A high-speed optical communication system equalization method

Abstract

The present invention provides a high-speed optical communication system equalization method. The method constructs a neural network equalizer based on Volterra series, adopts mutual correlation learning to enhance a joint neural network, combines linear and nonlinear compensation, eliminates the need for an additional linear compensation module in the network, and enhances the overall compensation capability of the network. Through an additional enhanced mutual correlation learning layer, the neural network can better learn the second-order and third-order mutual correlation terms of the input signal, thereby strengthening the neural network's compensation capability for system nonlinearity. Through a high-order fully connected layer, high-order mutual correlation terms of the input signal are learned from low-order autocorrelation input signals. At the same time, a clustering algorithm is used in densely weighted areas in the network to reduce network complexity.

Description

Technical Field

[0001] The present invention relates to the field of optical communications, in particular to a high-speed optical fiber communication system with severe linear and nonlinear distortion. Background Art

[0002] The rapid growth of data traffic in the 5G era places higher demands on system communication capacity. However, in high-speed optical communication systems, as signal rates increase, inter-symbol interference (ISI) caused by components introduces destructive distortion, limiting increases in signal rates and transmission distances. To improve the transmission rate of communication systems and ensure reliable information transmission, equalizers are required at the receiving end to compensate for linear and nonlinear distortion in the system. Equalizers also face complexity limitations, making them difficult to implement in practical applications. When designing an equalizer, both performance and complexity must be considered. The Volterra equalizer, based on the Volterra series, is a common solution. It is used to compensate for linear and nonlinear distortion in systems. However, this equalizer has a significant drawback: its complexity increases exponentially with the order. Therefore, Volterra equalizers typically only reach third order, making them difficult to effectively equalize in higher-speed optical communication systems. In recent years, with the development of machine learning and neural networks, they have gradually been applied to equalizers. However, most equalizers based on neural networks have the disadvantage of high complexity. Traditional multi-layer fully connected neural networks have been proven to be very complex, but they cannot actually achieve good learning effects.

[0003] The present invention mainly designs a low-complexity neural network equalizer suitable for high-speed optical communication based on the Volterra series, to replace the traditional Volterra equalizer to achieve higher-speed information transmission without increasing complexity. The proposed neural network equalizer is based on the Volterra series, and its input and output ports and the number of neural network layers are designed. An additional enhanced cross-correlation learning layer is proposed. At the same time, the high-order fully connected layer contained in the neural network equalizer strengthens the nonlinear equalization capability of the network by converging low-order autocorrelation signals and processing them with nonlinear activation functions to learn higher-order signal cross-correlation terms, making the neural network more consistent with the Volterra series to achieve better equalization effect. Summary of the Invention

[0004] The present invention provides an equalizer based on cross-correlation learning enhanced joint neural network, which is arranged at the receiving end and is used to compensate for linear and nonlinear distortion in the system to achieve higher-speed information transmission with lower complexity.

[0005] The equalizer is implemented based on cross-correlation learning enhanced joint neural network.

[0006] In terms of mathematical model, the cross-correlation learning enhanced joint neural network modeling is mainly based on Volterra series, and its mathematical model is:

[0007]

[0008] φ i ={l1, l2, ..., l i |1≤l1,l2,...,l i ≤L3} where the first-order terms in the first row are the outputs of the first-order linear neural network, the second-order and third-order cross-correlation terms in the second row are output by the enhanced cross-correlation learning layer, and the second-order and third-order autocorrelation terms in the third row and some high-order cross-correlation terms in the fourth row are output by the high-order fully connected layer in the cross-correlation learning enhanced neural network. In the formula, δ(·) and wω(·) represent the Dirac function and weights determined by the neural network's autonomous learning, respectively.

[0009] In terms of implementation structure, the mutual correlation learning enhanced joint neural network is a joint neural network structure that combines a first-order linear neural network and a mutual correlation learning enhanced neural network.

[0010] The first-order linear neural network of the mutual correlation learning enhanced joint neural network includes a first-order linear input layer, a linear layer, and a linear output layer:

[0011] The first-order linear input layer takes the first-order autocorrelation signal of a specified length from the data set and transmits it to the linear layer;

[0012] The linear layer performs linear operations on the transmitted first-order autocorrelation signal to compensate for the linear distortion in the system;

[0013] The linear output layer passes the output result of the linear layer to the output end of the mutual correlation learning enhanced joint neural network, and linearly adds it to the learning result of the mutual correlation learning enhanced neural network for output; at the same time, the linear output layer also performs linear summation processing on the output signal and passes it to the third-order autocorrelation input layer of the mutual correlation learning enhanced neural network as the input signal.

[0014] The mutual correlation learning enhanced neural network of the mutual correlation learning enhanced joint neural network includes a third-order autocorrelation input layer, an enhanced mutual correlation learning layer, a high-order fully connected layer and an output layer:

[0015] The third-order autocorrelation input layer is connected to the first-order linear neural network. It takes the output signal of a specified length, squares the collected input signal, and performs cubic autocorrelation processing to simultaneously obtain the first, second, and third-order autocorrelation terms of the signal. At the same time, the target signal is sparsely dimensionalized and coded, making the overall system more suitable for subsequent enhanced cross-correlation learning and improving system performance.

[0016] The enhanced cross-correlation learning layer is based on a simplified factorization machine, and its mathematical model is as follows:

[0017]

[0018] The model includes a second-order cross-correlation term, and the model involves a complexity of n 2 , its computational complexity can be reduced by perfect square, and the simplified process is as follows

[0019]

[0020] After this process, the complexity is reduced from n 2 It is reduced to k*n, where k is a custom random parameter that can be changed as needed. However, this optimization step alone cannot be used for equalization in high-speed optical communication systems. As the transmission rate increases, the second-order Volterra equalizer can no longer effectively compensate. Therefore, the cross-correlation learning is further improved. Assuming that the input is a, b, and c, the output after the above second-order cross-correlation learning is y cross It should be a k-column matrix as follows:

[0021] y cross1 =[k 11 (ab+ac+bc), k 12 (ab+ac+bc), k 13 (ab+ac+bc), k 14 (ab+ac+bc)]

[0022] By adding y cross1 By multiplying the matrix elements with a random set of input items, we can get the third-order cross-correlation terms as follows:

[0023] y crosss =y cross1 *[k 21 (a+b+c), k 22 (a+b+c), k 23 (a+b+c), k 24 (a+b+c)]

[0024] Here, (ab+ac+bc)*(a+b+c) gives all the terms in the Volterra third-order term except the autocorrelation term. k2 is a random matrix of the same dimension as k1.

[0025] The high-order fully connected layer is a two-layer fully connected network structure. This layer is primarily used to supplement the missing first-order terms and second- and third-order autocorrelation terms in the enhanced mutual correlation learning layer. By combining low-order autocorrelation signals and processing them through a nonlinear activation function, it can autonomously learn some higher-order Volterra series, further improving the overall balancing ability of the network.

[0026] The clustering algorithm is used in the high-order fully connected layer to cluster the weight-dense areas. The process is as follows:

[0027] Outputting all weights as a set is represented as:

[0028] W=[w1,w2,...,w n ]

[0029] Randomly select a point from the set W as the initial cluster center C, then calculate the distance between other weights in W and the center C, record it as D, then calculate the probability of each weight being selected as the next cluster center, and finally select the sample point corresponding to the maximum probability value as the next center point. Repeat the above steps until the specified number of centers are selected. The mathematical model for calculating probability is as follows:

[0030]

[0031] The mathematical model of the output layer is as follows:

[0032] y=Softmax(y cross +yDNN)

[0033]

[0034] where y cross and y DNN They are the output results of the enhanced cross-correlation learning layer and the fully connected layer respectively. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The accompanying drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute a limitation of the present invention.

[0036] In the attached figure:

[0037] Figure 1 Schematic diagram of the overall model of the mutual correlation learning enhanced joint neural network in the present invention;

[0038] Figure 2 Schematic diagram of the cross-correlation learning enhanced neural network model in the present invention;

[0039] Figure 3 This is a comparison chart of the bit error rates of the present invention, the traditional Volterra equalizer, and the fully connected neural network. DETAILED DESCRIPTION

[0040] The technical methods in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. These embodiments are merely exemplary and are not intended to limit the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention. The specific embodiments of the present invention will be described below in conjunction with the accompanying drawings.

[0041] Embodiment 1:

[0042] The network model of the equalizer method based on cross-correlation learning enhanced joint neural network is as follows: Figure 1 As shown, it is divided into two parts: first-order linear neural network and cross-correlation learning enhanced neural network. Figure 1 The "enhanced mutual correlation learning" part is the mutual correlation learning enhanced neural network, the specific model is as follows Figure 2 shown.

[0043] The input layer of the model is a two-part neural network that learns from input data using input sequences of their respective lengths. The first-order linear neural network also performs dimensionality reduction on the results before sending them to the input of the cross-correlation learning-enhanced neural network. The target sequence target must first be sparsely dimensionalized and encoded, and the target signal must be converted into categorical features for learning. An example of this invention, as shown in Table 1, converts the PAM4 signal into a 4-bit binary sequence through sparse dimensionality reduction coding, facilitating feature learning by the neural network.

[0044] Table 1 Results of PAM4 after sparse dimensionality reduction coding

[0045]

[0046] The final overall output

[0047] y inal =y LP +y NLP

[0048] The first-order linear neural network is a single-layer fully connected neural network that uses the following linear activation function. The purpose of this network is to compensate for linear distortion in the system.

[0049] y Linear =x

[0050] Figure 2The mutual correlation learning enhancement neural network part in the joint neural network mainly includes a third-order autocorrelation input layer, an enhanced mutual correlation learning layer, a high-order fully connected layer, and an output layer.

[0051] The input signal of the third-order autocorrelation input layer is Figure 1 L in NLP The square and cubic autocorrelation of the signal of the segment is expressed as:

[0052] Input=[x(tL),...,x(t+L),x(tL) 2 ,...,x(t+L) 2 ,...,x(tL) 3 ,...,x(t+L) 3 ]

[0053] Example 2:

[0054] The enhanced cross-correlation learning layer only uses the first-order terms in the input layer, and then the second-order and third-order cross-correlations are learned in the enhanced cross-correlation learning network. The first step of the second-order cross-correlation uses perfect square to reduce the complexity. Its mathematical model is as follows:

[0055]

[0056] Where k is a custom parameter. Experiments have shown that the overall performance of the network can be changed by adjusting k. For ease of understanding, we assume that the input is a, b, and c. Assume that the input is a, b, and c. After the above second-order cross-correlation learning, the output is y. cross It should be a k-column matrix as follows:

[0057] y cross1 =[k 11 (ab+ac+bc), k 12 (ab+ac+bc), k 13 (ab+ac+bc), k 14 (ab+ac+bc)]

[0058] By adding y cross1 The third-order cross-correlation term can be obtained by multiplying the matrix elements with a random set of input items, as follows:

[0059] Y crosss =y cross1 *[k 21 (a+b+c),k 22 (a+b+c),k 23 (a+b+c), k 24 (a+b+c)]

[0060] Here, (ab+ac+bc)*(a+b+c) yields all Volterra third-order terms except the autocorrelation term. k2 is a random matrix of the same dimension as k1. In summary, the enhanced cross-correlation learning layer has the ability to learn the third-order cross-correlation of signals. This ability improves with increasing k and is also related to the number of neurons in the layer.

[0061] The high-order fully connected layer in the cross-correlation learning enhanced neural network adopts a two-layer fully connected structure. The main purpose is to make up for the missing signal autocorrelation terms in the feature cross layer. At the same time, experiments have shown that through nonlinear activation functions, this network structure can also learn some high-order cross-correlation terms, which is beneficial for compensating for the high-order nonlinear distortion problem that is difficult to solve in high-speed optical communication systems. The present invention uses a clustering algorithm at the connection between the input layer and the fully connected layer, and outputs all weights as a set represented as:

[0062] W=[w1,w2,...,w n ]

[0063] Randomly select a point from the set W as the initial cluster center C, then calculate the distance between other weights in W and the center C and record it as D, then calculate the probability of each weight being selected as the next cluster center, and finally select the sample point corresponding to the maximum probability value as the next center point, repeat the above steps until the specified number of centers are selected. The mathematical model for calculating probability is as follows

[0064]

[0065] Clustering is used to reduce the complexity of this layer. The principle is as follows:

[0066] When two weights are close, they can be roughly regarded as:

[0067] w i x i +w j x i ≈w′ i (x i +x j )

[0068] Through clustering processing, w i With w j Unified as w k At this point, the above equation can be considered to be true.

[0069] The activation function from the high-order fully connected layer and the enhanced cross-correlation learning layer to the output layer all uses the Softmax function, which is expressed as follows:

[0070]

[0071] Then the argmax function is used to output only one valid digit in order to comply with the sparse dimensionality reduction coding principle in Table 1.

[0072]

[0073] Example 3:

[0074] The rapid growth of data traffic in the 5G era is placing higher demands on system communication capacity. To meet these demands for high bandwidth and high speed, pulse amplitude modulation (PAM-4 and PAM-8) systems based on intensity modulation direct detection (IM / DD) have attracted significant attention due to their simple structure and low power consumption. However, as data rates and transmission distances increase, nonlinear and linear distortion in the channel seriously impacts system performance. Therefore, effectively compensating for this distortion is a critical issue.

[0075] In order to evaluate the compensation performance during the application of the present invention, a 120Gbps high-speed PAM4 communication system was built. The system realizes 5km PAM4 signal transmission at a rate of 120Gbps. A 200,000-length received signal is collected at the receiving end and the present invention is used to compensate for linear and nonlinear distortion in the system. In order to evaluate the performance and complexity of the present invention, a common third-order Volterra equalizer and a traditional fully connected neural network are used for control experiments. The performance is presented in the form of bit error rate, and the complexity comparison is compared by the number of multiplications used in a single round. The specific results of the bit error rate are as follows: Figure 3 As shown in the figure, "net" represents the neural network of the present invention, with the numbers in parentheses indicating the number of neurons in the input, hidden, and output layers. DDLMS, LE, and Volterra represent three standard equalization methods, respectively, and DNN represents a traditional fully connected neural network. The figure shows a bit error rate of 0.0038 (7% HD-FEC threshold). As can be seen in the figure, the networks of the present invention are located in the bottom three lines, and their performance is significantly better than that of the traditional third-order Volterra equalizer.

Claims

1. A high-speed optical communication system equalization method, characterized in that: Enhanced joint neural network implementation based on cross-correlation learning; The cross-correlation learning enhanced joint neural network includes: A first-order linear neural network, including a linear input layer, a linear layer, and a linear output layer, is used to compensate for linear distortion in the system and input the compensated signal into a cross-correlation learning enhanced neural network; The cross-correlation learning enhanced neural network is used to learn the cross-correlation information of signals and compensate for nonlinear distortion in the system. It includes: a third-order autocorrelation input layer, which reads the output of the first-order linear neural network, processes and outputs it, making the data easier to enhance cross-correlation learning; an enhanced cross-correlation learning layer, which learns high-order cross-correlation signals by operating on the first-order signals; a high-order fully connected layer, which processes signals of all orders and supplements the low-order autocorrelation items that may be missing in the enhanced cross-correlation learning layer, while using clustering to reduce complexity; and an output layer, which combines the results of the linear and nonlinear networks, predicts the probability of outputting each level of the signal, and outputs the item with the highest probability as the result. The third-order autocorrelation input layer is connected to the first-order linear neural network, reads the output of the first-order linear neural network and takes a signal sequence of a specified length, squares the collected input signal, and performs a cubic autocorrelation process to simultaneously obtain the first, second, and third-order autocorrelation terms of the signal. At the same time, the target signal is subjected to sparse dimensionality reduction coding processing, making the overall system more compatible with subsequent enhanced cross-correlation learning and improving system performance. The enhanced cross-correlation learning layer solves a simplified second-order cross-correlation operation on the original signal using a perfect square mathematical formula; the original signal is randomly summed and cross-correlated with the solved second-order cross-correlation signal again to learn and mine the majority of third-order cross-correlation terms at a deeper level; the missing third-order autocorrelation terms are supplemented by the high-order fully connected layer; The high-order fully connected layer performs nonlinear processing on the first-order, second-order and third-order autocorrelation terms of the input signal through a nonlinear activation function. The autocorrelation terms are merged and processed through a nonlinear activation function to form higher-order cross-correlation terms, thereby supplementing the low-order autocorrelation terms missing in the enhanced cross-correlation learning layer and improving the performance of the system. A clustering algorithm is used between the input layer with the densest weights and the first hidden layer to reduce the complexity of the network.

2. An electronic device, characterized in that: It includes a processor, a memory, a communication interface and a communication bus, wherein: A processor, configured to execute a program stored in the memory to implement the method steps described in claim 1; Memory, used to store computer programs and data; Communication interface, used for communication between electronic equipment and the outside world; Communication bus: used for communication between processors, memory and communication interfaces.

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