Numerology of a pulse-tone modulation scheme

Abstract

Methods and systems directed to numerologies of a pulse-tone modulation scheme are described. An example method includes allocating transmission resources to one or more transmissions in a wireless network according to a first numerology that defines a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two-dimensional resource plane, and generating, based on allocated transmission resources, one or more transmission waveforms for N receiving devices, where N is a positive integer. An example system includes one or more processors configured to implement the above-described method.

Description

International Patent Application Attorney Docket No.: 119314.8126.WO00 NUMEROLOGY OF A PULSE-TONE MODULATION SCHEME CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to U.S. Provisional Application No.63 / 695,777, filed on September 17, 2024, entitled “NUMEROLOGY OF A PULSE-TONE MODULATION SCHEME,” the disclosure of which is hereby incorporated by reference herein in its entirety. TECHNICAL FIELD

[0002] The present document relates to digital communication. BACKGROUND

[0003] Due to an explosive growth in the number of wireless user devices and the amount of wireless data that these devices can generate or consume, current wireless communication networks are fast running out of bandwidth to accommodate such a high growth in data traffic and provide high quality of service to users.

[0004] Various efforts are underway in the telecommunication industry to come up with next generation of wireless technologies that can keep up with the demand on performance of wireless devices and networks. Many of those activities involve situations in which a large number of user devices may be served by a network. SUMMARY

[0005] This document discloses techniques that may be used in wireless networks to provide wireless connectivity between a network device and one or more user devices, or between user devices, using a physical layer having flexible numerology, where transmission signal waveforms are generated from a set of pulse-tone signals having mathematical properties disclosed herein.

[0006] In an example aspect, a digital communication method includes allocating transmission resources to one or more transmissions in a wireless network according to a first numerology that defines a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two-dimensional resource plane, and generating, by a transmitting device based on allocated transmission resources, one or more transmission waveforms for N receiving devices, where N is a positive integer.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0007] In another example aspect, a digital communication method includes receiving, by a receiving device, a wireless signal transmission according to a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two- dimensional resource plane, and performing a signal reception operation based on the wireless signal transmission. In this digital communication method, a first numerology is indicated by a transmitting device to the receiving device or is implicitly determined from a property of a wireless channel over which the wireless signal transmission is received.

[0008] In yet another example aspect, a digital communication method includes configuring a periodicity of pilot signal transmission along a first resource dimension of a two-dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension, and performing pilot signal transmissions according to the periodicity.

[0009] In yet another example aspect, a digital communication method includes receiving the pilot signals that are configured to have a periodicity of a pilot signal transmission along a first resource dimension of a two-dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension, and performing a reception operation based on the pilot signals.

[0010] In yet another example aspect, a digital communication method includes determining to use a first numerology that defines a first set of transmission resources from transmission resources in a two-dimensional time-frequency resource plane, and determining to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources. The digital communication method further includes mapping a first set of information bits to a first set of resource blocks in a two-dimensional delay-Doppler resource plane and a second set of information bits to a second set of resource blocks in the two-dimensional delay-Doppler resource plane, where a plurality of information bits comprises the first set of information bits for a first user device operating based on a legacy wireless protocol and the second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol. The digital communication method then includes generating, using a two-dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks, and transmitting, over aInternational Patent Application Attorney Docket No.: 119314.8126.WO00 wireless channel, the first set of transmission waveforms and the second set of transmission waveforms. In this digital communication method, each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and the transmission resources in the two-dimensional time-frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol.

[0011] In yet another example aspect, a digital communication apparatus includes transceiver circuitry and circuitry configured to be compatible with a legacy wireless protocol and provide a plurality of information bits comprising a first set of information bits for a first user device operating based on the legacy wireless protocol and a second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol. In this example apparatus, the transceiver circuitry configured to determine to use a first numerology that defines a first set of transmission resources from transmission resources in a two-dimensional time-frequency resource plane, and determine to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources. The transceiver circuitry is further configured to map the first set of information bits to a first set of resource blocks in a two-dimensional delay-Doppler resource plane and the second set of information bits to a second set of resource blocks in the two- dimensional delay-Doppler resource plane, generate, using a two-dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks, and transmit, over a wireless channel, the first set of transmission waveforms and the second set of transmission waveforms. In this digital communication apparatus, wherein each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and wherein the transmission resources in the two-dimensional time-frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol.

[0012] In yet another example aspect, a wireless communication apparatus that implements the above-described methods is disclosed. The wireless communication apparatus may include a transmitter circuit and / or a receiver circuit to perform signal transmissions or receptions and atInternational Patent Application Attorney Docket No.: 119314.8126.WO00 least one processor to implement various signal processing techniques described in the present document.

[0013] In yet another example aspect, a wireless system in which one or more of the above- described methods are implemented is disclosed.

[0014] In yet another example aspect, the method may be embodied as processor-executable code and may be stored on a computer-readable program medium.

[0015] These, and other, features are described in this document. DESCRIPTION OF THE DRAWINGS

[0016] FIG.1 shows an example communication network.

[0017] FIG.2 shows a simplified example of a wireless communication system in which uplink and downlink transmissions are performed.

[0018] FIG.3 shows an example of a backward-compatible communication apparatus.

[0019] FIG.4 shows an example of a resource grid in the two-dimensional time-frequency plane.

[0020] FIG.5 shows delay-Doppler resource block supported numerologies for different Physical Resource Block (PRB) lengths.

[0021] FIG.6 shows examples of time-frequency allocations of different numbers of RBs using different time durations.

[0022] FIG.7 shows an example of the delay-Doppler plane for an i-th orthogonal time frequency space (OTFS) block.

[0023] FIG.8 shows examples of time and frequency offsets applied to different OTFS blocks in the construction of a subframe.

[0024] FIG.9 shows an example of selecting a delay-Doppler numerology of one UE allocation.

[0025] FIGS.10A and 10B show examples of arranging sensing pilots in a resource grid that supports up to 3 kHz Doppler spread.

[0026] FIGS.11-13 show examples of arranging sensing pilots in a resource grid that support up to 6 kHz, 12 kHz, and 8 kHz Doppler spread, respectively.

[0027] FIG.14 shows a block diagram of an example orthogonal frequency division multiplexing (OFDM) transmitter.

[0028] FIG.15 shows a block diagram of an example OTFS transmitter.

[0029] FIG.16A shows an example pulse used as a basis signal for wireless communication.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0030] FIG.16B shows an example of rotations undergone by a delay-Doppler domain pulse.

[0031] FIG.16C is an example of a quasi-periodic delay Doppler domain pulse.

[0032] FIG.16D shows details of an example OTFS waveform.

[0033] FIG.17 shows an example of a resource block in the delay-Doppler plane.

[0034] FIG.18 shows an example of a delay-Doppler grid.

[0035] FIG.19 shows an example of a delay-Doppler plane divided into resource blocks, illustrating that the delay-Doppler signals are quasi-periodic.

[0036] FIG.20 shows the delay-Doppler plane of FIG.19 for the case where the delay-Doppler signal is a delta function.

[0037] FIG.21 shows an example of a Pulsone™ being generated at the transmitter.

[0038] FIG.22 shows additional details related to the Pulsone generation shown in FIG.21.

[0039] FIG.23 shows a block diagram of an example implementation of an OTFS transmitter.

[0040] FIG.24 shows an example of the processing performed by an OTFS demodulator.

[0041] FIG.25 shows a block diagram of an example implementation of an OTFS receiver.

[0042] FIG.26 shows an example of a point pilot with a guard band.

[0043] FIG.27 shows an example of a point pilot with a guard band and a set of effective channel reflections.

[0044] FIG.28 shows an example of an overlaid point pilot.

[0045] FIG.29 shows an example of an overlaid point pilot and a set of effective channel reflections.

[0046] FIG.30 shows an example of a spread pilot.

[0047] FIG.31 shows a block diagram of an example where a spread pilot is used in OTFS transmission.

[0048] FIG.32 shows an example of the adjustment of a calculated channel response.

[0049] FIG.33 shows an example of a graph representation of an adjusted channel response.

[0050] FIG.34 shows the reciprocal of the graph depicted in FIG.33, which represents the channel equation.

[0051] FIG.35 shows the adjusted channel response graph depicted in FIG.33 for the case where MAP equalization is used.

[0052] FIG.36 shows the graph depicted in FIG.35 for an example initialization condition.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0053] FIG.37 shows an example of the observation nodes for MAP equalization.

[0054] FIG.38 shows additional detail of the observation nodes depicted in FIG.37.

[0055] FIG.39 shows a block diagram of an example implementation of an iterative OTFS receiver.

[0056] FIG.40 shows an example of a hardware platform.

[0057] FIGS.41-45 are flowcharts for various example methods of digital communication. DETAILED DESCRIPTION

[0058] Section headings are used in the present document to improve readability of the description and do not in any way limit the discussion or the embodiments to the respective sections only. Furthermore, certain standard-specific terms are used for illustrative purpose only, and the disclosed techniques are applicable to any wireless communication systems.

[0059] 1 Wireless communication environment examples

[0060] The wireless or time-variant nature of the communication channel poses several challenges in design a transmission protocol suitable for wireless communication scenarios. These days, users expect their wireless devices to work everywhere and in a variety of mobile or stationary situations.

[0061] The relative movement of transmitters and receivers with respect to each other cause signal distortions such as varying channel delay, Doppler and / or angular spread, signal degradation due to ground clutter, sea clutter, and so on. Another example of signal degradation is flat fading in which an entire channel occupied by a transmission signal will experience fading or attenuation that may be relatively constant across the channel. In practice, a transmission scheme may need to be designed to fit within a certain link budget, maximum power constraint, or linearity of electronics used for transmitting or receiving signals.

[0062] Existing wireless systems, such as those defined by the Third Generation Partnership Project (3GPP) including 3G, 4G and 5G protocols, use orthogonal frequency division multiplexing (OFDM) modulation scheme as the underlying technology for generating transmission waveforms. To cope up with the differing channel characteristics, the existing wireless systems have incorporated features such as reference signal based channel estimation and allocation of transmission resources based on resource elements (RE) as basic building blocks that are defined by a time period, and a subcarrier width. Furthermore, to cope up withInternational Patent Application Attorney Docket No.: 119314.8126.WO00 different frequency bands in which the signals may be transmitted and also other operational parameters, the existing wireless systems use pre-determined subcarrier bandwidths (or subcarrier spacings). However, implementation of such features in the existing systems requires a large amount of overhead of message transmission, is less flexible to time variations in channels and typically requires complex signal processing both on the transmit side and on the receive side.

[0063] The various techniques described in the present document overcome the above discussed problems and others.

[0064] For example, in one example aspect, transmission signals use pulse-tone waveforms that have a mathematical basis in the delay-Doppler domain. Because wireless channels are primarily defined based on their delay spread and Doppler shifts (e.g., delay and Doppler distortions introduced by reflectors), the pulse-tone signals enable a less complex estimation of channel. In an example, these pulse-tone signals are generated using basis functions that are invariant under operations of time, delay, and Doppler shift. These properties may be used as a basis for orthogonal time frequency space (OTFS) modulation, further disclosed herein.

[0065] In another example aspect, the disclosed techniques allow for a flexible control over numerology used in a wireless system such that the numerology can be specified and controlled on a per-user device or a per-user device group basis. The numerology may also be flexible and alterable during run-time by providing scheduling flexibility to be able to signal changes to numerology without having to re-define or re-design a wireless system implementation.

[0066] In another example aspect, the disclosed techniques may be used to control use of pilot or reference signals in a more flexible manner than conventional wireless systems. For example, pilot bandwidth and periodicity may be controlled according to a target delay and / or Doppler behavior of the underlying channel between a transmitting device and a receiving device. In an example, the pilot bandwidth and periodicity may be configured separately for each user device. The disclosed techniques are also amenable to use a sensing pilot transmission in a seamlessly compatible manner.

[0067] These, and other, techniques are further described throughout the present document.

[0068] 2 Examples of wireless systemsInternational Patent Application Attorney Docket No.: 119314.8126.WO00

[0069] FIG.1 shows an example of a wireless communication system 100 in which a transmitter device 102 transmits signals to a receiver 104. The signals may undergo various wireless channels and multipaths, as depicted. Some reflectors such as buildings and trees may be static, while others such as cars, may be moving scatterers. The transmitter device 102 may be, for example, a user device, a mobile phone, a tablet, a computer, or another Internet of Things (IoT) device such as a smartwatch, a camera, and so on. The receiver device 104 may be a network device such as the base station. The signals transmitted from the base station to the transmitter 102 may experience similar channel degradations produced by static or moving scatterers. The techniques described in the present document may be implemented by the devices in the wireless communication system 100. The terms “transmitter” and “receiver” are simply used for convenience of explanation. As further described herein, depending on the direction of transmission (uplink or downlink), the network station may be transmitting or receiving and user device may be receiving or transmitting.

[0070] FIG.2 shows a simplified wireless network to highlight certain aspects of the disclosed technology. A transmitter transmits wireless signals to a receiver in the wireless network. Some transmissions in the network, variously called as downlink or downstream transmissions, a network-side node such as a base station acts as a transmitter of wireless signals and one or more user devices act as the receiver of these wireless signals. For some other transmissions, as depicted in FIG.2, the direction of transmission may be reversed. Such transmissions are often called uplink or upstream transmissions. For such transmissions, one or more user devices act as transmitters of the wireless signals and a network-side node such as the base station acts as the receiver of these signals (as depicted in FIG.2). Other type of transmissions in the network may include device-to-device transmissions, sometimes called direct or sideband transmissions. While the present document primarily uses the terms “downlink” and “uplink” for the sake of convenience, similar techniques may also be used for other situations in which transmissions in two directions are performed - e.g., inbound or incoming transmissions that are received by a wireless device and outbound or outgoing transmissions that are transmitted by a wireless device. For example, downlink transmissions may be inbound transmissions for a user device, while outbound transmissions for a network device. Similarly, uplink transmission may be inbound transmissions for a network device while outbound transmissions from a wireless device.International Patent Application Attorney Docket No.: 119314.8126.WO00 Therefore, for some embodiments, the disclosed techniques may also be described using terms such as “inbound” and “outbound” transmission without importing any 3GPP-specific or other wireless protocol-specific meaning to the terms “uplink” and “downlink.”

[0071] In frequency division multiplexing (FDM) networks, the transmissions to a base station and the transmissions from the base station may occupy different frequency bands (each of which may occupy continuous or discontinuous spectrum). In time division multiplexing (TDM) networks, the transmissions to a base station and the transmissions from the base station occupy a same frequency band but are separated in time domain using a TDM mechanism such as time slot-based transmissions.

[0072] 3 Examples of OTFS use cases

[0073] An OTFS waveform generated as described herein may be used in a variety of different digital communication scenarios such as underwater acoustic wave communications, deep-space communication, communication with non-terrestrial equipment such as satellites, airborne devices such as airplanes, balloons, drones, etc. The communication channel in such cases may comprise aerial-to-ground, ground-to-aerial or ariel-to-ariel communication, underwater acoustic wave communication, deep space communication and so on. More generally, the OTFS waveform may be used in doubly-spread channels, i.e., a channel that is both time-selective (due to Doppler spread) and frequency-selective (due to delay spread), making it a complex environment for wireless communication systems. Furthermore, the disclosed techniques may be applied in generally any frequency range - from sub-MHz (e.g., underwater acoustics that uses 10 Hz to 1 MHz), MHz, GHz or THz and beyond.

[0074] 4 Examples of numerology-defined OTFS

[0075] Currently, most popular cellular wireless technology deployments are based on interoperability standards (or protocols) published by the third generation partnership project (3GPP) consortium. These technologies are known by various acronyms, and generally grouped into third generation (3G), 4G, 5G (also called new radio NR) and the upcoming 6G technologies. In particular, the transmission signals defined by these standards use certain architectural building blocks referred to as numerology (frequency planning), logical groupings of transmission resources. For example, a resource element (RE) represents a basic minimum unit of transmission resource. Along the time axis, the resources are represented in various unitsInternational Patent Application Attorney Docket No.: 119314.8126.WO00 such a frame, divided into two subframes, which are divided into a number of slots, which carry a number of transmission symbols and so on. Along the frequency axis, the resources are represented by a subcarrier bandwidth or a resource block (comprising an integer number of subcarriers) and so on. Furthermore, these standards define some reference signals such as the primary and secondary synchronization signals (PSS, SSS), demodulation reference signal (DMRS), channel state information reference signal (CSI-RS), sounding reference signal (SRS), phase-tracking reference signal (PTRS), and so on. Each standard (or protocol) defines various rules of how the reference signals are constructed and transmitted, and also rules of how the reference signals are received and processed.

[0076] 5 Examples of backward-compatible implementations

[0077] The numerological flexibility offered by the disclosed techniques may be used advantageously to implement transmission / reception devices in which the physical layer may implement the OTFS transmission / reception techniques disclosed in the present document, while re-using building blocks of Medium Access Control (MAC) and higher layers of the protocol stack. An example implementation is depicted in FIG.3. Here, communication apparatus 300 (e.g., implemented using the wireless hardware platform disclosed with respect to FIG.40), may include OTFS transceiver circuitry 304 and a legacy-derived upper layer implementation 302. In an example, the upper-layer implementation is circuitry configured to perform both networking (e.g., routing, scheduling) and application (e.g., user input and output) operations. Signals received from or transmitted to the transmission channel from the OTFS transceiver circuitry 304 may use the pulse-tone waveforms disclosed herein, while at the same time, interactions with user apps and higher layer protocol stack (e.g., protocol data unit formation, encryption, use of service flows, quality of service, etc.) may benefit from existing legacy protocols. It will be appreciated that such an implementation will allow the hybrid deployment of new device that selectively uses a legacy transmission waveform or the newly disclosed waveform, depending on the capabilities of the wireless device on the other side of the channel and / or the characteristics of the wireless channel.

[0078] 6 Example implementations of 6G using OTFS technology

[0079] This section provides an example of a technical specification that illustrates how OTFS technology may be used for implementing a physical (PHY) layer to meet the requirements of aInternational Patent Application Attorney Docket No.: 119314.8126.WO00 6th Generation (6G) wireless system. In particular, examples of frame structure and the organization of physical resources for transmission are discussed below. In the described embodiments, resource elements are defined in the delay-Doppler plane and resource allocation is performed using resource blocks that are OTFS blocks. In some examples, the numerology for the resource blocks is compatible with (e.g., identical to or overlapping) a legacy transmission waveform (e.g., a 5G wireless system waveform).

[0080] In the described examples and embodiments, the following symbols apply:

[0081] ^^^^^^^, ^^^ A quasi-periodic delta function in the delay-Doppler domain

[0082] Resolution of Doppler grid of the delay-Doppler plane of OTFS block ^^

[0083] Resolution of the delay grid of the delay-Doppler plane of OTFS block ^^

[0084] ^^^^^^^15 kHz

[0085] ^^^^^^, ^^^ The two-dimensional Root-Raised-Cosine pulse of OTFS block ^^

[0086] ^^^,^Doppler period of OTFS block ^^

[0087] ^^^,^Delay period of OTFS block ^^

[0088] ^^^^^^^^^,^Bandwidth of OTFS block ^^

[0089] ^^^^ீாBandwidth of a basic grid element

[0090] ^^^^ோ^Bandwidth of an RB

[0091] ^^^^,^^^^^Frequency offset of the centre of OTFS block ^^

[0092] ^^^Sampling frequency

[0093] Sampling rate of OTFS block ^^

[0094] ^^^,^^^Number of ^^^^^^^defining the sampling frequency

[0095] ^^ீா,்,^Length of an OTFS block ^^ in number of basic grid elements

[0096] ^^ீௌா^^,்௧Number of basic grid elements per slot in the time domain

[0097] ^^ఛ^Number of grid points in the delay dimension of OTFS block ^^

[0098] ^^ఔ^Number of grid points in the Doppler dimension of OTFS block ^^

[0099] ^^ோ^,^Bandwidth of an OTFS block ^^ in number of RBs

[0100] ^^ோ^Maximum number of RBs that fit in the available bandwidth

[0101] ^^ோோா^Number of REs per RBInternational Patent Application Attorney Docket No.: 119314.8126.WO00

[0102] ^^ோோா^,ఛNumber of REs in delay dimension of an OTFS block of size one RB

[0103] ^^ோோா^,ఔNumber of REs in Doppler dimension of an OTFS block of size one RB

[0104] ^^ோா,^Total number of REs in OTFS block ^^

[0105] ^^^^^^ The time-domain signal of an OTFS slot

[0106] ^^^ ^^^^^, ^^^ The continuous delay-Doppler OTFS block ^^

[0107] ^^^^^^^^,^^^ A sampled version of the continuous delay-Doppler OTFS block ^^

[0108] ^^^^^^^ Time domain waveform of OTFS block ^^ after it is re-centred

[0109] ^^^,^^^^^^ Continuous baseband time-domain realization of OTFS block ^^

[0110] ^^^,^^^^^^ Discrete equivalent of the baseband time-domain signal ^^^,^^^^^^

[0111] ^̅^^,^^^^^^ Upsampled version of discrete baseband time-domain signal

[0112] ^^^^^^^,^Length in time of OTFS block ^^

[0113] ^^^^,^^^^^Time offset of the centre of OTFS block ^^

[0114] ^^^Radio frame duration

[0115] ^^ ா Time duration of a basic grid element

[0116] ^^^Basic time unit

[0117] ^^^^Subframe duration

[0118] ^^^^^௧Slot duration

[0119] ^^^^^^^^,^^^ Discrete delay-Doppler symbols of OTFS block ^^

[0120] ^^^ ^^^^^, ^^^ Continuous signal of the delay-Doppler symbols of OTFSblock ^^

[0121] In the described examples and embodiments, the abbreviations apply:

[0122] DD Delay-Doppler

[0123] OTFS Orthogonal time frequency spaceInternational Patent Application Attorney Docket No.: 119314.8126.WO00

[0124] PRB Physical resource block

[0125] RB Resource block

[0126] RE Resource Element

[0127] In the described embodiments, the sampling frequency is defined as ^^^(Hz), andthe basic time unit (or reference) is expressed as ^^^ ൌ 1 / ^^^ (seconds). The size of various fieldsin the time domain is expressed as a number of time units ^^^. Transmissions are organized intoframes with ^^^ ൌ 10 ^^^^ duration, each consisting of ten subframes of ^^^^ ൌ 15360 / ^^^ ൌ 1 ^^^^duration. In some embodiments, ^^^ is programmable to the following values: ^^^ ൌ ^^^^^^^ ∙ ^^^,^^^where Δ^^^^^ ൌ 15 ∙ 10ଷ Hz and ^^^,^^^ ൌ 1024 (for up to 10 MHz BW).

[0128] In the described embodiments:

[0129] − An OTFS slot has a duration of ^^^^^௧ ൌ 1 ^^^^, equivalent to a subframe.

[0130] − For each carrier, a resource grid of ^^ீௌா^^,்௧in time by ^^ீா,ிin frequency of basicgrid elements is defined, where a basic grid element is a time-frequency block of duration ^^ ா ൌ^^^^^௧ / 15 and bandwidth of ^^^^ீா ൌ 180 ^^^^^^. FIG. 4 illustrates an example of the resource grid.

[0131] − Resource elements (RE) are defined in the delay-Doppler plane.

[0132] − An RB is defined as a bandwidth of ^^^^ோ^ ൌ ^^^^ீா ൌ 180 ^^^^^^ in frequencydomain.

[0133] In some embodiments, when allocating resources, the starting time, length, and frequency offset may be defined, where the length in time of OTFS block ^^ is define as ^^^^^^^,^ൌ^^ீா,்,^ ∙ ^^ ா where ^^ீா,்,^ ൌ 1, 2, .. , 15 is the number of basic grid elements in the time domainconstructing an OTFS block ^^.

[0134] An allocation of one RB results in a delay-Doppler plane grid with the number of REs in the delay dimension ^^ோோா^,ఛand the number of REs in the Doppler dimension ^^ோோா^,ఔsatisfying: ^^ோ ோா^,ఛ ∙ ^^ோ ோா^,ఔ ൌ ^^ோோா^

[0135] Here, ^^ோோா^ ൌ ^^^^^^^ ∙ ^^^^ோ^ ൌ 12,000 ∙ ^^ீா,் ∙ ^^^^^௧. The supported combinationsof ^^^ோோா^,ఛ,^^ோோா^,ఔ^ for the different values of ^^ீாare listed in the tables shown in FIG.5.

[0136] In the described embodiments, an OTFS block ^^ is constructed by selecting ablock of time duration ^^^^^^^,^ ൌ ^^ீா,்,^ ∙ ^^ ா and bandwidth of ^^^^^^^^^,^ ൌ ^^ோ^,^ ∙ ^^^^ோ^ whereInternational Patent Application Attorney Docket No.: 119314.8126.WO00^^ோ^,^ ൌ 1, 2, … ,^^ோ^ and ^^ோ^ is the maximum number of RBs that fit in the available band asspecified in the table below, wherein the values are compatible with 3GPP TS 38.101, section 5.3.2. Table: Maximum transmission bandwidth configuration ^^^^^^5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz MHz 25 52 79 106 133 160 188 216 242 270 324 378 434 490 546 per OTFS block, using different time durations (^^^^^^^,^) is illustrated in the tables in FIG.5.

[0138] Examples of delay-Doppler processing

[0139] The delay-Doppler symbols ^^^^^^^^,^^^ of OTFS block ^^ having a bandwidth ^^^^^^^^^,^and a duration ^^^^^^^,^are assigned to a two-dimensional grid defined in a delay- Doppler plane of size ^^^,^in the delay dimension and ^^^,^in the Doppler dimension, and with anarea of ^^^,^ ∙ ^^^,^ ൌ 1 as shown in the table below and in FIG. 7.Table: Delay-Doppler plane grid of OTFS block ^^ Dimension # of grid points Resolution Delay-Doppler Plane Period Doppler ^^^ఔ ∆^^^ ൌ 1 / ^^^^^^^ ^ ^^^ ^ ൌ ^^^ఔ ∙ ∆^^^[0014^^^,^ ∙^^^^^^^^^,^ ൌ ^^ீா^^^^ ∙ ^^ ா ∙ ^^ோ^,^ ∙ ^^^^ோ^. To keep the dimensions of the DD plane ^^^^,^ , ^^^,^^unchanged for different OTFS block sizes sent over similar channel conditions (delay and Doppler spreads), the grid points should be set as follows: ^^^ఛ ^^^ோ^,^^^^^^ ൌ ^^^ఛ ^^^ோ^,^^^^ െ 1^^ ∙ ^^ோ^,^^^^^ / ^^ோ^,^^^^ െ 1^െ 1^

[0141] FIG.7 provides a visual depiction example of a delay-Doppler plane of OTFS block i. The discrete delay-Doppler symbols correspond to a continuous delay-Doppler symbols’ signal given by: ^^ഓ^^ഌ

[0142] International Patent Application Attorney Docket No.: 119314.8126.WO00 ^^^^൫^^ ^ ^^^^^, ^^ ^ ^^^^^൯ ൌ ^^^ଶగఔ^ఛ^^^^^^, ^^^

[0143] for any ^^ൌ0 ^^^^ℎ^^^^^^^^^^^^.

[0144] A two-dimensional Root-Raised-Cosine (RRC) pulse is defined as ^^^^^^, ^^^ ൌ ^^^^^^^^^^,^ ∙ ^^^^^^ఉഓ൫^^^^^^^^^,^ ∙ ^^൯ ∙ ^^^^^^^^,^ ∙ ^^^^^^ఉഌ൫^^^^^^^,^ ∙ ^^൯

[0145] ^^^^^^ఉ^^^^ ൌ ^^^^^1 ^4^^^^^ଶ^

[0146] set to ^^ఛ ൌ ^^ఔ ൌ 0.1.

[0147] The a (∗ఙ) t n oand the con i u us delay-Doppler symbols’ signal ^^^ ^^^^^, ^^^ ൌ ^^^^^^, ^^^ ∗ఙ ^^^ ^^^^^, ^^^

[0148] Let the^^^^^ ^^^, ^^^ sampled onthe grid ^^^ ^^^^^,^^^ ൌ ^^^ ^^^^^ ∙ ∆^^,^^ ∙ ∆^^^

[0149] The continuous baseband time-domain realization of the delay-Doppler OTFS block ^^ is the inverse Zak transform of the discrete delay-Doppler signal: ഓ ഌ 1^^^^^ ^^^^^^^^^,^ ∙ ^1 ^ ^^ఔ^ ^ ^^ ^ ^ ^^^^^^^,^ ∙ ^1 ^ ^^ఔ^

[0151] In somea different sampling rate ^^^^^ఛ^ ^ ∙ ^^ఔ^

[0152] and has an equivalenttime-domain signalInternational Patent Application Attorney Docket No.: 119314.8126.WO00 ഓ ഌ ^ 1^^^^^ ^^,^^^^^^ ൌ ^ ^^^^ ^^^^^,^^^ ^ ^^^ଶగ^∆ఔ^^ఛ^,^ ∙ ^^^^^ െ ^^ െ ^^ ∙ ^^^ఛ^

[0153] ^,^^^ / ^ೞ ೞ,^

[0154] Examples of time-

[0155] The time-domain from multiple OTFS blocks, tiled together in a time-frequency plane of ^^ Hz and ^^ sec.^^^௧^ ^ ^ ^ ^^ ^^ ൌ^^^ ^^^^ ^^^^^

[0156] Herein, the time block ^^ centered at time ^^ and^,^^^^^^frequency offset ^^ is^,^್^^^ೖ್^^^ೖ^ଶగி ^௧ି^^^^^^ ^,^ ^்,^^ ^ ^^ ^^ ൌ ^^ ൫^^ െ ^^ ൯ ∙ ^^^ ^,^^ ^,^

[0157] FIG.8 applied to differentOTFS blocks in the constructions of a subframe.

[0158] In some embodiments, modulation and upconversion to the carrier frequency ^^^^ ^ of the complex-valued OTFS baseband signal ^^ ^^ of a slot assumed to start at ^^ ൌ 0 is given by^ଶగ^^௧ି௧ ^బ ೞ^ೌ^^^ ^ ^^^^^^^ ^^ ∙ ^^ ^

[0159] In some per UE results in number ofallocated RBs for the UE. After deciding on the number of RBs allocated for the UE, the scheduler can decide on the dimensions of the PRB in the time-frequency plane, e.g. based on latency requirements. Once all the UE allocations are tiled in the time-frequency domain, the scheduler switches to the delay-Doppler domain and performs the following:

[0160] − Calculates the delay and Doppler grid resolutions ∆^^ and ∆^^ respectfully^ ^

[0161] − Based on the estimated delay and Doppler spreads of the UE channel, selects a ఛఔpair of ^^ and ^^ such that the delay spread of the channel is smaller than the delay period ^^ ൌ^,^^ ^ఛఔ^^∙ ∆^^ and the Doppler spread of the channel is smaller than half the Doppler period ^^ ൌ ^^∙^ ^,^^ ^∆^^ under the restriction that ^^ ∙ ^^ ൌ 1. This formulates the delay-Doppler grid of the^ ^,^ ^,^specific OTFS block.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0162] − Generates delay-Doppler symbols, assigns them to the RE of the OTFS block, and converts them to the time domain as described above in the delay-Doppler processing discussion.

[0163] − Places each OTFS block in the time-frequency plane by applying time and frequency offsets as described above in the time-domain processing discussion.

[0164] − Combines the time domain waveforms of all the OTFS blocks of the slot.

[0165] FIG.9 shows an example of selecting a delay-Doppler numerology of one UE allocation of 6 RBs using time-frequency allocation of 9 / 15 ms by 1080 KHz assuming the delay and Doppler spreads of the target UE channel is 10^^^^ and 2^^^^^^, respectively.

[0166] 7 Example OTFS implementations with sensing pilot signals

[0167] The described embodiments and implementations can optionally use sensing pilot signals to facilitate channel estimation, as described in this section. In these examples, sensing pilots may be implemented using pulse-tone based signal waveforms.

[0168] In some example embodiments, the sensing pilots are configured with a 6 kHzrate, i.e., one sensing pilot is used every 5 basic grid element columns with ^^^^^௧ ൌ 0.5 ^^^^, andthe OTFS block duration is limited to ^^ ൌ 4 (when avoiding overlapping the pilots), resulting in48 REs per block. In an example, with a duration of 4 / 15 msec, setting the DD dimension to 12 in the delay dimension and 4 in the Doppler dimension will support 66.67 us and 15 kHz delay and Doppler spreads, respectively. In another example, with a duration of 1 msec, the DD dimensions can be set as follows:

[0169] − 30 in the delay dimension and 6 in Doppler dimension supporting 6 kHz Doppler spread. This configuration supports overlapping with the 6 column pilots per 1 msec, as shown in FIG.11, by not populating the first 6 delay columns.

[0170] − 15 in delay and 12 in Doppler supporting 12 kHz Doppler spread. This configuration supports overlapping with the 12 column pilots per 1 msec, as shown in FIG.12, by not populating the first 3 delay columns.

[0171] In both the above cases, a relatively low-complexity equalizer can be deployed to support reasonable delay and Doppler spreads. In these examples, the following numerology can be used: Δ^^^ൌ 1 ^^ / 15 ^^^^ൌ 15 / ^^ ^^^^^^International Patent Application Attorney Docket No.: 119314.8126.WO00 Δ^^^ൌ 1 180 ^^^^^^ൌ 5.56 ^^^^^^ For ^^^ൌ 180For ^ ൌ 48

[0172] When the OTFS block is fixed to 180 kHz, when scheduling multiple RBs for a UE, the PHY layer creates multiple equal size OTFS blocks that are placed in the time-frequency (T-F) plane. In some examples, the OTFS blocks can be placed contiguously, whereas in other examples, the OTFS blocks can be interleaved to improve diversity. In both examples, the forward error correction (FEC) can cover multiple OTFS blocks.

[0173] In the following examples of using sensing pilots, and with reference to FIGS. 10A to 13, a 100 msec observation window is assumed (for this discussion, although other durations for the window may be used), and the following numerology can be deployed: Δ^^^ൌ 1 ൌ 10^^^^ 100 ^^^^ൌ 1,000,000 ^^^,^ൌ 0.33ms ⇒^^ఔ^ൌ 300 ^^^ఛൌ 3333

[0174] The examples shown in FIGS.10A and 10B support up to a 3 kHz Doppler spread. As shown in FIG.10A, for a delay spread of 3 µs and Doppler spread of 3 kHz, the number of grid points in the delay dimension required per pilot is ( 3 µs / 100 ns ) = 30, which implies that the number of sensing pilots needed is ( 3333 / 30 ) = 111. Similarly, for a Doppler spread of 1.5 kHz, the number of sensing pilots needed is 222, which can be achieved by using 2 pilots in the Doppler direction, or stretching the delay dimension by 2x and interleaving the pilots in time.

[0175] FIG.10B shows an example of sensing pilots and data transmissions being multiplexed in delay and Doppler (e.g., as was shown in FIG.10A), as well as in frequency (asInternational Patent Application Attorney Docket No.: 119314.8126.WO00 annotated in FIG.10B) and time (by using multiples of the basic Doppler dimension for some pilots which results in skipping some pilot columns). As seen in FIG.10B, some sensing pilot transmissions are skipped (compared to the configuration in FIG.10A).

[0176] In this example, the delay dimension of the DD plane of the pilots is equal to the distance between the pilot columns in the T-F plane. Furthermore, when allocating data over the pilot columns, the delay dimension of the DD plane of the allocated OTFS block is n times the distance between the pilot columns to minimize the overhead. With 1 / n of the pilot DS, the overhead will a factor of n.

[0177] FIGS.11 and 12 show examples of resource allocation when using 6 and 10 sensing pilots per millisecond, respectively, and which can support channels in which a Doppler spread of up to 6 kHz and 12 kHz, respectively, can be expected. In the latter case of FIG.12, each slot duration is 250 msec.

[0178] FIG.13 shows an example of using a 1 / 64 msec resolution (providing the advantage of a power-of-two implementation that can be compactly signaled using binary representation), and for which the following alternative numerology can be used: Δ^^^ൌ 1 ൌ 10^^^^ ^^^^^^^,^ൌ 1 / 8 ms ⇒^^ఔ^ൌ 800 ^^^ఛൌ 1250

[0179] This configuration can support up to 8 kHz Doppler shift in the wireless channel.

[0180] Herein, for a delay spread of 3 µs and Doppler spread of 8 kHz, the number of grid points in the delay dimension required per pilot is ( 3 µs / 100 ns ) = 30, which implies that the number of sensing pilots needed is ( 1250 / 30 ) = 41. Similarly, for a Doppler spread of 4 kHz, the number of sensing pilots needed is 82, which can be achieved by using 2 pilots in theDoppler direction. In this example, the size of an OTFS block is 2ఓ ∙ 180 kHz × 1 / 2ఓ msec,where ^^ ൌ 0, 1, 2, 3. Furthermore, ^^ோா,^ ൌ 180, Δ^^^ ൌ 2ఓ kHz, andInternational Patent Application Attorney Docket No.: 119314.8126.WO00 Δ^^^ൌ 1 180 ^^^^^^ ∙ 2ఓ ൌ 5.56 ∙ 2ିఓ μs.

[0181] Herein, the width of the pilot column is 1 / 64=15.625 µs. To be able to overlap over the pilots, the following cases are considered:

[0182] − 1 msec × 180 kHz OTFS block with 3 delay columns to be removed,which can be achieved by ^^^,^ ൌ 1 / 8 msec, ^^ఛ^ ൌ 22, and ^^^ఔ ൌ 8, resulting in overhead of 3 / 22 =13.6%

[0183] − 0.5 msec × 180 kHz OTFS block with 6 delay columns to be removed,which can be achieved by (Option 1) ^^^,^ ൌ 1 / 8 msec, ^^ఛ^ ൌ 44, ^^ఔ^ ൌ 4, and an overhead of 6 / 44= 13.6%, or (Option 2) ^^^,^ ൌ 1 / 16 msec, ^^^ఛ ൌ 22, ^^^ఔ ൌ 8, and an overhead of 6 / 22 = 27.3%, or(Option 3) shrinking ^^^^^௧to 0.5 msec; the resolution being 1 / 128 msec with 16 pilot columns.

[0184] 8 Examples of OTFS numerology and transmit / receive processing

[0185] In some embodiments, the disclosed technology advantageously provides a system design that supports resource allocations to multiple UEs, resource allocation granularity close to legacy 5G system, minimal impact on 5G upper layers, transmissions of all physical channels (Physical Downlink Shared Channel (PDSCH), Physical Downlink Control Channel (PDCCH), Physical Broadcast Channel (PBCH), etc.) and signals (DMRS, PTRS, CSI-RS, SRS, Synchronization Signal Block (SSB), etc.), different delay and Doppler spreads per scheduled transmission, and low-complexity implementations.

[0186] As previously discussed, an example numerology that is compatible with 5Gwireless systems includes using ^^^^^௧ ൌ 1 ^^^^, ^^ ா ൌ ^^^^^௧ / 15, and ^^^^ீா ൌ 180 ^^^^^^ (for gridelement “GE” in the two-dimensional resource grid), with a resource block (RB) being definedsuch that ^^^^ோ^ ൌ ^^^^ீா ൌ 180 ^^^^^^, and the starting time, length (in number of basic gridelements), and frequency offset being defined when allocating resources.

[0187] In some embodiments, and with reference to FIG.6, an OTFS block in the time-frequency plane can be constructed by first selecting a T-F block of size ^^^^^^^,^ ൌ ^^ீா,்,^ ∙ ^^ ாand ^^^^^^^^^,^ ൌ ^^ோ^,^ ∙ ^^^^ோ^. Here, resource elements (REs) are defined in the delay-Dopplerplane, and the total number of REs in the block is given by: ^^ோா,^ ൌ ^^^^^^^,^ ∙ ^^^^^^^^^,^ .International Patent Application Attorney Docket No.: 119314.8126.WO00

[0188] For this configuration, the dimensions of the DD plane are selected based on the delay spread and Doppler spread of the channel, and the following numerology can be deployed: ∆^^^ ൌ 1 / ^^^^^^^,^∆^^^ ൌ 1 / ^^^^^^^^^,^∙ 1

[0189] In any numerology

[0190] − Decide on # of REs to allocate

[0191] − Pick # of RBs and OTFS block length based on allocation size and latency

[0192] − Calculate ∆^^^and ∆^^^

[0193] − Select ^^^ఛand ^^ఔ^such that the i-th delay period (^^^,^) and the i-th Doppler period (^^^,^) are greater than delay and Doppler spreads of the wireless channel, respectively

[0194] − Generate DD symbols and assign them to the DD grid

[0195] − Apply the inverse Zak transform to transfer the signal to a time waveform

[0196] − Shift the signal in time and frequency to its allocated T-F location

[0197] − Combine the time domain waveforms of all the OTFS blocks of the slot

[0198] FIG.14 shows a block diagram of an example OFDM transmitter. As shown therein, a transport block is coded and segmented, followed by rate matching, followed by scrambling, followed by modulation, mapping the resources to time-frequency plane, and finally performing an inverse fast Fourier transform (IFFT) and cyclic prefix insertion to generate an OFDM block.

[0199] FIG.15 shows a block diagram of an example single-layer OTFS transmitter. As shown therein, the initial four stages may be same as the OFDM processing described in FIG.14. Next, a DD-domain remapping is performed, followed by 2D filtering, which is then followed by an inverse Zak transform, an upsampling, and a time / frequency shifting to generate an OTFS block.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0200] The described embodiments use linear time invariant (LTI) channel models, as depicted in FIG.16A, where a time-domain (TD) pulse is a geometric mode of the LTI channel – the I / O relation is made up of delays that move the pulse about in time. The I / O relation can be read off from the response to a single TD pulse. After waiting longer than the delay spread, embodiments can read off the I / O relation, and equalize the data. Because delay-Doppler profile of a channel typically is static over long time periods, this approach can provide predictability, which means that the I / O relation does not change with time. And predictability can enable a model-free mode of operation under the condition where delay spread is less than a delay period of the pulse being used as a basis signal.

[0201] FIG.16B is an example of rotations undergone by a delay-Doppler domain pulse. In FIG.16B, a pulse in the delay-Doppler domain is shown, which can, for example, have a delay spread ^^^= 50 µs and a Doppler spread ^^^= 20 KHz.

[0202] However, defining a pulse in the delay-Doppler (DD) domain is subject to the Heisenberg Uncertainty Principle (HUP), which implies that it is not possible to simultaneously localize a signal in delay and in Doppler. Embodiments of the disclosed technology work around the HUP by starting with a pulse in the DD domain and extending it quasi-periodically.

[0203] The DD domain pulse can be represented as a configuration of infinitely many pulses which repeat at integer multiples of the delay period ^^^along the delay axis and at integer multiples of the Doppler period ^^^along the Doppler axis. A box of width ^^^and height ^^^isreferred to as the fundamental period, and it is assumed that ^^^^^^ ൌ 1.

[0204] In these examples, the phase of the pulse changes when the pulse location shifts by an integer multiple of ^^^along the delay axis, but there is no change in phase when the pulse location shifts by an integer multiple of ^^^along the Doppler axis. Accordingly, the DD realization of a TD signal is a quasi-periodic function. FIG.16C shows an example of a quasi- periodic delay-Doppler domain pulse.

[0205] A DD domain pulse can be transformed to a TD pulse-tone waveform by applying an (inverse time) Zak transform. That is, an (inverse time) Zak transform may be applied to get a TD pulse-tone from a quasi-periodic DD domain pulse. There is also an inverse (frequency) Zak transform that transforms a DD domain pulse to a frequency-domain (FD) pulse-tone.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0206] In these examples, a DD domain pulse is located at (^^^, ^^^) within the fundamental period. The DD domain pulse is spread along the delay axis over a length 1 / B (i.e., B−1) and is spread along the Doppler axis over a length 1 / T (i.e., T−1). The TD realization x(t) can be obtained by applying the Zak transform to the DD domain pulse ^^^^^^(^^, ^^). The TD realization x(t) is a pulse train of finite duration T, with each pulse in the train spread over time duration 1 / B. Consecutive pulses of the pulse train are separated by the delay period ^^^– moving the pulse location ^^^along the delay axis displaces the TD pulse-tone in time. The pulse train is modulated by a sinusoid of frequency ^^^– moving the pulse location ^^^along the Doppler axis displaces the modulating tone in frequency.

[0207] Herein, time division multiplexing (TDM) is a limiting case. As the delay period ^^^grows, the TD pulses grow further apart, the tone structure disappears, and only a single TD pulse at ^^^remains. Similarly, frequency division multiplexing (FDM) is also a limiting case. As delay period ^^^shrinks, the pulses grow closer and closer together in time, and in the limit, the pulse structure disappears and only the tone remains. Pulse-tones parametrized by ^^^and ^^^interpolate between TDM and FDM; that is, they live on the hyperbola ^^^^^^ ൌ 1, with aparticular value of ^^^optimizing predictability.

[0208] Pulse-tones are optimal as time- and band- limited signals because there is almost no overlap between two DD pulses whose delay domain locations differ by 1 / B or whose Doppler locations differ by 1 / T. In the example depicted in FIG.16C, B= 1 / 100ns = 10MHz, T = 1 / 1kHz = 1ms, N = 50μs / 100ns = 500, and M = 20kHz / 1kHz = 20, with ^^^= 20 KHz (Doppler spread) and ^^^= 50 ms (delay spread).

[0209] FIG.16D shows an example of an OTFS waveform. The waveform shows a delay-Doppler domain pulse that has been filtered and converted into a time-domain train of pulses, where each pulse (pulse-tone) has a phase shift that varies (middle portion of the drawing) such that the resulting waveform is invariant under time, delay or Doppler domain shifts. As discussed in this patent document, the invariance of the resulting waveform to time, delay or Doppler domain shifts can be achieved by configuring each pulse of the train of pulses with a delay period and a Doppler period that are greater than an expected (or maximum) delay spread and an expected (or maximum) Doppler spread, respectively.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0210] 9 Examples of signal processing in the delay-Doppler domain

[0211] The described embodiments provide numerologies that can be implemented in OTFS systems that are backward-compatible with legacy (e.g., 5G) wireless systems. Examples of transmitting and receiving OTFS signals (e.g., pulse-tone signals) are discussed in this section.

[0212] In some embodiments, and as discussed above, a two-dimensional resource plane can be a two-dimensional delay-Doppler plane. The delay-Doppler plane can be divided into resource blocks, which are defined in one dimension by a delay period, ^^^, and in a second dimension by a Doppler period, ^^^, such that the area, ^^^ ∙ ^^^, is equal to one. FIG. 17 illustratesan example resource block.

[0213] In additional embodiments, a two-dimensional resource plane can be a delay- Doppler grid. FIG.18 depicts an example delay-Doppler grid. The delay-Doppler grid is made up of discrete points, and a point is defined by coordinates (^^∆^^,^^∆^^^, where ^^ and ^^ are integers, ∆^^ represents the distance between points in the first dimension (i.e., a delay resolution), and ∆^^ represents the distance between points in the second dimension (i.e., a Doppler resolution). The possible values for ∆^^ obey the relationship Δ^^ ^ ^^^, and the values for ∆^^ obey the relationship Δ^^ ^ ^். As shown in FIG.18, the delayis defined as ^^^^ ^^∆^^ and the Doppler period is defined as ^^^ ^ ^^∆^^.

[0214] In these examples, each point, ^^, in the delay-Doppler plane is defined by coordinates (^^,^^). A twisted convolution of a function, ℎ^, operating on a delay-Doppler signal ℎଶ^^^^ is defined as ℎ^ ∗ఙ ℎଶ^^^^ ≜ ^ ^^^ଶగఉ൫௨ᇲ,௨ି௨ᇲ൯ℎ^ଶ^^^ െ ^^ᇱ^^^^^ᇱ, where ^^^^^^, ^^ଶ^ ൌ^^^^^ଶ. The termwhile ℎ^^^^ᇱ^ℎଶ^^^ െ ^^ᇱ^^^^^ᇱ is a standard convolution of two functions. The twisted convolutionis non-commutative.

[00215] In one example, let ^^(^^) be a delta function at ^^^,^ given by ^^^^^^ ൌ^^ ^^൫^^ െ ^^ ൯, where ^^^^^^ ൌ ^1 ^^ ൌ ^0,0^0 ^^^^^^^^, and let ^^(^^) be a function defined on theof ^^(^^) and ^^(^^) is given by the following: ^^^^^^ ^^^^^^ ∗ ^^^^^^ ^^ ^ ^^^ଶగఉ൫௨ᇲ,௨ି௨ᇲ൯^^^^^ᇱ^ ^^ᇱ ^^ ᇱInternational Patent Application Attorney Docket No.: 119314.8126.WO00 ൌ^^^,^^^^ଶగ^ఔିఔ^^ఛ^^^൫^^ െ ^^^,^൯

[0216] In this ^^^ଶగ^ఔିఔ^^ఛ^which is a function of the location of the delta function,centered at the delta location.

[0217] Further, an inverse Zak transform of a delay-Doppler signal is defined as ^^ି^^^^^^^, ^^^^ ≜ ^ఔ^^ ^^^^^, ^^^^^^^. The inverse Zak transform transforms a signal, ^^(^^,^^), from delay-Doppler to time by integrating along one Doppler period, ^^^.

[0218] FIG.19 illustrates an example delay-Doppler plane divided into resource blocks. In this example, the delay-Doppler signals are quasi-periodic. The signals are periodic along the Doppler dimension and quasi-periodic along the delay dimension, with an additional phase.

[0219] FIG.20 depicts the delay-Doppler plane of FIG.19 in the case of a delta function, ^^^^൫^^ െ ^^^,^൯.In some embodiments, OTFS modulation in the delay-Doppler grid consists of the following steps. First, symbols are assigned to the delay-Doppler grid elements, ^^[^^,^^]. Some examples of symbols that can be assigned include quadrature amplitude modulation (QAM) symbols and channel estimation related symbols, such as pilot or guard symbols. Second, a two- dimensional delay-Doppler filter is applied. The two-dimensional delay-Doppler filter is used for shaping the OTFS waveform. This filter, ^^, may be constructed as a twisted convolution of two orthogonal filters, ^^ఛ on delay, and ^^ఔ on Doppler, such that ^^ ൌ ^^ఛ ∗ఙ ^^ఔ. The function of thedelay filter is to shape the signal in frequency, and the function of the Doppler filter is to shape the signal in time. Overall, the OTFS modulated signal is described by the following equations: ெ ே ^^^^^^ ^^^ ^ ^^

[0221] to a time-waveform, ^^^^^^, using the inverse Zak transform according to the following equation: ^^^^^^ ൌ^^ି^^^^^^^, ^^^^. In one example, where ^^^^^^ ൌ ^^^^^, ^^^ ∙ ^^^^൫^^ െ ^^^,^൯, the time-waveform iscalculated as the following: ^^^^^^ ൌ ^^ି^^^^ ∗ఙ ^^^^^^^ൌ ^^^^^,^^^ ∙ ^^ି^^^^ఛ ∗ఙ ^^ఔ ∗ఙ ^^^^൫^^ െ ^^^,^൯^International Patent Application Attorney Docket No.: 119314.8126.WO00 ൌ^^^^^, ^^^ ∙ ^^ఛ ∗ ^^ି^^^^ఔ ∗ఙ ^^^^൫^^ െ ^^^,^൯^∙ ^ ∙ ^^ି^

[0222] Along of a quasi-periodic delta is:^^ି^^^^ఔ^^^^^^ െ ^^^^^ ൌ ^ ^^^ଶగఔ^ఛ^^^^^^^ െ ^^^^^^^^ ൌ ^^^ଶగఔ^^ఛ^

[0223] periodic delta is:^^ି^^^^^^൫^^ െ ^^^,^൯^ ൌ ^ ^^^ଶగ^^ఔ^ఛ^^^൫^^ െ ^^Δ^^ െ ^^^^^൯

[0224]

[0225] In certain embodiments, the OTFS carrier waveform is a combination of a pulse and a tone. One implementation of the pulse-tone signal is the PulsoneTM, ^^^^,^^^^^^, which is defined as:^^^^,^^^^^^ ≜ ^^ି^^^^ ∗ఙ ^^^^൫^^ െ ^^^,^൯^where^ ^^^ ^^,^^^^^^ ^ ^^^ଶగ^^ఔ

[0226] Theof all Pulsones, asdescribed by: ^^^^^^ ൌ ∑ெ^ିୀ^^ ∑ே^ୀି^^ ^^^^^,^^^ ∙ ^^^^,^^^^^^

[0227] be generated on the transmitter-side. First, an infinite Dirac delta train, ^^^^^,^^^^^^, is convolved with a window function, ^^௧. The result is then convolved with a delay filter, ^^ఛ. The Pulsone generation operation is further detailed in FIG.22. As shown therein, the window function ^^௧is applied to each column of modulated symbols, and the roll-off factor ^^ఔis selected such that the each column is within the passband of the window function.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0228] FIG.23 describes a block diagram of an example implementation of an OTFS transmitter, similar to the implementation described in FIG.15, which includes applying a forward error correction (FEC) code that converts information bits into coded bits, an optional interleaving operation, a symbol mapper that converts coded (interleaved) bits to constellation symbols, which are mapped onto a delay-Doppler grid along with sensing pilots, and finally processed by an OTFS modulator.

[0229] When an OTFS signal is transmitted, the signal may interact with a wireless channel that introduces distortions in the received OTFS signals. The channel ℎ^^^^ can be represented as a super-position of reflectors, where each reflector is characterized by a delay ^^^, aDoppler ^^^, and a complex gain ^^^, according to ℎ^^^^ ൌ ∑^ ^^^^^^^^ െ ^^^^ , where ^^^ ൌ ^^^^ , ^^^^.

[0230] For a delay-Doppler signal ^^(^^), where ^^(^^) is by: ெି^ ேି^^^^^^^ ൌ ^^ ^^^^^^ ൌ ^^ ^ ^ ^^^^^, ^^^ ∙ ^^^^൫^^ െThe interaction^^^^^^

[0231] For a time-domain signal ^^(^^), the channel is a super position of time shifts, phaserotations and complex gains: ^^^^^^^ ൌ ∑^ ^^^^^^ଶగఔ^^௧ିఛ^^ ∙ ^^^^^ െ ^^^^

[0232] In certain embodiments, OTFSbe performed in the delay- Doppler domain. The received signal is described by: ^^^^^^^ ൌ ℎ ∗ఙ ^^^^^^ ൌ ℎ ∗ఙ ^^௧௫ ∗ఙ ^^^^^^

[0233] A two-dimensional filter is applied to obtain the received delay-Doppler signal, according to: ^^^^^^ ൌ ^^^௫ ∗ఙ ^^^^^^^ ൌ ^^^௫ ∗ఙ ℎ ∗ఙ ^^௧௫ ∗ఙ ^^^^^^

[0234] channel and the transmitand receive filters, as the effective channel ℎ^^^^^^^ ൌ ^^^௫ ∗ఙ ℎ ∗ఙ ^^௧௫. Therefore, the receiveddelay-Doppler signal can be described as ^^^^^^ ൌ ℎ^^^ ∗ఙ ^^^^^^.

[0235] When determining the filter to be applied, there are filter design tradeoffs that should be considered. The more localized the filter is in the delay / Doppler dimensions, the more it is spread out in frequency / time and interferes with other OTFS frames. The more localized the filter in frequency / time, the more spread out the filter in delay / Doppler, spreading out also the effective channel response.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0236] In certain embodiments, OTFS demodulation may be performed in the time- frequency domain. FIG.24 depicts an example of processing performed by a practical OTFS demodulator. To convert the received time domain OTFS signal, ^^^^^^^, to a delay-Doppler signal, the same operations as the transmit side are applied, but in reverse order: ^^^^^^ ൌ ^^^^^௧^௫ ∙ ൫^^ఛ^௫ ∗ ^^^^^^^൯^.Then, ^^^^^^ is sampled on the௧∙ ఛThe grid-sampled Zak transform^^^^^, ^^^ ൌ1 ^^^ ^^ି^ଶగ^^ఔ^ఛ^^^ᇱ൫^^ െ ^^Δ^^ െ ^^^^^൯

[0237] As shown therein, the OTFS receiver includes performing OTFS demodulation, demapping from the delay- Doppler grid, performing channel estimation and equalization, demapping the constellation symbols to bits, optionally deinterleaving, and finally performing an FEC decoding operation.

[0238] In some embodiments, a pilot signal may be used in an OTFS system in order to perform channel estimation. Some types of pilots that may be used in the OTFS system include a point pilot with a guard band, an overlaid point pilot, and a spread pilot. There are many different methods for adding pilots to the OTFS signal and estimating the effective channel response. Each method has different tradeoffs of performance, power and capacity.

[0239] FIG.26 depicts an example of a point pilot with a guard band, in which the pilot is a single delta function in the delay-Doppler plane in each transmission layer. The pilot is surrounded by a guard band of zeros, which match the delay and Doppler spread of the channel. The pilot may be boosted by the size of the guard band. To perform channel estimation using apoint pilot, the delay and Doppler offsets ^^^^ , ^^^^, relative to the pilot location, and the complexvalues ℎ^^^^,^, of every element in the guard band satisfying หℎ^หଶ^ ^^ℎ, are measured. Thatis, the channel estimation procedure when using a pointdetermining if any channel coefficient in the guard band have magnitudes greater than a threshold. FIG.27 depicts a pointInternational Patent Application Attorney Docket No.: 119314.8126.WO00 pilot with a guard band and a set Ω, of effective channel reflections that would be measured, e.g., if their magnitude exceeded a threshold value.

[0240] FIG.28 illustrates an example of an overlaid point pilot, in which the pilot is a single delta function in the delay-Doppler plane in each transmission layer. The overlaid point pilot may be boosted at the expense of the data symbols’ energy. To perform channel estimation ^^ using an overlaid point pilot, the delay and Doppler offsets ^^ , ^^ , relative to the pilot location,^ ^and the complex values ℎ^, of every element in the channel spread area satisfying หℎ^หଶ ^^^,^ ^^^,^^ ^^ℎ, are measured. FIG.29 depicts an overlaid point pilot and a set of effectivereflections within the channel spread area that would be measured. The data points the channel response can be erased for equalization. In the case where an iterative receiver is used, the channel response can be removed and separated from the data.

[0241] FIG.30 depicts an example of a spread pilot, in which a discrete spreading function is applied to a point pilot in the delay-Doppler plane, resulting in a pilot which is spread over the entire delay-Doppler plane. As an example, for a discrete filter based on a two- dimensional chirp, where ൫^^ ,^^ ൯ is the location of the point pilot, and ⊛ is ^^^^-periodic^ ^ ఙtwisted convolution: మమ൫ ൯^ ^ ା^1^ଶగ ெே^ ^ ^^ ^^,^^ ൌ^^ ^^^^

[0242] beoverlaid on the data after energy scaling, as shown in FIG.31. In some embodiments, multiple pilots may also be overlaid on top of each other with different spreading coefficients.

[0243] To perform channel estimation using a spread pilot, the effective channel can be computed using the cross-ambiguity function, as described by the following: ^^ ൌ ℎ ∗ ^^ ^ ^^^^^^^^^^^ ^^^ ఙ ^^International Patent Application Attorney Docket No.: 119314.8126.WO00 ேି^ ெି^ ൌ^ ^ ^^^^^^ᇱ,^^′^^^^∗^^^ᇱ െ ^^, ^^ᇱ െ ^^^^^^ଶగ^൫^ᇲି^൯ெே

[0244] After be subtracted from thereceived signal and

[0245] In each of the previous cases, the computed at ℎ^is related to a point pilot located at ൫^^^,^^^൯. The channel response a different location ℎ^^must beadjusted according to theℎ^^ ൌ ^^^ଶగ^^൫^ି^^൯ / ெே ∙ ℎ^. FIG. 32 depictsof thisadjustment.

[0246] In certain embodiments, equalization may be used in the processing of OTFS signals. Some examples of equalization methods include minimum mean square error (MMSE) and message-passing equalization.

[0247] In the case where MMSE equalization is used, the estimated effective channel response can be adjusted to all locations on the delay-Doppler grid. The delay-Doppler plane can be vectorized and the channel equation can be rewritten using matrices as: ^^ெேൈ^ ൌ ^^ெேൈெே ∙ ^^ெேൈ^ ^ ^^ெேൈ^The MMSE equalizer requires an inversion of an ^^^^×^^^^ matrix and is defined as: ^^^ ൌு^^ு^^ ^^ ^ ^^^^^^^

[0248] In the case where message passing is used, the adjusted channel response, originated from a delay-Doppler grid element ^^, can be represented as a graph connected to multiple ^^’s, as illustrated in FIG.33. FIG.34 depicts the reciprocal graph, which represents thechannel equation. The channel equation is defined as: ^^^^^,^^^ ≅ ∑|^ఆୀ|^ ℎ^^^^,^^^^^ି,^^^ି^ ∙^^^^^ି^,^^ି^^. The sparse graph representation of connectionsand variables (^^’s), is utilized for a message-passing equalizer. The messages or probabilities are passed back and forth between the observation nodes and the variables nodes along their connections.

[0249] One example of message passing equalization is maximum a posteriori (MAP) equalization. The maximum a posteriori equalizer, computes for each delay-Doppler data symbol, ^^[^^,^^], the estimated symbol given by:International Patent Application Attorney Docket No.: 119314.8126.WO00^^^^^^, ^^^ ൌ ar^gೖm∈^ax Pr൫^^^^^, ^^^ ൌ ^^^|^^,ℎ^^^^൯, where ^^ is the symbol constellation.The estimated symbol can beBayes’ theorem as: ^^^^^^, ^^^ ൌ ^^^^^^ೖ^^∈^^^^^^ ^^^^ ൫^^|^^^^^, ^^^ ൌ ^^^,ℎ^^^^൯^^^^^^^^^^,^^^ ൌ ^^^^

[0250] the messages,^^^^^^, ^^^, are^^^ ൌ ^^^^. In thisexample, the messages are extrinsic, meaning that they do not have information originating from the connected observation node.

[0251] Furthermore, in MAP equalization, each data symbol, ^^^^^,^^^ is associated withan a priori probability vector, ^^^^^^^^^, ^^^^, where its ^^-th element is Pr^^^^^^, ^^^ ൌ ^^^^. At thebeginning, ∀^^,^^, the probability vector is initialized to: 1 / |^^|^^^^൪

[0252] FIG.36 depicts ancondition. This initialization isfurther assigned to all messages, as described by: ^^^^^^, ^^^ ൌ ^^^^^^^^^,^^^^, ∀^^.

[0253] Additionally, in the channel equation for MAP equalization (and more generally, for message-passing equalization), the inter-symbol-interference (ISI) is approximated by a Gaussian random variable, according to the following: |ఆ| ^^^ ^

[0254] and 38, are described by the following equations: ^^^^^^,^^^ ^ ^^^^^^^,^^^International Patent Application Attorney Docket No.: 119314.8126.WO00 |^| ^^^^^^^, ^^^ ൌ ℎ^^^^,^^^^^ି,^^^ି^ ∙ ^ ^^^ ∙ ^^^^^^ି^,^^^ି^^The ^^−^^ℎ equations:^^^^^^,^^^^ ൌ ^^^^^^^^^, ^^^^^ ∙ ^ ^^^^^^^మ

[0255] Forthese equations.

[0256] Using the observation and variable node equations, the equalizer iterates multiple times, sending observation nodes messages to variables nodes and vice versa. At the end of the iterations, the symbol probabilities are computed as: ^^^^^,^^^^ ൌ ^^^^^^^^^, ^^^^^ ∙ ^ ^^^^^^^

[0257] In certainsuch as an iterative receiver may be used. FIG.39 illustrates an example of an iterative receiver. In this example, the output of the equalizer is converted to log-likelihood ratios (LLRs), which are passed to the FEC decoder. If decoding is unsuccessful, coded bit LLRs are computed and converted to symbol probabilities, which are then fed back to the equalizer as updated priors, ^^^(^^[^^,^^]).

[0258] 10 Examples and embodiments of the disclosed technology

[0259] Embodiments of the disclosed technology provide the following aspects and features, which advantageously enable flexible numerologies to be deployed on a per-user basis to support both legacy device users and current device users.

[0260] − Number of RE in a resource block is similar to 5G

[0261] − Each allocation of resources can be adjusted for the delay and Doppler spreads of the specific channel independent of T-F shape of the OTFS block. This provides anInternational Patent Application Attorney Docket No.: 119314.8126.WO00 improvement over existing 5G systems where different subcarrier spacing (SCS) parameters are needed to handle different Doppler spreads

[0262] − OTFS blocks are flexible in T-F, and are configured to be allocated around any special signals (e.g., SSB) and can support lower latencies by reducing allocation length in time with (or without) changing the slot length

[0263] − The upper layers of user devices (e.g., Layer 2 and above) remain almost unchanged from existing 5G implementations

[0264] − Complexity is lower than OFDM; specifically,

[0265] (1) Complexity of OFDM FFT is 12^^ோ^ ∙ ^^^௬^ ∙ log ^12^^ோ^)

[0266] (2) Complexity of OTFS Zak transform is ^^^ఛ ∙ ^^^ఔ ∙ log ^^^^ఔ)

[0267] − Supports all physical channels and signals currently being used in the 5G system

[0268] FIG.40 is a block diagram representation of a wireless hardware platform 4000 which may be used to implement the various methods described in the present document. The hardware platform 4000 may be incorporated within a base station or a user device. The hardware platform 4000 includes at least one processor 4002, a memory 4004 (this may be optional and in some cases the memory may be internal to the processor) and a transceiver circuitry 4006. The one or more processors may execute instructions, e. g., by reading from the memory 4004, and control the operation of the transceiver circuitry 4006 and the hardware platform 4000 to perform the methods described herein. In some embodiments, the memory 4004 and / or the transceiver circuitry 4006 may be partially or completely contained within the processor 4002 (e.g., same semiconductor package).

[0269] The following solutions may be preferably implemented by some embodiments.

[0270] S1. An apparatus for digital communication, comprising: circuitry (e.g., the one or more processors 4002 and one or more memories 4004 depicted in FIG.40) configured to be compatible with a legacy wireless protocol and provide a plurality of information bits comprising a first set of information bits for a first user device operating based on the legacy wireless protocol and a second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol; and transceiver circuitry (e.g., 4006) configured to: determine to use a first numerology that defines a first set ofInternational Patent Application Attorney Docket No.: 119314.8126.WO00 transmission resources from transmission resources in a two-dimensional time-frequency resource plane, determine to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources, map the first set of information bits to a first set of resource blocks in a two-dimensional delay-Doppler resource plane and the second set of information bits to a second set of resource blocks in the two- dimensional delay-Doppler resource plane, generate, using a two-dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks, and transmit, over a wireless channel, the first set of transmission waveforms and the second set of transmission waveforms, wherein each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and wherein the transmission resources in the two-dimensional time- frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol. For example, the circuitry being configured to be compatible with a legacy wireless protocol means that the circuitry is able to transmit and receive signals and extract (or insert) information bits from / in the signals, that are specified by the legacy protocols.

[0271] S2. The apparatus of solution S1, wherein the transmission resources comprise a slice of the two-dimensional time-frequency resource plane with a 1 msec duration and a 180kHz bandwidth. For example, this slice configuration is identical to that used in the 5G protocol.

[0272] S3. The apparatus of solution S1 or S2, wherein the first set of transmission resources and the second set of transmission resources are defined based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel.

[0273] S4. The apparatus of solution S3, wherein the first set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the first user device and the second set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the second user device.

[0274] S5. The apparatus of solution S1 or S2, wherein the first set of resource blocks are allocated for the first set of information bits and a first set of sensing pilot symbols.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0275] S6. The apparatus of solution S5, wherein a number of the first set of sensing pilot symbols is based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel between the apparatus and the first user device. For example, with reference to FIGS.10A and 11-13, sensing pilots may be added with different periodicities to support operation in a wireless channel with a maximum Doppler spread of 3 kHz, 6 kHz, 12 kHz, and 8 kHz, respectively.

[0276] S7. The apparatus of solution S5, wherein the first set of sensing pilot symbols comprises 30 sensing pilot symbols in a delay dimension and 6 sensing pilot symbols in a Doppler dimension to support a 6 kHz Doppler spread.

[0277] S8. The apparatus of solution S5, wherein the first set of sensing pilot symbols comprises 15 sensing pilot symbols in a delay dimension and 12 sensing pilot symbols in a Doppler dimension to support a 12 kHz Doppler spread.

[0278] S9. The apparatus of any of solutions S1 to S8, wherein the two-dimensional transform is a two-dimensional inverse Zak transform.

[0279] S10. The apparatus of any of solutions S1 to S9, wherein the legacy wireless protocol comprises a 5th Generation (5G) wireless protocol.

[0280] S11. A method of digital communication (e.g., method 4100 in FIG.41), comprising: allocating (4110) transmission resources to one or more transmissions in a wireless network according to a first numerology that defines a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two- dimensional resource plane; and generating (4120), by a transmitting device based on allocated transmission resources, one or more transmission waveforms for N receiving devices, where N is a positive integer. For example, the first two-dimensional resource plane is a time-frequency (or T-F) plane.

[0281] S12. The method of solution S11, wherein the one or more transmissions include a data transmission or a pilot signal transmission.

[0282] S13. The method of solution S11 or S12, including: determining to use a second numerology for at least some of the N receiving devices, and generating an additional transmission waveform according to the second numerology such that the first numerology and the second numerology are concurrently used in the wireless network.International Patent Application Attorney Docket No.: 119314.8126.WO00

[0283] S14. The method of solution S13, wherein a control signal transmission indicates to a given wireless device whether the first numerology or the second numerology is being used for transmissions to the given wireless device. For example, the network device may configure a wireless device with a number of possible numerologies via a high layer signaling such as a radio resource control (RRC) signal. Thereafter, the network device may use a triggering signal to activate one of the numerologies. The triggering signal may be, e.g., a downlink control indication (DCI) signal that may, based on its format, or based on explicitly signaling one or more bits in the DCI message, activate a particular numerology.

[0284] S15. The method of solution S12, wherein the pilot signal transmission is allocated resources according to a target property of a wireless channel over which the pilot signal transmission is communicated. For example, the target property may be the maximum delay spread or the maximum Doppler spread of the wireless channel. Alternatively, using the maximum value can be replaced by using an average value or a modal value (and more generally, an “expected” value from a statistical standpoint). For example, Section 7 describes how the expected delay spread or Doppler spread of wireless a channel is used to determine the periodicity of a pilot signal transmission.

[0285] S16. The method of any of solutions S11 to S15, wherein the one or more transmission waveforms are generated by mapping to a resource block along a third resource dimension and a fourth resource dimension in a second two-dimensional resource plane. For example, the second two-dimensional resource plane is a delay-Doppler resource plane. For example, the mapping may be to resource elements in the delay-Doppler domain, as described in the embodiments in Sections 6-9.

[0286] S17. The method of solution S16, wherein the one or more transmission waveforms are generated using an inverse Zak transform. Section 9 provides additional details regarding using the inverse Zak transform.

[0287] In the above (and other) solutions, the first resource dimension / second resource dimension may be time-frequency or delay-Doppler dimensions, and correspondingly the third resource dimension / fourth resource dimension may be the other (i.e., delay-Doppler or time- frequency dimensions, respectively). In some cases, N may be equal to one such that the transmissions are sent to one specific user device. In some cases, N may be greater than 1, suchInternational Patent Application Attorney Docket No.: 119314.8126.WO00 as when devices are grouped for transmission (e.g., using same code of a code division multiplexing, or using a same beam for all co-located UEs). As discussed in Sections 6 and 7, two different numerologies in the delay-Doppler domain may be used for simultaneous transmission of different signals.

[0288] S18. A method of wireless communications (e.g., method 4200 in FIG.42), comprising: receiving (4210), by a receiving device, a wireless signal transmission according to a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two-dimensional resource plane, wherein a first numerology is indicated by a transmitting device to the receiving device or is implicitly determined from a property of a wireless channel over which the wireless signal transmission is received; and performing (4220) a signal reception operation based on the wireless signal transmission.

[0289] S19. A method of transmitting pilot signals in a wireless communication network (e.g., method 4300 in FIG.43), comprising: configuring (4310) a periodicity of pilot signal transmission along a first resource dimension of a two-dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension; and performing (4320) pilot signal transmissions according to the periodicity. Some example implementations for this solution are discussed in Section 7 and 8.

[0290] S20. A method of receiving pilot signals in a wireless communication network (e.g., method 4400 in FIG.44), comprising: receiving (4410) the pilot signals that are configured to have a periodicity of a pilot signal transmission along a first resource dimension of a two- dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension; and performing (4420) a reception operation based on the pilot signals. Some example implementations for this solution are discussed in Section 7 and 8.

[0291] S21. The method of solution S19 or S20, wherein the at least some pilot signal transmissions selectively occupy less than the entirety of the second resource dimension.

[0292] S22. The method of solution S20, wherein the reception operation comprises a channel estimation operation or a channel sensing operation.23. An apparatus for digital communication comprising at least one processor and a transceiver, wherein the at least one processor is configured to cause the apparatus to perform signal processing operations recited inInternational Patent Application Attorney Docket No.: 119314.8126.WO00 any of solutions S11 to 22, and wherein the transceiver is configured to transmit or receive signals under control of the at least one processor.

[0293] S23. A method of wireless communications (e.g., method 4500 in FIG.45), comprising: determining (4510) to use a first numerology that defines a first set of transmission resources from transmission resources in a two-dimensional time-frequency resource plane; determining (4520) to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources; mapping (4530) a first set of information bits to a first set of resource blocks in a two-dimensional delay-Doppler resource plane and a second set of information bits to a second set of resource blocks in the two- dimensional delay-Doppler resource plane, wherein a plurality of information bits comprises the first set of information bits for a first user device operating based on a legacy wireless protocol and the second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol; generating (4540), using a two- dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks; and transmitting (4550), over a wireless channel, the first set of transmission waveforms and the second set of transmission waveforms, wherein each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and wherein the transmission resources in the two-dimensional time-frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol.

[0294] S24. The method of solution S23, wherein the transmission resources comprise a slice of the two-dimensional time-frequency resource plane with a 1 msec duration and a 180kHz bandwidth.

[0295] S25. The method of solution S23 or S24, wherein the first set of transmission resources and the second set of transmission resources are defined based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel.

[0296] S26. The method of solution S25, wherein the first set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the first user device and the second set of transmissionInternational Patent Application Attorney Docket No.: 119314.8126.WO00 resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the second user device.

[0297] S27. The method of solution S23 or S24, wherein the first set of resource blocks are allocated for the first set of information bits and a first set of sensing pilot symbols.

[0298] S28. The method of solution S27, wherein a number of the first set of sensing pilot symbols is based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel between the apparatus and the first user device.

[0299] S29. The method of any of solutions S23 to S28, wherein the two-dimensional transform is a two-dimensional inverse Zak transform, and wherein the legacy wireless protocol comprises a 5th Generation (5G) wireless protocol.

[0300] S30. A computer-readable medium having code stored thereon; the code, upon execution by at least one processor, causing the at least one processor to control an apparatus to implement the method recited in any of solutions S11 to S29.

[0301] It will be appreciated that the present document provides various techniques for designing numerologies for OTFS transmission systems. In some embodiments, the numerologies may be pre-determined. In some embodiments, numerology may be defined on a user device or a user device set basis and a control signaling may convey to the receiving device which numerology to use. In some embodiments, pilot sensing signals may be transmitted according to a delay or a doppler characteristic or property of a wireless channel.

[0302] The disclosed and other embodiments, modules and the functional operations described in this document can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this document and their structural equivalents, or in combinations of one or more of them. The disclosed and other embodiments can be implemented as one or more computer program products, i.e., one or more modules of computer program instructions encoded on a computer readable medium for execution by, or to control the operation of, data processing apparatus. The computer readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, a composition of matter effecting a machine-readable propagated signal, or a combination of one or more of them. The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example aInternational Patent Application Attorney Docket No.: 119314.8126.WO00 programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them. A propagated signal is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode information for transmission to suitable receiver apparatus.

[0303] A computer program (also known as a program, software, software application, script, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a standalone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0304] The processes and logic flows described in this document can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).

[0305] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read -only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled toInternational Patent Application Attorney Docket No.: 119314.8126.WO00 receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. However, a computer need not have such devices. Computer readable media suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0306] While this patent document contains many specifics, these should not be construed as limitations on the scope of an invention that is claimed or of what may be claimed, but rather as descriptions of features specific to particular embodiments. Certain features that are described in this document in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable sub-combination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a sub-combination or a variation of a sub-combination. Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results.

[0307] Only a few examples and implementations are disclosed. Variations, modifications, and enhancements to the described examples and implementations and other implementations can be made based on what is disclosed.

Claims

International Patent Application Attorney Docket No.: 119314.8126.WO00 WHAT IS CLAIMED IS:

1. An apparatus for digital communication, comprising: circuitry configured to be compatible with a legacy wireless protocol and provide a plurality of information bits comprising a first set of information bits for a first user device operating based on the legacy wireless protocol and a second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol; and transceiver circuitry configured to: determine to use a first numerology that defines a first set of transmission resources from transmission resources in a two-dimensional time- frequency resource plane, determine to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources, map the first set of information bits to a first set of resource blocks in a two- dimensional delay-Doppler resource plane and the second set of information bits to a second set of resource blocks in the two-dimensional delay-Doppler resource plane, generate, using a two-dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks, and transmit, over a wireless channel, the first set of transmission waveforms and the second set of transmission waveforms, wherein each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and wherein the transmission resources in the two-dimensional time-frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol.International Patent Application Attorney Docket No.: 119314.8126.WO00 2. The apparatus of claim 1, wherein the transmission resources comprise a slice of the two- dimensional time-frequency resource plane with a 1 msec duration and a 180kHz bandwidth.

3. The apparatus of claim 1 or 2, wherein the first set of transmission resources and the second set of transmission resources are defined based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel.

4. The apparatus of claim 3, wherein the first set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the first user device and the second set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the second user device.

5. The apparatus of claim 1 or 2, wherein the first set of resource blocks are allocated for the first set of information bits and a first set of sensing pilot symbols.

6. The apparatus of claim 5, wherein a number of the first set of sensing pilot symbols is based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel between the apparatus and the first user device.

7. The apparatus of claim 5, wherein the first set of sensing pilot symbols comprises 30 sensing pilot symbols in a delay dimension and 6 sensing pilot symbols in a Doppler dimension to support a 6 kHz Doppler spread.

8. The apparatus of claim 5, wherein the first set of sensing pilot symbols comprises 15 sensing pilot symbols in a delay dimension and 12 sensing pilot symbols in a Doppler dimension to support a 12 kHz Doppler spread.

9. The apparatus of any of claims 1 to 8, wherein the two-dimensional transform is a two- dimensional inverse Zak transform.

10. The apparatus of any of claims 1 to 9, wherein the legacy wireless protocol comprises a 5th Generation (5G) wireless protocol.International Patent Application Attorney Docket No.: 119314.8126.WO00 11. A method of digital communication, comprising: allocating transmission resources to one or more transmissions in a wireless network according to a first numerology that defines a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two-dimensional resource plane; and generating, by a transmitting device based on allocated transmission resources, one or more transmission waveforms for N receiving devices, where N is a positive integer.

12. The method of claim 11, wherein the one or more transmissions include a data transmission or a pilot signal transmission.

13. The method of claim 11 or 12, including: determining to use a second numerology for at least some of the N receiving devices, and generating an additional transmission waveform according to the second numerology such that the first numerology and the second numerology are concurrently used in the wireless network.

14. The method of claim 13, wherein a control signal transmission indicates to a given wireless device whether the first numerology or the second numerology is being used for transmissions to the given wireless device.

15. The method of claim 12, wherein the pilot signal transmission is allocated resources according to a target property of a wireless channel over which the pilot signal transmission is communicated.

16. The method of any of claims 11 to 15, wherein the one or more transmission waveforms are generated by mapping to a resource block along a third resource dimension and a fourth resource dimension in a second two-dimensional resource plane.

17. The method of claim 16, wherein the one or more transmission waveforms are generated using an inverse Zak transform.International Patent Application Attorney Docket No.: 119314.8126.WO00 18. A method of wireless communications, comprising: receiving, by a receiving device, a wireless signal transmission according to a first resource unit along a first resource dimension and a second resource unit along a second resource dimension in a first two-dimensional resource plane, wherein a first numerology is indicated by a transmitting device to the receiving device or is implicitly determined from a property of a wireless channel over which the wireless signal transmission is received; and performing a signal reception operation based on the wireless signal transmission.

19. A method of transmitting pilot signals in a wireless communication network, comprising: configuring a periodicity of pilot signal transmission along a first resource dimension of a two-dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension; and performing pilot signal transmissions according to the periodicity.

20. A method of receiving pilot signals in a wireless communication network, comprising: receiving the pilot signals that are configured to have a periodicity of a pilot signal transmission along a first resource dimension of a two-dimensional resource plane such that at least some pilot signal transmissions occupy an entirety of a second resource dimension; and performing a reception operation based on the pilot signals.

21. The method of claim 19 or 20, wherein the at least some pilot signal transmissions selectively occupy less than the entirety of the second resource dimension.

22. The method of claim 20, wherein the reception operation comprises a channel estimation operation or a channel sensing operation.

23. An apparatus for digital communication comprising at least one processor and a transceiver, wherein the at least one processor is configured to cause the apparatus to perform signal processing operations recited in any of claims 11 to 22, and wherein the transceiver is configured to transmit or receive signals under control of the at least one processor.

23. A method of wireless communications, comprising: determining to use a first numerology that defines a first set of transmission resources from transmission resources in a two-dimensional time-frequency resource plane;International Patent Application Attorney Docket No.: 119314.8126.WO00 determining to use a second numerology, different from the first numerology, that defines a second set of transmission resources from the transmission resources; mapping a first set of information bits to a first set of resource blocks in a two- dimensional delay-Doppler resource plane and a second set of information bits to a second set of resource blocks in the two-dimensional delay-Doppler resource plane, wherein a plurality of information bits comprises the first set of information bits for a first user device operating based on a legacy wireless protocol and the second set of information bits for a second user device operating based on a current wireless protocol different from the legacy wireless protocol; generating, using a two-dimensional transform, a first set of transmission waveforms based on the first set of resource blocks and a second set of transmission waveforms based on the second set of resource blocks; and transmitting, over a wireless channel, the first set of transmission waveforms and the second set of transmission waveforms, wherein each transmission waveform in the first set of transmission waveforms and the second set of transmission waveforms uses basis functions that are invariant under operations of time, delay, and Doppler shift, and wherein the transmission resources in the two-dimensional time-frequency resource plane are divided into resource blocks with numerologies compatible with the legacy wireless protocol.

24. The method of claim 23, wherein the transmission resources comprise a slice of the two- dimensional time-frequency resource plane with a 1 msec duration and a 180kHz bandwidth.

25. The method of claim 23 or 24, wherein the first set of transmission resources and the second set of transmission resources are defined based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel.

26. The method of claim 25, wherein the first set of transmission resources are defined based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the first user device and the second set of transmission resources are definedInternational Patent Application Attorney Docket No.: 119314.8126.WO00 based on the maximum delay spread or the maximum Doppler spread for the wireless channel between the apparatus and the second user device.

27. The method of claim 23 or 24, wherein the first set of resource blocks are allocated for the first set of information bits and a first set of sensing pilot symbols.

28. The method of claim 27, wherein a number of the first set of sensing pilot symbols is based on a maximum delay spread or a maximum Doppler spread associated with the wireless channel between the apparatus and the first user device.

29. The method of any of claims 23 to 28, wherein the two-dimensional transform is a two- dimensional inverse Zak transform, and wherein the legacy wireless protocol comprises a 5th Generation (5G) wireless protocol.

30. A computer-readable medium having code stored thereon; the code, upon execution by at least one processor, causing the at least one processor to control an apparatus to implement the method recited in any of claims 11 to 29.

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