Nonlinear damage compensation method for modular division multiplexing communication system

Abstract

The invention relates to a nonlinear damage compensation method for a mode division multiplexing communication system, and belongs to the field of optical fiber communication. According to the invention, by capturing the signal features of the input data and performing sufficient feature serialization fusion processing on the input data, when the signal data at the current moment is processed, the preorder signal data information in the training data can be combined and utilized, that is, serialization feature fusion is performed on the signal data sequence; and the nonlinear interference relationship between the current signal and the preorder signal can be better represented. According to the method, the nonlinear model, with high randomness and complexity, of the orbital angular momentum mode division multiplexing system can be accurately fitted. The method has lower calculation complexity, and can efficiently recover data symbols transmitted in the mode division multiplexing system, thereby compensating device nonlinearity of the mode division multiplexing optical communication system, and solving the problem that the received signal reduction degree is not high enough due to random nonlinear damage in the orbital angular momentum mode division multiplexing system.

Description

Technical Field

[0001] The invention relates to a nonlinear damage compensation method for a mode division multiplexing communication system, and in particular to a mode division multiplexing emphasized direct detection PAM transmission nonlinear compensation method based on a Koopman probabilistic neural network, and belongs to the field of optical fiber communication. Background Art

[0002] In the intensity modulated direct detection system, the nonlinear damage caused by various optoelectronic devices (such as modulators, electronic amplifiers and photodetectors) severely limits the system performance and causes strong signal distortion. Especially in the orbital angular momentum mode division multiplexing system, the spatial light modulator used to generate the orbital angular momentum beam contains many nonlinear materials (such as liquid crystal, nonlinear polymers, photorefractive materials, etc.), which introduces serious nonlinear damage. Generally speaking, nonlinear damage can be mitigated by adjusting the operating parameters of the optoelectronic device, such as the output power of the electronic amplifier or the bias voltage of the modulator. However, these operations will lead to a decrease in the signal-to-noise ratio, resulting in system performance degradation. Therefore, using digital signal processing algorithms to equalize and compensate the signal has become another method to mitigate the nonlinear damage of the communication system, such as the Volterra series method, digital pre-distortion method and lookup table method. Digital signal processing algorithms mitigate nonlinear damage in optical fiber communication systems by fitting the nonlinear mathematical model of the system. However, there are two difficulties in the traditional digital signal processing algorithms in mitigating the nonlinear damage of devices in the orbital angular momentum mode division multiplexing system. First, when multiple optoelectronic devices work in an OAM mode-division multiplexing system, the nonlinearities of different devices will couple with each other, resulting in a high complexity of the overall nonlinear model of the system. Second, the mode coupling in the OAM mode-division multiplexing system also makes the nonlinear damage have a strong random characteristic. Therefore, it is difficult to mitigate the nonlinear damage in the OAM mode-division multiplexing system using traditional digital signal processing algorithms.

[0003] In recent years, machine learning has become a breakthrough in compensating for nonlinear damage in optical fiber communications. Machine learning algorithms can learn the nonlinear characteristics of the channel from the signal through training, and establish an accurate fitting model to compensate for the nonlinear damage of the system, including deep neural networks, convolutional neural networks, and long short-term memory networks. These algorithms can accurately fit complex nonlinear models and effectively compensate for nonlinear damage. However, most machine learning algorithms must learn nonlinear characteristics through training data sets. The strong random nonlinearity in the orbital angular momentum mode division multiplexing system makes the training data and the test data differ greatly, resulting in inaccurate model fitting. In addition, the computational complexity of most machine learning algorithms is high and they are not suitable for high-speed optical fiber communications.

[0004] Based on the nonlinear damage mechanism of system components, the present invention proposes a nonlinear equalization technology for a mode division multiplexing system based on a Koopman probabilistic neural network. The technology can realize the characteristics of arbitrary nonlinear approximation and compensate for the nonlinearity of the mode division multiplexing system. Summary of the invention

[0005] In order to solve the problem that the random nonlinear damage in the orbital angular momentum mode division multiplexing system leads to insufficient restoration of the received signal, the purpose of the present invention is to provide a nonlinear damage compensation method for a mode division multiplexing communication system, which can effectively capture the signal characteristics of the input data, and by fully performing feature serialization and fusion processing on the input data, when processing the signal data at the current moment, it can be combined with the use of the preceding signal data information in the training data, that is, the signal data sequence is serialized and feature fused, so as to better characterize the nonlinear interference relationship between the current signal and the preceding signal. Therefore, the nonlinear model with high randomness and complexity of the orbital angular momentum mode division multiplexing system can be accurately fitted. Compared with the traditional nonlinear compensation algorithm, this method has lower computational complexity, and can efficiently restore the data symbols transmitted in the mode division multiplexing system, thereby compensating for the device nonlinearity of the mode division multiplexing optical communication system.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] The present invention discloses a method for compensating nonlinear damage in a mode division multiplexing communication system, comprising the following steps:

[0008] Step 1: The signal sent by the transmitter is pulse amplitude modulated, and then pulse shaped by data to obtain the input signal, and then the input signal is sent to the analog division multiplexing communication system for transmission to obtain the data symbol X m ;

[0009] Step 2: Convert the received data symbol X m Perform clock recovery and get the symbol Y m ; Then, according to the memory length, the symbol Y m Together with adjacent symbols, form a data set;

[0010] Step 3: Use the Koopman probabilistic neural network to perform compensation classification on the data set obtained in step 2;

[0011] The Koopman probabilistic neural network is divided into three layers. The first layer is the input layer, the second layer is the fully connected layer, and the third layer is the Koopman layer.

[0012] The training data in the data set is input to the second layer after the input layer to capture the signal characteristics; the ReLu activation function is used to fit the nonlinear characteristics of the training data according to the captured signal characteristics; the output feature vector z∈R L×s , z is represented by z={z1,z2,…,zs}, R L×s It means that the eigenvector z is a matrix with L rows and s columns, where s represents the sth symbol;

[0013] z=ReLu(W*Y q +b) (1)

[0014] Among them, W and b represent weights and biases, Y q Represents the training dataset.

[0015] Feed z into the Koopman layer and use singular value decomposition on z to obtain the left singular matrix U, the right-left singular matrix V and the singular value matrix ∑;

[0016] z=U∑V * (2)

[0017] According to formula (2), the characteristic matrix A is constructed and the eigenvalue matrix D and the orthogonal matrix T are obtained by solving the equation, and the Koopman linear operator K is further constructed:

[0018]

[0019] z s ∈R L×1 Multiplying with the Koopman linear operator gives the compensation output z s ′∈R L×1 ;

[0020] z s ′=K*z s (4)

[0021] Among them, z s ′ represents the output signal after compensation using the Koopman probabilistic neural network.

[0022] The gradient back propagation algorithm and Adam parameters are used to optimize the Koopman probabilistic neural network to determine the optimal network parameters; the training data set Y constructed above is used q , train a Koopman probabilistic neural network, and perform nonlinear damage compensation on the signal through the trained Koopman probabilistic neural network.

[0023] The z in step 3 s ′ is compared with the input signal of step 1, and the bit error rate is obtained by demapping, thereby obtaining the compensation performance of the nonlinear damage compensation method;

[0024] The output signal z s After demapping, the output bit stream and the input bit stream are obtained. The number of error bits and the total number of transmitted bits are obtained by comparing the output bit stream and the input bit stream. The bit error rate is calculated according to formula (5);

[0025]

[0026] Step 3: q The process of processing using a fully connected layer is:

[0027] For the training data set Y q Perform a linear transformation, that is, multiply the input signal by the weight matrix and add the bias term. The linear transformation result is y=W*Y q +b, where W and b are the weights and biases of the fully connected layer respectively; the ReLU activation function is applied to the result y of the linear transformation, that is, z = max(0,y). This step will activate neurons nonlinearly, truncating negative signals to zero while retaining positive signals.

[0028] The process of using singular value decomposition on z in step 3 is:

[0029] A data matrix is ​​constructed according to the eigenvector z, where each column of the data matrix represents a symbol and each row represents a system variable; the constructed data matrix is ​​subjected to singular value decomposition, which decomposes the information of the data matrix into a series of modes and corresponding singular values, which describe the dynamic behavior of the system; the singular value decomposition is truncated to retain the main part of the singular value matrix, that is, to retain the largest several singular values ​​and the corresponding left and right singular vectors; and the left singular matrix U, the right-left singular matrix V and the singular value matrix ∑ are obtained.

[0030] The specific method of constructing the feature matrix A in step 3 is:

[0031] Get the singular value matrix ∑, select the first r singular values ​​from the singular value matrix ∑, and form an r×r diagonal matrix ∑ r , where the elements on the diagonal are selected singular values ​​and the other elements are zero;

[0032] At the same time, select the first r columns from the left singular matrix U to form an L×r matrix U r , these column vectors are called eigenvectors, L represents the length of the input signal; select the first r rows from the right singular matrix V to form an r×L matrix V r ;

[0033] according to Solve to obtain the characteristic matrix A;

[0034] The specific method of optimizing the Koopman probabilistic neural network with Adam parameters described in step 3 is:

[0035] Initialize the parameters of the neural network, including weights and biases, using random initialization; determine the hyperparameters of the Adam algorithm, including learning rate, batch size, weight initialization method, optimization method, and number of iterations; repeat iterative training until the preset number of iterations is reached or the loss function converges to a good degree.

[0036] Beneficial Effects

[0037] 1. The present invention discloses a method for compensating nonlinear damage of a mode division multiplexing communication system, which is a method for compensating nonlinear damage of PAM transmission of a mode division multiplexing communication system based on a Koopman probabilistic neural network. It compensates for nonlinear damage of signals according to the nonlinear signal damage characteristics of devices in a mode division multiplexing optical fiber communication system. Compared with traditional nonlinear compensation algorithms, it has better equalization effect, reduces computational complexity, and is close to the needs of actual systems.

[0038] 2. The present invention discloses a method for compensating nonlinear damage in a mode-division multiplexing communication system, which performs full feature serialization and fusion processing on training data through a Koopman probabilistic neural network. When processing the signal data at the current moment, it can combine and utilize the previous signal data information in the training data, that is, perform serialization feature fusion on the signal data sequence, so as to better characterize the nonlinear interference relationship between the current signal and the previous signal.

[0039] 3. The present invention discloses a method for compensating nonlinear damage in a mode-division multiplexing communication system. In a Koopman probabilistic neural network, the eDMD dynamic equation is used to independently calculate the corresponding Koopman operator K for the input data to fit the probability distribution function between the input and the output. In a data-driven manner, the network model can adapt to the ever-changing data distribution and environment to achieve the function of dynamically adjusting system parameters, and fully learn the characteristics of different inputs to accurately output compensation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The figure is a flow chart of the nonlinear compensation method for PAM transmission in a mode division multiplexing communication system based on Koopman probabilistic neural network.

[0041] Figure 2 This is a mode division multiplexing and direct detection PAM transmission system described in the embodiment.

[0042] Figure 3 The diagram shows the structure of a Koopman probabilistic neural network suitable for symbol compensation in a mode-division multiplexing communication system.

[0043] Figure 4 It is the bit error rate performance of mode 3 PAM symbol after KP compensation.

[0044] Figure 5It is the bit error rate performance of mode 4 PAM symbol after KP compensation. DETAILED DESCRIPTION

[0045] In order to better illustrate the purpose and advantages of the present invention, the invention is further described below with reference to the accompanying drawings and examples.

[0046] like Figure 1 As shown, the specific implementation steps of a nonlinear impairment compensation method for a mode division multiplexing communication system disclosed in this embodiment are as follows:

[0047] Step 1: Prepare training data with a length of 61440 bits. The data is mapped to PAM8 symbols and pulse-formed to pass through the mode division multiplexing direct modulation and direct detection communication system.

[0048] Mode division multiplexing direct modulation and direct detection communication system, such as Figure 2 As shown. At the transmitting end, the data through the digital signal processing (DSP) block is encoded into the waveform generated by the arbitrary waveform generator (AWG) with a sampling rate of 60GSa / s. A laser with a wavelength of 1550nm is used to generate an optical carrier, and the electrical signal is modulated onto the optical carrier by a Mach-Zehnder modulator (MZM). In order to increase the transmission distance of the signal, an erbium-doped fiber amplifier (EDFA) is used to amplify the signal. The signal is coupled from the optical fiber into space through a polarization controller (PC), a collimator (Col) and a linear polarization (LP). Two spatial light modulators (SLMs) are used to modulate the light in different mode division multiplexing modes, respectively, with topological charge numbers l=-3 and l=4. The multiplexed mode division multiplexing beams are then combined into one beam through the BS. Due to reflection, the multiplexed mode division multiplexing beam contains two modes of l=3 and l=4. A quarter wave plate (QWP) is used to convert the multiplexed mode division multiplexing beam from linear polarization to circular polarization, thereby coupling it into a 1.6km ring core fiber for transmission.

[0049] At the receiving end, the mode-division multiplexing beam is converted into linearly polarized light by a quarter-wave plate and split into two beams by a BS, and then passes through a spiral phase plate (VPP) with opposite topological charges. After transmission through the VPP with opposite topological charges, the mode-division multiplexing beam of the corresponding mode can be converted into a Gaussian beam and coupled into a single-mode fiber (SMF) through a collimator. The optical signal is received by a photon detector. In a time-invariant nonlinear system, the received signal can be characterized by the Volterra series as follows:

[0050]

[0051] Where M is the memory length of the system, h0 is a constant, and h p (·) indicates p thHowever, in the mode division multiplexing system, due to the random coupling between modes, the system will cause time-varying nonlinear interference to the signal, so the traditional nonlinear equalization method is not applicable to the mode division multiplexing system.

[0052] In this example, the received signal y consists of p+q PAM8 data symbols:

[0053] y=[y1,y2,y3…y p+q ] T (2)

[0054] Step 2: Perform clock recovery on the received data, i.e., the PAM8 data symbols. Subsequently, the PAM8 data symbols are grouped into symbol vectors according to the memory length M. The data set is:

[0055]

[0056] Step 3: Divide the data set Y into a training set and a test set, each containing p and q groups of symbol vectors. Furthermore, the training set data is divided into i categories according to the data symbol level, and each training set contains k symbol vectors. Test data Y q are sequentially sent to the Koopman probabilistic neural network for symbol compensation in the mode division multiplexing communication system, such as Figure 3 As shown. Training data Y q After the input layer, it is input into the second layer to capture the signal feature process as shown in formula (4). The ReLu activation function is used to fit the nonlinear characteristics of the feature vector, z∈R L×s is the feature vector of the third layer output. The output z is represented by z={z1,z2,…,z s}, feed z into the Koopman probabilistic neural network, and calculate the eDMD rolling equation for z to obtain the Koopman linear operator K. The process of constructing the Koopman linear operator K is as follows: First, use the singular value decomposition of the input matrix z as shown in formula (5) to obtain the orthogonal matrices U, V and the diagonal matrix ∑; then construct the characteristic matrix A and solve it to obtain the eigenvalue matrix D; finally, construct K, and the process is shown in formula (6). s ∈R L×1 Multiplying with the Koopman linear operator gives the compensation output z s ′∈R L×1 , the process is shown in formula (7);

[0057] The test data enters the fully connected layer through the input layer. The fully connected layer calculates the matching relationship between the input feature vector and each pattern in the training set. When processing the current moment signal, it can combine and utilize the previous signal data information in the test data, that is, perform serialized feature fusion on the signal data to better characterize the nonlinear interference relationship between the current signal and the previous signal. In the Koopman layer, the corresponding Koopman operator K is independently calculated for the input data through the eDMD dynamic equation to fit the probability distribution function between the input and output. In a data-driven manner, the characteristics of different inputs can be fully learned. The Koopman layer better judges the category of the input data symbol level, and then constructs a Koopman probabilistic neural network that can calculate the nonlinear discrimination boundary. The network model can adapt to the ever-changing data distribution and environment to achieve the function of dynamically adjusting system parameters and accurately output compensation results.

[0058] z=ReLu(W*Y q +b) (4)

[0059] z=U∑V * (5)

[0060]

[0061] z s ′=K*z s (7)

[0062] Step 4: Compare the judgment symbol with the transmitted symbol, and calculate the PAM8 symbol bit error rate to obtain the bit error rate performance of the test data at different receiving powers after KP compensation. Compare the bit error rate performance of the KP-based equalization results with the three cases of no equalization compensation, digital signal processing algorithm, and convolutional neural network equalization. Figure 4 As shown, the minimum bit error rate is 1e-5. Compared with different equalization algorithms, the bit error rate performance of the KP algorithm is outstanding. In the two mode division multiplexing modes, with the increase of the received optical power, the bit error rate of KP has a faster decline rate. When the bit error rate is 1e-2, the bit error rate performance of KP in mode division multiplexing mode 3 and 4 is about 1.5dB and 2.5dB better than CNN, respectively, which further confirms the effectiveness and superiority of the KP algorithm in nonlinear equalization of mode division multiplexing system.

[0063] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and does not limit the scope of protection of the present invention. Any modifications, replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for compensating nonlinear impairments in a mode division multiplexing communication system, characterized in that: The following steps are included: Step 1: The signal sent by the transmitter is pulse amplitude modulated, and then pulse shaped by data to obtain the input signal, and then the input signal is sent to the analog division multiplexing communication system for transmission to obtain the data symbol X m ; Step 2: Convert the received data symbol X m Perform clock recovery and get the symbol Y m ; Then, according to the memory length, the symbol Y m Together with adjacent symbols, form a data set; Step 3: Use the Koopman probabilistic neural network to perform compensation classification on the data set obtained in step 2; The Koopman probabilistic neural network is divided into three layers. The first layer is the input layer, the second layer is the fully connected layer, and the third layer is the Koopman layer. The training data in the dataset is fed into the second layer after the input layer to capture the signal features; Use the ReLu activation function to fit the nonlinear characteristics of the training data based on the captured signal characteristics; Output feature vector z∈R L×s , z is represented by z={z1,z2,…,z s }, R L ×s It means that the eigenvector z is a matrix with L rows and s columns, where s represents the sth symbol; z=ReLu(W*Y q +b) (1) Among them, W and b represent weights and biases, Y q represents the training data set; Feed z into the Koopman layer and use singular value decomposition on z to obtain the left singular matrix U, the right-left singular matrix V and the singular value matrix ∑; z=U∑V * (2) According to formula (2), the characteristic matrix A is constructed and the eigenvalue matrix D and the orthogonal matrix T are obtained by solving the equation, and the Koopman linear operator K is further constructed: z s ∈R L×1 Multiplying with the Koopman linear operator gives the compensation output z s ′∈R L×1 ; With s ′=K*z s (4) Among them, z s ′ represents the output signal after compensation using the Koopman probabilistic neural network; The gradient back propagation algorithm and Adam parameters are used to optimize the Koopman probabilistic neural network and determine the optimal network parameters; the training data set Y q , train a Koopman probabilistic neural network, and perform nonlinear damage compensation on the signal through the trained Koopman probabilistic neural network.

2. A method for compensating nonlinear impairments in a mode division multiplexing communication system as claimed in claim 1, characterized in that: The z in step 3 s ′ is compared with the input signal of step 1, and the bit error rate is obtained by demapping, thereby obtaining the compensation performance of the nonlinear damage compensation method; The output signal z s After demapping the ′ and input signals, output bit stream and input bit stream are obtained, and the number of error bits and the total number of transmitted bits are obtained by comparing the output bit stream and the input bit stream; The bit error rate is calculated according to formula (4); 3. A method for compensating nonlinear impairments in a mode division multiplexing communication system as claimed in claim 1, characterized in that: Step 3: q The process of processing using a fully connected layer is: For the training data set Y q Perform a linear transformation, that is, multiply the input signal by the weight matrix and add the bias term. The linear transformation result is y=W*Y q +b, where W and b are the weights and biases of the fully connected layer respectively; the ReLU activation function is applied to the result y of the linear transformation, that is, z = max(0,y). This step will activate neurons nonlinearly, truncating negative signals to zero while retaining positive signals.

4. A method for compensating nonlinear impairments in a mode division multiplexing communication system as claimed in claim 1, characterized in that: The process of using singular value decomposition on z in step 3 is: A data matrix is ​​constructed according to the eigenvector z, where each column of the data matrix represents a symbol and each row represents a system variable; the constructed data matrix is ​​subjected to singular value decomposition, which decomposes the information of the data matrix into a series of modes and corresponding singular values, wherein the modes describe the dynamic behavior of the system; the singular value decomposition is truncated to retain the main part of the singular value matrix, that is, retain the largest number of singular values ​​and the corresponding left and right singular vectors; and the left singular matrix U, the right-left singular matrix V and the singular value matrix ∑ are obtained.

5. A method for compensating nonlinear impairments in a mode division multiplexing communication system as claimed in claim 1, characterized in that: The specific method of constructing the feature matrix A in step 3 is: Get the singular value matrix ∑, select the first r singular values ​​from the singular value matrix ∑, and form an r×r diagonal matrix ∑ r , where the elements on the diagonal are selected singular values ​​and the other elements are zero; At the same time, select the first r columns from the left singular matrix U to form an L×r matrix U r , the column vector is called the eigenvector, L represents the length of the input signal; select the first r rows from the right singular matrix V to form an r×L matrix V r ; according to Solve and obtain the characteristic matrix A.

6. A method for compensating nonlinear impairments in a mode division multiplexing communication system as claimed in claim 1, characterized in that: The specific method of optimizing the Koopman probabilistic neural network with Adam parameters described in step 3 is: Initialize the weight parameters and bias parameters of the neural network by random initialization; determine the hyperparameters of the Adam algorithm, including learning rate, batch size, weight initialization method, optimization method and number of iterations; Repeat the iterative training until the preset number of iterations is reached or the loss function converges to a good level.

Images