A coherent optical communication residual equalization method based on first-order perturbation characteristics and bidirectional gated recurrent network

Abstract

The application discloses a kind of based on first-order perturbation feature and bidirectional gated recurrent network coherent optical communication residual equalization method.First, the double polarization received complex signal preprocessed by receiving end DSP and completed power normalization is obtained, and the estimated symbol is obtained according to the target constellation hard decision;Rely on the estimated symbol to extract the first-order perturbation feature and complete time alignment, use the standardized and principal component analysis parameters calibrated in the training stage to realize feature dimension reduction;Intercept feature window and input pre-training bidirectional GRU residual equalization network, predict the two-dimensional residual of central symbol, and obtain the equalization output by subtracting the residual from the received symbol.The application uses residual learning, only the transmission label is needed in the training stage, and the inference does not need the signal of transmitting end;Feature transformation parameters are fitted by training set, and information leakage of test set is eliminated, and the physical meaning of model output is clear.

Description

Technical Field

[0001] This invention relates to the field of digital signal processing technology for optical fiber communication, and in particular to a coherent optical communication residual equalization method and system based on first-order perturbation characteristics and bidirectional gated cyclic network (BiGRU). Background Technology

[0002] In high-speed coherent optical communication systems, the receiver signal is affected by factors such as fiber link nonlinearity, polarization-dependent impairments, carrier phase disturbances, and non-ideal device characteristics, resulting in amplitude, phase, and inter-symbol correlation errors between the receiver constellation points and the transmitter tags. Conventional digital signal processing can compensate for some linear impairments and phase disturbances, but for nonlinear residuals with memory effects, further equalization using symbol neighborhood information is still necessary.

[0003] First-order perturbation features can extract combined terms related to nonlinear perturbations from dual-polarization symbol sequences. Since there are numerous combinations of lag indices for the perturbation terms, effective combinations can be selected through constraints, retaining the main cross-terms related to nonlinear damage while controlling the feature dimension. These features still exhibit contextual relationships between adjacent symbols on the time axis, making them suitable for further input into sequence models for residual estimation.

[0004] In offline equalization or receiver processing where latency is acceptable, the symbol to be equalized can be located at the center of a complete observation window. If only a unidirectional recurrent network is used and the hidden state at the end of the sequence is taken, the model struggles to directly fuse the contextual information on both sides of the central symbol. A bidirectional gated recurrent network can perform forward and backward recursive modeling separately within the complete window and form a bidirectional hidden state at the center, making it suitable for residual compensation of the central symbol.

[0005] Furthermore, in data-driven equalization methods, using training, validation, and test data simultaneously for parameter fitting during data standardization, principal component analysis, and gain alignment can easily lead to information leakage and overly optimistic evaluation results. If the transmitter label signal corresponding to the symbol to be equalized is still required during the actual equalization inference stage, the method is difficult to deploy in real-world links. Therefore, a complete equalization method is needed that clearly distinguishes between the training or calibration stage and the equalization inference stage: during the training or calibration stage, the transmitter label signal should be allowed to complete sample alignment, parameter fitting, and residual supervision; during the actual equalization inference stage, compensation should only rely on the received signal to be equalized, pre-fitted feature transformation parameters, and a pre-trained BiGRU residual equalization network, thereby avoiding using the transmitter label signal as a necessary input for online equalization. Summary of the Invention

[0006] The purpose of this invention is to provide a coherent optical communication residual equalization method and system based on first-order perturbation features and a bidirectional gated cyclic network, to solve the problems existing in the background art. This method clearly distinguishes between the training or calibration phase and the equalization inference phase: In the training or calibration phase, a dual-polarization received complex signal and its corresponding transmitter tag complex signal are acquired for time alignment, data-assisted dynamic carrier phase compensation, training segment complex gain alignment, standardization and principal component analysis parameter fitting, and residual supervision target construction; In the equalization inference phase, the dual-polarization received complex signal to be equalized is acquired after preprocessing by the receiver's DSP, its power is normalized and hard-decision is performed, first-order perturbation features are extracted based on the dual-polarization predicted symbols, and the standardized parameters, principal component analysis parameters, and BiGRU residual equalization network obtained in the training phase are used to predict the two-dimensional residual. Finally, the equalization output is obtained by subtracting the predicted residual from the received two-dimensional symbol at the center position; thus, the transmitter tag signal is only used for training or calibration and is not a necessary input for the actual equalization inference phase.

[0007] To achieve the above objectives, the first aspect of the present invention provides a coherent optical communication residual equalization method based on first-order perturbation features and a bidirectional gated cyclic network, comprising the following steps: S1. Obtain the dual-polarization received complex signal to be equalized after preprocessing by a coherent receiver and a receiver DSP. The receiver DSP preprocessing includes one or more of I / Q imbalance correction, dispersion compensation, clock phase recovery, adaptive time-domain equalization MIMO-CMA, downsampling, carrier frequency recovery, and carrier phase recovery, and performs power normalization on the dual-polarization received complex signal to be equalized. S2. Based on the target constellation set used by the coherent optical communication signal, perform hard decision on the normalized dual-polarization received complex signal to be equalized to obtain the dual-polarization prediction symbol used to extract perturbation features. S3. Extract first-order perturbation features based on the combination of the dual-polarization prediction symbol and the constrained hysteresis index, and perform time alignment on the first-order perturbation features. The time alignment includes: for perturbation features whose length is shortened due to offset, padding the front end with zero values ​​of the offset line and the rear end with zero values ​​of the corresponding length, so that the length of the padded perturbation feature is consistent with the length of the corresponding received signal. S4. Using the feature standardization parameters and principal component analysis parameters prefitted during the training or calibration phase, transform the aligned first-order perturbation features to obtain the dimension-reduced real-valued feature sequence. S5. Taking the symbol to be balanced as the center, extract a complete window from the reduced real-valued feature sequence to form the input of the bidirectional gated recurrent network residual balance network. S6. Input the complete window into the bidirectional gated recurrent network residual equalization network obtained in the training phase, and obtain the two-dimensional residual prediction value corresponding to the center symbol through the input projection module, bidirectional GRU module and residual output module. S7. Subtract the predicted two-dimensional residual from the two-dimensional symbol received at the center position to obtain the balanced two-dimensional symbol output; The transmitter tag signal is only used in the training or calibration phase of the bidirectional gated recurrent network residual equalization network. It is not necessary to obtain the transmitter tag signal corresponding to the symbol to be equalized in the equalization inference phase.

[0008] In the above technical solution, preferably, during the equalization inference stage, the transmitter tag complex signal corresponding to the symbol to be equalized is not acquired, and the standardized parameters, principal component analysis parameters and BiGRU residual equalization network are all parameters and models obtained in advance during the training or calibration stage.

[0009] In the above technical solution, preferably, the training or calibration phase of the bidirectional gated recurrent network residual equalization network includes: S21. Obtain the dual-polarization receiving complex signal for training and its corresponding transmitting tag complex signal, and normalize the power of the dual-polarization receiving complex signal for training and the transmitting tag complex signal respectively. S22. Determine the time delay based on the cross-correlation result of the amplitude sequence of the training dual-polarization received complex signal and the transmitting tag complex signal, and trim and align the training dual-polarization received complex signal and the transmitting tag complex signal according to the time delay. S23. Based on the aligned training dual-polarization received complex signal and the transmitter tag complex signal, perform data-assisted carrier phase compensation to obtain the phase-compensated training dual-polarization received complex signal. S24. Perform hard decision on the phase-compensated dual-polarization received complex signal for training to obtain the dual-polarization predicted symbol for training. S25. Extract first-order perturbation features based on the training dual-polarization prediction symbols, and fit the complex gain alignment parameters, feature normalization parameters, and principal component analysis parameters of the received signal using only the training segment samples. S26. Using the difference between the two-dimensional symbol received at the center position and the two-dimensional symbol labeled at the center position as the residual supervision target, the mean square error loss is used to train the bidirectional gated recurrent network residual equalization network.

[0010] In the above technical solution, the training samples are divided into training segment, verification segment and test segment in chronological order. The training segment and verification segment are divided according to a preset ratio, and the remaining samples are used as the test segment. A protection interval is set between adjacent data segments, and the protection interval is determined by the full window radius and the perturbation memory length.

[0011] In the above technical solution, preferably, the data-assisted carrier phase compensation includes: Calculate the phase of the conjugate product of the current polarization training received signal and the corresponding transmitter tag signal to obtain the phase difference sequence; The phase difference sequence is phase-expanded, and the expanded phase difference sequence is smoothed by moving average to obtain a smoothed phase sequence; The current polarization training received signal is reversed and rotated according to the smoothed phase sequence to obtain the phase-compensated training received complex signal. The moving average smoothing uses a preset smoothing window length, which is determined based on the carrier phase disturbance velocity, symbol rate, or phase noise intensity.

[0012] In any of the above technical solutions, preferably, the hard decision includes: making a nearest constellation point decision on the normalized received complex signal to be equalized or the training received complex signal after phase compensation, based on the target constellation set used by the coherent optical communication signal. ; Where r represents the normalized received complex symbol to be equalized or the received complex symbol after phase compensation, and C represents the target constellation set; the decision result of the nearest constellation point is used as the predicted symbol under the unit power scale.

[0013] In any of the above technical solutions, preferably, the extraction of the first-order perturbation features includes: S51. Construct a two-dimensional grid with indices i and j, where i∈[-m,m] and j∈[-n,n]; S52. Based on physical constraints, retain the condition that |i|+|j|≤min(m,n) and |i The index combination of j|≤min(m,n); S53. Based on the range constraints, retain the index combinations that satisfy i≤0, j≤0 and i+j≤0; S54. The index combination that simultaneously satisfies the physical constraint and the range constraint is taken as the effective hysteresis index combination. S55. Calculate the complex first-order perturbation term based on the effective lag index combination, and take the real part and imaginary part of the complex first-order perturbation term as the perturbation feature real part and perturbation feature imaginary part, respectively.

[0014] In the above technical solution, m and n are preset perturbation memory length parameters, and the offset is determined by m and n; after the physical constraints and the range constraints are jointly filtered, multiple complex perturbation feature terms are obtained, and the real and imaginary parts of each complex perturbation feature term are separated to form the original real-valued perturbation feature dimension.

[0015] In the above technical solution, preferably, in step S55, for the estimated symbol sequence Bx of the current polarization to be extracted and the estimated symbol sequence By of another polarization, the complex first-order perturbation term is calculated according to the following formula: ; Where k represents the center time position, i and j are indices in the effective lag index combination, and conj(·) represents complex conjugate; when extracting Y polarization, the input order of Bx and By is swapped; the real and imaginary parts of At are taken as the real and imaginary parts of the perturbation feature, respectively.

[0016] Furthermore, in a specific embodiment, m=n=5, and offset=m+n=10; under the combined effect of the physical constraints and range constraints, each polarization obtains 19 complex perturbation feature terms, and after separating the real and imaginary parts, 38 original real-valued perturbation feature dimensions are formed.

[0017] Furthermore, in step S3, for the perturbation feature whose length is shortened due to the offset, zero values ​​of the offset line are added at the front end and zero values ​​of the corresponding length are added at the rear end, so that the perturbation feature after being padded is consistent with the received signal in time position.

[0018] Furthermore, during the training phase, the training segment ratio is 0.60, the validation segment ratio is 0.20, and the remaining samples are used for testing. The guard interval is determined by the full window radius and perturbation memory; specifically, the guard interval is split. guard =half window + perturb memory Excluding the first and last edges, edge = max(half) window perturb edge ).

[0019] Furthermore, during the training phase, the complex gain alignment only uses the training segment index to calculate the tag average power, the normalization ratio of the received signal, and the least squares complex gain, without using the validation and test segment data to fit the alignment parameters; the inference phase uses the alignment parameters determined during the training or calibration phase.

[0020] Furthermore, the principal component analysis (PCA) processing includes: calculating the mean and standard deviation using the training segment features; performing singular value decomposition on the standardized features of the training segment; selecting principal components according to the proportion of cumulative explained variance, with the number of principal components not exceeding a preset maximum value; projecting the features to be balanced in the training segment, validation segment, test segment, and inference stage onto the selected principal components and scaling them again according to the standard deviation of the principal components in the training segment. In one specific embodiment, the proportion of cumulative explained variance is 0.995, and the maximum number of principal components is 64.

[0021] In any of the above technical solutions, preferably, in step S5, the complete window length L satisfies: L = 2H+1 Where H is the half-window length; the complete window is composed of positions from center-H to center+H in the dimensionality-reduced real-valued feature sequence, and the center position is the position of the symbol to be balanced; The half-window length H is a preset positive integer, and the full window length L is an odd number that satisfies L=2H+1.

[0022] In any of the above technical solutions, preferably, in step S6, the bidirectional GRU module adopts a batch-first data format, the input dimension is the projection dimension, the hidden dimension is the preset BiGRU hidden dimension, the number of layers is the preset number of layers, and GRU inter-layer Dropout is enabled when the number of layers is greater than 1. The preset BiGRU hidden dimension, preset number of layers, and GRU inter-layer Dropout ratio are determined based on the input feature dimension, window length, and target model complexity. In step S6, the bidirectional gated cyclic network residual equalization network reads the bidirectional hidden state at the center position of the complete window as the input of the residual output module, but does not read the hidden state at the end of the complete window as the input of the residual output module. The bidirectional hidden state at the center of the complete window includes the hidden state obtained by the forward GRU recursively from the left side of the window to the center, and the hidden state obtained by the reverse GRU recursively from the right side of the window to the center.

[0023] Further, in step S6, the BiGRU residual equalization network includes: an input projection module, used to map the features after principal component analysis at each time step to a fixed projection dimension; a bidirectional GRU module, used to perform forward recursive modeling and backward recursive modeling on the full window respectively; and a residual output module, used to output two-dimensional residual prediction values ​​based on the bidirectional hidden state at the center position.

[0024] Further, the input projection module sequentially includes a first fully connected layer, a GELU activation layer, a Dropout layer, and a second fully connected layer. The output dimension of the first fully connected layer is twice the projection dimension, and the output dimension of the second fully connected layer is the projection dimension; in one specific embodiment, the projection dimension is 64. The bidirectional GRU module adopts a batch-first data format, with the input dimension being the projection dimension, the hidden dimension being a preset BiGRU hidden dimension, and the number of layers being a preset number. GRU inter-layer Dropout is enabled when the number of layers is greater than 1; in one specific embodiment, the BiGRU hidden dimension is 38, the number of GRU layers is 2, and the Dropout ratio is 0.10.

[0025] Furthermore, the BiGRU residual equalization network does not take the hidden state at the end of the complete window as the output feature, but instead takes the bidirectional hidden state at the center of the window as the input of the residual output module. This bidirectional hidden state at the center contains the information accumulated by the forward GRU from the left side of the window to the center, and the information accumulated by the reverse GRU from the right side of the window to the center.

[0026] The residual output module consists of a fully connected layer, a GELU activation layer, a Dropout layer, and a two-dimensional output fully connected layer. The input dimension of the residual output module is twice the BiGRU hidden dimension, the intermediate dimension is 64, and the output dimension is 2. The two output components represent the real part and the imaginary part of the residual to be compensated, respectively.

[0027] Furthermore, during model training, the difference between the received two-dimensional symbol at the center position and the label two-dimensional symbol is used as the residual supervision target, and the BiGRU residual equalization network is trained using mean squared error loss. During inference, the complex signal of the transmitting label corresponding to the symbol to be equalized is not obtained. Instead, the two-dimensional residual output by the network is subtracted from the received two-dimensional symbol at the center position to obtain the final equalization result.

[0028] In any of the above technical solutions, preferably, the received signal complex gain alignment includes: S91. Calculate the tag scaling factor based on the average power of the tag signal in the training segment, and use the tag scaling factor to normalize the tag signal and the received signal. S92. Calculate the least squares complex gain based on the received signal and the tag signal of the training segment; S93. Apply the least squares complex gain to the received signal; wherein neither the tag scaling factor nor the least squares complex gain is fitted using the verification segment samples and the test segment samples.

[0029] In any of the above technical solutions, preferably, the fitting and transformation of the principal component analysis parameters includes: S101. Calculate the feature mean and feature standard deviation using the features of the training segment, and protect the dimension with near-zero standard deviation; S102. Perform singular value decomposition on the standardized features of the training segment; S103. Select the number of principal components based on the cumulative explained variance ratio, and the number of principal components shall not exceed the preset maximum number of principal components; S104. Project the features of the training segment, validation segment, and test segment onto the selected principal components and scale them according to the standard deviation of the principal components of the training segment.

[0030] In the above technical solution, the cumulative explained variance ratio is a preset threshold, and the number of principal components does not exceed the preset maximum number of principal components.

[0031] In the above technical solution, preferably, the projection dimension is a preset projection dimension, and the dropout ratio of the Dropout layer is a preset dropout ratio.

[0032] In the above technical solution, preferably, the preset BiGRU hidden dimension, preset number of layers, and GRU inter-layer Dropout ratio are determined based on the input feature dimension, window length, and target model complexity.

[0033] In the above technical solution, preferably, the bidirectional hidden state of the center position of the complete window includes the hidden state obtained by the forward GRU recursively from the left side of the window to the center position, and the hidden state obtained by the reverse GRU recursively from the right side of the window to the center position.

[0034] In the above technical solution, preferably, in step S6, the residual output module sequentially includes a fully connected layer, a GELU activation layer, a Dropout layer, and a two-dimensional output fully connected layer; the two-dimensional output fully connected layer outputs a two-dimensional residual prediction value, and the two components of the two-dimensional residual prediction value represent the real part and the imaginary part of the residual to be compensated, respectively.

[0035] In the above technical solution, preferably, when the bidirectional gated recurrent network residual equalization network is trained, the difference between the two-dimensional symbol received at the center position and the two-dimensional symbol of the label at the center position is used as the residual supervision target, and mean square error loss is used for training; during inference, without obtaining the transmitter label signal corresponding to the symbol to be equalized, the two-dimensional symbol output by the network is subtracted from the two-dimensional symbol received at the center position to obtain the equalized two-dimensional symbol output.

[0036] Compared with existing technologies, the coherent optical communication residual equalization method based on first-order perturbation features and bidirectional gated cyclic networks provided by this invention has the following advantages: First, in the perturbation feature generation stage, the present invention filters the lag index combination through constraints, and retains the effective cross terms related to nonlinear damage while controlling the feature dimension. Second, the present invention uses dual polarization prediction symbols to jointly construct perturbation terms, which can incorporate the relevant nonlinear combination information of the current polarization and another polarization into the feature representation; Third, this invention combines first-order perturbation features with the BiGRU central state fusion mechanism, enabling the network to simultaneously utilize forward and backward context information for residual estimation at the center of the complete window. Fourth, this invention adopts a residual learning method. During the training phase, it directly learns the two-dimensional difference between the received symbol and the tag symbol. During the inference phase, it does not require the transmitter tag corresponding to the symbol to be equalized. Instead, it obtains the compensation result by subtracting the prediction residual from the received symbol, and the output has a clear physical meaning. Fifth, the data standardization, principal component analysis, and complex gain alignment of this invention are all based on the training segment fitting only, avoiding information leakage in the validation and test segments, and enabling the inference stage to directly use the parameters obtained in the training stage to complete feature transformation and residual compensation. Sixth, this invention limits the input dimension through principal component analysis and maps features to a fixed projection dimension through an input projection module, which helps to reduce the parameter size and training complexity of subsequent recurrent networks. Seventh, this invention takes the hidden state at the center position in the bidirectional GRU instead of the hidden state at the end, so that the network structure is consistent with the task form of "complete window center symbol compensation". Attached Figure Description

[0037] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments are briefly described below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of the coherent optical communication system and the receiver DSP preprocessing process of the present invention.

[0039] Figure 2 This is a flowchart of the residual equalization method based on first-order perturbation features and BiGRU of the present invention.

[0040] Figure 3 This is a block diagram of the module structure of the residual equalization system of the present invention.

[0041] Figure 4 This is a flowchart of the preprocessing and feature saving of dual-polarization received signals in this invention.

[0042] Figure 5 This is a schematic diagram of the first-order perturbation feature extraction process in this invention.

[0043] Figure 6 This is a schematic diagram illustrating the data relationship between the first-order perturbation feature, PCA dimensionality reduction feature, complete window, and center symbol in this invention.

[0044] Figure 7 This is a schematic diagram of the structure of the BiGRU residual equalization network of the present invention.

[0045] Figure 8 This is a performance curve diagram from an embodiment of the present invention. Detailed Implementation

[0046] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0047] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0048] Example 1 (e.g.) Figure 1 and Figure 2 , Figures 4 to 8 (As shown)

[0049] This embodiment uses a dual-polarization 16QAM coherent optical communication signal as an example to illustrate a residual equalization method based on first-order perturbation features and BiGRU. This embodiment includes a training or calibration stage and an equalization inference stage: the training or calibration stage includes receiver DSP preprocessing, alignment of the received signal and the tag, perturbation feature generation, and training and testing of the BiGRU residual equalization network; the equalization inference stage uses the parameters and model obtained in the training stage to complete residual prediction and symbol compensation based solely on the received signal to be equalized.

[0050] First, during the training or calibration phase, the coherent receiver performs coherent detection, photoelectric conversion, low-pass filtering, and analog-to-digital conversion on the dual-polarized optical signal transmitted through the fiber optic link to obtain a dual-polarized digital sampled signal. The receiver's DSP preprocessing sequentially includes I / Q imbalance correction, dispersion compensation, clock phase recovery, adaptive time-domain equalization MIMO-CMA, downsampling, carrier frequency recovery, and carrier phase recovery. After the above processing, the training receiver data and the transmitter tag data are read. The receiver data includes the X-polarized received complex signal RxX and the Y-polarized received complex signal RxY, and the transmitter tag data includes the X-polarized tag complex signal sigX. complex and the complex signal sigY of the Y-polarized tag complex The above signals are uniformly converted into column vectors to avoid calculation errors caused by inconsistent row and column directions.

[0051] Subsequently, during the training or calibration phase, the unit average power of both the receiving signal and the transmitting tag signal used for training is normalized. Specifically, each signal is divided by the square root of its average power. After normalization, based on |RxX| and |sigX|... complex The cross-correlation of | is used to calculate the delay, and the received signal or tag signal is truncated according to the sign of the delay to obtain the time-aligned BX, BY, and TX. LabelX and TX LabelY .

[0052] Next, data-aided dynamic carrier phase compensation is performed during the training or calibration phase. For X-polarization, the phase is calculated. X = angle(BX · conj(TX LabelX )), for the phase after phase expansion X Perform a moving average with a window length of 51 to obtain the phase. Xsmooth And let BX = BX · exp(-j · phase Xsmooth For Y-polarization, the phase is calculated in the same way. Y phase Ysmooth And update BY. This step uses the aligned tag to assist in estimating the dynamic phase difference, so that the subsequent hard decision and perturbation feature extraction have a more stable input; in the equalization inference stage, the receiver DSP, pilot-assisted or decision-assisted carrier phase recovery results are used, and the transmitter tag corresponding to the symbol to be equalized is not required to be input.

[0053] Then, 16QAM hard decision is performed on the phase-compensated BX and BY. Specifically, BX and BY are multiplied by a scaling factor (scale = √10), and the decision function is executed on the real and imaginary parts respectively: d(x) = min( max( 2·round((x-1) / 2) + 1, -3 ), 3 ) This allows us to determine the real and imaginary parts to be within the range {-3, -1, 1, 3}, and then divide by the scale to obtain BX at the unit power scale. dec and BY dec The predicted sign mentioned above is used for subsequent perturbation feature extraction. The nearest constellation point decision is equivalent to solving: ; Where r is the received complex symbol to be decided, and C is the target constellation set.

[0054] Furthermore, the first-order perturbation feature extraction function is invoked. Assuming m=5 and n=5, a two-dimensional index grid of I and J is first constructed; then, a physical constraint mask is formed based on |I|+|J| ≤ min(m, n) and |I·J| ≤ min(m, n); simultaneously, a range constraint mask is formed based on I ≤ 0, J ≤ 0 and I+J ≤ 0; the two are ANDed to obtain the effective index combination. In this embodiment, 19 effective complex perturbation terms are finally obtained.

[0055] For X-polarization, the feature extraction function uses BX_dec as the current polarization input and BY_dec as the other polarization input; for Y-polarization, it uses BY_dec as the other polarization input.dec As the current polarization input, BX dec As another polarization input. For each valid index combination (i, j, i+j), calculate based on the time center position k: ; The function vectorizes the above perturbation terms along the time axis, outputting the real part RT and the imaginary part IT of At. This yields RTX, ITX, and lagPairsX for X-polarization, and RTY, ITY, and lagPairsY for Y-polarization.

[0056] Since perturbation feature calculation requires offset symbols (offset = m + n = 10), the feature length is shortened relative to the original received signal. Therefore, for the perturbation features of X-polarization and Y-polarization, zero values ​​are padded at the offset line at the front end and at the rear end to obtain the corresponding length of zero values, resulting in RTX. aligned ITX aligned ,RTY aligned and ITY aligned This process ensures that the lengths of the padded perturbation features are consistent with those of BX and BY, respectively. Subsequently, the X-polarization perturbation feature files, Y-polarization perturbation feature files, corresponding tag files, and the received signal files with alignment and phase compensation completed are saved for subsequent reading by the neural network.

[0057] In the neural network training and testing process, the feature and tag files mentioned above are first read from the directory of each transmit power point. For X-polarization, the aligned received signal, tag real part, tag imaginary part, real part of perturbation feature, and imaginary part of perturbation feature are read; for Y-polarization, the corresponding aligned received signal, tag, and perturbation feature are read. The real and imaginary perturbation features of the same polarization are concatenated along the feature dimension to form the original real-valued feature matrix. If there is a difference in the length of the received signal and tag, the shorter length is used for consistency.

[0058] Then, the samples are divided into training, validation, and test segments in chronological order. In this embodiment, the training ratio is 0.60, the validation ratio is 0.20, and the remaining samples are used as the test segment. (Full window radius half) window = 15, perturbation memory memory = 5, feature generation with leading and trailing zeros corresponds to perturbation. edge = 10, therefore the guard interval is split guard =half window + perturb memory = 20, edge = max(half) window perturb edge=15. The indices of the training segment, validation segment, and test segment avoid the boundaries of adjacent segments to prevent information sharing between adjacent segments due to window or perturbation memory.

[0059] Subsequently, complex gain alignment of the received signal is performed using only the training segment. Specifically, the label is first calculated based on the average power of the label signal in the training segment. scale And divide both the tag signal and the received signal by the label. scale Next, the least-squares complex gain g is calculated based on the received signal and the label signal from the training segment, making g·rx approximate the label, and then g is applied to the received signal. This step does not use the fitting parameters from the validation or test segment samples.

[0060] Next, standardized and principal component analysis parameters are fitted using only the training segment features. First, the mean and standard deviation of the training segment features are calculated, with the standard deviation of the near-zero standard deviation dimension set to 1 to avoid numerical anomalies. Then, singular value decomposition is performed on the standardized features of the training segment, and the number of principal components is selected based on the cumulative explained variance proportion. In this embodiment, the cumulative explained variance proportion is 0.995, and the maximum number of principal components is 64. All samples are transformed using the mean, standard deviation, and principal component matrix obtained from the training segment fitting, and then divided by the standard deviation of the principal components in the training segment to obtain the real-valued feature sequence after principal component analysis.

[0061] Then, a complete window is constructed for each center symbol to be balanced. Let the half-window length be H, and the complete window length be L = 2H + 1. In this embodiment, H = 15, therefore the complete window length is 31. The window data consists of positions from center-H to center+H in the feature sequence after principal component analysis. During training or testing, two-dimensional label symbols and two-dimensional receiver symbols at the center position are provided simultaneously for supervised training and metric statistics. During inference, only the receiver two-dimensional symbols at the center position are needed for residual subtraction output. Data sets for X-polarization and Y-polarization are constructed separately and then concatenated for unified training and evaluation.

[0062] In the BiGRU residual equalization network, the input tensor is a complete window of shape [B, L, D], where B is the batch size, L is the window length, and D is the feature dimension after principal component analysis. The network first calculates the center position mid = L / / 2. For BiGRU mode, the network uses the complete window as input, without truncating the features on the right side of the window.

[0063] The complete window is first input to the input projection module. The input projection module performs the following transformation at each time step: mapping from the input dimension D to 2P dimensions, then through GELU activation and Dropout, and finally mapping back to P dimensions. In this embodiment, P=64, and the Dropout ratio is 0.10. Through this module, the features after principal component analysis are uniformly projected into a fixed-dimensional representation suitable for recurrent network processing.

[0064] The projected sequence is input into a bidirectional GRU module. The bidirectional GRU module has an input dimension of P, a hidden dimension of Hb, and N layers, and uses a batch-first approach. first The format is as follows. In this embodiment, Hb=38, N=2; since the number of layers is greater than 1, the dropout between GRU layers is set to 0.10. The bidirectional GRU performs forward recursion and backward recursion on the same complete window respectively, and outputs the bidirectional hidden state at each time position, with an output dimension of 2Hb.

[0065] After the bidirectional GRU outputs, the network reads the bidirectional hidden state at the center position `mid` as the feature representation of the center symbol. That is, the network does not use the end-of-window state, but rather the center position state. This center state is formed by concatenating the states from the left end of the window to the center position of the forward GRU and the states from the right end of the window to the center position of the reverse GRU, thus corresponding to the fusion of the preceding and following contexts of the center symbol to be equalized.

[0066] The central bidirectional hidden state is then input into the residual output module. The residual output module first maps from 2Hb dimensions to 64 dimensions, then performs GELU activation and Dropout, and finally maps back to 2 dimensions. The output 2-dimensional vector represents the residual prediction value of the central symbol to be equalized, corresponding to the real and imaginary components in the complex plane, respectively.

[0067] During training, the received complex signal and the labeled complex signal are converted into two-dimensional real-valued representations, respectively. The residual supervision objective is defined as: Δ = R - Y Where R represents the two-dimensional symbol received at the center location, Y represents the two-dimensional symbol labeled at the center location, and Δ represents the two-dimensional residual target. The network output is denoted as... The training loss is the mean squared error between the network output and Δ. The optimizer used is AdamW with a learning rate of 1×10⁻⁶. -3 The weight decays to 1×10 -4 The gradient norm is pruned to a maximum value of 1.0. During training, the optimal model is saved based on the validation set loss, and a learning rate plateau descent strategy and an early stopping strategy are employed.

[0068] During inference or testing, the BiGRU residual equalization network outputs residual predictions based on the full window, and the final equalization output is: ; in, This represents a two-dimensional symbol after equalization. The actual equalization inference stage does not require obtaining the transmitter tag corresponding to this symbol; however, during offline testing or performance evaluation, the tag can be used to calculate metrics such as bit error rate, symbol error rate, normalized mean square error, and error vector magnitude. For 16QAM decision-making, in this embodiment, the output and tag are multiplied by √10, and then hard-determined to {-3, -1, 1, 3} for both the real and imaginary parts, and the bit error rate and symbol error rate are calculated according to the Gray mapping.

[0069] In this embodiment, the hidden dimension of the BiGRU network is set to 38. This is intended to match the number of trainable parameters as closely as possible to the unidirectional GRU comparison model, given a projection dimension of 64, two GRU layers, and a residual output head intermediate dimension of 64. This parameter setting does not limit the scope of this invention; the projection dimension, hidden dimension, number of GRU layers, and Dropout ratio can be adjusted for different input dimensions, window lengths, or system complexities.

[0070] Example 2 (e.g.) Figure 3 (As shown)

[0071] This embodiment illustrates the composition of the BiGRU residual equalization system. The system includes a training sample construction module, an online receiving and preprocessing module, a hard decision module, a perturbation feature extraction module, a feature alignment and storage module, a training segment alignment module, a feature dimensionality reduction module, a window construction module, a BiGRU residual prediction module, and a residual compensation module.

[0072] The training sample construction module is used to read the dual-polarization complex signal from the receiver and the dual-polarization tag complex signal from the transmitter during the training or calibration phase, and convert them into column vectors for time alignment, data-assisted phase compensation, residual supervision target construction, and performance evaluation.

[0073] The online receiver preprocessing module is used to read the dual-polarization received complex signal to be equalized during the equalization inference stage, and to perform I / Q imbalance correction, dispersion compensation, clock phase recovery, adaptive time-domain equalization MIMO-CMA, downsampling, carrier frequency recovery, carrier phase recovery, and unit average power normalization on the dual-polarization digital sampled signal output by the coherent receiver. During the training or calibration stage, this module can also combine the transmitter tag signal to perform cross-correlation time alignment and data-assisted dynamic carrier phase compensation.

[0074] The hard decision module is used to map the phase-compensated received signal into a predicted symbol at a unit power scale, which serves as the input to the perturbation feature extraction module.

[0075] The perturbation feature extraction module is used to construct lag index combinations and filter effective perturbation terms through physical constraints and range constraints. This module outputs the real part of the perturbation feature, the imaginary part of the perturbation feature, and the lag index combination for X polarization and Y polarization, respectively.

[0076] The feature alignment and saving module is used to pad the beginning and end of the perturbation features with zeros so that their length is consistent with the received signal. During the training phase, the module saves the X-polarization features, Y-polarization features, tag signal and received signal as data files that can be read by the subsequent neural network training. During the inference phase, the module outputs the perturbation features aligned with the received signal to be equalized.

[0077] The training segment alignment module is used to normalize the signal based on the average power of the tags in the training segment, and to calculate the least squares complex gain from the received signal to the tag signal based on the training segment samples, so as to achieve amplitude alignment of the received signals.

[0078] The feature dimensionality reduction module is used to fit the mean, standard deviation, principal component matrix, and principal component standard deviation to the features of the training segment, and applies the fitting parameters to all features of the training, validation, and test segments.

[0079] The window construction module is used to extract a complete window centered on the symbol to be balanced from the feature sequence after principal component analysis according to the preset half-window length. During training or testing, the received two-dimensional symbol and the label two-dimensional symbol at the center position are provided simultaneously. During inference, only the received two-dimensional symbol at the center position is provided for residual compensation.

[0080] The BiGRU residual prediction module is used to perform input projection, bidirectional GRU recursive modeling, bidirectional state reading at the center position, and two-dimensional residual output. The core of this module is to take the bidirectional hidden state at the center position of the complete window as the basis for center symbol compensation.

[0081] The residual compensation module is used to subtract the two-dimensional residual prediction value output by the BiGRU residual prediction module from the two-dimensional symbol received by the center to obtain a balanced output, and can be further connected to the decision module or performance statistics module.

[0082] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

[0083] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the coherent optical communication residual equalization method based on first-order perturbation features and bidirectional gated cyclic networks in any of the above embodiments.

[0084] Based on this understanding, the technical solution of this application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as CD-ROM, USB flash drive, mobile hard drive, etc.) and includes several instructions to cause a computer device (such as personal computer, server, or network device, etc.) to execute the methods of various implementation scenarios of this application.

[0085] This application also provides a computer device, including a storage medium and a processor; the storage medium is used to store a computer program; the processor is used to execute the computer program to implement the steps of the coherent optical communication residual equalization method based on first-order perturbation features and bidirectional gated cyclic networks in any of the above embodiments.

[0086] Optionally, the computer device may also include a user interface, a network interface, a camera, radio frequency (RF) circuitry, sensors, audio circuitry, a Wi-Fi module, etc. The user interface may include a display screen, input units such as a keyboard, etc., and optional user interfaces may also include USB ports, card reader ports, etc. The network interface may optionally include standard wired interfaces, wireless interfaces (such as Bluetooth interfaces, Wi-Fi interfaces), etc.

[0087] Those skilled in the art will understand that the computer device structure provided in this embodiment does not constitute a limitation on the computer device, and may include more or fewer components, or combine certain components, or have different component arrangements.

[0088] The storage medium may also include an operating system and a network communication module. The operating system is a program that manages and stores the hardware and software resources of a computer device, supporting the operation of information processing programs and other software and / or programs. The network communication module is used to enable communication between the various components within the storage medium, as well as communication with other hardware and software within the physical device.

[0089] In this invention, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the term "multiple" refers to two or more unless otherwise explicitly defined. The terms "install," "connect," "link," and "fix" should be interpreted broadly. For example, "connect" can be a fixed connection, a detachable connection, or an integral connection; "link" can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0090] In the description of this invention, it should be understood that the terms "upper," "lower," "left," "right," "front," "rear," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or unit referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0091] In the description of this specification, the terms "one embodiment," "some embodiments," "specific embodiment," etc., refer to a specific feature, structure, material, or characteristic described in connection with that embodiment or example, which is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0092] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A coherent optical communication residual equalization method based on first-order perturbation features and bidirectional gated cyclic networks, characterized in that, Includes the following steps: S1. Obtain the dual-polarization received complex signal to be equalized after preprocessing by a coherent receiver and a receiver DSP. The receiver DSP preprocessing includes one or more of I / Q imbalance correction, dispersion compensation, clock phase recovery, adaptive time-domain equalization MIMO-CMA, downsampling, carrier frequency recovery, and carrier phase recovery, and performs power normalization on the dual-polarization received complex signal to be equalized. S2. Based on the target constellation set used by the coherent optical communication signal, perform hard decision on the normalized dual-polarization received complex signal to be equalized to obtain the dual-polarization prediction symbol used to extract perturbation features. S3. Extract first-order perturbation features based on the combination of the dual-polarization prediction symbol and the constrained hysteresis index, and perform time alignment on the first-order perturbation features. The time alignment includes: for perturbation features whose length is shortened due to offset, padding the front end with zero values ​​of the offset line and the rear end with zero values ​​of the corresponding length, so that the length of the padded perturbation feature is consistent with the length of the corresponding received signal. S4. Using the feature standardization parameters and principal component analysis parameters prefitted during the training or calibration phase, transform the aligned first-order perturbation features to obtain the dimension-reduced real-valued feature sequence. S5. Taking the symbol to be balanced as the center, extract a complete window from the reduced real-valued feature sequence to form the input of the bidirectional gated recurrent network residual balance network. S6. Input the complete window into the bidirectional gated recurrent network residual equalization network obtained in the training phase, and obtain the two-dimensional residual prediction value corresponding to the center symbol through the input projection module, bidirectional GRU module and residual output module. S7. Subtract the predicted two-dimensional residual from the two-dimensional symbol received at the center position to obtain the balanced two-dimensional symbol output; The transmitter tag signal is only used in the training or calibration phase of the bidirectional gated recurrent network residual equalization network. It is not necessary to obtain the transmitter tag signal corresponding to the symbol to be equalized in the equalization inference phase.

2. The coherent optical communication residual equalization method according to claim 1, characterized in that, The training or calibration phase of the bidirectional gated recurrent network residual equalization network includes: S21. Obtain the dual-polarization receiving complex signal for training and its corresponding transmitting tag complex signal, and normalize the power of the dual-polarization receiving complex signal for training and the transmitting tag complex signal respectively. S22. Determine the time delay based on the cross-correlation result of the amplitude sequence of the training dual-polarization received complex signal and the transmitting tag complex signal, and trim and align the training dual-polarization received complex signal and the transmitting tag complex signal according to the time delay. S23. Based on the aligned dual-polarization received complex signal for training and the transmitted tag complex signal, perform data-assisted carrier phase compensation to obtain the phase-compensated dual-polarization received complex signal for training. S24. Perform hard decision on the phase-compensated dual-polarization received complex signal for training to obtain the dual-polarization predicted symbol for training. S25. Extract first-order perturbation features based on the training dual-polarization prediction symbols, and fit the complex gain alignment parameters, feature normalization parameters, and principal component analysis parameters of the received signal using only the training segment samples. S26. Using the difference between the two-dimensional symbol received at the center position and the two-dimensional symbol labeled at the center position as the residual supervision target, the mean square error loss is used to train the bidirectional gated recurrent network residual equalization network.

3. The coherent optical communication residual equalization method according to claim 2, characterized in that, The data-assisted carrier phase compensation includes: Calculate the phase of the conjugate product of the current polarization training received signal and the corresponding transmitter tag signal to obtain the phase difference sequence; The phase difference sequence is phase-expanded, and the expanded phase difference sequence is smoothed by moving average to obtain a smoothed phase sequence; The current polarization training received signal is reversed and rotated according to the smoothed phase sequence to obtain the phase-compensated training received complex signal. The moving average smoothing uses a preset smoothing window length, which is determined based on the carrier phase disturbance velocity, symbol rate, or phase noise intensity.

4. The coherent optical communication residual equalization method according to claim 1 or 2, characterized in that, The hard decision includes: based on the target constellation set used by the coherent optical communication signal, performing a nearest constellation point decision on the normalized received complex signal to be equalized or the phase-compensated training received complex signal. ； Where r represents the normalized received complex symbol to be equalized or the received complex symbol after phase compensation, and C represents the target constellation set; the decision result of the nearest constellation point is used as the predicted symbol under the unit power scale.

5. The coherent optical communication residual equalization method according to claim 1 or 2, characterized in that, The extraction of the first-order perturbation features includes: S51. Construct a two-dimensional grid with indices i and j, where i∈[-m,m] and j∈[-n,n]; S52. Based on physical constraints, retain the condition that |i|+|j|≤min(m,n) and |i The index combination of j|≤min(m,n); S53. Based on the range constraints, retain the index combinations that satisfy i≤0, j≤0 and i+j≤0; S54. The index combination that simultaneously satisfies the physical constraint and the range constraint is taken as the effective hysteresis index combination. S55. Calculate the complex first-order perturbation term based on the effective lag index combination, and take the real part and imaginary part of the complex first-order perturbation term as the perturbation feature real part and perturbation feature imaginary part, respectively.

6. The coherent optical communication residual equalization method according to claim 5, characterized in that, In step S55, for the estimated symbol sequence Bx of the current polarity to be extracted and the estimated symbol sequence By of another polarity, the complex first-order perturbation term is calculated according to the following formula: ； Where k represents the center time position, i and j are indices in the effective lag index combination, and conj(·) represents complex conjugate; when extracting Y polarization, the input order of Bx and By is swapped.

7. The coherent optical communication residual equalization method according to claim 1 or 2, characterized in that, In step S5, the complete window length L satisfies: L = 2H+1 Where H is the half-window length; the complete window is composed of positions from center-H to center+H in the dimensionality-reduced real-valued feature sequence, and the center position is the position of the symbol to be balanced; The half-window length H is a preset positive integer, and the full window length L is an odd number that satisfies L=2H+1.

8. The coherent optical communication residual equalization method according to claim 2, characterized in that, In step S6, the bidirectional GRU module adopts a batch-first data format, with the input dimension being the projection dimension, the hidden dimension being the preset BiGRU hidden dimension, the number of layers being the preset number of layers, and GRU inter-layer Dropout being enabled when the number of layers is greater than 1. The preset BiGRU hidden dimension, preset number of layers, and GRU inter-layer Dropout ratio are determined based on the input feature dimension, window length, and target model complexity. In step S6, the bidirectional gated cyclic network residual equalization network reads the bidirectional hidden state at the center position of the complete window as the input of the residual output module, but does not read the hidden state at the end of the complete window as the input of the residual output module. The bidirectional hidden state at the center of the complete window includes the hidden state obtained by the forward GRU recursively from the left side of the window to the center, and the hidden state obtained by the reverse GRU recursively from the right side of the window to the center.

9. The coherent optical communication residual equalization method according to claim 2, characterized in that, The received signal complex gain alignment includes: S91. Calculate the tag scaling factor based on the average power of the tag signal in the training segment, and use the tag scaling factor to normalize the tag signal and the received signal. S92. Calculate the least squares complex gain based on the received signal and the tag signal of the training segment; S93. Apply the least squares complex gain to the received signal; wherein neither the tag scaling factor nor the least squares complex gain is fitted using verification segment samples and test segment samples.

10. The coherent optical communication residual equalization method according to claim 1 or 2, characterized in that, The fitting and transformation of the principal component analysis parameters include: S101. Calculate the feature mean and feature standard deviation using the features of the training segment, and protect the dimension with near-zero standard deviation; S102. Perform singular value decomposition on the standardized features of the training segment; S103. Select the number of principal components based on the cumulative explained variance ratio, and the number of principal components shall not exceed the preset maximum number of principal components; S104. Project the features of the training segment, validation segment, and test segment onto the selected principal components and scale them according to the standard deviation of the principal components of the training segment.

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