0,0,0], 0, 0, the second GCP = ( );or [2,1,0,3], [0,0,0,1], 0, 0, the second GCP = ( );or [0,1,2], [0,0,0], 0, 1, the second GCP = ( );or [0,1,2], [0,0,1], 0, 1, the second GCP = ( );or [0,1,2,3], [0,1,0,0], 0, 0, the second GCP = ( );or [0,1,2,3], [0,1,0,1], 0, 0, the second GCP = ( );or [0,1,2,3], [0,1,1,0], 0, 0, the second GCP = ( );or [0,1,2,3], [0,1,1,1], 0, 0, the second GCP = ( );or [0,2,1,3], [0,0,1,0], 0, 1, the second GCP = ( );or [0,2,1,3], [0,0,1,1], 0, 1, the second GCP = ( );or [1,0,2,3], [1,1,0,0], 0, 1, the second GCP = ( );or [1,0,2,3], [1,1,0,1], 0, 1, the second GCP = ( );or [1,0,2,3], [1,1,1,0], 0, 1, the second GCP = ( );or [1,0,2,3], [1,1,1,1], 0, 1, the second GCP = ( );or [1,2,0,3], [1,1,0,0], 0, 0, the second GCP = ( );or [1,2,0,3], [1,1,0,1], 0, 0, the second GCP = ( );or [1,2,0,3], [1,1,1,0], 0, 0, the second GCP = ( );or [1,2,0,3], [1,1,1,1], 0, 0, the second GCP = ( ).
11. The method according to claim 9 or 10, characterized in that, When N equals 320, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4], [0,0,0,0,0], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,0,0,1], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,0,1,0], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,0,1,1], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,1,0,0], 0, 1, the second GCP = ( );or [0,1,2,3,4], [0,0,1,0,1], 0, 1, the second GCP = ( );or [0,1,2,3,4], [0,0,1,1,0], 0, 1, the second GCP = ( );or [0,1,2,3,4], [0,0,1,1,1], 0, 1, the second GCP = ( );or [0,1,3,2,4], [1,0,0,0,0], 0, 0, the second GCP = ( );or [0,1,3,2,4], [1,0,0,0,1], 0, 0, the second GCP = ( );or [0,1,3,2,4], [1,0,0,1,0], 0, 0, the second GCP = ( );or [0,1,3,2,4], [1,0,0,1,1], 0, 0, the second GCP = ( );or [0,1,3,4,2], [1,1,0,0,0], 0, 1, the second GCP = ( );or [0,1,3,4,2], [1,1,1,0,0], 0, 1, the second GCP = ( );or [0,1,3,4,2], [1,1,0,1,1], 0, 1, the second GCP = ( );or [0,1,3,4,2], [1,1,1,1,1], 0, 1, the second GCP = ( );or [0,2,4,3,1], [0,0,0,0,1], 0, 1, the second GCP = ( );or [0,2,4,3,1], [0,1,0,0,1], 0, 1, the second GCP = ( );or [0,2,4,3,1], [0,0,0,1,0], 0, 1, the second GCP = ( );or [0,2,4,3,1], [0,1,0,1,0], 0, 1, the second GCP = ( ).
12. The method according to any one of claims 9-11, characterized in that, When N equals 640, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4,5], [0,0,0,0,0,0], 0, 0, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,0,1], 0, 0, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,0,0], 0, 1, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,0,1], 0, 1, the second GCP = ( );or [0,1,3,4,2,5], [1,0,1,1,0,0], 0, 1, the second GCP = ( );or [0,1,3,4,2,5], [1,0,1,1,0,1], 0, 1, the second GCP = ( );or [0,2,4,3,1,5], [0,0,0,1,1,0], 0, 0, the second GCP = ( );or [0,2,4,3,1,5], [0,0,0,1,1,1], 0, 0, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,0,0], 0, 1, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,0,1], 0, 1, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,1,0], 0, 0, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,1,1], 0, 0, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,1,0], 0, 1, the second GCP = ( );or [0,1,2,3,4,5], [0,0,0,0,1,1], 0, 1, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,0,0], 0, 0, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,0,1], 0, 0, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,1,0], 0, 0, the second GCP = ( );or [0,1,2,4,3,5], [1,0,0,0,1,1], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,0,0,0], 0, 1, the second GCP = ( );or [0,1,2,3,4], [0,0,0,0,1], 0, 1, the second GCP = ( ).
13. The method according to any one of claims 9-12, characterized in that, When N equals 832, the parameters used to generate the GCP are any one of the following sets: [0,1,2,3,4], [0,0,0,0,0], 0, 0, the second GCP = ( );or [0,1,2,3,4], [0,0,0,0,1], 0, 0, the second GCP = ( );or [0,3,1,2,4], [1,0,1,0,0], 0, 1, the second GCP = ( );or [0,3,1,2,4], [1,0,1,0,1], 0, 1, the second GCP = ( );or [0,1,3,2,4], [1,0,0,1,0], 0, 0, the second GCP = ( );or [0,1,3,2,4], [1,0,0,1,1], 0, 0, the second GCP = ( );or [2,0,1,4,3], [0,1,0,0,0], 0, 0, the second GCP = ( );or [2,0,1,4,3], [0,1,0,1,0], 0, 0, the second GCP = ( );or [1,0,3,2,4], [0,0,0,0,0], 0, 0, the second GCP = ( );or [1,0,3,2,4], [0,0,0,0,1], 0, 0, the second GCP = ( );or [2,0,1,3,4], [0,1,0,1,0], 0, 1, the second GCP = ( );or [2,0,1,3,4], [0,1,0,1,1], 0, 1, the second GCP = ( );or [0,1,2,3,4], [0,0,1,0,0], 0, 1. The second GCP = ( );or [0,1,2,3,4], [0,0,1,0,1], 0, 1, the second GCP = ( );or [0,1,3,2,4], [1,0,0,0,0], 0, 1. The second GCP = ( );or [0,1,3,2,4], [1,0,0,0,1], 0, 1. The second GCP = ( );or [1,0,2,3,4], [0,1,1,0,0], 0, 0, the second GCP = ( );or [1,0,2,3,4], [0,1,1,0,1], 0, 0, the second GCP = ( );or [1,3,2,0,4], [0,0,1,1,0], 0, 1. The second GCP = ( );or [1,3,2,0,4], [0,0,1,1,1], 0, 1. The second GCP = ( ).
14. A device sensing method, characterized in that, The method includes: A sensing signal is transmitted, which is generated based on a Gray complement pair GCP of length N, where N is greater than or equal to 32. When the sensing signal is a multi-carrier signal, the difference between the length N of the GCP and the target value is less than a threshold. The target value is determined by the subcarrier spacing, sensing bandwidth, and resource element (RE) mapping method. Receive the echo signal of the sensed signal; Process the echo signal accordingly; When N equals 128, the GCP is any one of the following pairs: 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1,-1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1,1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1,-1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1,1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1,-1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1,1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1,1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1,1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1,1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1,-1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1； or, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1,1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1,1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1； 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1,1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1,1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1,-1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1,-1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1； 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1,1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1,-1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1； -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1,1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1,1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1； -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1,-1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1,1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1,-1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1,1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1,-1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1,-1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1,1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1,-1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1； -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1,-1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1,1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1,1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1,1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1,-1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1,1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1,-1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1,1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1,-1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1,1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1,1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1,1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1,-1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1,-1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1,1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； or, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1,1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1,1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1； -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1,1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1,1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1,1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1,1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1,-1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1； -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1,1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1,-1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1,1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1,1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1,1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1,1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1,-1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1； 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1,-1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1,-1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1； 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1,-1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1,-1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1,-1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1,1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1,-1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1,-1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1； 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1,1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1,-1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1,1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1,-1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1,1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1,-1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1,-1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1； 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1,1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1,1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1,1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1,1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1,-1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1,1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1,1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1,1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1,-1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1； -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1,-1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1,-1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1,-1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1； or, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1,-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1； 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1,-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1,1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1； or, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1,-1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1,-1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1,-1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1,-1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1； 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1,-1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1； or, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1,-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1； -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1,1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1,1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1,-1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1； or, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1,-1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1,-1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1,-1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1,-1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1； -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1,-1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1； or, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1,1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1,-1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1； 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1,1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1,-1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1,1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1； or, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1,1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1； 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1,1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1,1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1； or, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1,1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1,-1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1； -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1,-1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1,1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1,-1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1； or, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1,1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1； -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1,-1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1,-1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1,-1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1； or, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1,-1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1,1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1,-1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1,-1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1,-1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1； or, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1,-1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1,1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1,1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1,-1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1； 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1,-1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1,1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1,1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1,-1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1； or, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1,-1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1,1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1,-1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1,1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； or, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1,-1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1,1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1,1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1,-1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1； -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1,1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1,1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1,1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1,1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1,1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1,1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1,-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1； 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1,1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1,1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1； 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1,1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1,-1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1,1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1,1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1,-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1； -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1,-1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1,1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1,1, 1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1,1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1； -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1,-1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1,1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1,1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1,1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1； 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1,1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1,1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1,-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1,1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1,-1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1； 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1,1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1,1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1； 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1,1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1,1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1,-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1,1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1,-1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1； 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1,1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1。 15. The method according to claim 14, characterized in that, When N equals 64, the GCP is any one of the following pairs: 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1,1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； or, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1,1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1,-1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1； -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1,1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1,1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1,1； or, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1,-1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1,-1； -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1,-1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1,-1； or, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1,1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1,1； 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1,1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1,1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1； or, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1,-1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1,1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1； 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1,-1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1； or, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1,-1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1,1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； or, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1,-1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1,1； -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1,1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1,1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1； or, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1,-1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1； -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1； or, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1,1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1； -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1,-1； or, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1,1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1； 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1,1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1,-1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1； 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1,1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1； 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1,1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1,1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1； 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1,-1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1,-1； or, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1,-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1； 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1,-1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1； or, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1,-1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1； 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1； or, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1,1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1,-1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1； -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1,-1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1； or, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1； -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1； or, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1； 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1； or, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1,1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1； 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1,1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1,-1； or, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1,-1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1,1； 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1,1, 1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1,1, 1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1； 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1,-1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1,1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1,1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1,1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1,1； -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1,-1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1,1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1； -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1,-1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1,-1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1,1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1,1, 1； -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1,-1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1； or, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1,1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1； 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1,1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1； or, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1,1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1,1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1； 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1,1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1,1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1,-1； or, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1,1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1； 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1,1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1,1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1； or, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1,-1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1,-1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1,-1； 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1,-1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1,1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1； or, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1,1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1； -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1,-1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1,-1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1,1； or, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1,-1； -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1,1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1,-1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1； or, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1,1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1,1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1,1, -1； -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1,1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1,1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1,1, -1； or, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1,-1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1,1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1； -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1,1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1,1, 1； or, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1； 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1,1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1； or, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1,-1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1,1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1； 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1,-1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1,-1, -1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1,-1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1,-1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, 1,1； 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1,-1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1,-1； or, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1,-1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1,1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1； 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1,-1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1,-1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, -1, 1,1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1,1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1,1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1,-1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1,-1； -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1,-1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1,-1。 16. The method according to claim 14 or 15, characterized in that, When N equals 32, the GCP is any one of the following pairs: 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1,-1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1； 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1； or, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1； or, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1,-1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1； -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1,-1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1； or, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1； -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1； or, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1,1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1； -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1,1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1； or, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1； -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1,1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1； or, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1,1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1； 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1,-1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1； or, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1； 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1,1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1； or, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1； -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1； or, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1,1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1； -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1； or, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1； -1, -1, 1, 1, -1, 1, -1, 1, -1, -1,-1, -1, -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1； or, 1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1； -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1； or, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1,-1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1； 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1,1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1； or, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1,1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1； 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1,1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1； or, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1,1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1； -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1； or, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1,1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1； -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1； or, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1,-1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1； 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1,-1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1； or, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1,1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1； 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1； or, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1； -1, -1, -1, 1, -1, -1, 1, -1, 1, 1,1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1； or, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1； -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1,1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1； or, 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1,-1, 1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1； -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1,-1, 1, -1, 1, -1, -1, -1, 1, 1, 1, -1, -1, 1； or, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1； -1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1,1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, -1； or, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1,-1, -1, 1, -1, 1, 1, 1, -1, -1, 1, -1, -1, 1； 1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1,-1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1； or, 1, -1, -1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1； 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1,1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1； or, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1,-1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1； 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1； or, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, -1, 1,-1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1； 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1,1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1； or, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1,1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1； 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1； or, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1,1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1； 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1； or, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1, -1,1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1； 1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1,-1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1； or, 1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1,1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1； 1, -1, -1, 1, 1, 1, -1, -1, -1, 1,1, -1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1； or, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1,1, -1, -1, -1, 1, -1, 1, -1, 1, 1, -1； 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1； or, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1,-1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1； 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1,1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, -1。 17. The method according to any one of claims 1-16, characterized in that, The RE mapping method maps one element of the GCP to every M REs; the target value, the subcarrier spacing, the sensing bandwidth, and M satisfy the following formula: in, For the subcarrier spacing, The sensing bandwidth is [the bandwidth of the sensor]. This indicates rounding down to the nearest integer.
18. The method according to any one of claims 1-17, characterized in that, The processing based on the echo signal includes: The distance to the target object is sensed based on the echo signal, where the target object is the object that reflects the sensed signal to form the echo signal.
19. The method according to claim 18, characterized in that, The step of sensing the distance to the target object based on the echo signal includes: Perform aperiodic autocorrelation calculation on the GCP and the GCP corresponding to the echo signal; The signal propagation delay between the sensing device and the target object is determined based on the result of the aperiodic autocorrelation calculation. The distance to the target object is determined based on the signal propagation delay.
20. A communication device, characterized in that, The communication device includes a module for performing the method as described in any one of claims 1 to 19.
21. A communication device, characterized in that, The communication device includes: a processor; The processor is configured to execute computer programs or instructions to implement the method as described in any one of claims 1 to 19.
22. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program or instructions that, when executed by a communication device, implement the method as described in any one of claims 1 to 19.
23. A computer program product, characterized in that, When the computer program product is run on a communication device, the method as described in any one of claims 1 to 19 is performed.