Nonlinear equalization method and apparatus for optical transmission system

Abstract

Disclosed are a nonlinear equalization method and apparatus for an optical transmission system, relating to the technical field of optical communications. The method comprises: on the basis of a specifically structured frame received, training a noise-filtering network and a main network, wherein the noise-filtering network is configured for tracking and filtering out time-varying noise, and the main network is configured for static nonlinear equalization; the specifically structured frame comprises a reference frame, an interference frame, and a test frame, wherein the reference frame is configured for training the main network so as to achieve convergence of a weight coefficient of the main network, the interference frame and the reference frame are configured for training the noise-filtering network so as to achieve real-time convergence of the noise-filtering network, and the test frame is configured for carrying a random service signal and testing system performance; performing nonlinear equalization on the test frame using the trained noise-filtering network and the trained main network, and outputting an equalized test frame. The present invention solves the problems of large nonlinear equalization convergence errors and poor generalization performance caused by the introduction of time-varying noise, has good anti-noise performance and low algorithmic complexity, and meets practical application requirements.

Description

A nonlinear equalization method and apparatus for optical transmission systems Technical Field

[0001] This invention relates to the field of optical communication technology, specifically to a nonlinear equalization method and apparatus for optical transmission systems. Background Technology

[0002] In optical transmission systems, signals are affected by various optoelectronic components and fiber nonlinearities during transmission, making it difficult to improve system transmission capacity and distance. Therefore, it is necessary to incorporate efficient nonlinear equalizers into the DSP (Digital Signal Processing) algorithms at the coherent optical receiver to improve optical transmission performance. Neural network equalizers, as a type of nonlinear equalizer, have relatively low algorithm complexity and have received widespread attention and application in recent years.

[0003] However, the nonlinear compensation performance of neural network equalizers is highly dependent on reliable parameter training. As the optical transmission system rate increases, the baud rate and modulation order also gradually increase, leading to a greater impact from noise, including bandwidth limitations and nonlinear disturbances. Obtaining high-quality received signals for training the neural network equalizer becomes extremely difficult. Furthermore, the time-varying nature of system disturbance noise further degrades the received signal-to-noise ratio (SNR), making it difficult for conventional neural network equalizers to converge to a low error level.

[0004] Currently, there are two main research approaches to improve the noise resistance of neural network equalizers. One approach involves designing the activation elements or recursive convolutions for individual neurons within a single node of the equalizer. This method can effectively reduce the impact of Gaussian white noise, static nonlinearity, and inter-symbol interference in the system, but it cannot fundamentally solve the noise impact introduced by time-varying impairments. With the introduction of time-varying noise, nonlinear neural network equalizers suffer from problems such as misconvergence and poor generalization performance. The other approach focuses on the structural design of a single neural network, maximizing the complexity of the neural network by increasing the number of nodes and layers to improve equalization performance. However, this leads to problems such as high algorithm complexity.

[0005] Therefore, how to design nonlinear equalization algorithms to improve their noise resistance and generalization ability in optical transmission systems and reduce their complexity is a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear equalization method and apparatus for optical transmission systems, which can solve the problems of large convergence error and poor generalization performance of nonlinear equalization caused by the introduction of time-varying noise. It has good noise resistance and low algorithm complexity, meeting the needs of practical applications.

[0007] To achieve the above objectives, in a first aspect, embodiments of the present invention provide a nonlinear equalization method for an optical transmission system. The method includes: training a noise filtering network and a main network based on a received specific structure frame; wherein the noise filtering network is used to track and filter time-varying noise, and the main network is used for static nonlinear equalization; the specific structure frame includes a reference frame, an interference frame, and a test frame; the reference frame is used for training the main network to achieve convergence of the weight coefficients of the main network; the interference frame and the reference frame are used for training the noise filtering network to achieve real-time convergence of the noise filtering network; the test frame is used to carry random service signals and test system performance; the trained noise filtering network and main network are used to perform nonlinear equalization on the test frame, and the equalized test frame is output.

[0008] In conjunction with the first aspect, in one implementation, both the reference frame and the interference frame are known modulation signals agreed upon with the transmitting end and have the characteristic of having the same information sequence. The test frame is the modulation signal corresponding to the random service signal to be transmitted. Furthermore, the reference frame is received only once during system initialization, while the interference frame and the test frame are received cyclically after the reference frame.

[0009] In conjunction with the first aspect, in one embodiment, the noise filtering network includes a first input terminal and a second input terminal. The first input terminal receives a reference frame, and the second input terminal receives an interference frame / test frame. The noise filtering network internally includes two parallel and independent conventional neural networks. Each conventional neural network contains an activation layer, and the nonlinear activation neurons in the activation layer are used for time-varying nonlinear noise equalization. The inputs of both conventional neural networks are connected to the interference frame / test frame at the second input terminal. The output signal of one conventional neural network is connected to the reference frame at the first input terminal via a multiplier to eliminate amplitude variations. The output signal of the other conventional neural network is connected to the reference frame at the first input terminal via an adder to eliminate DC bias variations.

[0010] In conjunction with the first aspect, in one implementation, the noise filtering network and the main network are trained separately based on the received specific structure frames, and nonlinear equalization is performed on the test frames, including:

[0011] Upon receiving a reference frame, it is input into the main network for training until convergence, at which point the node weights remain constant. Upon receiving an interference frame, both the interference and reference frames are input into a noise filtering network. The noise filtering network outputs a signal with a transformed distribution, which is then input into the main network. The node weights of the noise filtering network are adjusted based on the error in the main network's output signal. When the error in the main network's output signal is minimized, the training of the noise filtering network is complete, and convergence is determined, with the node weights remaining constant. Upon receiving a test frame, both the test and reference frames are input into the noise filtering network. The nodes in the noise filtering network undergo distribution transformation to filter out time-varying noise, and the filtered signal is output. The filtered signal is then input into the main network for static nonlinear equalization. This process continues cyclically, receiving interference and test frames, and repeatedly training and converging the noise filtering network while performing time-varying noise filtering and static nonlinear equalization on the test frames.

[0012] In conjunction with the first aspect, in one embodiment, the nonlinear equalization method for optical transmission systems further includes initializing the noise filtering network and the main network using a clustering coarse-tuning method; the clustering coarse-tuning method is as follows: clustering the digital signals obtained after linear equalization to obtain the degree of nonlinear deformation of the constellation diagram; obtaining the coarse initial setting parameters of the corresponding network structure according to the degree of nonlinear deformation of the constellation diagram, and initializing the noise filtering network and the main network according to the parameters.

[0013] In conjunction with the first aspect, in one embodiment, the nonlinear equalization method for optical transmission systems further includes optimizing and pruning the initialized noise filtering network and the main network using an iterative pruning method: first, optimizing and pruning the noise filtering network using an iterative pruning method, and then optimizing and pruning the main network using an iterative pruning method; wherein, the two parallel and independent conventional neural networks in the noise filtering network are treated as a whole for pruning.

[0014] In conjunction with the first aspect, in one implementation, when using iterative pruning to optimize and prune the noise filtering network, the time-varying nature of the weight coefficients of each node is used as the pruning strategy to determine the priority of each node and whether it is pruned; when using iterative pruning to optimize and prune the main network, a comprehensive evaluation of network complexity and balance performance is used as the pruning strategy to determine the priority of each node and whether it is pruned.

[0015] Secondly, embodiments of the present invention also provide a nonlinear equalization device for an optical transmission system based on the method in the first aspect embodiment. The device includes: a noise filtering network for tracking and filtering time-varying noise; a main network for static nonlinear equalization; a training module for training the noise filtering network and the main network respectively based on received specific structure frames; wherein the specific structure frames include reference frames, interference frames, and test frames, the reference frames are used for training the main network to achieve convergence of the weight coefficients of the main network, the interference frames and reference frames are used for training the noise filtering network to achieve real-time convergence of the noise filtering network, and the test frames are used to carry random service signals and test system performance; and an equalization processing module for performing nonlinear equalization on the test frames using the trained noise filtering network and main network, and outputting the equalized test frames.

[0016] In conjunction with the second aspect, in one embodiment, the device further includes:

[0017] The clustering coarse adjustment module is used to initialize the noise filtering network and the main network using a clustering coarse adjustment method. The clustering coarse adjustment method is as follows: cluster the digital signal obtained after linear equalization to obtain the degree of nonlinear deformation of the constellation diagram; obtain the coarse initial setting parameters of the corresponding network structure according to the degree of nonlinear deformation of the constellation diagram, and initialize the noise filtering network and the main network according to the parameters.

[0018] In conjunction with the second aspect, in one embodiment, the device further includes:

[0019] The pruning optimization module is used to optimize and prune the noise filtering network and the main network after initialization using an iterative pruning method to obtain the optimized noise filtering network and the main network; the equalization processing module is also used to perform nonlinear equalization on the test frame using the optimized noise filtering network and the main network, and output the equalized test frame.

[0020] The beneficial effects of the technical solutions provided in this application include:

[0021] By training the noise filtering network and the main network separately using specific structure frames, time-varying noise and inherent nonlinearity can be trained and equalized separately, resulting in higher stability, faster convergence speed, and smaller error. Furthermore, the trained noise filtering network and the main network can be used to equalize time-varying impairments and static nonlinearities in the system, effectively filtering out time-varying noise and constant nonlinear noise. This solves the problems of large convergence error and poor generalization performance of traditional nonlinear equalization caused by various time-varying impairments in high-speed, high-order modulation, and low signal-to-noise ratio optical transmission systems. The overall noise resistance is good and the algorithm complexity is low, meeting the needs of practical applications. Attached Figure Description

[0022] Figure 1 is a schematic diagram of an optical transmission system applying the nonlinear equalization method of this application in a first embodiment;

[0023] Figure 2 is a flowchart of the first embodiment of the nonlinear equalization method for optical transmission systems;

[0024] Figure 3 is a schematic diagram of the frame structure signal sequence in the prior art;

[0025] Figure 4 is a schematic diagram of a specific structural frame in an embodiment of the present invention;

[0026] Figure 5 is a schematic diagram of the specific structure of the noise filtering network in an embodiment of the present invention;

[0027] Figure 6 is a schematic diagram showing the different distributions of signals affected by time-varying noise at different times in an optical communication system;

[0028] Figure 7 is a schematic diagram of the training and balancing process in an embodiment of the present invention;

[0029] Figure 8 is a block diagram illustrating the implementation of training and balancing in an embodiment of the present invention;

[0030] Figure 9 is a schematic diagram of an optical transmission system applying the nonlinear equalization method of this application in a second embodiment;

[0031] Figure 10 is a comparison of network structure settings using clustering coarse adjustment and existing methods under different nonlinearity scenarios;

[0032] Figure 11 is a comparison of the performance and complexity of the clustering coarse-tuning method and the existing method;

[0033] Figure 12 is a schematic diagram of the initialization settings of the noise filtering network and the main network using cluster coarse tuning in an embodiment of the present invention.

[0034] Figure 13 is a schematic diagram of the grouping results obtained after clustering of the constellation diagram, as well as the ideal decision threshold and the optimal decision threshold;

[0035] Figure 14 is a schematic diagram of an optical transmission system applying the nonlinear equalization method of this application in a third embodiment.

[0036] Figure 15 is a schematic diagram of the process of optimizing and pruning the noise filtering network and the main network using an iterative pruning method in an embodiment of the present invention;

[0037] Figure 16 is a flowchart illustrating a specific example corresponding to the third embodiment of the present invention. Detailed Implementation

[0038] To make the technical problems, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] However, it should be noted that the examples described below are merely specific examples and are not intended to limit the embodiments of the present invention to the specific steps, values, conditions, data, order, etc. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0040] The technical solution provided in this embodiment is applicable to the typical optical transmission system application scenario shown in Figure 1. As shown in Figure 1, in a typical optical transmission system, the receiver performs coherent detection and digital-to-analog conversion on signals containing nonlinearity; the RX DSP (coherent optical receiver DSP) processes the signal through three parts: linear equalization (including resampling, clock recovery, IQ imbalance compensation, dispersion compensation, polarization demultiplexing, frequency offset estimation, and carrier phase recovery), nonlinear equalization, and decoding (including QAM decoding and FEC decoding). Referring to Figure 1, by applying the technical solution provided in this embodiment, the designed noise filtering network and main network can be used to equalize time-varying impairments and static nonlinearities in the system during the nonlinear equalization process. This effectively alleviates the problems of high complexity, large convergence error, and poor generalization performance of traditional nonlinear equalization caused by various time-varying impairments in high-speed, high-order modulation, and low signal-to-noise ratio optical transmission systems.

[0041] Specifically, in the first aspect, embodiments of this application provide a nonlinear equalization method for optical transmission systems.

[0042] Example 1

[0043] In the first embodiment, referring to Figure 2, which is a flowchart illustrating the first embodiment of the nonlinear equalization method for an optical transmission system according to this application, the nonlinear equalization method for an optical transmission system includes:

[0044] Step S1: Based on the received specific structure frames, train the noise filtering network and the main network respectively; wherein, the noise filtering network is used to track and filter out time-varying noise, and the main network is used for static nonlinear equalization; the specific structure frames include reference frames, interference frames and test frames, the reference frames are used for training the main network to achieve convergence of the weight coefficients of the main network, the interference frames and reference frames are used for training the noise filtering network to achieve real-time convergence of the noise filtering network, and the test frames are used to carry random service signals and test system performance.

[0045] Step S2: Use the trained noise filtering network and main network to perform nonlinear equalization on the test frame and output the equalized test frame.

[0046] It is understandable that, unlike the single neural networks in existing technologies, this application embodiment includes two parts: a noise filtering network and a main network. The main network is a conventional neural network, primarily used for compensating for static nonlinearities in the receiving-end DSP of the optical fiber transmission system, i.e., equalizing the static nonlinearities. The noise filtering network is a unique network added before the main network, mainly used for tracking and filtering time-varying noise such as time-varying amplitude, bias, and crosstalk. Compared to traditional single complex neural networks, this structure of a main network superimposed with a noise filtering network can effectively improve the convergence performance and equalization effect of the nonlinear neural network equalizer in time-varying noise scenarios. At the same time, precisely because this application embodiment includes both a noise filtering network and a main network, a different implementation method is used when training the noise filtering network and the main network compared to existing technologies.

[0047] Referring to Figure 3, in the prior art, the frame structure signal sequence transmitted at the transmitting end of the optical transmission system only includes training frames and test frames. The training frames are used to converge the weight coefficients of each node in the single neural network equalizer in the receiver's DSP, while the test frames are used to carry random service signals. In the prior art, training a single neural network using training frames involves simultaneously training against time-varying noise and inherent nonlinearity, and then using test frames for equalization. This results in poor overall training stability, slow convergence, and large errors. In optical communication systems with strong nonlinearity and rapidly changing system impairments, it is difficult to effectively and quickly converge and track time-varying impairments in real time. In this embodiment, however, a specific structure frame, as shown in Figure 4, is transmitted at the transmitting end of the optical transmission system, including a reference frame, an interference frame, and a test frame. At the receiving end of the optical transmission system, the noise filtering network and the main network are trained separately based on the received specific structure frame. The reference frame is used to train the main network, enabling the convergence of its weight coefficients and allowing the main network to balance strong nonlinearities in the fiber optic transmission system. The interference frame and reference frame are used to train the noise filtering network, achieving real-time convergence and enabling it to track time-varying nonlinearities, amplitude, DC bias, and other impairments in the system while filtering out time-varying noise. The test frame is used to carry random service signals and test system performance. By training the noise filtering network and the main network separately using these specific frame structures, time-varying noise and inherent nonlinearities can be trained and balanced separately, resulting in higher stability, faster convergence, and smaller errors.

[0048] Specifically, in this embodiment, the reference frame is a known modulation signal (such as QPSK / 16QAM) agreed upon with the transmitting end. During the training of the main network, the reference frame is processed within the main network (the noise filtering network is disabled). Based on the error relationship between the demodulated signal output by the neural network and the known reference frame signal sequence, the weight coefficients of the nodes in the main network are adjusted to complete the training of the nonlinear equalization of the main network. The interference frame shares the same information sequence as the reference frame; that is, the interference frame is also a known modulation signal (such as QPSK / 16QAM) agreed upon with the transmitting end. During the training of the noise filtering network, the interference frame is processed within the overall neural network (the noise filtering network is enabled). Based on the error relationship between the demodulated signal output by the neural network and the known reference frame signal sequence, the weight coefficients of the nodes in the noise filtering network are adjusted to complete the training of the noise filtering network. This allows the noise filtering network to transform the amplitude probability distribution of the interference frame at different times to the same amplitude probability distribution as the reference frame, filtering out time-varying noise. The test frame is the modulated signal (such as QPSK / 16QAM) corresponding to the random service signal to be transmitted, used for service signal transmission and testing system performance. The test frame is filtered by a noise filtering network and then nonlinearly equalized by the main network to compensate for signal transmission impairments.

[0049] In practical applications, the reference frame is received only once at the receiving end during system initialization, while interference frames and test frames are received cyclically after the reference frame (i.e., the reference frame is sent only once at the sending end during system initialization, while interference frames and test frames are sent cyclically after the reference frame). For example, during system initialization, the receiving end receives a reference frame once, which is used to train the main network. After the main network converges, the coefficients of each layer's nodes are fixed, and no more reference frames are received for training. After the reference frame, interference frames are received, which are used to train the noise filtering network, enabling it to transform the distribution of interference frames at different times to the reference frame, filtering out time-varying noise. After the interference frames, test frames are received. These test frames are filtered by the noise filtering network and then nonlinearly equalized by the main network to compensate for signal transmission impairments. The nonlinearly equalized received signal is then sent to the decoding module to output the decoded data. Afterward, interference frames and test frames will continue to be received cyclically for real-time adjustment of the time-varying noise filtering network parameters and for equalization of the random service signals to be carried.

[0050] In this embodiment, the typical length ratio of the reference frame, interference frame, and test frame can be 3:3:7. For example, taking 100Gbaud 16QAM as an example, the frame length (the sum of the lengths of the interference frame and the test frame) can be 10,000 symbols. Then, a reference frame of 3,000 symbols (30ns) is sent at a time for the convergence of the weight coefficients of each node in the main network. The period of the interference frame and the test frame is 100ns, corresponding to an interference frame length of 3,000 symbols (30ns) and a test frame length of 7,000 symbols (70ns). They are sent cyclically for real-time adjustment of time-varying noise filtering network parameters and equalization and demodulation of the service signals to be carried. However, in practical applications, the length ratio of the reference frame and the test frame can be adjusted accordingly based on the rate and magnitude of change of the time-varying noise, but it is generally not greater than 5:5, otherwise it will affect the total transmission capacity of the system.

[0051] Further, referring to Figure 5, as an optional implementation, the noise filtering network in this embodiment includes two signal input terminals: a first input terminal and a second input terminal. The signal input to the first input terminal is the reference frame (i.e., the original training signal) received by the receiver, which has the original reference amplitude and probability distribution D1; the signal input to the second input terminal is the interference frame (i.e., the training signal at the time of testing) or the test frame (i.e., the service signal to be equalized and decoded at the time of testing) received by the receiver. Using the interference frame as the input signal to the second input terminal can achieve the training convergence of the coefficients of each node in the noise filtering network, that is, the amplitude and probability distribution D1 of the training signal at the time of testing... X The signal is converted to the original reference amplitude and probability distribution D1 to filter out time-varying nonlinearity, amplitude, DC bias, and other noise. When the test frame is used as the input signal of the second input terminal, the coefficients of each node of the noise filtering network remain unchanged from the weights after training and convergence using the interference frame at the same time. At this time, the amplitude and probability distribution D1 of the test frame (i.e., the service signal at the time of the test) can be converted to the original reference amplitude and probability distribution D1. X The signal is converted to the original reference amplitude and probability distribution D1 to filter out time-varying nonlinearity, amplitude, DC bias and other noises; the test frame processed by the noise filtering network can be sent to the main network for static nonlinear equalization.

[0052] As shown in Figure 5, the noise filtering network includes two parallel and independent conventional neural networks. Each conventional neural network contains an activation layer with nonlinear activation neurons for time-varying nonlinear noise equalization. The inputs of both parallel and independent conventional neural networks are connected to the interference frame / test frame at the second input terminal. In practical applications, the interference frame / test frame can be copied twice and input to the inputs of the two parallel and independent conventional neural networks respectively. The output signal of one conventional neural network is connected to the reference frame (i.e., the original training signal) at the first input terminal via a multiplier to eliminate amplitude variations caused by the time-varying amplification gain and modulator modulation point drift in the optical fiber transmission system. The output signal of the other conventional neural network is connected to the reference frame (i.e., the original training signal) at the first input terminal via an adder to eliminate DC bias variations caused by the time-varying amplification gain and modulator modulation point drift in the optical fiber transmission system. As shown in Figure 5, the overall noise filtering network outputs a noise-filtered signal φ. out It can be input into the main network for static nonlinear equilibrium.

[0053] As can be seen from the above, the noise filtering network in this embodiment consists of two parallel and independent conventional neural networks (as shown in Figure 5). The nonlinear activation neurons in the activation layers of the two neural networks can perform a nonlinear inverse transform on the received test frame signal and multiply it by the corresponding weight coefficients to achieve equalization compensation for residual time-varying nonlinearity. At the same time, the test frame is multiplied by one of the neural networks (the neural network on the left in Figure 5) with the received reference frame signal to track and compensate for time-varying amplitude noise in the optical fiber transmission system; and is added by the other neural network (the neural network on the right in Figure 5) with the received reference frame signal to track and compensate for time-varying DC bias noise in the optical fiber transmission system. Thus, the residual, time-varying nonlinearity, amplitude, and DC bias noise in the test frame signal have all been compensated.

[0054] Furthermore, as shown in Figure 6, in an optical communication system, due to time-varying noise, the signal exhibits different distributions at different times, as shown in Figure 6 at times t0, t1, and t2. In this embodiment, the noise filtering network shown in Figure 5 is used to train and converge the weights of the neural nodes in each layer of the network based on the error of the main network output signal. When the error converges to a threshold, the amplitude and probability distribution of the training signal (interference frame) at the current receiving end at the measured time are transformed to the same distribution as the original training signal (reference frame), i.e., the distributions at times t1, t2, ..., t2 are transformed. nThe amplitude and probability distribution of signals at different times are transformed to the amplitude and probability distribution of the signal at time t0, thereby filtering out time-varying noise. Then, the main network is used to perform nonlinear equalization processing on the signal with filtered time-varying noise to further eliminate the effects of static nonlinearity. Thus, both time-varying noise and static nonlinearity in the optical fiber transmission system are well compensated. This embodiment has good overall noise resistance and low algorithm complexity, meeting the needs of practical applications.

[0055] Further, referring to Figure 7, as an optional implementation, in this embodiment, the noise filtering network and the main network are trained separately based on the received specific structure frames, and nonlinear equalization is performed on the test frames, including:

[0056] S11. As shown in Figure 8, after receiving the reference frame (reference frame t0 in Figure 8), the reference frame is input into the main network. The main network is trained using the reference frame until the main network converges and the node weight coefficients in the network remain unchanged.

[0057] S12. As shown in Figure 8, after receiving the interference frame (interference frame t1 in Figure 8), the interference frame and the aforementioned received reference frame (reference frame t0 in Figure 8) are input into the noise filtering network. The noise filtering network outputs a signal with a transformed distribution (interference frame with the same distribution as the reference frame in Figure 8), which is input into the main network. The performance of the main network output signal is monitored, and the node weight coefficients of the noise filtering network are adjusted based on the error of the main network output signal. When the error of the main network output signal is minimized, the training of the noise filtering network is completed, and it is determined that the noise filtering network has converged. The node weight coefficients of the noise filtering network remain unchanged.

[0058] S13. As shown in Figure 8, after receiving the test frame (test frame t2 in Figure 8), the test frame and the aforementioned received reference frame (reference frame t0 in Figure 8) are input into the noise filtering network. The distribution transformation of each node in the noise filtering network is performed to filter out time-varying noise and output the noise-filtered signal (as shown in Figure 8, the output distribution is the same as the reference frame).

[0059] S14. As shown in Figure 8, the noise-filtered signal is input into the main network to further equalize the static nonlinearity, thereby filtering out constant nonlinear noise.

[0060] S15. Continue to receive interference frames and test frames in a loop, repeat steps S12 to S14, and perform training and convergence of the noise filtering network in a loop, as well as filter out time-varying noise and static nonlinear equalization of the test frames.

[0061] Understandably, the above steps complete the training of the noise filtering network and the main network, as well as the nonlinear equalization of the test frames.

[0062] To better understand the training process of the noise filtering network and the main network, as well as the nonlinear equalization of the test frames, the specific steps described above are explained in detail below:

[0063] 1. The transmitting end first sends a reference frame signal y(n) for training and convergence of the weight coefficients of each network node in the main network. The reference frame signal y(n) is a known modulation signal (such as QPSK / 16QAM) agreed upon between the transmitting and receiving devices. It undergoes photoelectric conversion via an optoelectronic modulator and is transmitted through optical fiber. At the receiving end, it is photoelectrically detected by a coherent receiver and then undergoes a series of linear equalization processes as shown in Figure 1 in the receiver's DSP, outputting the reference frame signal x to be nonlinearly equalized at the receiving end. ref .

[0064] With the noise filtering network disabled, the reference frame signal x at the receiver... ref The input is only fed into the main network, and the main network is trained using reference frames until the main network converges. The node weight coefficients in the network remain unchanged.

[0065] The equivalent transfer function of the main network is denoted as H. main Then the reference frame signal x ref The signal after passing through the main network is denoted as H. main {x ref , D1}, where D1 is the reference frame signal x ref Over a period of time, the amplitude and probability distribution at the two-dimensional constellation points reflect the changes in signal transmission probability and system nonlinearity, crosstalk, bias, amplitude, etc. (as shown in Figure 6, which illustrates the changes in amplitude and probability distribution of in-phase signals in 16QAM modulation due to time-varying impairments). The main network is trained using the following model parameters that minimize the conventional error function to adjust the node weight coefficients:

[0066] In equation (1), n ​​is the nth symbol, N is the total length of the reference frame sequence, and n = 1, 2, ..., N. When equation (1) satisfies that the MSE (Minimum Mean Square Error) is less than the threshold, it indicates that the main network has converged and that the coefficient distribution is optimal for the distribution D1 at the time of reference frame transmission. At this point, the node weight coefficients in the main network remain unchanged and are no longer adjusted.

[0067] 2. The transmitting end then sends an interference frame signal y′(n) for training and convergence of the weight coefficients of each network node in the noise filtering network. The interference frame signal y′(n) is identical to the reference frame signal y(n), being a known modulation signal (such as QPSK / 16QAM) agreed upon between the transmitting and receiving devices; that is, y′(n) equals y(n). Photoelectric conversion is achieved through an optoelectronic modulator and transmitted in optical fiber. At the receiving end, photoelectric detection is performed by a coherent receiver, and the signal undergoes a series of linear equalization processes as shown in Figure 1 in the DSP at the receiving end, outputting the interference frame signal x to be nonlinearly equalized at the receiving end. noisy .

[0068] Understandably, due to time-varying noise, the signal distribution varies at different times. Interference frame x is received. noisy Afterwards, although the interfering frame x noisy With reference frame x ref They have exactly the same data to send, but

[0069] Due to the influence of time-varying noise, x noisy Distribution Deviating from the reference frame distribution D1, it is directly input into the main network H. main Therefore, performance is limited. Thus, as shown in Figure 5, the received interference frame signal x can be... noisy The signal is copied into two copies and used as the input signals of two independent parallel neural networks in the noise filtering network for equalization processing (as shown in Figure 5). The outputs of the two independent parallel neural networks are then processed by multipliers and adders and compared with the reference frame signal x mentioned in equation (1) above. ref After multiplication and addition, the output of the noise filtering network is the noise-filtered signal, which can be passed to the main network for static nonlinear equalization.

[0070] Specifically, assuming the equivalent transfer function of the noise filtering network is H sub Its output is a noise-filtered signal H. sub (x noisy x ref The processing of the noise filtering network can be considered as adjusting the coefficients of each node in the network to filter out the interference frame x at another time. noisy The distribution inverse transformation is applied to the original reference frame x. ref The time frame changes, and the original reference frame x is used at this point. ref Even with the node coefficients processed at each time step, a good balancing effect can still be achieved. Therefore, during the training process of the noise-filtering network, the aforementioned noise-filtering signal H is used. sub (x noisy x ref The signal is transmitted to the main network, while ensuring that the coefficients of each node in the main network remain unchanged, thus obtaining the output signal H. main (Hsub (x noisy x ref Furthermore, the noise filtering subnetwork H is adjusted using the following conventional formula for MSE. sub Weight coefficients of each node:

[0071] When equation (2) satisfies that MSE is less than the threshold, the output signal H of the noise filtering subnetwork is... sub (x noisy x ref The distribution of the noise filtering network is approximately the same as the distribution of the reference frame D1, which means that the noise filtering network has completed training and convergence.

[0072] 3. The transmitting end then sends a test frame signal. This test frame signal is the modulated signal (such as QPSK / 16QAM) corresponding to the random service signal to be transmitted by the equipment, used for service signal transmission and reception detection. This test frame signal undergoes photoelectric conversion via an optoelectronic modulator and is transmitted through optical fiber. At the receiving end, it is photoelectrically detected by a coherent receiver and then undergoes a series of linear equalization processes as shown in Figure 1 in the receiving end's DSP, outputting the test frame signal x to be nonlinearly equalized at the receiving end. test .

[0073] Test frame signal x at the receiving end test Within a certain time period, it is assumed that the amplitude and probability distribution of the interfering frame are the same as those of the previous moment. Before equalizing the test frame at the receiving end, the aforementioned receiving end reference frame signal x is first divided into G segments (G can be an integer or a non-integer). ref The preceding and following frames are concatenated in the DSP's memory to form a segment that is connected to the received test frame x. test The same length of reference frame signal sequence x reef Next, the test frame x from the receiving end... test The signal is copied into two copies and input into two independent parallel neural networks of the noise filtering network (as shown in Figure 5). The outputs of the two independent parallel neural networks of the noise filtering network are multiplied and added by a multiplier and an adder, and then combined with the previously concatenated reference frame signal sequence x. ref After calculation and processing, a signal is obtained that has been filtered out of time-varying amplitude, DC bias, and nonlinear noise, and has the same characteristics as the original reference frame x. ref The amplitude and probability distribution D1 are the same at the same time. Finally, the signal output from the noise filtering network is input into the main network to achieve static nonlinear noise equalization of the signal under the D1 distribution. At this point, the service signal carried by the test frame has completed nonlinear equalization processing and can be output to the subsequent decoding module of the DSP for signal demodulation (decoding).

[0074] 4. After that, the transmitting end will continue to send interference frames and test frames in a loop. After receiving the interference frames and test frames, the receiving end repeats steps 2 and 3 above to train the noise filtering network to converge and track, and to filter out time-varying noise and static nonlinear equalization on the test frames.

[0075] As can be seen from the above, in this embodiment, by training the noise filtering network and the main network separately using specific structure frames, time-varying noise and inherent nonlinearity can be trained and equalized separately, thereby achieving higher stability, faster convergence speed, and smaller error. Furthermore, the trained noise filtering network and the main network can be used to equalize the time-varying impairments and static nonlinearities in the system, effectively filtering out time-varying noise and constant nonlinear noise. This solves the problem of large convergence error and poor generalization performance of traditional nonlinear equalization caused by various time-varying impairments in high-speed, high-order modulation, and low signal-to-noise ratio optical transmission systems. The overall noise resistance is good and the algorithm complexity is low, meeting the needs of practical applications.

[0076] Example 2

[0077] It is understandable that current structural designs for nonlinear neural network equalizers are based on blind manual tuning. For the varying degrees of nonlinearity present in fiber optic transmission systems, they cannot adapt to different code patterns and varying transmit / receive / input optical power in different scenarios to achieve optimal performance and complexity design, resulting in over-design and excessive complexity. Therefore, in order to be applicable to systems with varying degrees of nonlinearity and avoid the high complexity, high power consumption, and high latency caused by over-design of the nonlinear equalizer, the second embodiment further includes: initializing the noise filtering network and the main network using a clustering coarse-tuning method.

[0078] Referring to Figure 9, which is a schematic diagram of an optical transmission system applying the nonlinear equalization method of this application in a second embodiment, as shown in Figure 9, the technical solution provided in the second embodiment can be used to initialize the noise filtering network and the main network using a clustering coarse-tuning method. Specifically, in this embodiment, the clustering coarse-tuning method is as follows: the digital signal obtained after linear equalization is clustered to obtain the degree of nonlinear deformation of the constellation diagram; the coarse initial setting parameters of the corresponding network structure are obtained according to the degree of nonlinear deformation of the constellation diagram, and the noise filtering network and the main network are initialized according to these parameters.

[0079] Compared to existing methods that manually and blindly tune the nonlinear neural network equalizer structure, the clustering coarse-tuning initialization scheme can adaptively and automatically initialize the noise filtering network and main network for different degrees of nonlinearity in different optical transmission systems. Furthermore, it can reduce complexity, energy waste, and processing latency while maintaining equalization performance. Referring to Figure 10, which compares the network structure settings using the clustering coarse-tuning method with existing methods under different nonlinearity levels, in fiber optic transmission systems, when nonlinearity is low, the clustering coarse-tuning method of this embodiment can optimize the neural network structure, reducing the number of nodes and network layers, and controlling complexity. When nonlinearity is high, the clustering coarse-tuning method of this embodiment can adaptively set the neural network structure, appropriately increasing the number of nodes and network layers. In contrast, the traditional method of manually setting the neural network structure requires reserving sufficient layers and nodes regardless of the nonlinearity level, resulting in an overly complex neural network structure. Referring again to Figure 11, which compares the performance and complexity benefits of the clustering coarse-tuning method with existing methods. As shown in Figure 11, taking a 40Gbad PM-64QAM BTB transmission system as an example, different transmission nonlinearities are obtained by adjusting the modulation depth of the modulator. Measurements show that when the system nonlinearity coefficient is 0.464, the initial network structure of the main network generated using the clustering coarse-tuning method in this embodiment is (57, 46, 46, 1), meaning there are four layers of neural networks, with each layer (1-4) having 57, 46, 46, and 1 neural nodes respectively. When the system nonlinearity coefficient is 0.2, the initial network structure of the main network is (38, 33, 33, 1). While the traditional method of manually setting the neural network structure can also achieve a single network structure of (57, 46, 46, 1) by reserving sufficient complexity, resulting in better balanced performance, this method struggles to achieve the optimal balance between performance and complexity when the system has uncertain or time-varying nonlinear impairments. Therefore, when the nonlinearity coefficient is 0.2, this method can adaptively adapt to the system's nonlinearity and achieve a complexity reduction of over 40%.

[0080] It should be noted that the initialization settings included in this embodiment are typically completed before the noise filtering network and the main network are trained and used, i.e., during the network structure construction phase. However, in practical applications, these initialization settings can also be applied to noise filtering networks and the main network that have already been trained or built, performing re-initialization settings, i.e., during the network usage phase. In other words, these initialization settings can be performed at different stages according to actual application needs; this embodiment is merely an example and does not impose specific limitations.

[0081] Further, referring to Figure 12, in one embodiment, the initialization settings for the noise filtering network and the main network using a clustering coarse-tuning method include:

[0082] S01. Obtain the signal sequence after linear equalization.

[0083] By using a pre-processing digital signal algorithm, a signal sequence after linear equalization can be obtained, which is the complex-valued signal after linear impairment compensation. The compensated complex-valued signal is expressed as: x(t)=[x(1),x(2),...,x(t)] =[I(1)+Q(1)i,I(2)+Q(2)i,...,I(t)+Q(t)i]=I(t)+Q(t)i;

[0084] Where x(t) is the original complex-valued symbol sequence, and I(t) and Q(t) are the real and imaginary parts of the complex-valued symbol, respectively. Due to the nonlinearity present in optical transmission systems, conventional linear equalization cannot compensate for this nonlinearity, resulting in issues such as constellation diagram rotation or inconsistent distances between constellation points within the inner and outer rings of the signal after linear equalization.

[0085] S02. Cluster the signal sequence after linear equalization to obtain A received signal clusters that deviate from the ideal modulation constellation point A-QAM signal and their central constellation points; take the vector average of the central constellation points of the A received signal clusters to obtain the optimal decision threshold under nonlinear conditions.

[0086] For example, a density-based unsupervised machine learning algorithm can be used to cluster I(t) and Q(t) to obtain A received signal clusters of A-QAM signals that deviate from the ideal modulation constellation point and their central constellation points as: Rx_QAM (Center) ={Rx_QAM C1 Rx_QAM C2 ,….,Rx_QAM CA};

[0087] Where A is a positive integer representing the modulation order, such as A = 32, which represents a 32QAM signal; A = 64, which represents a 64QAM signal. A clustering algorithm is used to obtain A clusters containing transmission noise, each corresponding to the demodulated signal at the receiver for each constellation point of the A-QAM signal. Taking the vector average of the center points of the A received signal clusters yields the optimal decision threshold for the nonlinear case: D_opti_QAM a =(Rx_QAM Ca +Rx_QAM Ca+1 ) / 2 D_opti_QAM={D_opti_QAM1,D_opti_QAM2,...,D_opti_QAM A-1} D_opti_I=real(D_opti_QAM), D_opti_Q=imag(D_opti_QAM) D_opti_I={real(D_opti_QAM1),real(D_opti_QAM2)...,real(D_opti_QAM A-1 )} D_opti_Q={imag(D_opti_QAM1),imag(D_opti_QAM2)...,imag(D_opti_QAM A-1 )

[0088] Where a belongs to {1,2,…A-1}.

[0089] S03. Obtain the nonlinear measurement factor by comparing the optimal decision threshold with the ideal decision threshold.

[0090] For a standard A-QAM signal, there are sqrt(A) constellation points on I and Q respectively. The ideal decision threshold corresponding to the standard constellation point distribution is: I(Q)=-sqrt(A)+1:2:sqrt(A)-1,QAM_A=I+1j*Q D_thero_I(D_thero_Q)=-sqrt(A)+2:2:sqrt(A)-2;

[0091] Where -sqrt(A)+1:2:sqrt(A)-1 represents the set of all values ​​from -sqrt(A)+1 to sqrt(A)-1, with an interval of 2. For example, for 16QAM, the amplitudes of constellation points in the in-phase and orthogonal directions are I(Q) = -sqrt(16)+1:2:sqrt(16)-1, which is the matrix [-3,-1,1,3]; and the corresponding decision points are D_thero_I(D_thero_Q) = [-2,0,2]. The grouping results obtained after clustering the constellation diagram, as well as the ideal decision threshold and the optimal decision threshold, are shown in Figure 13. Based on the difference between the optimal decision threshold and the ideal decision threshold in this scenario, the nonlinear measurement factor β is obtained. For example, the nonlinear measurement factor β can be obtained according to the following formula (3): β=0.5*abs((D_thero_I+D_thero_Q)-(D_opti_I+D_opti_Q))(3);

[0092] It reflects the current degree of nonlinear damage and is positively correlated with the magnitude of nonlinear damage. Different optical transmission systems have different degrees of nonlinearity, and the aforementioned nonlinearity measurement factor β can effectively measure the magnitude of nonlinearity.

[0093] S04. Based on the nonlinear measurement factor, the structure of the noise filtering network and the main network is coarsely adjusted to obtain the corresponding rough initial setting parameters.

[0094] It is understandable that increasing the complexity of a neural network equalizer will lead to overfitting after reaching a certain threshold, resulting in a decrease in equalization performance instead of an increase. Using a nonlinear metric β to coarsely adjust the structure of the noise filtering network and the main network, so that they are close to the point where the complexity benefit is high, can be used to provide a rough range and complexity boundary for subsequent optimization algorithms, thus helping to optimize.

[0095] For A-QAM signals, the default initial network layer number is K=3, and the number of nodes in the k-th layer is denoted as L. k Then the initial L = (L1, L2, L3) = (3, 2, 1). That is, the first layer has 3 neural network nodes, the second layer has 2 neural network nodes, and the third layer has 1 neural network node.

[0096] For example, in practical applications, since higher-order modulation formats and enhanced nonlinear effects require more neural network layers and nodes for processing, the following formula (4) can be used, based on the nonlinearity measure factor β for K and L. k Perform coarse adjustments to obtain rough initial settings parameters:

[0097] Where, round() is the rounding function, pk and pL are the optimization factors for the number of layers and nodes, respectively, usually taking values ​​of about 1 and 3. The number of layers that need to optimize the number of nodes is k = 1, 2, ..., K-1. The Kth layer is the last node of the multi-input single-output neural network, so the number of output network nodes is always 1. Assuming that according to equation (4), K_ opt =round(K(1+p) k *β)) The optimal number of layers K_ of the main network after nonlinear optimization is calculated. opt If you need to increase to 4 layers or more, then the formula is... On the right side, the default initial value is L = (L1, L2, L3, ..., L k )=(3,2,2, , ...,1).

[0098] In this embodiment, the main network, as a multi-input single-output (MIMO) neural network, always has only one node in its last layer. The denoising network, composed of two parallel and independent conventional neural networks, is also a multi-input multi-output (MIMO) neural network. The number of output nodes in its last layer should be the same as the number of input nodes in the main network. The number of input nodes (in the first layer) in the denoising network is the same as the number of input nodes in the main network. Therefore, for the two parallel and independent neural networks of the denoising network, the corresponding formulas are... On the right side, the default initial value is L = (L1, L2, L3, ..., L k )=(3,2,2,, ...,3).

[0099] For example, in practical applications, a method for coarse clustering of 16QAM format signals for the main network can be recorded in the coarse adjustment lookup table based on the nonlinear metric β (as shown in Table 1) as follows:

[0100] Table 1

[0101] Taking the first row of Table 1 as an example, the nonlinear coefficient is equal to 0.1, which is a network with virtually no nonlinearity. This can be addressed by increasing the number of nodes in each layer of the neural network while keeping the number of layers unchanged. That is, K_ is calculated according to equation (4). opt =3, and at the same time, L1 = sqrt(16)*3*1*(1+3*0.1) = 15; L2 = sqrt(16)*3*1*(1+2*0.1) = 10; L3 is the last node of the multi-input single-output neural network, and the number of output network nodes is always 1.

[0102] Similarly, taking a 16QAM format signal as an example, a coarse clustering adjustment is performed on two parallel and independent neural networks in the noise filtering network. Table 1 can then be updated to Table 2 as shown below:

[0103] Table 2

[0104] The noise filtering network contains two parallel and independent neural networks. Except for the number of output nodes of the last layer being the same as the number of input nodes of the first layer, the number of layers and the number of nodes in each layer are the same as the main network.

[0105] S05. Initialize the noise filtering network and the main network according to the corresponding rough initial setting parameters.

[0106] Example 3

[0107] Furthermore, to further prune network nodes with small contributions based on the initial settings, thereby reducing the complexity of the noise-filtering network and the main network while maintaining performance, the nonlinear equalization method for optical transmission systems in the third embodiment further includes: using an iterative pruning method to optimize and prune the initialized noise-filtering network and the main network to obtain optimized noise-filtering network and main network. Based on this, the optimized noise-filtering network and main network are used to perform nonlinear equalization on the test frame, and the equalized test frame is output.

[0108] Referring to Figure 14, which is a schematic diagram of an optical transmission system applying the third embodiment of the nonlinear equalization method of this application, as shown in Figure 14, the technical solution provided in the third embodiment can optimize and prune the noise filtering network and the main network after initialization by using an iterative pruning method based on the initial settings of cluster coarse adjustment. Specifically, this includes: first optimizing and pruning the noise filtering network using an iterative pruning method, and then optimizing and pruning the main network using an iterative pruning method; wherein, the two parallel independent conventional neural networks in the noise filtering network are treated as a whole for pruning. That is, each node in the two parallel independent conventional neural networks of the noise filtering network is regarded as a node in the same noise filtering network that may have the same importance, and pruning is performed simultaneously, without having to prune them separately or in a specific order.

[0109] Understandably, while it's possible to prune network structures using neural network pruning to adaptively reduce complexity, the initial network structure in existing technologies is still manually determined. Traditional pruning schemes require traversing a huge number of pruning options, resulting in high algorithm complexity and long processing time. Therefore, this embodiment combines a clustering-based coarse-tuning initialization scheme with an iterative pruning scheme to optimize the pruning of both the noise filtering network and the main network. This significantly reduces the number of iterative traversals, resulting in lower algorithm complexity, shorter processing time, and lower energy consumption.

[0110] Furthermore, in this embodiment, when optimizing and pruning the noise filtering network using an iterative pruning method, the time-varying nature of the weight coefficients of each node is used as the pruning strategy to determine the priority of each node and whether it is pruned; when optimizing and pruning the main network using an iterative pruning method, a comprehensive evaluation of network complexity and balance performance is used as the pruning strategy to determine the priority of each node and whether it is pruned.

[0111] Understandably, traditional pruning schemes use bit error rate (BER) as the pruning strategy (i.e., selecting the neural network with the lowest BER as the optimal network structure after pruning, assuming that unpruned nodes have higher priority and importance for signal nonlinearity equalization compared to other pruned nodes). However, in practical applications, for noise filtering networks used to remove noise, the importance of each node should be reflected by the time-varying nature of its coefficients, rather than the BER. Therefore, this embodiment proposes a new pruning strategy suitable for noise filtering networks, determining the priority of a node and whether it should be pruned based on the time-varying nature of its weight coefficients, thus achieving more reasonable and high-quality optimization pruning of the noise filtering network. Similarly, for the main network, this embodiment proposes using a comprehensive evaluation of network complexity and equalization performance as the pruning strategy to determine the priority of each node and whether it should be pruned. Compared to the traditional BER-based scheme, this approach more reasonably simplifies the complexity of the main network and improves the efficiency and quality of designing and debugging the main network structure.

[0112] For example, referring to Figure 15, as an optional implementation, in this embodiment, an iterative pruning method is used to optimize and prune the initialized noise filtering network and the main network to obtain optimized noise filtering network and main network, including:

[0113] S31. Keeping the main network unchanged, generate S alternative pruning denoising networks for pruning the denoising network through the pruning strategy generator.

[0114] Specifically, the process begins by pruning different nodes in the noise filtering network, while keeping the main network unchanged. The two parallel, independent conventional neural networks within the noise filtering network are treated as a single entity. This entire noise filtering network is then input into a pruning policy generator. This generator randomly removes any node from any layer of the noise filtering network, generating a candidate pruned noise filtering network. This process is repeated, pruning different nodes sequentially, resulting in a maximum of S candidate pruned noise filtering networks. Here, S equals the sum of the number of nodes in the two independent neural networks of the original noise filtering network before pruning.

[0115] S32. For each candidate pruning and noise filtering network, perform M training convergence cycles to obtain the node weight coefficients of the noise filtering network after each training convergence. Based on node weight coefficients Calculate the time-varying characteristic coefficients α for each candidate pruning and noise filtering network. s Using the time-varying characteristic coefficient α s The clipping performance of each alternative clipping and noise filtering network is evaluated.

[0116] Specifically, in practical applications, the interference frame signal can be cyclically transmitted M times at the transmitting end, and the interference frames x before nonlinear equalization can be obtained by detection and processing at the receiving end. noisy ; Using M groups of interference frames x before nonlinear equalization noisy For each candidate pruning and denoising network, train and update the coefficients of each node of the denoising network M times until convergence. After each training iteration, record the weight coefficients of each node of the candidate pruning and denoising network. Where m = 1, 2, ..., M; ks represents the k-th neuron node in the s-th candidate pruning and denoising network, and s = 1, 2, ..., S represents the s-th candidate pruning and denoising network.

[0117] Then, according to The characteristic coefficient α of the time-varying characteristics can be calculated. s The calculation formula is as follows:

[0118] In the formula, the `rmse` function represents the root mean square error (RMSE) of the weight coefficients obtained for the `ks`-th node after `m` training iterations, and the `mean` function represents the average of the RMSEs of the weight coefficients of all nodes in the `s`-th candidate pruning and denoising network. Following the above method, the time-varying characteristic coefficients α corresponding to the S candidate pruning and denoising networks can be obtained. s .

[0119] Finally, the time-varying characteristic coefficient α is used. s The pruning performance of each alternative pruning and noise filtering network is evaluated, i.e., α s The larger the value, the faster the weight coefficients of the alternative pruning and denoising network change, and the greater the contribution of the alternative pruning and denoising network to time-varying noise suppression.

[0120] S33. Select the characteristic coefficient α of the time-varying characteristics. s The largest candidate pruning and noise filtering network is used as the output of the pruned noise filtering network. This can be understood as the selected set of time-varying characteristic coefficients α... s The most suitable alternative pruning noise filtering network can be considered as the pruned noise filtering network that meets the performance requirements.

[0121] S34. Take the selected candidate pruning and noise filtering networks from the previous step as new networks to be pruned and input them into the pruning strategy generator. Repeat the operations of S31 to S33 until further pruning will result in α. s The value is less than a certain threshold (preferably α in this embodiment). sA threshold of 0.05 indicates that all network nodes in the neural network to be pruned are highly important for suppressing time-varying impairments, and further pruning would lead to severe performance degradation of the denoising neural network. At this point, pruning is stopped, and the pruned output network is considered the best-performing pruned network, which can be used as the optimized denoising network, i.e., the optimal output of the denoising network.

[0122] After the above steps (S31-S34), the optimization and pruning of the noise filtering network is completed, and the optimized noise filtering network is obtained. The next step is to optimize and prune the main network.

[0123] S35. Keeping the noise filtering network unchanged, generate P alternative pruning main networks for main network pruning through the pruning strategy generator.

[0124] Specifically, different nodes of the main network can be pruned while the noise filtering network remains unchanged. The main network is then input into a pruning policy generator, which randomly removes any neural network node from any layer of the main network, generating a candidate pruned main network. This process is repeated to prune different nodes in the main network, resulting in at most P candidate pruned main networks. Here, P equals the sum of the number of nodes in the original main network before pruning.

[0125] S36. Perform a single-pass equalization process on each candidate pruning master network to obtain the network complexity MAC of the corresponding candidate pruning master network. main(sub) and the equilibrium performance evaluation value (MSE) after each equilibrium. val Based on network complexity MAC main(sub) and convergence evaluation value MSE val Calculate the overall evaluation value F of the main network, and use the overall evaluation value F to evaluate the pruning performance of the main network.

[0126] Specifically, in practical applications, a test frame signal can be sent once at the transmitting end and detected at the receiving end. The signal is then fed into the linear equalization processing of the DSP to obtain the test frame signal x to be nonlinearly equalized. test ; Test frame signal x test Duplicate the network P times and feed each copy into the converged noise filtering network and one of the P candidate pruning main networks for equalization. The network complexity MAC of each candidate pruning main network is... main(sub) and the equilibrium performance evaluation value (MSE) after each equilibrium. val These are represented by the following formulas (6) and (7), respectively:

[0127] Where MAC (the required number of multipliers and accumulations) represents the complexity of the overall network, and K and L in equation (6) are... k Here are the structural parameters of a fully connected network, where K is the number of network layers and L is the number of layers. k Let x be the number of nodes in the k-th layer. In equation (7), x eq,val x(n) is the signal sequence after network equalization. The mean square error is calculated by combining it with the decision value x(n), yielding the equalization performance evaluation value MSE. val via MSE val To evaluate the equalization performance. In equation (7), x(n) is x eq,val (n) The QAM signal decision value obtained by making a decision based on the decision value given by the ideal decision threshold formula. The ideal decision threshold formula is as follows: I(Q)=-sqrt(A)+1:2:sqrt(A)-1,QAM_A=I+1j*Q D_thero_I(D_thero_Q)=-sqrt(A)+2:2:sqrt(A)-2

[0128] For example, for a 16QAM signal, the I / Q modulation points are [-3, -1, 1, 3], and the I / Q decision values ​​are [-2, 0, 2]. When the signal x obtained by the nth equalization... eq,val When x(n) = -1.5 + 3j, the decision value x(n) is -1 + 3j.

[0129] Then, based on the network complexity MAC main(sub) and the balanced performance evaluation value MSE val The overall evaluation value F of the main network can be calculated using the following formula: F = MAC main(sub) *MSE val (8)

[0130] In this embodiment, a comprehensive evaluation value F based on network complexity and balance performance is used to evaluate the pruning performance of the main network. The smaller the F, the better the balance performance of the corresponding candidate pruning main network can be achieved with less complexity.

[0131] S37. Select the candidate pruning master network with the smallest overall evaluation value F as the output of the pruned master network.

[0132] S38. Input the selected candidate pruning master networks from the previous step into the pruning strategy generator as new networks to be pruned. Repeat the operations of S35 to S37 until the minimum F value is obtained, and further pruning would cause the F value to exceed a certain threshold (preferably F threshold is 1 in this embodiment). Stop pruning at this point. It is considered that further pruning would cause serious performance degradation. The final output candidate pruning master network is considered to be the best pruned master network considering both complexity and balanced performance, and it is used as the optimized master network, i.e., the best output of the master network.

[0133] After the above steps (S35~S38), the optimization and pruning of the main network is completed, and the optimized main network is obtained.

[0134] To better understand the overall flow of the third embodiment of the nonlinear equalization method for optical transmission systems in this application, the overall implementation process of the third embodiment will be illustrated below with reference to Figure 16, using a specific example. As shown in Figure 16, the nonlinear equalization method for optical transmission systems includes:

[0135] Step 100: Initialize the noise filtering network and the main network using a clustering coarse-tuning method: Cluster the digital signal obtained after linear equalization to obtain the degree of nonlinear deformation of the constellation diagram; obtain the coarse initial setting parameters of the corresponding network structure according to the degree of nonlinear deformation of the constellation diagram, and initialize the noise filtering network and the main network according to these parameters.

[0136] Step 200: Based on the received specific structure frames, train the noise filtering network and the main network separately: First, input the reference frame into the main network and train the main network using the reference frame until the main network converges and the node weight coefficients in the network remain unchanged; then input the interference frame and the reference frame into the noise filtering network and train the noise filtering network until the noise filtering network converges and the node weight coefficients in the network remain unchanged; then input the test frame and the reference frame into the noise filtering network, and filter out time-varying noise by performing distribution transformation on each node in the noise filtering network; then input the noise-filtered signal into the main network to further equalize the static nonlinearity; finally, continue to receive interference frames and test frames in a loop, and repeatedly train and converge the noise filtering network and filter out time-varying noise and equalize the static nonlinearity on the test frames.

[0137] Step 300: For the initialized noise filtering network and main network, an iterative pruning method is used to first optimize and prune the noise filtering network, and then an iterative pruning method is used to optimize and prune the main network. Specifically, the two parallel and independent conventional neural networks in the noise filtering network are treated as a whole for pruning. When optimizing and pruning the noise filtering network, the time-varying nature of the weight coefficients of each node is used as the pruning strategy to determine the priority of each node and whether it is pruned. When optimizing and pruning the main network, a comprehensive evaluation of network complexity and balance performance is used as the pruning strategy to determine the priority of each node and whether it is pruned.

[0138] Step 400: Use the pruned and optimized noise filtering network and the main network to perform nonlinear equalization on the test frame, and output the equalized test frame.

[0139] The following examples illustrate the pruning optimization effects of the above embodiments:

[0140] Taking a 40Gbad PM-64QAM BTB transmission system as an example, different transmission nonlinearities can be obtained by adjusting the modulation depth of the modulator. Measurements show that when the system nonlinearity coefficient is 0.464, the initial network structure parameters of the main network are set to (57, 46, 46, 1) using the clustering coarse-tuning method in this embodiment, and the two parallel independent neural network structures in the noise filtering network are (57, 46, 46, 57). After pruning according to the pruning optimization method in this example, the pruned main network structure is (21, 26, 20, 1), and the pruned noise filtering network structure is (21, 25, 21, 21), with a total complexity of 2577. Manually scanning and adjusting the network parameters to achieve the same performance as the pruned network structure, the unpruned network structure is (21, 23, 20, 1), and the noise filtering network is (21, 30, 30, 21), with a total complexity of 3123. In comparison, the main network and noise-filtering network optimized by pruning have a 17% lower complexity than the unpruned network; and the pruned main network and noise-filtering network have a 16% higher bit error rate performance compared to the existing single fully connected network.

[0141] Secondly, embodiments of the present invention also provide a nonlinear equalization device for an optical transmission system.

[0142] Example 4

[0143] In a fourth embodiment, a nonlinear equalization device for an optical transmission system includes: a noise filtering network for tracking and filtering time-varying noise; a main network for static nonlinear equalization; a training module for training the noise filtering network and the main network based on received specific structure frames; wherein the specific structure frames include reference frames, interference frames, and test frames, the reference frames are used for training the main network to achieve convergence of the weight coefficients of the main network, the interference frames and reference frames are used for training the noise filtering network to achieve real-time convergence of the noise filtering network, and the test frames are used to carry random service signals and test system performance; and an equalization processing module for performing nonlinear equalization on the test frames using the trained noise filtering network and main network, and outputting the equalized test frames.

[0144] As can be seen from the above, in this embodiment, the training module can use specific structure frames to train the noise filtering network and the main network separately, which can achieve separate training and equalization of time-varying noise and inherent nonlinearity, thereby achieving higher stability, faster convergence speed and smaller error. Furthermore, the equalization processing module can use the trained noise filtering network and the main network to equalize the time-varying impairments and static nonlinearities in the system separately, effectively filtering out time-varying noise and constant nonlinear noise. This solves the problem of large convergence error and poor generalization performance of traditional nonlinear equalization caused by various time-varying impairments in high-speed, high-order modulation, and low signal-to-noise ratio optical transmission systems. The overall noise resistance is good and the algorithm complexity is low, meeting the needs of practical applications.

[0145] Example 5

[0146] In the fifth embodiment, the nonlinear equalization device for the optical transmission system further includes a clustering coarse-tuning module, which is used to initialize the noise filtering network and the main network using a clustering coarse-tuning method. In this embodiment, the clustering coarse-tuning initialization scheme can adaptively and automatically initialize the noise filtering network and the main network for different degrees of nonlinearity in different optical transmission systems. This reduces complexity, energy consumption, and processing latency while ensuring algorithm performance.

[0147] Example 6

[0148] In the sixth embodiment, the nonlinear equalization device for the optical transmission system further includes a pruning optimization module, which optimizes and trims the initialized noise-filtering network and main network using an iterative pruning method to obtain optimized noise-filtering network and main network. Based on this, the equalization processing module is further used to perform nonlinear equalization on test frames using the optimized noise-filtering network and main network, and outputs the equalized test frames. In this embodiment, an initialization setting scheme based on clustering coarse tuning is combined with an iterative pruning strategy to achieve optimized trimming of the noise-filtering network and main network. Compared with the prior art, this embodiment can more reasonably simplify the complexity of the noise-filtering network and main network, and improve the efficiency and quality of designing and debugging the noise-filtering network and main network structure.

[0149] It should be noted that the various variations and specific examples in the foregoing method embodiments are also applicable to the device in this embodiment. Through the detailed description of the foregoing method, those skilled in the art can clearly understand the implementation method of the device in this embodiment. Therefore, for the sake of brevity, they will not be described in detail here.

Claims

1. A nonlinear equalization method for optical transmission systems, characterized in that, The method includes: Based on the received specific structure frames, the noise filtering network and the main network are trained separately. The noise filtering network is used to track and filter out time-varying noise, and the main network is used for static nonlinear equalization. The specific structure frames include reference frames, interference frames, and test frames. The reference frames are used to train the main network to achieve convergence of the weight coefficients of the main network. The interference frames and reference frames are used to train the noise filtering network to achieve real-time convergence of the noise filtering network. The test frames are used to carry random service signals and test the system performance. The trained noise filtering network and the main network are used to perform nonlinear equalization on the test frames, and the equalized test frames are output.

2. The nonlinear equalization method for optical transmission systems as described in claim 1, characterized in that: Both the reference frame and the interference frame are known modulation signals agreed upon with the transmitting end and have the same information sequence. The test frame is the modulation signal corresponding to the random service signal to be transmitted. Furthermore, the reference frame is received only once during system initialization, while the interference frame and the test frame are received cyclically after the reference frame.

3. The nonlinear equalization method for optical transmission systems as described in claim 1, characterized in that: The noise filtering network includes a first input terminal and a second input terminal. The first input terminal inputs a reference frame, and the second input terminal inputs an interference frame / test frame. The noise filtering network includes two parallel and independent conventional neural networks. Each conventional neural network contains an activation layer, and the nonlinear activation neurons in the activation layer are used for time-varying nonlinear noise equalization. The inputs of both conventional neural networks are connected to the interference frame / test frame at the second input terminal; the output signal of one conventional neural network is connected to the reference frame at the first input terminal through a multiplier to eliminate amplitude changes; the output signal of the other conventional neural network is connected to the reference frame at the first input terminal through an adder to eliminate DC bias changes.

4. The nonlinear equalization method for optical transmission systems as described in claim 3, characterized in that, The noise filtering network and the main network are trained separately based on the received frames with specific structures, and nonlinear equalization is performed on the test frames, including: After receiving the reference frame, the reference frame is input into the main network, and the main network is trained using the reference frame until the main network converges and the node weight coefficients in the network remain unchanged. After receiving the interference frame, the interference frame and the reference frame are input into the noise filtering network. The noise filtering network outputs a signal with a transformed distribution, which is then input into the main network. The node weight coefficients of the noise filtering network are adjusted based on the error of the main network output signal. When the error of the main network output signal is minimized, the training of the noise filtering network is completed, and the noise filtering network is determined to have converged. The node weight coefficients of the noise filtering network remain unchanged. After receiving the test frame, the test frame and the reference frame are input into the noise filtering network. The distribution transformation of each node in the noise filtering network is performed to filter out time-varying noise and output the noise-filtered signal. The noise-filtered signal is input into the main network for static nonlinear equalization. The system continues to receive interference frames and test frames in a loop, and then trains and converges the noise filtering network in a loop, while filtering out time-varying noise and static nonlinear equalization from the test frames.

5. The nonlinear equalization method for optical transmission systems as described in claim 3, characterized in that, The nonlinear equalization method for optical transmission systems also includes initializing the noise filtering network and the main network using a clustering coarse-tuning approach. The cluster coarse adjustment method is as follows: cluster the digital signals obtained after linear equalization to obtain the degree of nonlinear deformation of the constellation diagram; Based on the degree of nonlinear deformation of the constellation diagram, obtain the rough initial setting parameters of the corresponding network structure, and initialize the noise filtering network and the main network according to these parameters.

6. The nonlinear equalization method for optical transmission systems as described in claim 5, characterized in that, The nonlinear equalization method for optical transmission systems further includes optimizing and pruning the initialized noise filtering network and main network using an iterative pruning approach. First, an iterative pruning method is used to optimize and prune the noise filtering network, and then an iterative pruning method is used to optimize and prune the main network. In this process, the two parallel and independent conventional neural networks in the noise filtering network are treated as a whole for pruning.

7. The nonlinear equalization method for optical transmission systems as described in claim 6, characterized in that: When optimizing and pruning the noise filtering network using an iterative pruning method, the time-varying nature of the weight coefficients of each node is used as the pruning strategy to determine the priority of each node and whether it should be pruned. When optimizing and pruning the main network using an iterative pruning method, the pruning strategy is based on a comprehensive evaluation of network complexity and balanced performance to determine the priority of each node and whether it should be pruned.

8. A nonlinear equalization device for an optical transmission system based on the method of any one of claims 1 to 7, characterized in that, The device includes: A noise filtering network is used to track and filter out time-varying noise; The main network is used for static nonlinear equilibrium. The training module is used to train the noise filtering network and the main network respectively based on the received specific structure frames; wherein, the specific structure frames include reference frames, interference frames and test frames, the reference frames are used for training the main network to achieve convergence of the weight coefficients of the main network, the interference frames and reference frames are used for training the noise filtering network to achieve real-time convergence of the noise filtering network, and the test frames are used to carry random service signals and test system performance; The equalization processing module is used to perform nonlinear equalization on the test frames using the trained noise filtering network and the main network, and output the equalized test frames.

9. The nonlinear equalization device for an optical transmission system as described in claim 8, characterized in that, The device also includes: The clustering coarse adjustment module is used to initialize the noise filtering network and the main network using a clustering coarse adjustment method. The clustering coarse adjustment method is as follows: cluster the digital signal obtained after linear equalization to obtain the degree of nonlinear deformation of the constellation diagram; obtain the coarse initial setting parameters of the corresponding network structure according to the degree of nonlinear deformation of the constellation diagram, and initialize the noise filtering network and the main network according to the parameters.

10. The nonlinear equalization device for an optical transmission system as described in claim 9, characterized in that, The device also includes: The pruning optimization module is used to optimize and trim the noise filtering network and the main network after initialization using an iterative pruning method, so as to obtain the optimized noise filtering network and the main network. The equalization processing module is also used to perform nonlinear equalization on the test frame using the optimized noise filtering network and the main network, and output the equalized test frame.

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