Signal processing system, multi-signal processing system, signal processing method, and signal processing program

Abstract

To provide a signal processing system capable of suppressing a decline of success probability of time alignment even under a condition where the peak of cross correlation is low.SOLUTION: A cross correlation calculation unit calculates, for a plurality of received signals having temporal expanse and coupling with each other during propagation and pilot signals included respectively in portions of the received signals, a cross correlation spectrum representing the similarity between the received signals and the pilot signals. A correlation forming unit applies arithmetic processing which forms the peak of the cross correlation spectrum so that it becomes higher than the original peak. A first peak determination processing unit detects the peak of the cross correlation spectrum after the arithmetic processing has been applied. A synchronization processing unit uses the detected peak to perform temporal alignment of aligning a temporal origin for which the pilot signals and the reception signals are synchronized.SELECTED DRAWING: Figure 24

Description

[Technical Field]

[0001] The present invention relates to a signal processing system for processing optical signals, a multi-signal processing system, a signal processing method, and a signal processing program. [Background technology]

[0002] In optical communication transmission systems using optical fibers that exhibit spatial mode dispersion (SMD), time alignment is performed using a known signal, such as a pilot signal.

[0003] Patent Document 1 discloses a method of using cross-correlation when synchronizing a transmitter and a receiver using a preamble. In the method described in Patent Document 1, the cross-correlation between a received signal and a preamble is calculated, and when the calculated value exceeds a predetermined threshold, the peak of the cross-correlation is detected and synchronization is performed. Here, the threshold is empirically determined based on Monte Carlo simulation. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Special Publication No. 2010-531572 Summary of the Invention [Problem to be solved by the invention]

[0005] Under conditions where the cross-correlation peak is low, the probability of successful time alignment using cross-correlation decreases because it is difficult or impossible to determine an appropriate threshold value under such conditions.

[0006] An object of the present invention is to provide a signal processing system, a multi-signal processing system, a signal processing method, and a signal processing program that can suppress a decrease in the probability of successful time alignment even under conditions where the above-mentioned cross-correlation peak is low. [Means for solving the problem]

[0007] The signal processing system according to the present disclosure is characterized by comprising: a cross-correlation calculation unit that calculates a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a temporal spread and that couple with each other during propagation, and a pilot signal included in each of the received signals; a correlation shaping processing unit that performs arithmetic processing to shape the peak of the cross-correlation spectrum so as to raise it from its original peak; a first peak determination processing unit that detects the peak of the cross-correlation spectrum after the arithmetic processing has been performed; and a synchronization processing unit that uses the detected peak to perform time alignment to align the time origin for synchronizing the pilot signal and the received signal.

[0008] The multi-signal processing system according to the present disclosure is characterized in that the signal processing systems are configured in parallel, and each signal processing system receives at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal.

[0009] The signal processing method according to the present disclosure is characterized in that it calculates a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a temporal extent and that couple with each other during propagation, and a pilot signal that is included as part of each of the received signals, performs arithmetic processing to shape the peak of the cross-correlation spectrum so that it is higher than the original peak, detects the peak of the cross-correlation spectrum after the arithmetic processing has been performed, and uses the detected peak to perform time alignment to align the time origin for synchronizing the pilot signal and the received signal.

[0010] A signal processing program according to the present disclosure causes a computer to execute a cross-correlation calculation process that calculates a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a time spread and that couple with each other during propagation, and a pilot signal included in each of the received signals; a correlation shaping process that performs an arithmetic process to shape the peak of the cross-correlation spectrum so as to make it higher than the original peak; a first peak determination process that detects the peak of the cross-correlation spectrum after the arithmetic process has been performed; and a synchronization process that uses the detected peak to align the time origin for synchronizing the pilot signal and the received signal. [Effects of the Invention]

[0011] According to the present invention, even under conditions where the cross-correlation peak is low, it is possible to prevent a decrease in the probability of successful time alignment. [Brief explanation of the drawings]

[0012] [Figure 1] 1 is a block diagram illustrating an example configuration of a signal processing system according to the present disclosure. [Figure 2] 10 is a flowchart illustrating an example of the operation of the signal processing system of the present disclosure. [Figure 3] FIG. 10 is a block diagram showing another example configuration of a signal processing system according to the present disclosure. [Figure 4] 10 is a flowchart showing another example of the operation of the signal processing system of the present disclosure. [Figure 5] FIG. 10 is a block diagram showing another example configuration of a signal processing system according to the present disclosure. [Figure 6] 10 is a flowchart showing another example of the operation of the signal processing system of the present disclosure. [Figure 7] FIG. 10 is a block diagram showing another example configuration of a signal processing system according to the present disclosure. [Figure 8] 10 is a flowchart showing another example of the operation of the signal processing system of the present disclosure. [Figure 9] FIG. 1 is an explanatory diagram showing an example of a configuration using a signal processing device. [Figure 10] FIG. 2 is an explanatory diagram showing an example of a received signal. [Figure 11] FIG. 1 is a block diagram illustrating a configuration example of a time alignment device. [Figure 12] 10 is a flowchart illustrating an example of the operation of the time alignment device. [Figure 13] FIG. 10 is an explanatory diagram showing an example of change in the success probability of peak determination. [Figure 14] FIG. 10 is an explanatory diagram showing another example of a configuration using a signal processing device. [Figure 15] FIG. 10 is a block diagram showing another example of the configuration of the time alignment device. [Figure 16] 10 is a flowchart illustrating another example of the operation of the time alignment device. [Figure 17] FIG. 10 is an explanatory diagram showing an example of change in the success probability of peak determination when a shaping parameter is changed. [Figure 18] FIG. 10 is an explanatory diagram showing another example of a configuration using a signal processing device. [Figure 19] FIG. 10 is a block diagram showing another example of the configuration of the time alignment device. [Figure 20] 10 is a flowchart illustrating another example of the operation of the time alignment device. [Figure 21] FIG. 10 is an explanatory diagram showing another example of a configuration using a signal processing device. [Figure 22] FIG. 10 is a block diagram showing another example of the configuration of the time alignment device. [Figure 23] 10 is a flowchart illustrating another example of the operation of the time alignment device. [Figure 24] 1 is a block diagram showing an overview of a signal processing system according to the present disclosure. [Figure 25] 1 is a block diagram illustrating an overview of a multi-signal processing system according to the present disclosure. [Figure 26] FIG. 1 is a schematic block diagram illustrating the configuration of a computer according to at least one embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0013] First, a method for time synchronization between a received signal and a known signal will be described.

[0014] In recent years, MIMO (Multiple-Input Multiple-Output) technology has been developed for optical fiber communications as a technology to expand communication capacity. MIMO in optical communications is used in polarization multiplexing of single-mode fiber, multimode fiber (MMF), multicore fiber (MCF), etc., and aims to expand communication capacity and increase communication speeds.

[0015] In MIMO processing in optical communications, received signals in multiple modes (polarization, propagation mode, core) are input, and a signal is output that has been compensated for crosstalk between modes and distortion incurred during propagation. In particular, in MIMO processing in optical communications using coupled MCFs, the use of data-aided processing using pilot signals is being considered (see, for example, Reference 1 below).

[0016] <Reference 1> M. Arikawa et al., “Long-Haul WDM / SDM Transmission Over Coupled 4-Core Fibers Installed in Submarine Cable,” in Journal of Lightwave Technology, vol. 41, no. 6, pp. 1649-1657

[0017] In data-aided processing, pilot signals are included in the transmitted signal. The MIMO processing filter is initially converged to restore the pilot signal affected by crosstalk or distortion to the original pilot signal, and then switched to blind adaptive equalization, which does not use the pilot signal, to achieve stable compensation.

[0018] To perform data-aided processing, it is necessary to identify a portion of the received signal that corresponds to a pilot signal from among the distorted signals in advance, and to time-align the time origin of the received signal with the pilot signal. One method for performing such time-alignment is to use cross-correlation. Examples of such signal processing methods are the methods described in Patent Document 1 and Reference 2 below.

[0019] <Reference 2> JP 2005-064567 A

[0020] Reference 2 discloses a method for calculating the cross-correlation between a received signal and a known signal to time synchronize them, and then averaging the calculated cross-correlation to calculate a moving average value to mitigate the effects of noise mixed in the signal. In communications, it is desirable for the length of a pilot signal to be short. This is because pilot signals are used only for time alignment and data-aided processing, and cannot actually transmit information. While using a short pilot signal can increase transmission capacity, if a pilot signal is not long enough, the height of the cross-correlation peak will be low, reducing the probability of successful time alignment.

[0021] In addition to a short pilot signal, the peak height can also be reduced due to factors such as a large SMD, a large number of modes coupled due to crosstalk, etc. In particular, in data-aided processing in long-distance optical communications using coupled MCFs, the pilot signal length, SMD, and number of coupled modes all affect the peak height.

[0022] While a simple moving average of the cross-correlation, as disclosed in Reference 2, can mitigate the effects of noise in the signal, it does not aim to improve the probability of successful time alignment in situations where the peak height is low.

[0023] Therefore, the present disclosure describes a method that can suppress a decrease in the probability of successful time alignment even under conditions where the cross-correlation peak is low.

[0024] Hereinafter, the similarity between the received signal and the pilot signal will be referred to as the cross-correlation spectrum. Specifically, the spectrum consisting of the value C[m] that indicates the similarity between the pilot signal and a continuous portion of the received signal starting from the mth symbol, using all or part of the received signal and the pilot signal, is called the cross-correlation spectrum. A basic example of a cross-correlation spectrum is cross-correlation.

[0025] Hereinafter, embodiments of the present disclosure will be described with reference to the drawings. Note that the unidirectional arrows shown in each block diagram simply indicate the direction of information flow and do not exclude bidirectionality.

[0026] [First embodiment] [Configuration Description] 1 is a block diagram showing a configuration example of a first embodiment of a signal processing system according to the present disclosure. The signal processing system 100 of the first embodiment includes a cross-correlation calculation unit 101, a correlation shaping processing unit 102, a peak determination processing unit 103, and a synchronization processing unit 104.

[0027] [Explanation of operation] These means operate roughly as follows.

[0028] The cross-correlation calculation unit 101 calculates a cross-correlation spectrum from a pilot signal and a received signal provided as input. In this embodiment, the received signal has a time spread and is made up of multiple signals that couple with each other during propagation. The pilot signals are signals that are included as part of the received signals. As described above, the cross-correlation spectrum represents the similarity between the received signal and the pilot signal. The cross-correlation calculation unit 101 may calculate the cross-correlation spectrum using a known method.

[0029] The correlation shaping processor 102 receives the cross-correlation spectrum calculated by the cross-correlation calculator 101 and performs a calculation process to shape the peak of the cross-correlation spectrum so that it is relatively higher than the original peak. This calculation process is performed on the entire cross-correlation spectrum, resulting in a higher peak. A specific example of the calculation process will be described later.

[0030] The peak determination processing unit 103 performs peak determination based on a threshold value on the cross-correlation spectrum that has been subjected to the arithmetic processing by the correlation shaping processing unit 102. That is, the peak determination processing unit 103 detects peaks in the cross-correlation spectrum that has been subjected to the arithmetic processing. If the peak detection is successful, the peak determination processing unit 103 outputs information on the position of the peak, and if the peak detection is unsuccessful, it outputs information indicating the failure.

[0031] When the peak determination processing unit 103 has succeeded in detecting a peak, the synchronization processing unit 104 determines the portion of the received signal that corresponds to the pilot signal, using information on the position of the peak detected by the peak determination processing unit 103. Then, using the detected peak, the synchronization processing unit 104 performs time alignment to align the point at which the pilot signal and the received signal are synchronized (hereinafter referred to as the time origin).

[0032] The cross-correlation calculation unit 101, the correlation shaping processing unit 102, the peak determination processing unit 103, and the synchronization processing unit 104 are realized by a computer processor (e.g., a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit)) that operates according to a program (signal processing program). For example, the program may be stored in a storage unit (not shown) provided in the signal processing system 100, and the processor may read the program and operate as the cross-correlation calculation unit 101, the correlation shaping processing unit 102, the peak determination processing unit 103, and the synchronization processing unit 104 according to the program.

[0033] Furthermore, the functions of the cross-correlation calculation unit 101, the correlation shaping processing unit 102, the peak determination processing unit 103, and the synchronization processing unit 104 may be provided in the form of SaaS (Software as a Service). Furthermore, the cross-correlation calculation unit 101, the correlation shaping processing unit 102, the peak determination processing unit 103, and the synchronization processing unit 104 may each be realized by dedicated hardware.

[0034] Furthermore, some or all of the components of each device may be realized by general-purpose or dedicated circuits, processors, etc., or a combination of these. These may be configured by a single chip, or by multiple chips connected via a bus. Some or all of the components of each device may be realized by a combination of the above-mentioned circuits, etc., and programs.

[0035] Furthermore, when some or all of the components of the cross-correlation calculation unit 101, the correlation shaping processing unit 102, the peak determination processing unit 103, and the synchronization processing unit 104 are realized by a plurality of information processing devices, circuits, etc., the plurality of information processing devices, circuits, etc. may be centrally or decentralized. For example, the information processing devices, circuits, etc. may be realized as a client-server system, a cloud computing system, or the like, in a form in which each device is connected via a communication network.

[0036] Next, the operation of this embodiment will be described with reference to a flowchart shown in FIG.

[0037] First, a received signal and a pilot signal are input to cross-correlation calculation section 101 (step A1 in FIG. 2). Next, cross-correlation calculation section 101 calculates the cross-correlation spectrum between the received signal and the pilot signal, and inputs the result to correlation shaping processing section 102 (step A2).

[0038] The correlation shaping processor 102 performs a calculation process to increase the peak of the input cross-correlation spectrum, and inputs the cross-correlation spectrum after the calculation process to the peak determination processor 103 (step A3). The peak determination processor 103 performs a peak determination process on the cross-correlation spectrum after the calculation process, determining and detecting a portion exceeding a threshold as a peak (step A4).

[0039] If peak determination processing unit 103 does not detect a peak (No in step A5), time alignment fails and processing ends. On the other hand, if peak determination processing unit 103 detects a peak (Yes in step A5), peak determination processing unit 103 inputs the position of the detected peak to synchronization processing unit 104 (step A6). Then, synchronization processing unit 104 performs time alignment between the received signal and the pilot signal based on information about the position of the detected peak (step A7).

[0040] [Effect description] Next, the effects of this embodiment will be described. In this embodiment, the correlation shaping processor 102 performs arithmetic processing on the cross-correlation spectrum calculated by the cross-correlation calculator 101 to relatively increase the peak of the cross-correlation spectrum, thereby increasing the probability of successful peak determination. Therefore, even under conditions where the cross-correlation peak is low, it is possible to prevent a decrease in the probability of successful time alignment.

[0041] For example, when the length of the pilot signal is shortened, the height of the peak of the cross-correlation spectrum decreases, making it difficult to determine an appropriate threshold. On the other hand, in this embodiment, the correlation shaping processor 102 performs calculations to make the peak of the cross-correlation spectrum relatively higher than the original peak. This prevents a decrease in the probability of successful time alignment. This also reduces the proportion of pilot signals in the signal, thereby increasing transmission capacity.

[0042] Furthermore, the correlation shaping processor 102 performs arithmetic processing, which makes the peak of the cross-correlation spectrum relatively high compared to the entire spectrum. Therefore, even under conditions where the peak of the cross-correlation spectrum is low, the probability of success of time alignment using the cross-correlation spectrum can be improved. This is because it becomes easier to determine an appropriate value for the threshold used to search for the peak required for time alignment.

[0043] [Second embodiment] [Configuration Description] Next, a second embodiment of the signal processing system of the present disclosure will be described. Fig. 3 is a block diagram showing an example configuration of the second embodiment of the signal processing system of the present disclosure. A signal processing system 200 of the second embodiment includes a cross-correlation calculation unit 201, a parameter determination unit 202, a correlation shaping processing unit 203, a peak determination processing unit 204, and a synchronization processing unit 205.

[0044] [Explanation of operation] These means operate roughly as follows: The operations of the cross-correlation calculation unit 201, peak determination processing unit 204, and synchronization processing unit 205 are similar to the operations of the cross-correlation calculation unit 101, peak determination processing unit 103, and synchronization processing unit 104 in the first embodiment.

[0045] Parameter determination section 202 determines parameters (hereinafter referred to as shaping parameters) used in a calculation process for shaping the peaks of the cross-correlation spectrum, using at least one of parameters indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal. The shaping parameters will be described in detail later. Then, correlation shaping processing section 203 performs a calculation process for shaping the peaks, using the shaping parameters.

[0046] The cross-correlation calculation unit 201, the parameter determination unit 202, the correlation shaping processing unit 203, the peak determination processing unit 204, and the synchronization processing unit 205 are realized by a processor of a computer that operates according to a program (signal processing program).

[0047] Next, the operation of this embodiment will be described. Fig. 4 is a flowchart showing an example of the operation of the signal processing system of this embodiment. The processing up to the calculation of the cross-correlation spectrum is the same as the processing from step A1 to step A2 in Fig. 2.

[0048] In this embodiment, parameters indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal are input to parameter determination section 202 (step B3). Then, parameter determination section 202 determines shaping parameters using the input information, such as the input parameters indicating the characteristics of the transmission system and the information indicating the modulation method of the pilot signal, and inputs the shaping parameters to correlation shaping processing section 203 (step B4).

[0049] The correlation shaping processing unit 203 performs calculations on the cross-correlation spectrum input from the cross-correlation calculation unit 201 using the shaping parameters input from the parameter determination unit 202 to shape the peak of the cross-correlation spectrum, and inputs the cross-correlation spectrum after the calculations to the peak determination processing unit 204 (step B5).

[0050] The subsequent processing from peak determination to time alignment is the same as the processing from step A4 to step A7 in FIG.

[0051] [Effect description] Next, the effects of this embodiment will be described. In this embodiment, the parameter determination unit 202 specifically determines the shaping parameters used in the calculation process for shaping the peaks of the cross-correlation spectrum from parameters indicating the characteristics of the transmission path and information indicating the modulation method of the pilot signal. Therefore, in addition to the effects of the first embodiment, the effects of the calculation process performed on the cross-correlation spectrum can be optimized for various transmission systems.

[0052] [Third embodiment] [Configuration Description] Next, a third embodiment of the signal processing system of the present disclosure will be described. Fig. 5 is a block diagram showing an example configuration of the third embodiment of the signal processing system of the present disclosure. A signal processing system 300 of the third embodiment includes a cross-correlation calculation unit 301, a pre-peak determination processing unit 302, a branching processing unit 303, a correlation shaping processing unit 304, a post-peak determination processing unit 305, and a synchronization processing unit 306.

[0053] [Explanation of operation] These means operate roughly as follows: The operations of cross-correlation calculation section 301, correlation shaping processing section 304, and synchronization processing section 306 are similar to the operations of cross-correlation calculation section 101, correlation shaping processing section 102, and synchronization processing section 104 in the first embodiment.

[0054] The method by which the preceding peak determination processor 302 and the following peak determination processor 305 determine peaks is the same as the method by the peak determination processor 103 in the first embodiment. However, the cross-correlation spectrum for which peaks are detected differs between the preceding peak determination processor 302 and the following peak determination processor 305. Specifically, the preceding peak determination processor 302 detects peaks in the cross-correlation spectrum before arithmetic processing is performed, and the following peak determination processor 305 detects peaks in the cross-correlation spectrum after arithmetic processing is performed.

[0055] The branching processor 303 determines subsequent processing based on the success or failure of peak detection performed by the preceding peak determination processor 302. That is, if no peak is detected in the cross-correlation spectrum, the branching processor 303 causes the correlation shaping processor 304 and the following peak determination processor 305 to perform processing.

[0056] The cross-correlation calculation unit 301, the pre-peak determination processing unit 302, the branching processing unit 303, the correlation shaping processing unit 304, the post-peak determination processing unit 305, and the synchronization processing unit 306 are realized by a computer processor that operates according to a program (signal processing program).

[0057] Next, the operation of this embodiment will be described. Fig. 6 is a flowchart showing an example of the operation of the signal processing system of this embodiment. Note that the processing up to the calculation of the cross-correlation spectrum is the same as the processing from step A1 to step A2 in Fig. 2.

[0058] The pre-peak determination processor 302 performs peak determination on the input cross-correlation spectrum, determining and detecting portions exceeding a threshold as peaks (step C3). If the pre-peak determination processor 302 detects a peak (Yes in step C4), the process proceeds to step C5, and if not (No in step C4), the process proceeds to step C6. This branching process is determined by the branching processor 303.

[0059] That is, if a peak is detected, the preceding peak determination processor 302 inputs the position of the detected peak to the synchronization processor 306 and proceeds to step A7 (step C5). On the other hand, if a peak is not detected, the preceding peak determination processor 302 inputs the cross-correlation spectrum to the correlation shaping processor 304 (step C6).

[0060] The correlation shaping processor 304 performs arithmetic processing to increase the peak of the input cross-correlation spectrum, and inputs the cross-correlation spectrum after the arithmetic processing to the subsequent peak determination processor 305 (step C7). The subsequent peak determination processor 305 performs peak determination on the cross-correlation spectrum after the arithmetic processing, determining and detecting portions exceeding a threshold as peaks (step C8).

[0061] Thereafter, the process of performing synchronization according to the result of peak determination is the same as the process from step A5 to step A7 in FIG.

[0062] [Effect description] Next, the effects of this embodiment will be described. In this embodiment, the pre-peak determination processor 302 performs peak determination once before the calculation process for relatively increasing the peak of the cross-correlation spectrum is performed, and if a peak is detected, the pre-peak determination processor 302 is configured to perform synchronization processing immediately. Therefore, in addition to the effects of the first embodiment, the above calculation process can be omitted if it is not necessary, and unnecessary calculations required for the calculation process can be reduced.

[0063] Furthermore, the signal processing system 300 of this embodiment may include the parameter determination unit 202 of the second embodiment. With such a configuration, the effects shown in the second embodiment can also be obtained.

[0064] [Fourth embodiment] [Configuration Description] Next, a fourth embodiment of the signal processing system of the present disclosure will be described. Fig. 7 is a block diagram showing an example configuration of the fourth embodiment of the signal processing system of the present disclosure. A signal processing system 400 of the fourth embodiment includes a cross-correlation calculation unit 401, a detectability estimation unit 402, a branching processing unit 403, a correlation shaping processing unit 404, a peak determination processing unit 405, and a synchronization processing unit 406.

[0065] [Explanation of operation] These means operate roughly as follows: The operations of cross-correlation calculation section 401, correlation shaping processing section 404, peak determination processing section 405, and synchronization processing section 406 are similar to the operations of cross-correlation calculation section 101, correlation shaping processing section 102, peak determination processing section 103, and synchronization processing section 104 in the first embodiment.

[0066] The detectability estimation unit 402 estimates the possibility of successful peak detection using an index that distinguishes between the magnitude of the peak and non-peak portions of the cross-correlation spectrum. The content of the index and a method of estimating the possibility using the index will be described later.

[0067] The branching processing unit 403 determines the subsequent processing depending on the possibility of successful peak detection estimated by the detectability estimation unit 402. That is, when the possibility of successful peak detection is lower than a predetermined standard, the branching processing unit 403 causes the correlation shaping processing unit 404 to perform calculation processing (i.e., calculation processing to make the peak of the cross-correlation spectrum relatively higher than the original peak).

[0068] The cross-correlation calculation unit 401, the detectability estimation unit 402, the branching processing unit 403, the correlation shaping processing unit 404, the peak determination processing unit 405, and the synchronization processing unit 406 are realized by a computer processor that operates according to a program (signal processing program).

[0069] Next, the operation of this embodiment will be described. Fig. 8 is a flowchart showing an example of the operation of the signal processing system of this embodiment. The processing up to the calculation of the cross-correlation spectrum is the same as the processing from step A1 to step A2 in Fig. 2.

[0070] The detectability estimation unit 402 estimates the possibility of successful peak detection for the input cross-correlation spectrum using an index that distinguishes between the magnitude of the peak and non-peak portions of the cross-correlation spectrum (step D3).

[0071] If the probability of success is not higher than the predetermined standard (No in step D4), the process proceeds to step D5, and if it is higher than the predetermined standard (Yes in step D4), the process proceeds to step D7. Note that this branching process is determined by the branching processing unit 403.

[0072] That is, if the probability of success is not higher than a predetermined standard, detectability estimation unit 402 inputs the cross-correlation spectrum to correlation shaping processing unit 404 (step D5). Correlation shaping processing unit 404 then performs arithmetic processing on the input cross-correlation spectrum, inputs the cross-correlation spectrum after the arithmetic processing to peak determination processing unit 405, and proceeds to step D8 (step D6). On the other hand, if the probability of success is higher than a predetermined standard, detectability estimation unit 402 inputs the cross-correlation spectrum to peak determination processing unit 405 (step D7).

[0073] Peak determination processing unit 405 performs peak determination to detect a portion of the cross-correlation spectrum that exceeds a threshold value (step D8). After that, the process of performing synchronization according to the result of peak determination is the same as the process from step A5 to step A7 in FIG. 2.

[0074] [Effect description] Next, the effects of this embodiment will be described. In this embodiment, the detectability estimation unit 402 estimates the possibility of successful peak detection, and when the possibility of peak detection is low, the correlation shaping processing unit 404 performs calculation processing. Therefore, in addition to the effects of the first embodiment, unnecessary calculation processing can be reduced. Furthermore, in this embodiment, the cross-correlation spectrum and the processing unit that determines peaks in the cross-correlation spectrum that has been subjected to calculation processing are shared by the peak determination processing unit 405. Therefore, unnecessary signal processing blocks can be reduced.

[0075] Furthermore, the signal processing system 400 of this embodiment may include the parameter determination unit 202 of the second embodiment. With such a configuration, the effects shown in the second embodiment can also be obtained.

[0076] The signal processing systems 100 to 400 described above are used for time alignment of received signals in spatial mode multiplexed optical signal communication using a multicore fiber, time alignment of received signals in propagation mode multiplexed optical signal communication using a multimode fiber, and time alignment of received signals in polarization multiplexed optical signal communication using a single mode fiber.

[0077] [Specific example] Next, the operation of the embodiment of the present disclosure will be described using a specific example.

[0078] First, a specific example of the first embodiment will be described.

[0079] The signal processing device 500 in this specific example is used in the front stage of a data-aided MIMO processing device in optical signal communication using optical fibers having multiple propagation modes. Fig. 9 is an explanatory diagram showing an example of a configuration using the signal processing device 500.

[0080] The signal processing device 500 is used in optical signal communication using a coupled four-core MCF having four spatial modes (total of 4x2=8 modes), each of which is polarization-multiplexed, as illustrated in Fig. 9. As an optical fiber having multiple propagation modes, an MCF with a different number of cores may be used, or an MMF for mode division multiplexing (MDM) optical signal communication may be used.

[0081] Furthermore, the signal processing device 500 may be used in optical signal communication using polarization division multiplexing (PDM) in a single mode fiber (SMF), or in optical signal communication using a multiplexing method that combines these.

[0082] The signal processing device 500 includes time alignment devices 510 to 580. The time alignment devices 510 to 580 each correspond to the signal processing system 100 in the first embodiment. In other words, the signal processing device 500 can be said to be a device in which a plurality of the signal processing systems 100 in the first embodiment are configured in parallel.

[0083] Time alignment device 510 processes received signal 1X corresponding to the X polarization of core 1 of the MCF received by the coherent receiver. Time alignment device 520 processes received signal 1Y corresponding to the Y polarization of core 1. Time alignment device 530 processes received signal 2X corresponding to the X polarization of core 2. Time alignment device 540 processes received signal 2Y corresponding to the Y polarization of core 2. Time alignment device 550 processes received signal 3X corresponding to the X polarization of core 3. Time alignment device 560 processes received signal 3Y corresponding to the Y polarization of core 3. Time alignment device 570 processes received signal 4X corresponding to the X polarization of core 4. Time alignment device 580 processes received signal 4Y corresponding to the Y polarization of core 4.

[0084] FIG. 10 is an explanatory diagram showing an example of a received signal. As shown in FIG. 10, each received signal is a transmission signal that includes a pilot signal as part of the transmission signal and is subjected to crosstalk and distortion between modes during propagation. In this example, the modulation method for the transmission signal and pilot signal is assumed to be Quaternary Phase-Shift Keying (QPSK). However, other modulation methods may also be used. The pilot signals included in each transmission signal may be different from each other or may be the same.

[0085] 11 is a block diagram showing an example of the configuration of a time alignment device 510. The time alignment device 510 includes a cross-correlation calculation device 511, a correlation shaping device 512, a peak determination device 513, and a synchronization processing device 514. Here, each device may be realized in whole or in part by an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integration Circuit), or may be realized as a program executed on a computing device such as a computer.

[0086] The cross-correlation calculation device 511, correlation shaping device 512, peak determination device 513, and synchronization processing device 514 of this specific example correspond to the cross-correlation calculation unit 101, correlation shaping processing unit 102, peak determination processing unit 103, and synchronization processing unit 104 in the first embodiment, respectively. Using the above configuration, the time alignment device 510 generally operates as follows.

[0087] The cross-correlation calculation device 511 calculates the cross-correlation spectrum C[m] using, for example, the following equation 1. Here, the length of the received signal is N symbols, and m is a natural number ranging from 0 to N-1. Furthermore, x[j] (j=0, 1, ..., N-1) is the received signal, and y[k] (k=0, 1, ..., N-1) is the pilot signal.

[0088] However, the length of the pilot signal y[k] is actually M(M<N)であり、y[k]=0(k> M-1). The cross-correlation calculation device 511 may calculate the cross-correlation spectrum using a part of the pilot signal instead of the whole of the pilot signal. In this case, the length of the part of the pilot signal used to calculate the cross-correlation spectrum is M'(<M)として、y[k]=0(k> M'-1).

[0089]

number

[0090] Alternatively, the cross-correlation calculator 511 may use, as the cross-correlation spectrum, a further normalized C[m].

[0091] The correlation shaping device 512 performs an arithmetic operation to relatively increase the peak of the cross-correlation spectrum with respect to the cross-correlation spectrum calculated by the cross-correlation calculator 511. Hereinafter, specific examples of the arithmetic operation will be described.

[0092] First, a first example of the arithmetic operation will be described. When the optical signal-to-noise ratio (OSNR) is sufficiently large, two QPSK-modulated signals are uncorrelated, and all symbols of the pilot signal appear in the calculation of the cross-correlation spectrum. That is, it is assumed that m < N - M - 1. At this time, the component excluding the absolute value of C[m] follows a two-dimensional normal distribution on the complex plane, and its standard deviation σ1 is expressed by Equation 2 exemplified below. Here, it is assumed that the pilot signal and the received signal are each normalized by power.

[0093]

Equation

[0094] Normalize the cross-correlation spectrum by dividing it by σ1. When the two signals used in the calculation of the cross-correlation spectrum are uncorrelated, the value exemplified in Equation 3 below, which is the square of the part where m < N - M - 1 of the cross-correlation spectrum, is a random variable following a chi-square distribution with 2 degrees of freedom. Since the peak used for time alignment is not the value of the cross-correlation spectrum calculated by uncorrelated signals, it does not follow this chi-square distribution.

[0095] Furthermore, due to SMD, only the area around the peak of the cross-correlation spectrum is no longer a random variable following a chi-square distribution. Therefore, the correlation shaping device 512 can calculate a moving average with an appropriate window width w1 according to the equation shown in Equation 4 below. That is, the correlation shaping device 512 may shape the peak of the cross-correlation spectrum by performing a calculation process to calculate a moving average of the square of the normalized cross-correlation spectrum. This calculation process makes it possible to obtain a cross-correlation spectrum C1[m] that has been subjected to calculation and has a peak that is relatively higher than the original peak.

[0096] In this case, correlation shaping device 512 may experimentally determine σ1 using a portion of the received signal that is known not to include a pilot signal. If the influence of including a pilot signal can be ignored, correlation shaping device 512 may experimentally determine σ1 using the entire received signal.

[0097]

number

[0098]

number

[0099] Next, a second example of the arithmetic processing will be described. Of the cross-correlation spectrum C1[m] that has undergone the arithmetic processing described in the first example, the portion where the received signal and the pilot signal are uncorrelated is distributed around 2, which is the mean of a chi-squared distribution with two degrees of freedom. The correlation shaping device 512 may subtract this constant value according to Equation 5 shown below and output the result as the cross-correlation spectrum C2[m] that has undergone the arithmetic processing. In other words, the correlation shaping device 512 may shape the peak of the cross-correlation spectrum by performing arithmetic processing in which a constant value is subtracted from the moving average of the square of the normalized cross-correlation spectrum.

[0100]

number

[0101] Next, a third example of arithmetic processing will be described. The cross-correlation spectrum subjected to the arithmetic processing described in the second example follows a normal distribution with a standard deviation having a width σ2 represented by Expression 6 exemplified below according to the central limit theorem. Therefore, the correlation shaping device 512 normalizes the cross-correlation spectrum C2[m] subjected to the arithmetic processing described in the second example by dividing it by σ2. Then, the correlation shaping device 512 calculates a moving average with an appropriate window width w2 according to an expression represented by Expression 8 below for a value C2’[m] represented by Expression 7 exemplified below, which is the square of the portion where m < N - M - 1.

[0102] That is, the correlation shaping device 512 performs arithmetic processing to calculate a moving average of the square of the normalized cross-correlation spectrum after subtracting a constant value from the moving average of the square of the normalized cross-correlation spectrum, thereby shaping the peak of the cross-correlation spectrum. By this arithmetic processing, it is possible to obtain a cross-correlation spectrum C3[m] subjected to arithmetic processing in which components other than the peak used for time alignment are suppressed.

[0103] Also, at this time, the correlation shaping device 512 may experimentally obtain σ2 using a portion of the received signal where it is known that no pilot signal is included. If the influence due to the inclusion of the pilot signal can be ignored, the correlation shaping device 512 may experimentally obtain σ2 using the entire received signal.

[0104] [Number]

[0105] [Number]

[0106] [Number]

[0107] These calculations are effective when the cross-correlation spectrum peaks are broadened due to the SMD of the optical fiber.Similarly, these calculations are effective even when the signal has a temporal broadening due to factors other than SMD, such as polarization mode dispersion (PMD).

[0108] The calculation method is not limited to the above example. For example, the calculation may be performed based on the statistics of the cross-correlation spectrum, or arbitrary processing may be performed. In either case, any method may be used as long as the calculation process makes the peak of the cross-correlation spectrum relatively higher than the original peak.

[0109] Peak determination device 513 performs peak determination on the cross-correlation spectrum that has undergone this calculation processing based on peak determination threshold 1. Specifically, peak determination device 513 determines that symbol m, which has a value exceeding peak determination threshold 1 in the cross-correlation spectrum that has undergone the calculation processing, is the beginning of the portion corresponding to the pilot signal in the received signal. If there is no symbol m having a value exceeding peak determination threshold 1, time alignment fails.

[0110] Furthermore, if there are multiple symbols m having a value exceeding peak determination threshold 1, peak determination device 513 selects one appropriate symbol m. For example, peak determination device 513 selects symbol m having the largest value in the cross-correlation spectrum that has been subjected to arithmetic processing. Peak determination device 513 inputs the value of symbol m determined to be the beginning of the portion corresponding to the pilot signal in the received signal to synchronization processing device 514.

[0111] For example, the peak determination device 513 may use a value exceeding a constant multiple of the average value of the cross-correlation spectrum as a determination condition for peak detection. That is, the peak determination device 513 may detect the peak of the cross-correlation spectrum by using a value obtained by multiple of the average value of the cross-correlation spectrum after the arithmetic processing as a threshold value for detecting the peak.

[0112] For example, when the average of the cross-correlation spectrum that has been subjected to the arithmetic processing calculated by the following formula 9 is μ, the peak determination device 513 may use a value obtained by multiplying μ by a constant (for example, 5μ) as the peak determination threshold value 1.

[0113] Alternatively, the peak determination threshold 1 may be determined based on an index that combines other statistics (such as the mean, variance, median, and maximum value) of the cross-correlation spectrum that has been subjected to computational processing, or may be an arbitrarily determined value that can distinguish the peak from other parts.

[0114]

number

[0115] The synchronization processing device 514 performs time alignment to align the time origin so that the portion corresponding to the pilot signal in the received signal becomes the beginning, based on information about the beginning of the portion corresponding to the pilot signal in the received signal detected by the peak determination device 513. Here, the time alignment process may be performed by digital signal processing, or may be performed using a delay line or other signal delay function.

[0116] The configuration of time alignment devices 520 to 580 is the same as that of time alignment device 510. Specifically, when each time alignment device is represented as 5N0 with respect to time alignment device 510 (where N is 2 to 8), received signal 1 can be read as received signal N, pilot signal 1 as pilot signal N, and peak determination threshold 1 as peak determination threshold N, respectively. By time aligning the received signals, it becomes possible to perform MIMO processing at a later stage.

[0117] In this specific example, the signal processing device 500 is used in optical communications using MCF. Alternatively, the signal processing device 500 may be used for MIMO processing used in PDM in SMF or MDM using MMF.

[0118] Fig. 12 is a flowchart showing an example of the operation of the time alignment device of this example. The processes from step E1 to step E7 in the flowchart shown in Fig. 12 are specific examples of the processes from step A1 to step A7 in the flowchart shown in Fig. 2, so detailed explanations will be omitted.

[0119] Fig. 13 is an explanatory diagram showing an example of change in the probability of success in peak detection. Specifically, Fig. 13 shows the change in the possibility of peak detection before and after shaping by the correlation shaping device. As shown in Fig. 13, the arithmetic processing in the correlation shaping device increases the possibility of detecting a peak in the cross-correlation spectrum after arithmetic processing (corresponding to C2[m] shown above) compared to the possibility of detecting a peak in the cross-correlation spectrum. Therefore, information can be transmitted even using a shorter pilot signal.

[0120] Next, a specific example of the second embodiment will be described.

[0121] The signal processing device 600 in this specific example is used in the front stage of data-aided MIMO processing in optical signal communication using optical fibers having multiple propagation modes. Fig. 14 is an explanatory diagram showing an example of a configuration using the signal processing device 600.

[0122] The signal processing device 600 is used in optical signal communication using a coupled four-core MCF having four polarization-multiplexed spatial modes (a total of 4x2=8 modes), as illustrated in Fig. 14. As an optical fiber having multiple propagation modes, an MCF with a different number of cores may be used, or an MMF for MDM optical signal communication may be used.

[0123] Furthermore, the signal processing device 600 may be used in optical signal communication using PDM in SMF, or in optical signal communication employing a multiplexing method that combines these.

[0124] The signal processing device 600 includes time alignment devices 610 to 680. The time alignment devices 610 to 680 each correspond to the signal processing system 200 in the second embodiment. In other words, the signal processing device 600 can be said to be a device in which a plurality of the signal processing systems 200 in the second embodiment are configured in parallel. In this way, a configuration including a plurality of the signal processing systems 200 can be said to be a multi-signal processing system.

[0125] Time alignment device 610 processes received signal 1X corresponding to the X polarization of core 1 of the MCF received by the coherent receiver. Time alignment device 620 processes received signal 1Y corresponding to the Y polarization of core 1. Time alignment device 630 processes received signal 2X corresponding to the X polarization of core 2. Time alignment device 640 processes received signal 2Y corresponding to the Y polarization of core 2. Time alignment device 650 processes received signal 3X corresponding to the X polarization of core 3. Time alignment device 660 processes received signal 3Y corresponding to the Y polarization of core 3. Time alignment device 670 processes received signal 4X corresponding to the X polarization of core 4. Time alignment device 680 processes received signal 4Y corresponding to the Y polarization of core 4.

[0126] 15 is a block diagram showing an example of the configuration of the time alignment device 610. The time alignment device 610 includes a cross-correlation calculation device 611, a parameter determination device 612, a correlation shaping device 613, a peak determination device 614, and a synchronization processing device 615.

[0127] The cross-correlation calculation device 611, parameter determination device 612, correlation shaping device 613, peak determination device 614, and synchronization processing device 615 of this specific example correspond to the cross-correlation calculation unit 201, parameter determination unit 202, correlation shaping processing unit 203, peak determination processing unit 204, and synchronization processing unit 205 in the second embodiment, respectively. Using the above configuration, the time alignment device 610 generally operates as follows.

[0128] The cross-correlation calculation device 611, peak determination device 614, and synchronization processing device 615 operate in the same manner as the cross-correlation calculation device 511, peak determination device 513, and synchronization processing device 514, respectively, in the specific example of the first embodiment.

[0129] The parameter determination device 612 determines, for example, the SMD (σ SMD ) and transmission distance L, sample rate R s The moving average window w1, which is one of the shaping parameters used in the correlation shaping device 613, is determined using the following equation 10. In equation 10, the parentheses represent the maximum integer not to be exceeded. Furthermore, the cross-correlation calculation device 611 may determine the method of arithmetic processing performed in the correlation shaping device 613, for example, in accordance with the modulation method of the pilot signal.

[0130]

number

[0131] The correlation shaping device 613 operates in the same manner as the correlation shaping device 512 in the specific example of the first embodiment. However, for w1 used in the calculation process in the specific example of the first embodiment, the value determined by the parameter determining device 612 is used.

[0132] The configuration of time alignment devices 620 to 680 is the same as that of time alignment device 610. By time aligning the received signals, it becomes possible to perform MIMO processing at a later stage.

[0133] Fig. 16 is a flowchart showing an example of the operation of the time alignment device of this example. The processes from step F1 to step F9 in the flowchart shown in Fig. 16 are specific examples of the processes from step A1 to step A7 in the flowchart shown in Fig. 4, so detailed explanations will be omitted.

[0134] FIG. 17 is an explanatory diagram showing an example of how the probability of successful peak detection changes when the shaping parameters are changed. Specifically, FIG. 17 shows how the possibility of peak detection changes when the value of w1 used to shape the cross-correlation spectrum is changed. Each line in FIG. 17 represents the detectability of a peak in a cross-correlation spectrum that has been subjected to arithmetic processing when w1 is arbitrarily given. Furthermore, each diamond (◇) in FIG. 17 represents the detectability of a peak in a cross-correlation spectrum that has been subjected to arithmetic processing when w1 is determined according to Equation 10 above. As shown in FIG. 17, the detectability of a peak is improved when w1 calculated using Equation 10 is used compared to when w1 is determined arbitrarily.

[0135] Next, a specific example of the third embodiment will be described.

[0136] The signal processing device 700 in this specific example is used in the front stage of data-aided MIMO processing in optical signal communication using optical fibers having multiple propagation modes. Fig. 18 is an explanatory diagram showing an example of a configuration using the signal processing device 700.

[0137] The signal processing device 700 is used in optical signal communication using a coupled four-core MCF having four polarization-multiplexed spatial modes (a total of 4x2=8 modes), as illustrated in Fig. 18. As an optical fiber having multiple propagation modes, an MCF with a different number of cores may be used, or an MMF for MDM optical signal communication may be used.

[0138] Furthermore, the signal processing device 700 may be used in optical signal communication using PDM in SMF, or in optical signal communication employing a multiplexing method that combines these.

[0139] The signal processing device 700 includes time alignment devices 710 to 780. The time alignment devices 710 to 780 each correspond to the signal processing system 300 in the third embodiment. In other words, the signal processing device 700 can be said to be a device in which a plurality of the signal processing systems 300 in the third embodiment are configured in parallel. In this way, a configuration including a plurality of the signal processing systems 300 can be said to be a multi-signal processing system.

[0140] Time alignment device 710 processes received signal 1X corresponding to the X polarization of core 1 of the MCF received by the coherent receiver. Time alignment device 720 processes received signal 1Y corresponding to the Y polarization of core 1. Time alignment device 730 processes received signal 2X corresponding to the X polarization of core 2. Time alignment device 740 processes received signal 2Y corresponding to the Y polarization of core 2. Time alignment device 750 processes received signal 3X corresponding to the X polarization of core 3. Time alignment device 760 processes received signal 3Y corresponding to the Y polarization of core 3. Time alignment device 770 processes received signal 4X corresponding to the X polarization of core 4. Time alignment device 780 processes received signal 4Y corresponding to the Y polarization of core 4.

[0141] 19 is a block diagram showing an example of the configuration of the time alignment device 710. The time alignment device 710 includes a cross-correlation calculation device 711, a front-stage peak determination device 712, a branching device 713, a correlation shaping device 714, a rear-stage peak determination device 715, and a synchronization processing device 716.

[0142] The cross-correlation calculation device 711, the preceding peak determination device 712, the branching device 713, the correlation shaping device 714, the subsequent peak determination device 715, and the synchronization processing device 716 of this specific example correspond to the cross-correlation calculation section 301, the preceding peak determination processing section 302, the branching processing section 303, the correlation shaping processing section 304, the subsequent peak determination processing section 305, and the synchronization processing section 306 of the third embodiment, respectively. Using the above configuration, the time alignment device 710 generally operates as follows.

[0143] The cross-correlation calculation device 711, correlation shaping device 714, and subsequent peak determination device 715 operate in the same manner as the cross-correlation calculation device 511, correlation shaping device 512, and peak determination device 513 in the specific example of the first embodiment.

[0144] Previous peak determination device 712 performs peak determination on the cross-correlation spectrum calculated by cross-correlation calculation device 711 based on previous peak determination threshold 1. Specifically, previous peak determination device 712 determines that symbol m having a value exceeding previous peak determination threshold 1 in the cross-correlation spectrum is the beginning of a portion corresponding to a pilot signal in the received signal, and outputs to branching device 713 that the peak determination was successful. If there is no symbol m having a value exceeding previous peak determination threshold 1, it outputs to branching device 713 that the peak determination was unsuccessful.

[0145] Furthermore, if there are multiple symbols m having values ​​exceeding the peak determination threshold 1, the pre-peak determination device 712 selects one appropriate symbol m. For example, the pre-peak determination device 712 selects the symbol m having the largest value in the cross-correlation spectrum.

[0146] For example, the pre-peak determination device 712 may use a value exceeding a constant multiple of the average value of the cross-correlation spectrum as a determination condition for peak detection. That is, the pre-peak determination device 712 may detect peaks in the cross-correlation spectrum using a value that is a constant multiple of the average value of the cross-correlation spectrum as a threshold for detecting peaks.

[0147] For example, when the average of the cross-correlation spectrum calculated by the following equation 11 is μ, the previous peak determination device 712 may use a value obtained by multiplying μ by a constant (for example, 5μ) as the previous peak determination threshold value 1.

[0148] Alternatively, the pre-peak determination threshold 1 may be determined based on an index that combines other statistics of the cross-correlation spectrum (such as the mean, variance, median, and maximum value), or may be an arbitrarily determined value that can distinguish the peak from other parts.

[0149]

number

[0150] If the upstream peak determination device 712 succeeds in peak determination, the synchronization processing device 716 performs time alignment based on the symbol m input from the branching device 713 so that the portion of the received signal corresponding to the pilot signal comes to the beginning. If the upstream peak determination device 712 fails to detect a peak, the synchronization processing device 716 performs time alignment based on the symbol m input from the downstream peak determination device 715 so that the portion of the received signal corresponding to the pilot signal comes to the beginning. The time alignment process may be performed by digital signal processing, or may be performed using a delay line or other signal delay function.

[0151] The configuration of time alignment devices 720 to 780 is the same as that of time alignment device 710. Specifically, when each time alignment device is represented as 7N0 (where N is 2 to 8) with respect to time alignment device 710, previous peak determination threshold 1 can be read as previous peak determination threshold N. By time aligning each received signal, it becomes possible to perform MIMO processing at a later stage.

[0152] Fig. 20 is a flowchart showing an example of the operation of the time alignment device of this example. The processes from step G1 to step G11 in the flowchart shown in Fig. 20 are specific examples of the processes from step A1 to step A7 in the flowchart shown in Fig. 6, so detailed explanations will be omitted.

[0153] Next, a specific example of the fourth embodiment will be described.

[0154] The signal processing device 800 in this specific example is used in the front stage of data-aided MIMO processing in optical signal communication using optical fibers having multiple propagation modes. Fig. 21 is an explanatory diagram showing an example of a configuration using the signal processing device 800.

[0155] The signal processing device 800 is used in optical signal communication using a coupled four-core MCF having four polarization-multiplexed spatial modes (a total of 4x2=8 modes), as illustrated in Fig. 21. As an optical fiber having multiple propagation modes, an MCF with a different number of cores may be used, or an MMF for MDM optical signal communication may be used.

[0156] Furthermore, the signal processing device 800 may be used in optical signal communication using PDM in SMF, or in optical signal communication employing a multiplexing method that combines these.

[0157] The signal processing device 800 includes time alignment devices 810 to 880. The time alignment devices 810 to 880 each correspond to the signal processing system 400 in the fourth embodiment. In other words, the signal processing device 800 can be said to be a device in which a plurality of the signal processing systems 400 in the fourth embodiment are configured in parallel. In this way, a configuration including a plurality of the signal processing systems 400 can be said to be a multi-signal processing system.

[0158] Time alignment device 810 processes received signal 1X corresponding to the X polarization of core 1 of the MCF received by the coherent receiver. Time alignment device 820 processes received signal 1Y corresponding to the Y polarization of core 1. Time alignment device 830 processes received signal 2X corresponding to the X polarization of core 2. Time alignment device 840 processes received signal 2Y corresponding to the Y polarization of core 2. Time alignment device 850 processes received signal 3X corresponding to the X polarization of core 3. Time alignment device 860 processes received signal 3Y corresponding to the Y polarization of core 3. Time alignment device 870 processes received signal 4X corresponding to the X polarization of core 4. Time alignment device 880 processes received signal 4Y corresponding to the Y polarization of core 4.

[0159] 22 is a block diagram showing an example of the configuration of the time alignment device 810. The time alignment device 810 includes a cross-correlation calculation device 811, a detectability estimation device 812, a branching device 813, a correlation shaping device 814, a peak determination device 815, and a synchronization processing device 816.

[0160] The cross-correlation calculation device 811, detectability estimation device 812, branching device 813, correlation shaping device 814, peak determination device 815, and synchronization processing device 816 of this specific example correspond to the cross-correlation calculation unit 401, detectability estimation unit 402, branching processing unit 403, correlation shaping processing unit 404, peak determination processing unit 405, and synchronization processing unit 406 of the fourth embodiment, respectively. Using the above configuration, the time alignment device 810 generally operates as follows.

[0161] The cross-correlation calculation unit 811 and the synchronization processing unit 816 operate in the same manner as the cross-correlation calculation unit 511 and the synchronization processing unit 514 in the specific example of the first embodiment, respectively.

[0162] The detectability estimation device 812 estimates the possibility of successful peak detection using an index that distinguishes between the magnitude of the peak and non-peak portions of the cross-correlation spectrum calculated by the cross-correlation calculation device 811. This index may be, for example, an empirically obtained arbitrary value. Alternatively, the index may be determined using a statistical quantity such as the average, maximum value, or minimum value of the calculated cross-correlation spectrum. An example of a method for estimating detectability using a statistical quantity as an index is shown below.

[0163] First, a first example of estimating the detectability will be described.

[0164] The detectability estimation unit 812 estimates the maximum value C of the cross-correlation spectrum. max Next, the detectability estimation unit 812 calculates C max The maximum value C of the cross-correlation spectrum after removing the surrounding area of max2 The range indicating the periphery may be determined in advance to be a predetermined range. The detectability estimation device 812 calculates, for example, C[m]=C max Using the symbol m such that max2 Let's say.

[0165] Then, the detectability estimation device 812 calculates C max / C max2 That is, the detectability estimation unit 812 estimates the possibility of successful peak detection from the ratio of the maximum value of the cross-correlation spectrum to the maximum value of the cross-correlation spectrum obtained by deleting a predetermined range from the maximum value.

[0166] C max / C max2 is a value that indicates how high the peak of the cross-correlation spectrum is compared to its surroundings. Therefore, the detectability estimation device 812 may determine that there is a high possibility that a peak will be detected in the cross-correlation spectrum if this value is greater than a value that is sufficiently larger than 1 (for example, 2).

[0167] Next, a second example of estimating the detectability will be described.

[0168] The detectability estimation device 812 uses the average value μ of the cross-correlation spectrum calculated by the above equation 11 to calculate (C max -μ) / (C max2 -μ). That is, the detectability estimation unit 812 estimates the possibility of successful peak detection from the ratio of the difference between the maximum value of the cross-correlation spectrum and the average value of the cross-correlation spectrum to the difference between the maximum value of the cross-correlation spectrum, with a predetermined range removed from the maximum value, and the average value of the cross-correlation spectrum.

[0169] This value indicates how high the peak of the cross-correlation spectrum is compared to its surroundings, and the ratio becomes large even when μ is relatively large. Therefore, the detectability estimation device 812 may determine that there is a high possibility that a peak will be detected in the cross-correlation spectrum when this value exceeds a value sufficiently larger than 1 (for example, 2).

[0170] Next, a third example of estimating the detectability will be described.

[0171] The detectability estimation device 812 calculates the standard deviation σ of the cross-correlation spectrum calculated by the following equation (12):C Using (C max -μ) / σ C That is, the detectability estimation unit 812 estimates the possibility of successful peak detection from the ratio of the standard deviation of the cross-correlation spectrum to the difference between the maximum value of the cross-correlation spectrum and the average value of the cross-correlation spectrum.

[0172] This value indicates how large the peak of the cross-correlation spectrum is relative to the overall extent of the cross-correlation spectrum. If this value exceeds a sufficiently large value (e.g., 5), the detectability estimation device 812 may determine that there is a high possibility that a peak will be detected in the cross-correlation spectrum.

[0173]

number

[0174] If the detectability estimation device 812 determines that there is a high possibility that a peak of the cross-correlation spectrum will be detected, the branching device 813 determines that arithmetic processing to relatively increase the peak of the cross-correlation spectrum is not necessary, and inputs the cross-correlation spectrum to the peak determination device 815. If there is a low possibility that a peak of the cross-correlation spectrum will be detected, the branching device 813 determines that arithmetic processing to relatively increase the peak of the cross-correlation spectrum is necessary, and inputs the cross-correlation spectrum to the correlation shaping device 814.

[0175] The correlation shaping device 814 operates in the same manner as the correlation shaping device 512 in the specific example of the first embodiment when it is determined by the branching device 813 that calculation processing for relatively increasing the peak of the cross-correlation spectrum is necessary. At this time, the parameters used in the correlation shaping device 814 may be determined arbitrarily, or may be determined by a device that operates in the same manner as the parameter determination device 612 in the specific example of the second embodiment.

[0176] When the detectability estimation device 812 determines that there is a high possibility that a peak will be detected in the cross-correlation spectrum, the peak determination device 815 performs peak determination on the cross-correlation spectrum calculated by the cross-correlation calculation device 811 using peak determination threshold 1a. On the other hand, when it determines that there is a low possibility that a peak will be detected in the cross-correlation spectrum, the peak determination device 815 performs peak determination on the cross-correlation spectrum that has been subjected to calculation processing by the correlation shaping device 814 using peak determination threshold 1b.

[0177] Here, peak determination threshold 1a and peak determination threshold 1b may be determined by different methods, or the cross-correlation spectrum and the cross-correlation spectrum after arithmetic processing may be regarded as the same and determined by the same method. Symbol m in the cross-correlation spectrum or the cross-correlation spectrum after arithmetic processing, which has a value exceeding peak determination threshold 1a or peak determination threshold 1b, is determined to be the beginning of a portion corresponding to a pilot signal present in the received signal, and is input to synchronization processing device 816.

[0178] The peak determination device 815 determines that symbol m having a value exceeding peak determination threshold 1a in the cross-correlation spectrum is the beginning of a portion corresponding to a pilot signal in the received signal, and inputs this to the synchronization processing device 816. Similarly, the peak determination device 815 determines that symbol m having a value exceeding peak determination threshold 1b in the cross-correlation spectrum that has been subjected to arithmetic processing is the beginning of a portion corresponding to a pilot signal in the received signal, and inputs this to the synchronization processing device 816.

[0179] On the other hand, if there is no symbol m having a value exceeding peak determination threshold 1a or peak determination threshold 1b, synchronization processing fails. Also, if there are multiple symbols m having values ​​exceeding peak determination threshold 1a or peak determination threshold 1b, peak determination device 815 selects one appropriate symbol m. For example, peak determination device 815 selects symbol m having the largest value in the cross-correlation spectrum or the cross-correlation spectrum that has been subjected to arithmetic processing.

[0180] The configuration of time alignment devices 820 to 880 is the same as that of time alignment device 810. Specifically, when each time alignment device is represented as 8N0 with respect to time alignment device 810 (where N is 2 to 8), peak determination threshold 1a can be read as peak determination threshold Na, and peak determination threshold 1b can be read as peak determination threshold Nb, respectively. By time aligning the received signals, it becomes possible to perform MIMO processing at a later stage.

[0181] Fig. 23 is a flowchart showing an example of the operation of the time alignment device of this example. The processes from step H1 to step H11 in the flowchart shown in Fig. 23 are specific examples of the processes from step A1 to step A7 in the flowchart shown in Fig. 8, so detailed explanations will be omitted.

[0182] Next, an overview of the present disclosure will be described. Fig. 24 is a block diagram showing an overview of a signal processing system according to the present disclosure. A signal processing system 80 (e.g., signal processing system 100) according to the present disclosure includes a cross-correlation calculation unit 81 (e.g., cross-correlation calculation unit 101) that calculates a cross-correlation spectrum representing the similarity between a plurality of received signals that have a time spread and that couple with each other during propagation, and a pilot signal included in each of the received signals, a correlation shaping processing unit 82 (e.g., correlation shaping processing unit 102) that performs arithmetic processing to shape the peak of the cross-correlation spectrum so as to raise it from the original peak, a first peak determination processing unit 83 (e.g., peak determination processing unit 103) that detects the peak of the cross-correlation spectrum after the arithmetic processing has been performed, and a synchronization processing unit 84 (synchronization processing unit 104) that uses the detected peak to align the time origin for synchronizing the pilot signal and the received signal.

[0183] With such a configuration, even under conditions where the cross-correlation peak is low, it is possible to suppress a decrease in the probability of successful time alignment.

[0184] Furthermore, signal processing system 80 (e.g., signal processing system 200) may include a parameter determination unit (e.g., parameter determination unit 202) that determines a shaping parameter, which is a parameter used in a calculation process for shaping the peak of the cross-correlation spectrum, using at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal. Then, correlation shaping processing unit 82 may perform a calculation process for shaping the peak using the shaping parameter.

[0185] Specifically, the parameter determination unit may determine the shaping parameters using the product of spatial mode dispersion, transmission distance, and sample rate.

[0186] In addition, the first peak determination processing unit 83 may detect the peak of the cross-correlation spectrum by using a value that is a constant multiple of the average value of the cross-correlation spectrum after the arithmetic processing is performed as a threshold value for detecting the peak.

[0187] Furthermore, the signal processing system 80 (for example, the signal processing system 300) may include a second peak determination processor (for example, the pre-peak determination processor 302) that detects peaks in the cross-correlation spectrum before arithmetic processing is performed. Then, when no peak is detected by the second peak determination processor, the correlation shaping processor 82 may perform arithmetic processing to shape the peak on the cross-correlation spectrum. Furthermore, the first peak determination processor (for example, the post-peak determination processor 305) may detect peaks that have been subjected to arithmetic processing.

[0188] Specifically, the second peak determination processor may detect the peak of the cross-correlation spectrum by using a value obtained by multiplying the average value of the cross-correlation spectrum by a constant as a threshold value for detecting the peak.

[0189] Furthermore, the signal processing system 80 (for example, the signal processing system 400) may include a detectability estimation unit (for example, the detectability estimation unit 402) that estimates the possibility of successful peak detection using an index that distinguishes between the magnitude of the peak in the cross-correlation spectrum and the magnitude of the non-peak. Then, the correlation shaping processor 82 may perform a calculation process on the cross-correlation spectrum to shape the peak when the possibility is lower than a predetermined standard.

[0190] Fig. 25 is a block diagram showing an overview of a multi-signal processing system according to the present disclosure. A multi-signal processing system 90 according to the present disclosure is configured in parallel with signal processing systems 80 exemplified in Fig. 24, and each signal processing system receives at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal.

[0191] 26 is a schematic block diagram showing the configuration of a computer according to at least one embodiment. The computer 1000 includes a processor 1001, a main memory device 1002, an auxiliary memory device 1003, and an interface 1004.

[0192] The above-described signal processing system 80 is implemented in a computer 1000. The operations of the above-described processing units are stored in the form of a program (signal processing program) in an auxiliary storage device 1003. The processor 1001 reads the program from the auxiliary storage device 1003, loads it into the main storage device 1002, and executes the above-described processing in accordance with the program.

[0193] In at least one embodiment, the auxiliary storage device 1003 is an example of a non-transitory tangible medium. Other examples of non-transitory tangible media include a magnetic disk, a magneto-optical disk, a CD-ROM (Compact Disc Read-only memory), a DVD-ROM (Read-only memory), and a semiconductor memory connected via the interface 1004. In addition, when this program is distributed to the computer 1000 via a communication line, the computer 1000 that receives the program may load the program into the main storage device 1002 and execute the above processing.

[0194] The program may also be a program for realizing part of the above-described functions. Furthermore, the program may be a so-called differential file (differential program) that realizes the above-described functions in combination with another program already stored in the auxiliary storage device 1003.

[0195] A part or all of the above-described embodiments can be described as, but not limited to, the following supplementary notes.

[0196] (Supplementary Note 1) A cross-correlation calculation unit that calculates a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals; a correlation shaping processor that performs a calculation process to shape the peak of the cross-correlation spectrum so that it is higher than the original peak; a first peak determination processing unit that detects a peak in the cross-correlation spectrum after the calculation processing; a synchronization processing unit that performs time alignment to align the time origin for synchronizing the pilot signal and the received signal using the detected peak. A signal processing system comprising:

[0197] (Supplementary Note 2) A parameter determination unit is provided which determines a shaping parameter, which is a parameter used in the calculation process of the cross-correlation spectrum, using at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal; The correlation shaping processing unit performs calculation processing using the shaping parameters. 10. The signal processing system of claim 1.

[0198] (Appendix 3) The parameter determination unit determines the shaping parameters using the product of the spatial mode dispersion, the transmission distance, and the sample rate. 10. The signal processing system of claim 2.

[0199] (Note 4) The first peak determination processing unit detects peaks in the cross-correlation spectrum by using a value obtained by multiplying the average value of the cross-correlation spectrum after the calculation process by a constant as a threshold value for detecting peaks. 4. A signal processing system according to any one of claims 1 to 3.

[0200] (Supplementary Note 5) A second peak determination processing unit is provided that detects a peak in the cross-correlation spectrum before the calculation processing is performed, the correlation shaping processor performs a calculation process on the cross-correlation spectrum when no peak is detected by the second peak determination processor; The first peak determination processing unit detects the peak that has been subjected to the calculation processing. 5. A signal processing system according to any one of claims 1 to 4.

[0201] (Note 6) The second peak determination processor detects peaks in the cross-correlation spectrum by using a value obtained by multiplying the average value of the cross-correlation spectrum by a constant as a threshold value for detecting peaks. 6. The signal processing system of claim 5.

[0202] (Supplementary Note 7) A detection possibility estimation unit is provided which estimates the possibility of successful detection of a peak using an index which distinguishes between the magnitude of a peak in the cross-correlation spectrum and the magnitude of other peaks; The correlation shaping processor performs a calculation process on the cross-correlation spectrum when the possibility is lower than a predetermined standard. 10. A signal processing system according to any one of claims 1 to 3.

[0203] (Appendix 8) The detection possibility estimation unit estimates the possibility of successful peak detection from the ratio of the maximum value of the cross-correlation spectrum to the maximum value of the cross-correlation spectrum obtained by deleting a predetermined range from the maximum value. 8. The signal processing system of claim 7.

[0204] (Supplementary Note 9) The detection possibility estimation unit estimates the possibility of successful peak detection from the ratio of the difference between the maximum value of the cross-correlation spectrum and the average value of the cross-correlation spectrum to the difference between the maximum value of the cross-correlation spectrum obtained by deleting a predetermined range from the maximum value and the average value. 8. The signal processing system of claim 7.

[0205] (Appendix 10) The detection possibility estimation unit estimates the possibility of successful peak detection from the ratio of the standard deviation of the cross-correlation spectrum to the difference between the maximum value of the cross-correlation spectrum and the average value of the cross-correlation spectrum. 8. The signal processing system of claim 7.

[0206] (Appendix 11) The correlation shaping processor shapes the peak of the cross-correlation spectrum by performing a calculation process to calculate the moving average of the square of the normalized cross-correlation spectrum. 11. A signal processing system according to any one of claims 1 to 10.

[0207] (Appendix 12) The correlation shaping processor performs a calculation process to subtract a constant value from the moving average of the square of the normalized cross-correlation spectrum, thereby shaping the peak of the cross-correlation spectrum. 11. A signal processing system according to any one of claims 1 to 10.

[0208] (Appendix 13) The correlation shaping processor performs an arithmetic process to calculate a moving average of the square of the normalized cross-correlation spectrum by subtracting a constant value from the moving average of the square of the normalized cross-correlation spectrum, thereby shaping the peak of the cross-correlation spectrum. 11. A signal processing system according to any one of claims 1 to 10.

[0209] (Appendix 14) Used for time alignment of received signals in spatial mode multiplexed optical signal communication using multicore fiber 14. A signal processing system according to any one of claims 1 to 13.

[0210] (Appendix 15) Used for time alignment of received signals in propagation mode multiplexed optical signal communication using multimode fiber 14. A signal processing system according to any one of claims 1 to 13.

[0211] (Appendix 16) Used for time alignment of received signals in polarization multiplexed optical signal communications using single-mode fiber 14. A signal processing system according to any one of claims 1 to 13.

[0212] (Supplementary Note 17) The signal processing system according to any one of Supplementary Note 1 to Supplementary Note 16 is configured in parallel, Each signal processing system receives at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal. A multi-signal processing system comprising:

[0213] (Supplementary Note 18) A cross-correlation spectrum is calculated for a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals, the cross-correlation spectrum representing the degree of similarity between the received signal and the pilot signal; performing a calculation process to shape the peak of the cross-correlation spectrum so that it is higher than the original peak; Detecting peaks in the cross-correlation spectrum after the calculation process is performed; Using the detected peak, time alignment is performed to align the time origins for synchronizing the pilot signal and the received signal. A signal processing method comprising:

[0214] (Appendix 19) A shaping parameter, which is a parameter used in the calculation process of the cross-correlation spectrum, is determined using at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal; Performing calculation processing using the shaping parameters 19. The signal processing method of claim 18.

[0215] (Appendix 20) To the computer, a cross-correlation calculation process for calculating a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals; a correlation shaping process for performing a calculation process to shape the peak of the cross-correlation spectrum so as to increase the height of the peak; a first peak determination process for detecting a peak in the cross-correlation spectrum after the calculation process; and A synchronization process is performed to align the time origins of the pilot signal and the received signal using the detected peak. A signal processing program for executing the above.

[0216] (Appendix 21) To the computer, Execute a parameter determination process to determine a shaping parameter, which is a parameter used in a calculation process of a cross-correlation spectrum, using at least one of a parameter indicating a characteristic of a transmission system and information indicating a modulation method of a pilot signal; In the correlation shaping process, the shaping parameters are used to perform calculation processing. 21. The signal processing program according to claim 20.

[0217] Although the present disclosure has been described above with reference to the embodiments, the present disclosure is not limited to the above-described embodiments. Various modifications that can be understood by those skilled in the art can be made to the configuration and details of the present disclosure within the scope of the present disclosure. Furthermore, each embodiment can be combined with other embodiments as appropriate. [Industrial Applicability]

[0218] The present invention is suitable for use in a signal processing system for processing optical signals. Specifically, the present invention can be applied to time alignment required for data-aided signal processing using a pilot signal in optical communication transmission using optical fibers that generate modal dispersion. [Explanation of symbols]

[0219] 100,200,300,400 Signal Processing System 101 Cross-correlation calculation unit 102 Correlation shaping processing unit 103 Peak determination processing unit 104 Synchronization processing section 201 Cross-correlation calculation unit 202 Parameter determination unit 203 Correlation shaping processing unit 204 Peak determination processing unit 205 Synchronization processing section 301 Cross-correlation calculation unit 302 Pre-stage peak determination processing unit 303 Branching section 304 Correlation shaping processing unit 305 Post-stage peak determination processing unit 306 Synchronization processing section 401 Cross-correlation calculation unit 402 Detectability Estimation Unit 403 Branching section 404 Correlation shaping processing unit 405 Peak determination processing unit 406 Synchronization processing section 500,600,700,800 signal processing device 510,610,710,810 Time Alignment Device 5n0, 6n0, 7n0, 8n0 Time alignment device (n=2-8) 511 Cross-correlation calculation device 512 Correlation Shaping Device 513 Peak Detector 514 Synchronous Processing Device 611 Cross-correlation Calculation Device 612 Parameter Determination Device 613 Correlation Shaping Device 614 Peak Detector 615 Synchronous Processing Device 711 Cross-correlation Calculation Device 712 Pre-stage peak detector 713 Branching Device 714 Correlation Shaping Device 715 Post-stage peak determination device 716 Synchronous Processing Device 811 Cross-correlation calculation device 812 Detectability Estimation Device 813 Branching Device 814 Correlation Shaping Device 815 Peak Determining Device 816 Synchronous Processing Device

Claims

1. a cross-correlation calculation unit that calculates a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals; and a correlation shaping processor that performs a calculation process to shape the peak of the cross-correlation spectrum so that it is higher than the original peak; a first peak determination processing unit that detects a peak in the cross-correlation spectrum after the calculation processing; a synchronization processing unit that performs time alignment to align the time origin for synchronizing the pilot signal and the received signal using the detected peak. A signal processing system comprising:

2. a parameter determination unit that determines a shaping parameter, which is a parameter used in a calculation process of a cross-correlation spectrum, using at least one of a parameter indicating a characteristic of a transmission system and information indicating a modulation method of a pilot signal; The correlation shaping processing unit performs calculation processing using the shaping parameters.

2. The signal processing system of claim 1.

3. The parameter determination unit determines the shaping parameters using the product of the spatial mode dispersion, the transmission distance, and the sample rate.

3. The signal processing system according to claim 2.

4. The first peak determination processing unit detects peaks in the cross-correlation spectrum by using a value obtained by multiplying the average value of the cross-correlation spectrum after the calculation process by a constant as a threshold value for detecting peaks.

4. A signal processing system according to claim 1.

5. a second peak determination processing unit that detects a peak in the cross-correlation spectrum before calculation processing is performed; the correlation shaping processor performs a calculation process on the cross-correlation spectrum when no peak is detected by the second peak determination processor; The first peak determination processing unit detects the peak that has been subjected to the calculation processing. The signal processing system according to any one of claims 1 to 3.

6. The second peak determination processor detects peaks in the cross-correlation spectrum by using a value obtained by multiplying the average value of the cross-correlation spectrum by a constant as a threshold value for detecting peaks.

6. The signal processing system according to claim 5.

7. a detectability estimation unit that estimates the possibility of successfully detecting a peak using an index that distinguishes between the magnitude of a peak in a cross-correlation spectrum and the magnitude of other peaks; The correlation shaping processor performs a calculation process on the cross-correlation spectrum when the possibility is lower than a predetermined standard.

4. A signal processing system according to claim 1.

8. The signal processing system according to any one of claims 1 to 3 is configured in parallel, Each signal processing system receives at least one of a parameter indicating the characteristics of the transmission system and information indicating the modulation method of the pilot signal. A multi-signal processing system comprising:

9. calculating a cross-correlation spectrum representing a degree of similarity between a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals; performing a calculation process to shape the peak of the cross-correlation spectrum so that it is higher than the original peak; Detecting peaks in the cross-correlation spectrum after the calculation process is performed; Using the detected peak, time alignment is performed to align the time origins for synchronizing the pilot signal and the received signal. A signal processing method comprising:

10. On the computer, a cross-correlation calculation process for calculating a cross-correlation spectrum representing the degree of similarity between a plurality of received signals that have a time spread and are mutually coupled during propagation, and a pilot signal included in each of the received signals; a correlation shaping process for performing a calculation process to shape the peak of the cross-correlation spectrum so as to increase the height of the peak; a first peak determination process for detecting a peak in the cross-correlation spectrum after the calculation process; and A synchronization process for performing time alignment to align the time origins of the pilot signal and the received signal using the detected peak. A signal processing program for executing the above.

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