Optimization method and device for adaptive equalizer for coherent optical communication system

Abstract

This invention provides an optimization method and apparatus for an adaptive equalizer in a coherent optical communication system. The method includes: when updating the tap coefficients of the signal equalizer, acquiring the current input signal and the current output signal of the signal equalizer, and determining the data loss function for each tap point based on the error term corresponding to the current output signal, the current input signal, and the current output signal; determining the updated weights of each tap point according to the current weights of each tap point, the data loss function, and the weight sparsification function, so as to optimize the adaptive equalizer; wherein the weight sparsification function for each tap point is determined by setting an L1 regularization parameter and the current weights of each tap point. This invention can reduce the computational complexity of the adaptive equalizer while maintaining its performance.

Description

Technical Field

[0001] This invention relates to the field of optical communication technology, and in particular to an optimization method and apparatus for adaptive equalizers in coherent optical communication systems. Background Technology

[0002] With the continued explosive growth of global network traffic, traditional intensity modulation direct detection (IM / DD) systems require wider electro-optical bandwidth, higher complexity, and more advanced digital signal processing (DSP) algorithms to support higher transmission rates, leading to a significant increase in system cost and power consumption. In contrast, digital coherent optical transmission systems, with their superior spectral efficiency and receiver sensitivity, are highly competitive in next-generation high-speed and high-capacity optical communication solutions. However, coherent optical transmission systems still face challenges of high computational complexity and power consumption, especially the power consumption of the receiver-side DSP, which can account for more than 50% of the total power consumption of the optical module, severely limiting its practical deployment in industrial applications. Specifically, the complexity of coherent optical communication DSPs is mainly concentrated in adaptive equalizers (AEQs), such as traditional 4x4 MIMO AEQs and 2x2 MIMO AEQs. However, traditional AEQ calculations are still quite complex. Therefore, to reduce the computational burden on the receiver-side DSP, low-complexity AEQs have become a focus of extensive research.

[0003] Current research on reducing the computational complexity of AEQ (Adaptive Equalizer) mainly focuses on decomposing the traditional Multi-Input Multiple-Output (MIMO) equalizer architecture into two stages: polarization demultiplexing and signal equalization. In this two-stage AEQ design, an M-tap butterfly filter (which can be composed of four interconnected finite impulse response (FIR) filters) can be used for polarization demultiplexing, while an N-tap FIR filter can adaptively equalize the optical signal for each polarization state (where M < N). Existing two-stage AEQ architectures include various types such as MN CV AEQ, M-NRV (1x1) AEQ, and MN RV (2x2) AEQ. Compared to traditional AEQ, this type of design halves the number of N-tap FIR filters, significantly reducing computational complexity without significantly degrading system performance, thus achieving low-complexity adaptive equalization.

[0004] However, research has revealed that even with the simplified AEQ architecture employing the two-stage approach described above, a certain degree of coefficient redundancy still exists in the tap design of the FIR filter. There is still significant room for optimization in further reducing redundant tap coefficients. Therefore, how to maintain AEQ performance while further reducing its computational complexity is a pressing issue that needs to be addressed. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide an optimization method and apparatus for adaptive equalizers in coherent optical communication systems, which can significantly reduce the computational complexity of AEQ while maintaining AEQ performance.

[0006] One aspect of the present invention provides an optimization method for an adaptive equalizer (AEQ) in a coherent optical communication system. The adaptive equalizer includes a polarization demultiplexer and a signal equalizer that receives the output signal of the polarization demultiplexer. The method includes the following steps:

[0007] Obtain the current input signal and current output signal of the signal equalizer, and determine the data loss function of each tap point based on the error term corresponding to the current output signal, the current input signal, and the current output signal;

[0008] The new weights of each tap are determined based on the current weights of each tap, the data loss function, and the weight sparsification function to optimize the adaptive equalizer. The weight sparsification function of each tap is determined based on the set L1 regularization parameter and the current weights of each tap.

[0009] In some embodiments of the present invention, the weight sparsification function for each tap point is determined based on a set L1 regularization parameter and the current weight of each tap point, including:

[0010] The sign of the weight sparsification function at each tap point is determined by the sign of the current weight at each tap point, and the absolute value of the weight sparsification function at each tap point is determined by the absolute value of the product of the L1 regularization parameter and the convergence step size.

[0011] In some embodiments of the present invention, after determining the new weights of each tap point, the method further includes setting the new weights below the decision threshold to zero.

[0012] In some embodiments of the present invention, the L1 regularization term parameter is determined in the following manner:

[0013] During the training phase, the training input signals from the training set are introduced into the adaptive equalizer with initial L1 regularization parameters. The error term of the signal equalizer in the adaptive equalizer is updated based on the current training output signal. Then, the tap coefficients of the signal equalizer in the adaptive equalizer are updated based on the current training input signal and the current training output signal. The next training input signal is then input into the updated adaptive equalizer. The iterative tap coefficients corresponding to the initial L1 regularization parameters are obtained by iteratively updating multiple training input signals, thus obtaining the iterative adaptive equalizer corresponding to the initial L1 regularization parameters.

[0014] During the testing phase, the test input signals from the test set are input into the iterative adaptive equalizer, and it is determined whether the iterative adaptive equalizer meets the set regularization conditions based on the test input signals and the corresponding test output signals.

[0015] If the set regularization conditions are not met, the initial L1 regularization parameters are corrected and the training and testing phases are repeated. If the set regularization conditions are met, the initial L1 regularization parameters are used as the set L1 regularization parameters.

[0016] In some embodiments of the present invention, the regularization condition is set as follows: the bit error rate is less than a set bit error value and the sparsity is greater than a set sparsity quantity; wherein, the bit error rate is determined based on the output signal of the signal equalizer in the iterative adaptive equalizer during the test phase and the standard reference signal, and the sparsity is measured by the number of taps in the iterative adaptive equalizer whose weights are greater than a set weight value.

[0017] In some embodiments of the present invention, the signal equalizer is constructed using a finite impulse response filter, and the architecture of the adaptive equalizer is MN CV AEQ, MN RV(1x1)AEQ or MN RV(2x2)AEQ.

[0018] The data loss function for each tap point is determined based on the error term corresponding to the current output signal, the current input signal, and the current output signal, including:

[0019] In the MN CV AEQ architecture, for optical signals of various polarization states, the product of the conjugate operation result of the current input signal, the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0020] In the MN RV(1x1)AEQ architecture, for optical signals of various polarization states, the product of the real part of the current input signal, the real part of the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0021] In the MN RV(2x2)AEQ architecture, for optical signals of various polarization states, if both the current input signal and the current output signal are real or imaginary parts of the signal, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point; if the current input signal and the current output signal are real and imaginary parts of the signal, respectively, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0022] In some embodiments of the present invention, the initial weights of each tap point in the signal equalizer are determined in the following manner:

[0023] The initial weight of the tap point located in the middle of the signal equalizer is set to 1, and adaptive iteration is performed using sliding window convolution to determine the initial weight of each tap point in the signal equalizer.

[0024] In some embodiments of the present invention, the error term corresponding to the current output signal is obtained by using a cascaded multimode algorithm to calculate the difference between the square of the current output signal and the square of the reference magnitude.

[0025] In some embodiments of the present invention, the data loss function of each tap point in the signal equalizer is the same.

[0026] Another aspect of the present invention provides an optimization apparatus for an adaptive equalizer for a coherent optical communication system, comprising a processor, a memory, and a computer program / instructions stored in the memory, wherein the processor is configured to execute the computer program / instructions, and when the computer program / instructions are executed, the apparatus implements the steps of the method described in any of the above embodiments.

[0027] The proposed optimization method and apparatus for adaptive equalizers in coherent optical communication systems can achieve low power consumption and high efficiency in coherent optical communication systems by introducing L1 regularization parameters during the tap coefficient update process of the two-stage AEQ design, thereby suppressing redundant taps of the FIR filter in the signal equalizer.

[0028] Additional advantages, objects, and features of the invention will be set forth in part in the description which follows, and will also become apparent in part to those skilled in the art upon studying the description, or may be learned by practice of the invention. The objects and other advantages of the invention can be realized and obtained by means of the structures specifically pointed out in the description and drawings.

[0029] Those skilled in the art will understand that the objectives and advantages achievable with the present invention are not limited to those specifically described above, and that the above and other objectives achievable with the present invention will become clearer from the following detailed description. Attached Figure Description

[0030] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, are not intended to limit the scope of the invention. In the drawings:

[0031] Figure 1 This is a flowchart illustrating an optimization method for AEQ (Adaptive Equivalent Optimization) in a coherent optical communication system according to an embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram of an AEQ architecture with a two-stage MN tap configuration in one embodiment of the present invention.

[0033] Figure 3 This is a schematic diagram of the tap coefficient update of the filter in an AEQ according to an embodiment of the present invention.

[0034] Figure 4 This is a schematic diagram of a signal optical back-to-back transmission system according to an embodiment of the present invention.

[0035] Figure 5 This is a schematic diagram illustrating the performance verification results of optimized AEQ in one embodiment of the present invention. Detailed Implementation

[0036] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the embodiments and accompanying drawings. Here, the illustrative embodiments and descriptions of this invention are used to explain the invention, but are not intended to limit the invention.

[0037] It should also be noted that, in order to avoid obscuring the invention with unnecessary details, only the structures and / or processing steps closely related to the solution according to the invention are shown in the accompanying drawings, while other details that are not closely related to the invention are omitted.

[0038] It should be emphasized that the term "including / comprises" as used herein refers to the presence of a feature, element, step, or component, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0039] In the following description, embodiments of the invention will be illustrated with reference to the accompanying drawings. In the drawings, the same reference numerals represent the same or similar parts, or the same or similar steps.

[0040] This application is applicable to coherent optical communication systems, and the adaptive equalizer in this application is a two-stage architecture AEQ, that is, the adaptive equalizer in this application can be divided into a polarization demultiplexer and a signal equalizer, and the output signal of the polarization demultiplexer is the input signal equalizer. Considering that the polarization demultiplexer in the AEQ is used to eliminate the interference and damage caused by factors such as birefringence and polarization mode dispersion to various polarization state signals (including X polarization state and Y polarization state) in the optical communication system, the optimization pruning method of the adaptive equalizer proposed in this application does not include the update process of the polarization demultiplexer, but only involves optimizing the signal equalizer in the AEQ.

[0041] Furthermore, in digital filters, especially FIR filters and recursive filters (such as Infinite Impulse Response (IIR) filters), a tap can represent the position used to adjust filter parameters (i.e., a specific position on the filter's delay line), where the signal can be sampled or weighted. Considering that most existing AEQs are constructed using FIR filters, the following description uses an AEQ constructed with an FIR filter as an example. Other types of filters can also be used to construct the AEQ; this invention is not limited to this.

[0042] The tap coefficients of an FIR filter refer to the specific weight values ​​of each tap in the filter's transfer function (i.e., the tap coefficients can be regarded as the collective weights of each tap point in the filter). The input signal can be weighted and added through these tap points to generate the output signal. That is, an FIR filter contains many convolution operations consisting of multiplication and accumulation. The number of effective FIR tap points can indirectly indicate the number of calculations required.

[0043] Compared to traditional AEQs, although the computational complexity of AEQs combining polarization demultiplexers and signal equalizers has been simplified, the redundancy in their tap coefficients makes it difficult to further reduce the computational complexity. This application introduces an L1 regularization parameter during the tap coefficient update process of the FIR filter in the signal equalizer to optimize the pruning of the adaptive equalizer, adaptively sparsifying the filter's tap coefficients. Furthermore, by combining this parameter with a threshold value, the number of effective taps in the AEQ can be further controlled (i.e., reducing the number of unimportant taps in the AEQ), thereby reducing computational complexity while maintaining AEQ performance.

[0044] Figure 1 This is a schematic diagram illustrating the optimized AEQ (Advanced Electrification Parameter) for coherent optical communication systems proposed in this application. Figure 1 As shown, the method may include steps S110 to S120.

[0045] Step S110: Obtain the current input signal and current output signal of the signal equalizer, and determine the data loss function of each tap point based on the error term corresponding to the current output signal, the current input signal, and the current output signal.

[0046] In some embodiments of the present invention, the calculation methods for the data loss function differ between different two-stage AEQ architectures. For example, Figure 2 The architecture of the adaptive equalizer with the two-stage MN tap configuration shown can be MN CV AEQ, MN RV(1x1)AEQ, or MN RV(2x2)AEQ. Figure 2 In the example, (a)MN CV AEQ represents the use of a 4x4 MIMO filter with M taps to achieve polarization demultiplexing, and two independent CV 2x2 FIR filters with N taps to achieve signal equalization. Figure 2 In the example, (b)MN RV(1x1)AEQ represents the polarization demultiplexing achieved by using a 4x4 MIMO filter with M taps and equalization achieved by two independent RV 1x1 FIR filters with N taps. Figure 2 In the diagram, (c)MN RV(2x2)AEQ represents polarization demultiplexing achieved using a 4x4 MIMO with an M-tap, and equalization achieved using two independent RV 2x2 FIR filters with N-tap. For optical signals in various polarization states, Figure 2 The data loss function for each AEQ architecture can be calculated as follows:

[0047] In the MN CV AEQ architecture, the product of the conjugate operation result of the current input signal, the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0048] In the MN RV(1x1)AEQ architecture, the product of the real part of the current input signal, the real part of the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0049] In the MN RV(2x2)AEQ architecture, if both the current input signal and the current output signal are real or imaginary parts, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point. If the current input signal and the current output signal are real and imaginary parts, respectively, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

[0050] Specifically, the optical signal transmitted in a coherent optical communication system is a complex signal that can be represented as i+jq. Taking the X-polarized optical signal as an example, the calculation formula for the data loss function of the signal equalizer in the AEQ configured with the above three MN taps can be expressed as:

[0051]

[0052] Where μ is the convergence step size, which is an empirical value, and ε x X represents the error term corresponding to the current output signal. mid X represents the current input signal of the signal equalizer. out X represents the current output signal of the signal equalizer. mid * Re(X) represents the result of the conjugate operation of the current input signal. out ) represents X out The real part, X mid,a ′ represents part of X mid,a , The data loss function represents the input and output of a signal equalizer where both the input and output are either the real or imaginary parts of the signal. Let a and b represent the data loss function of a signal equalizer, where the input and output are the real and imaginary parts of the signal, respectively, and a and b represent the i-channel or q-channel.

[0053] From the above formula, it can be seen that in MN In the RV(2x2) AEQ architecture, if both the current input signal and the current output signal are real parts (a = i), the data loss function at each tap point is the product of the current input signal, the real part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal. If both the current input signal and the current output signal are imaginary parts (a = q), the data loss function at each tap point is the product of the current input signal, the imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal. If the current input signal is real and the current output signal is imaginary (a = i and b = q), the data loss function at each tap point is the product of the current input signal, the imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal. If the current input signal is imaginary and the current output signal is real (a = q and b = i), the data loss function at each tap point is the product of the current input signal, the real part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal. The aforementioned real and imaginary parts of the signal are only used for the signal type (i or q) of the input signal equalizer and are unrelated to the specific transmitted optical signal.

[0054] As an example, such as Figure 2As shown, optical signals with different polarization states need to be input into different signal equalizers. Therefore, the tap coefficient update process of the signal equalizer proposed in this application is described for a single signal equalizer. Furthermore, the data loss function of each tap point in a single signal equalizer is the same (but the data loss function of different signal equalizers may be different), that is, the error term corresponding to the current output signal of each tap point in each AEQ signal equalizer is the same.

[0055] In some embodiments of the present invention, considering that the length of the filter is determined by the number of taps, the number of taps in the signal equalization stage of AEQ can be customized as needed, and the initial weight of each tap can be determined in the following way:

[0056] The initial weight of the tap located in the middle of the signal equalizer is set to 1, and an adaptive iteration is performed using a sliding window convolution method to determine the initial weight of each tap in the signal equalizer. That is, assuming there are N taps in the signal equalizer, the initial weight of the tap at (N+1) / 2 (or N / 2+1 or N / 2-1) is set to 1, and the initial weight of each tap in the signal equalizer is determined using an adaptive iterative algorithm. The adaptive iterative algorithm mentioned in this application can be a sliding window convolution algorithm or other iterative algorithms, and this invention does not specifically limit it.

[0057] Step S120: Determine the updated weights of each tap point based on the current weights of each tap point, the data loss function, and the weight sparsity function to optimize AEQ.

[0058] More specifically, this application can increase the weight of important positions and decrease the weight of unimportant positions through sparsification. Theoretically, some weights can be sparsified to zero to optimize the tap coefficients and number of taps of the FIR filter, thereby improving the computational efficiency of the AEQ model while preserving the model's performance as much as possible. For example, sparsity regularization (such as L1 regularization) or pruning can be used. The following uses L1 regularization as an example to sparsify the tap coefficients of the filter in the signal equalizer.

[0059] This application introduces an L1 regularization parameter during the update process of FIR filter tap coefficients. Based on the set L1 regularization parameter λ and the current weight of each tap point, the weight sparsification function is determined. The sparsification objective is determined by using the data loss function and the weight sparsification function. Thus, the updated weight of each tap point of the filter is determined according to the current weight of each tap point and the sparsification objective.

[0060] In some embodiments of the present invention, the weight sparsity function can be used to represent the gradient of weight changes, and the weight sparsity function for each tap may be different. The weight sparsity function for each tap is determined based on a set L1 regularization parameter and the current weight of each tap, including: the sign of the weight sparsity function for each tap is determined by the sign of the current weight of each tap, and the absolute value of the weight sparsity function for each tap is determined by the absolute value of the product of the L1 regularization parameter and the convergence step size. That is, the weight sparsity function for each tap can be expressed as R = μ·λ·sign(W), where sign(·) is the sign function, and W can be the current weight of the tap.

[0061] Sparsity can affect both signal quality and computational complexity; therefore, this application requires setting a sparsity objective when defining the weight sparsity function. In this application, the sparsity objective is to minimize the data loss function and maximize sparsity; therefore, the sparsity objective can be expressed as: That is, sparsification objective = data loss function - weight sparsification function.

[0062] In some embodiments of the present invention, after determining the update weights of each tap point, the method further includes: step S130, setting the update weights of the updated tap coefficients of the signal equalizer that are below the decision threshold value to zero. That is, after sparsifying the tap coefficients, the tap coefficients can be further optimized using a threshold decision mechanism to reduce the number of redundant taps. This process ensures the sparsity of the FIR filter and significantly reduces the computational complexity without significantly affecting system performance. For example, a threshold value can be set, and any weights less than this threshold value will be set to zero, further improving the sparsity of the filter.

[0063] In some embodiments of the present invention, such as Figure 3 As shown, the L1 regularization parameter is determined before updating the tap coefficients of the FIR filter in the signal equalizer. The specific determination process is as follows:

[0064] During the training phase, the training input signals from the training set are introduced into the adaptive equalizer with initial L1 regularization parameters. The error term of the signal equalizer in the adaptive equalizer is updated based on the current training output signal. Then, the tap coefficients of the signal equalizer in the adaptive equalizer are updated using the current training input signal, the current training output signal, the error term corresponding to the current training output signal, and the initial L1 regularization parameters. The next training input signal is then input into the updated adaptive equalizer. The iterative tap coefficients corresponding to the initial L1 regularization parameters are obtained by iteratively updating multiple training input signals, thus obtaining the iterative adaptive equalizer corresponding to the initial L1 regularization parameters.

[0065] During the testing phase, the test input signals from the test set are input into the iterative adaptive equalizer, and it is determined whether the iterative adaptive equalizer meets the set regularization conditions based on the test input signals and the corresponding test output signals.

[0066] If the set regularization conditions are not met, the initial L1 regularization parameters are corrected and the training and testing phases are repeated. If the set regularization conditions are met, the initial L1 regularization parameters are used as the set L1 regularization parameters.

[0067] As an example, during the training and update phases, gradient descent algorithms (such as the Cascaded Multi-modulus Algorithm, CMMA) can be used to obtain the error term corresponding to the output signal, thereby minimizing the data loss function. Specifically, during the training phase, the Cascaded Multi-modulus Algorithm is used to calculate the difference between the squared modulus of the current training output signal and the squared modulus of the reference signal, thus obtaining the error term corresponding to the current training output signal; during the update phase, the Cascaded Multi-modulus Algorithm is used to calculate the difference between the squared modulus of the current output signal and the squared modulus of the reference signal, thus obtaining the error term corresponding to the current output signal. Furthermore, during the training phase, initial L1 regularization parameters and decision thresholds can be introduced during the signal equalizer update phase for iterative updates (e.g., ...). Figure 3 As shown, if the AEQ obtained through iterative updates during the testing phase satisfies the set regularization conditions, then the initial L1 regularization parameter is used as the set L1 regularization parameter, and the decision threshold is used as the threshold value. The initial regularization parameter and the decision threshold can be set according to the sparsity target, and this invention does not impose specific limitations.

[0068] In some embodiments of the present invention, the regularization condition is set as follows: the bit error rate is less than a set bit error value and the sparsity degree is greater than a set sparsity number; wherein, the bit error rate is determined based on the output signal of the signal equalizer in the iterative adaptive equalizer during the test phase and the standard reference signal, and the sparsity degree is measured by the number of taps in the iterative adaptive equalizer whose weights are greater than a set weight value.

[0069] As an example, a weighted approach can be used to comprehensively quantify and measure the bit error rate and sparsity of AEQ, or other methods can be used; this invention does not impose specific limitations on them. The bit error rate and the set weight value can be set independently; for example, the set bit error rate can be determined based on the current bit error rate, and the set weight value can be set to zero. Furthermore, the above-mentioned setting of regularization conditions is merely an example; for instance, the bit error rate can be used alone as an indicator to determine whether the set regularization conditions are met, and this invention is not limited to this.

[0070] As an example, this application may also set multiple initial L1 regularization parameters. After the training and testing phases, the bit error rate and sparsity of each initial L1 regularization parameter are determined. The initial L1 regularization parameter with the smallest change in bit error rate and the largest sparsity is selected from the multiple initial L1 regularization parameters and used as the set L1 regularization parameter λ.

[0071] Furthermore, based on the AEQ optimization method proposed in this application, taking an X-polarized optical signal as an example, such as... Figure 2 The tap coefficient update formulas for the three AEQs shown are as follows:

[0072] W x =W x-1 +μ·(ε x ·X out ·X mid * -λ·sign(W x-1 (4)

[0073] W x =W x-1 +μ·(ε x ·Re(X out )·Re(X mid )-λ·sign(W x-1 (5)

[0074]

[0075] Among them, W x-1 and W x These are the current tap coefficient and the updated tap coefficient, respectively, W. x,aa W represents the tap coefficients of the real-real and imaginary-imaginary filters with N1 taps. x,ab X represents the tap coefficients of the real-to-imaginary part filter with N2 taps. mid,a ′ represents the input signal vector X mid,a Part of, for example, X mid,a X represents the input signal with 21 taps. mid,a ′ can represent the signals of the first 13 tap points.

[0076] As an example, the optimization process of AEQ in this application can be as follows: input coherent optical signal; determine error terms based on output optical signal, and update the tap coefficients of adaptive equalizer using input optical signal, output optical signal, determined error terms, and set L1 regularization parameters; after the tap coefficients are updated, the tap coefficients of AEQ are further sparsed using a threshold decision mechanism, and finally an AEQ that can be used to optimize the equalized signal is obtained. The optimization method proposed in this application can be divided into three stages: in the training stage, initial L1 regularization parameters and decision thresholds are set and an iterative adaptive equalizer is obtained; in the testing stage, the initial L1 regularization parameters and decision thresholds corresponding to the iterative adaptive equalizer that meet the set regularization conditions are determined, and they are used as the set L1 regularization parameters and threshold values, respectively; in the update stage, steps S110, S120, and S130 are executed to update the weights of each tap point based on the set L1 regularization parameters and threshold values.

[0077] In a specific embodiment of the present invention, a CV filter refers to a filter that performs complex number operations on the input signal, and an RV filter refers to a filter that performs real number operations on the input signal. Furthermore, the input AEQ signal can be converted between complex and real numbers based on the applicable operation method of the filter (e.g., using Matlab for conversion). If the filter performs one complex multiplication, it is equivalent to four real number multiplications. Considering the poor equalization effect of traditional 2x2 MIMO AEQ, this application uses the traditional 4x4 RV MIMO AEQ as a reference and compares its computational complexity and performance with multiple two-stage AEQs. The comparison results of the computational complexity of different AEQs are as follows: compared with the traditional 4x4 MIMO RV AEQ, the computational complexity of MN CV AEQ, MN RV(1x1)AEQ, and MN RV(2x2)AEQ is reduced by 40.5%, 65.5%, and 50%, respectively.

[0078] (1) Assuming the number of taps N is 21, a traditional 4×4 MIMO RV AEQ requires 4×4×21=336 real number multiplications to equalize a signal.

[0079] (2) Assuming that M is 2 and N is 21 in the two-stage AEQ, then Figure 2 In the polarization demultiplexing stage, (a) MN CV AEQ performs multiplication on the real and imaginary parts of the input complex signal respectively. In the signal equalization stage, it performs complex multiplication on the complex signals of the two polarization states X and Y respectively. Therefore, MN CV AEQ requires 16×M+2×4×N=200 real multiplications to equalize a signal.

[0080] (3) Assuming that M is 2 and N is 21 in the two-stage AEQ, then Figure 2In the polarization demultiplexing stage, (b)MN RV(1x1)AEQ performs multiplication operations on the real and imaginary parts of the input complex signal respectively. In the signal equalization stage, real number operations are performed on the complex signals of the two polarization states x and y respectively (multiplication of the real and imaginary parts of the complex signal is performed respectively). Therefore, 16×M+2×2×N=116 real number multiplications are needed to equalize a signal.

[0081] (4) Assuming that M is 2, N1 is 21, and N2 is 13 in the two-stage AEQ, then Figure 2 In (c)MN RV(2x2)AEQ, the filter with tap M performs multiplication operations on the real and imaginary parts of the input complex signal during the polarization demultiplexing stage. The filter with tap N1 performs real multiplication operations on the real parts of the complex signals with polarization states x and y during the signal equalization stage. The filter with tap N2 performs real multiplication operations on the imaginary parts of the complex signals with polarization states X and Y during the signal equalization stage. Therefore, 16×M+2×2×N1+2×2×N2=168 real multiplications are needed to equalize a signal.

[0082] Furthermore, using the AEQ optimization method proposed in this application, based on the L1 regularization parameter λ and threshold value set in Table 1, the per-symbol computational complexity (i.e., the complexity of equalizing one signal) of 4x4 MIMO RV AEQ, MN CV AEQ, MN RV(1x1)AEQ, and MN RV(2x2)AEQ is reduced to 146, 160, 96, and 101 respectively after optimization, representing reductions of 56.5%, 52.4%, 71.5%, and 70% respectively. That is, compared to the traditional 4x4 MIMO RV AEQ, the method of this application can effectively reduce the computational complexity of AEQ.

[0083] Table 1. Example settings for L1 regularization parameter λ and threshold value for AEQ of various architectures.

[0084] AEQ architecture The set L1 regularization parameter λ Threshold 4x4 MIMO RV AEQ 0.01 0.02 MN CV AEQ 0.02 0.02 MN RV(1x1)AEQ 0.005 0.01 MN RV(2x2)AEQ 0.02 0.02

[0085] In some embodiments of the present invention, it is possible to utilize, such as Figure 4 The 50 GBaud polarization-multiplexed 16 quadrature amplitude modulation (PDM-16QAM) signal back-to-back transmission system shown verifies the optimized AEQ performance. The optical signal transmission process is as follows:

[0086] In the transmitter DSP, the generated 50 GBaud 16QAM signal is first pulse-shaped by a root-raised cosine filter with a roll-off factor of 0.1. After resampling, two polarization-independent signals are loaded into an arbitrary waveform generator operating at 120 GSa / s, and then the electrical signal is modulated onto a 1550 nm optical carrier using a modulator. A variable optical attenuator is used to control the received optical power (ROP). Subsequently, a digital sampling oscilloscope operating at 256 GSa / s is used to capture the output signal of the integrated coherent receiver. The offline receiver DSP includes resampling at 2 samples per symbol (two samples per signal) and IQ imbalance compensation. After matched filtering, AEQ is used for polarization demultiplexing and equalization. Then, a carrier recovery algorithm is executed to remove frequency offset and phase noise, followed by decision, symbol demapping, and bit error rate calculation.

[0087] Based on the above verification system, Figure 2 Three AEQ architectures were used to build adaptive equalizers, and performance tests were conducted. The verification results are as follows: Figure 3 As shown. Based on optical back-to-back transmission, Figure 5 (a) shows the transmission performance at different received optical powers, by Figure 5 As shown in (a), when the ROP (receiver, integrated coherent optical receiver) is -20.2 dBm, the bit error rates of each AEQ are not significantly different, and the receiver sensitivity is 2 × 10⁻⁶. -2 Almost at the same position. Even though the performance of the sparse AEQ optimized by the pruning scheme proposed in this patent is not only comparable to that of the traditional 4x4 MIMO RV AEQ, but also maintains receiver sensitivity comparable to existing AEQs, it proves that the AEQ optimized and pruned in this application can achieve a balance between reduced complexity and robust system performance. Figure 5 Figures (b) and (c) demonstrate the tolerance of the optimized pruning AEQ to IQ imbalance. Experimental results show that the AEQ using the optimized pruning scheme can still maintain robustness to IQ imbalance (amplitude and phase imbalance of the I and Q signals) comparable to the unpruned AEQ.

[0088] This application optimizes AEQ based on the idea of ​​model lightweighting. The core idea is to introduce an L1 regularization term and a decision threshold during the update process of the tap coefficients of the FIR filter in the AEQ to sparsify the filter's tap coefficients, thereby effectively reducing computational complexity. The introduction of L1 regularization parameters to achieve tap coefficient sparsity in this application is merely an example; other sparsity methods (such as Elastic Net regularization) can also be used to update the FIR filter of the signal equalizer in the AEQ, and the update process can be customized according to the sparsity target.

[0089] The proposed optimization method for AEQ (Advanced Equalization Filter) in coherent optical communication systems utilizes L1 regularization to adaptively sparsify the number of filter taps during weight updates, reducing invalid or minimally influential tap coefficients and thus lowering computational complexity. The updated AEQ adaptively suppresses redundant taps based on the received signal, significantly reducing equalizer computational complexity while effectively maintaining AEQ performance and high tolerance for IQ amplitude and phase imbalances. This provides a new technical path for achieving low-power, high-efficiency coherent optical communication systems.

[0090] Corresponding to the above method, the present invention also provides an optimization apparatus for an adaptive equalizer for a coherent optical communication system. The apparatus includes a computer device, which includes a processor and a memory. The memory stores computer programs / instructions, and the processor executes the computer programs / instructions stored in the memory. When the computer programs / instructions are executed by the processor, the apparatus implements the steps of the method described above.

[0091] Those skilled in the art will understand that the exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Whether implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention. When implemented in hardware, it can be, for example, electronic circuits, application-specific integrated circuits (ASICs), appropriate firmware, plug-ins, function cards, etc. When implemented in software, the elements of this invention are programs or code segments used to perform the desired tasks. The programs or code segments can be stored in a machine-readable medium or transmitted over a transmission medium or communication link via data signals carried in a carrier wave.

[0092] It should be clarified that the present invention is not limited to the specific configurations and processes described above and shown in the figures. For the sake of brevity, detailed descriptions of known methods are omitted here. In the above embodiments, several specific steps are described and shown as examples. However, the method process of the present invention is not limited to the specific steps described and shown. Those skilled in the art can make various changes, modifications, and additions, or change the order of steps, after understanding the spirit of the present invention.

[0093] In this invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or in place of features of other embodiments.

[0094] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, various modifications and variations of the embodiments of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An optimization method for an adaptive equalizer (AEQ) in a coherent optical communication system, wherein the adaptive equalizer includes a polarization demultiplexer and a signal equalizer that receives the output signal of the polarization demultiplexer, characterized in that, The method includes the following steps: The current input signal and current output signal of the signal equalizer are obtained, and the data loss function of each tap point is determined based on the error term corresponding to the current output signal, the current input signal, and the current output signal. The new weights of each tap are determined based on the current weights of each tap, the data loss function, and the weight sparsification function to optimize the adaptive equalizer. The weight sparsification function for each tap is determined based on a set L1 regularization parameter and the current weights of each tap. The set L1 regularization parameter is an L1 regularization parameter introduced into the iterative adaptive equalizer that meets the set regularization conditions, obtained during the training and testing phases. The set regularization conditions are determined based on the bit error rate (BER), which is determined based on the output signal of the signal equalizer in the iterative adaptive equalizer during the testing phase and the standard reference signal.

2. The method according to claim 1, characterized in that, The weight sparsity function for each tap point is determined based on the set L1 regularization parameter and the current weight of each tap point, including: The sign of the weight sparsification function at each tap point is determined by the sign of the current weight at each tap point, and the absolute value of the weight sparsification function at each tap point is determined by the absolute value of the product of the L1 regularization parameter and the convergence step size.

3. The method according to claim 1, characterized in that, After determining the new weights for each tap point, the method further includes setting the new weights below the decision threshold to zero.

4. The method according to claim 1, characterized in that, The L1 regularization parameters are determined in the following way: During the training phase, the training input signals from the training set are introduced into the adaptive equalizer with initial L1 regularization parameters. The error term of the signal equalizer in the adaptive equalizer is updated based on the current training output signal. Then, the tap coefficients of the signal equalizer in the adaptive equalizer are updated based on the current training input signal and the current training output signal. The next training input signal is then input into the updated adaptive equalizer. The iterative tap coefficients corresponding to the initial L1 regularization parameters are obtained by iteratively updating multiple training input signals, thus obtaining the iterative adaptive equalizer corresponding to the initial L1 regularization parameters. During the testing phase, the test input signals from the test set are input into the iterative adaptive equalizer, and it is determined whether the iterative adaptive equalizer satisfies the set regularization conditions based on the test input signals and the corresponding test output signals. If the set regularization conditions are not met, the initial L1 regularization parameters are corrected and the training and testing phases are repeated. If the set regularization conditions are met, the initial L1 regularization parameters are used as the set L1 regularization parameters.

5. The method according to claim 4, characterized in that, The set regularization conditions are that the bit error rate is less than a set bit error value and the sparsity degree is greater than a set sparsity quantity; wherein, the sparsity degree is measured by the number of taps in the iterative adaptive equalizer whose weights are greater than a set weight value.

6. The method according to claim 1, characterized in that, The signal equalizer is constructed using a finite impulse response (FIR) filter, and the architecture of the adaptive equalizer is MN CV AEQ, MN RV (1x1) AEQ, or MN RV (2x2) AEQ. The process of determining the data loss function for each tap point based on the error term corresponding to the current output signal, the current input signal, and the current output signal includes: In the MN CV AEQ architecture, for optical signals of various polarization states, the product of the conjugate operation result of the current input signal, the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point. In the MN RV (1x1) AEQ architecture, for optical signals of various polarization states, the product of the real part of the current input signal, the real part of the current output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point. In the MN RV (2x2) AEQ architecture, for optical signals of various polarization states, if both the current input signal and the current output signal are real or imaginary parts of the signal, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point; if the current input signal and the current output signal are real and imaginary parts of the signal, respectively, the product of the current input signal, the real or imaginary part of the AEQ output signal, the convergence step size, and the error term corresponding to the current output signal is calculated to obtain the data loss function for each tap point.

7. The method according to claim 1, characterized in that, The initial weights of each tap point in the signal equalizer are determined in the following way: The initial weight of the tap point located in the middle of the signal equalizer is set to 1, and adaptive iteration is performed using sliding window convolution to determine the initial weight of each tap point in the signal equalizer.

8. The method according to claim 1, characterized in that, The error term corresponding to the current output signal is obtained by using a cascaded multimode algorithm to calculate the difference between the square of the current output signal and the square of the reference magnitude.

9. The method according to claim 1, characterized in that, The data loss function is the same at each tap point in the signal equalizer.

10. An optimization device for an adaptive equalizer in a coherent optical communication system, comprising a processor, a memory, and a computer program / instructions stored in the memory, characterized in that, The processor is configured to execute the computer program / instructions, and when the computer program / instructions are executed, the device implements the steps of the method as described in any one of claims 1 to 9.

Images