A method for compensating for nonlinear impairments in a mode division multiplexing communication system

Abstract

The application relates to a nonlinear impairment compensation method of a mode division multiplexing communication system and belongs to the optical fiber communication field. The application captures the signal characteristics of input data, fully serializes and fuses the input data, combines the previous signal data information in the training data when processing the signal data at the current moment, serializes and fuses the signal data sequence, better represents the nonlinear interference relationship between the current signal and the previous signal, can accurately fit the nonlinear model of the orbital angular momentum mode division multiplexing system with high randomness and complexity, has lower calculation complexity, can efficiently recover the data symbols transmitted in the mode division multiplexing system, compensates the device nonlinearity of the mode division multiplexing optical communication system, and can solve the problem that the restoration degree of the received signal is not high due to the random nonlinear impairment in the orbital angular momentum mode division multiplexing system.

Description

TECHNICAL FIELD

[0001] The application relates to a nonlinear impairment compensation method of a mode division multiplexing communication system, in particular to a nonlinear compensation method of a mode division multiplexing direct detection PAM transmission based on a Kupfmann probability neural network, and belongs to the optical fiber communication field. BACKGROUND

[0002] In an intensity modulation direct detection system, the nonlinear impairment caused by various optoelectronic devices (such as modulators, electronic amplifiers and photodetectors) seriously limits the system performance and causes strong signal distortion. Especially in an orbital angular momentum mode division multiplexing system, the spatial light modulator used to generate an orbital angular momentum beam contains many nonlinear materials (such as liquid crystal, nonlinear polymer, photorefractive material, etc.), which introduces serious nonlinear impairment. Generally speaking, the nonlinear impairment can be alleviated by adjusting the operating parameters of the optoelectronic devices, such as the output power of the electronic amplifier or the bias voltage of the modulator. However, these operations will cause the signal-to-noise ratio to decrease, thereby causing the system performance to deteriorate. Therefore, using a digital signal processing algorithm to equalize and compensate the signal becomes another method to alleviate the nonlinear impairment of the communication system, such as the Volterra series method, the digital pre-distortion method and the look-up table method. The digital signal processing algorithm alleviates the nonlinear impairment in the optical fiber communication system by fitting the nonlinear mathematical model of the system. However, there are two difficulties in alleviating the nonlinear impairment of the device in the orbital angular momentum mode division multiplexing system using the traditional digital signal processing algorithm. First, when multiple optoelectronic devices are working in the orbital angular momentum mode division multiplexing system, the nonlinearities of different devices will be coupled with each other, resulting in high complexity of the overall nonlinear model of the system. Second, the mode coupling in the orbital angular momentum mode division multiplexing system also makes the nonlinear impairment have strong random characteristics. Therefore, it is difficult to alleviate the nonlinear impairment in the orbital angular momentum mode division multiplexing system using the traditional digital signal processing algorithm.

[0003] In recent years, machine learning has become a breakthrough in the compensation of nonlinear impairment in optical fiber communication. 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 impairment 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 impairment. However, most machine learning algorithms must learn the nonlinear characteristics through a training data set. 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, most machine learning algorithms have high computational complexity and are not suitable for high-speed optical fiber communication.

[0004] Based on the nonlinear damage mechanism of system devices, this invention proposes a nonlinear equalization technique for modular multiplexing systems based on a Koopman probabilistic neural network. This technique can achieve arbitrary nonlinear approximation and compensate for the nonlinearity of modular multiplexing systems. Summary of the Invention

[0005] To address the issue of insufficient signal reconstruction due to random nonlinear impairments in orbital angular momentum modular division multiplexing (EMD) systems, this invention provides a nonlinear impairment compensation method for EMD communication systems. This method effectively captures the signal characteristics of the input data. By performing sufficient feature serialization and fusion processing on the input data, it can combine the preceding signal data information from the training data when processing the current signal data. This serialization and feature fusion of the signal data sequence better characterizes the nonlinear interference relationship between the current signal and the preceding signals. Therefore, it can accurately fit the highly random and complex nonlinear model of the orbital angular momentum EMD system. Compared with traditional nonlinear compensation algorithms, this method has lower computational complexity and can efficiently recover the transmitted data symbols in the EMD system, thereby compensating for the device nonlinearity of the EMD optical communication system.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a method for compensating for nonlinear impairments in a modular division multiplexing (MDF) communication system, comprising the following steps:

[0008] Step 1: The signal transmitted by the transmitting end is pulse amplitude modulated, and then the data is pulse shaped to obtain the input signal. This input signal is then sent to the modulus-division multiplexing communication system for transmission, resulting in data symbol X. m ;

[0009] Step 2: Transfer the received data symbol X m Perform clock recovery to obtain symbol Y m Then, based on the memory length, the symbol Y is... m The dataset is composed of adjacent symbols;

[0010] Step 3: Use the Koopman probabilistic neural network to perform compensatory classification on the dataset obtained in Step 2;

[0011] The Koopman probabilistic neural network consists of 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 dataset is fed into the second layer after passing through the input layer to capture signal features; the ReLU activation function is used to fit the nonlinear characteristics of the training data based on the captured signal features; the output feature vector z∈R is then applied. L×s z is represented as z = {z1, z2, ..., z}s}, R L×s represents that the feature vector z is a matrix of L rows and s columns, and s represents the s-th symbol;

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

[0014] where W and b represent weights and biases, Y q represents a training data set.

[0015] z is fed into a Kupfmann layer, singular value decomposition is used on z to obtain a left singular matrix U, a right singular matrix V, and a singular value matrix ∑;

[0016] z = U∑V * (2)

[0017] A feature matrix A is constructed according to formula (2) and eigenvalue matrix D and orthogonal matrix T are solved, and a Kupfmann linear operator K is further constructed:

[0018]

[0019] z s ∈R L×1 is multiplied by the Kupfmann linear operator to obtain a compensation output z s ′∈R L×1 ;

[0020] z s ′ = K * z s (4)

[0021] where z s ′ represents an output signal compensated using the Kupfmann probabilistic neural network.

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

[0023] z s ′ of step three is compared with the input signal of step one, and a bit error rate is obtained by demapping, so that the compensation performance of the nonlinear damage compensation method is obtained;

[0024] The output signal z s ′ and the input signal are demapped to obtain an output bit stream and an input bit stream, and the error bit number 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 three is to use singular value decomposition on z q The process of using the full connection layer is:

[0027] Step two is to apply a linear transformation to the training data set Y q The linear transformation is to multiply the input signal by a weight matrix and add a bias term, and the result of the linear transformation is y = W * Y q + b, where W and b are the weight and bias of the full connection layer, respectively; apply the ReLU activation function to the result of the linear transformation, that is, z = max(0, y), which will non-linearly activate the neurons and cut off the negative signals to zero while preserving the positive signals.

[0028] Step three is to use singular value decomposition on z

[0029] According to the eigenvector z, a data matrix is constructed, each column of the data matrix represents a symbol, and each row represents a system variable; singular value decomposition is performed on the constructed data matrix, which decomposes the information of the data matrix into a series of modes and corresponding singular values, and these modes describe the dynamic behavior of the system; truncate the singular value decomposition to retain the main part of the singular value matrix, that is, retain the largest singular values and the corresponding left and right singular vectors; obtain the left singular matrix U, the right singular matrix V, and the singular value matrix ∑.

[0030] The specific method of step three is to construct the feature matrix A

[0031] Obtain the singular value matrix ∑, select the first r singular values from the singular value matrix ∑, and construct a r x r diagonal matrix ∑ r , where the elements on the diagonal are the 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 construct a L x r matrix U r , these column vectors are called eigenvectors, and L represents the length of the input signal; select the first r rows from the right singular matrix V to construct a r x L matrix V r ;

[0033] According to Solve to obtain the feature matrix A;

[0034] The specific method of step three is to use the Adam parameter optimization library to solve the Kupman probability neural network

[0035] The parameters of the neural network, including weights and biases, are initialized in a random initialization manner; the hyperparameters of the Adam algorithm are determined, including a learning rate, a batch size, a weight initialization manner, an optimization method, and an iteration number; and iterative training is repeatedly performed until a preset iteration number is reached or a loss function converges to a good degree.

[0036] Advantages

[0037] 1. The nonlinear impairment compensation method for a mode division multiplexing communication system disclosed in the application is a PAM transmission nonlinear compensation method for a mode division multiplexing communication system based on a Kupman probability neural network, which compensates for the nonlinear impairment of signals according to the signal impairment characteristics of the nonlinear devices of the mode division multiplexing optical fiber communication system, has better equalization effect compared with traditional nonlinear compensation algorithms, reduces the calculation complexity, and meets the requirements of an actual system.

[0038] 2. The nonlinear impairment compensation method for a mode division multiplexing communication system disclosed in the application can fully fuse and process the feature sequences of the training data through the Kupman probability neural network, can combine and utilize the previous signal data information in the training data when processing the signal data at the current time, that is, can fuse the sequence features of the signal data sequence, and better represents the nonlinear interference relationship between the current signal and the previous signal.

[0039] 3. The nonlinear impairment compensation method for a mode division multiplexing communication system disclosed in the application can independently calculate the corresponding Kupman operator K of the input data through an eDMD dynamic equation in the Kupman probability neural network to fit the probability distribution function between the input and the output, can adapt to the changing data distribution and environment in a data-driven manner, can achieve the function of dynamically adjusting the system parameters, can fully learn the characteristics of different inputs, and can accurately output the compensation results. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 The Kupman probability neural network-based mode division multiplexing communication system PAM transmission nonlinear compensation method flowchart.

[0041] Figure 2 The mode division multiplexing emphasis direct detection PAM transmission system described in the embodiment.

[0042] Figure 3 The Kupman probability neural network structure suitable for symbol compensation of a mode division multiplexing communication system.

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

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

[0045] To better illustrate the purposes and advantages of the present application, the following further describes the summary in conjunction with the accompanying drawings and examples.

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

[0047] Step one: prepare training data with a length of 61440 bits. After PAM8 symbol mapping and pulse shaping, the data passes through a mode division multiplexing direct modulation direct detection communication system.

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

[0049] At the receiving end, a quarter-wave plate is used to convert the mode division multiplexing beams into linearly polarized light and divide them into two beams through a BS, and then pass through a vortex phase plate (VPP) with opposite topological charges. After transmission through the VPP with opposite topological charges, the mode division multiplexing beams corresponding to the modes can be converted into Gaussian beams, which are coupled into a single mode fiber (SMF) through a collimator. The optical signal is received by a photodetector. In a time-invariant nonlinear system, the received signal can be characterized by a Volterra series as follows:

[0050]

[0051] In the formula, M is the memory length of the system, h0 is a constant, and h p (·) represents p thJacobi-Woltjer nonlinear term coefficients. However, in a 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 is composed of p+q PAM8 data symbols:

[0053] y = [y1, y2, y3… y p+q ] T (2)

[0054] Step two: clock recovery is performed on the received data, i.e., PAM8 data symbols. Then, the PAM8 data symbols are grouped into symbol vector groups according to the memory length (Memory Length) M. The data set is:

[0055]

[0056] Step three: the data set Y is divided into a training set and a test set, each containing p, q symbol vector groups. Further, the training set data is divided into i classes according to the data symbol level size, and each class of training set contains k symbol vectors. The test data Y q is sequentially input into the Kupman probability neural network for symbol compensation of the mode division multiplexing communication system, as shown in Figure 3 . The training data Y q is input to the second layer after the input layer to capture the signal feature process as shown in equation (4), and the ReLu activation function is used to fit the nonlinear characteristics of the feature vector, z ∈ R L×s is the feature vector output by the third layer. The output z is represented as z = {z1, z2, …, z s}. z is fed into the Kupman probability neural network, and the eDMD rolling equation calculation is performed on z to obtain the Kupman linear operator K. The process of constructing the Kupman linear operator K is as follows: first, singular value decomposition is performed on the input matrix z as shown in equation (5) to obtain the orthogonal matrices U, V and the diagonal matrix ∑; second, the feature matrix A is constructed and the eigenvalue matrix D is solved; finally, K is constructed, and the process is shown in equation (6). z s ∈ R L×1 is multiplied by the Kupman linear operator to obtain the compensation output z s ′ ∈ R L×1 , as shown in equation (7);

[0057] Test data enters the fully connected layer after passing through the input layer. The fully connected layer calculates the matching relationship between the input feature vector and various patterns in the training set. When processing the signal at the current moment, it can combine the preceding signal data information from the test data, i.e., perform serialized feature fusion on the signal data, to better characterize the nonlinear interference relationship between the current signal and the preceding signals. In the Koopman layer, the corresponding Koopman operator K is independently calculated for each input data using the eDMD dynamic equation to fit the probability distribution function between the input and output. In a data-driven manner, it can fully learn the characteristics of different inputs. The Koopman layer better judges the category of the input data symbol level, thus constructing a Koopman probabilistic neural network capable of calculating the nonlinear discrimination boundary. The network model can adapt to constantly changing data distributions and environments to dynamically adjust 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 discrimination symbol with the transmitted symbol and calculate the PAM8 symbol bit error rate to obtain the bit error rate performance of the test data after KP compensation at different received powers. Compare the KP-based equalization results with the bit error rate performance under three conditions: no equalization compensation, digital signal processing algorithm, and convolutional neural network equalization. Figure 4 As shown, the minimum bit error rate (BER) is 1e-5. Compared to different equalization algorithms, the KP algorithm exhibits superior BER performance. In both modulus-division multiplexing (MDD) modes, the BER of KP decreases faster with increasing received optical power. At a BER of 1e-2, KP outperforms CNN by approximately 1.5dB and 2.5dB in MMD modes 3 and 4, respectively, further confirming the effectiveness and superiority of the KP algorithm in nonlinear equalization of MMD systems.

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

Claims

1. A method for compensating for nonlinear impairments in a mode division multiplexing communication system, the method comprising: Comprising the following steps, ​ Step one: the signal sent by the sending end is subjected to pulse amplitude modulation, then subjected to pulse shaping, to obtain an input signal, and then the input signal is sent into a mode division multiplexing communication system for transmission, to obtain a data symbol X m ; Step two: received data symbols X m Clock recovery is performed to obtain symbols Y m Then, according to the memory length, the symbols Y m are grouped with adjacent symbols to form a data set; Step three: using the Kuppmann probabilistic neural network to compensate and classify the data set obtained in step two; The Kuppmann probabilistic neural network is divided into three layers, the first layer is the input layer, the second layer is the full connection layer, and the third layer is the Kuppmann layer; The training data in the data set is input to the second layer after the input layer to capture signal characteristics; Using the ReLu activation function, according to the captured signal characteristics, the nonlinear characteristics of the training data are fitted; Output feature vector z e R L×s , z is represented as z = {z1, z2,..., z s}, R L×s denotes that the feature vector z is a matrix of L rows and s columns, L denotes the length of the input signal, and s denotes the s-th symbol; z = ReLu(W * Y q + b) (1) where W and b represent weights and bias, Y q denotes a training data set; Feed z into the Kuppmann layer, and use singular value decomposition on z to obtain left singular matrix U, right singular matrix V and 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 solved, and the Kuppmann linear operator K is further constructed: z s ∈R L×1 z s ′∈R L×1 ; z s ′= K * z s (4) where z s represents the output signal after compensation using the Kupfmann probabilistic neural network; The gradient back propagation algorithm and Adam parameter optimization library are used to determine the optimal network parameters of the Kuppers probability neural network q , train the Kuppers probability neural network, and perform nonlinear damage compensation on the signal through the trained Kuppers probability neural network.

2. The method of claim 1, wherein the nonlinear impairment compensation is performed for each of the subcarriers of the subcarrier groups. The z s The error rate is obtained by comparing the input signal of step one with the demapping result, so as to obtain the compensation performance of the non-linear impairment compensation method. The output signal z s The output bit stream and the input bit stream are obtained after the output signal z and the input signal are de-mapped. 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. According to formula (4), the bit error rate is calculated; 3. The nonlinear impairment compensation method for a modular division multiplexing communication system as described in claim 1, characterized in that: The process of using singular value decomposition on z in step three is: According to the eigenvector z, a data matrix is constructed, each column of the data matrix represents a symbol, and each row represents a system variable; The constructed data matrix is singular value decomposed, and the singular value decomposition decomposes the information of the data matrix into a series of modes and corresponding singular values, and the mode describes the dynamic behavior of the system; Truncate the singular value decomposition, retain the main part of the singular value matrix, that is, retain the largest number of singular values and corresponding left and right singular vectors; Obtain left singular matrix U, right singular matrix V and singular value matrix ∑.

4. The nonlinear impairment compensation method for a modular division multiplexing communication system as described in claim 1, characterized in that: The specific method for constructing the characteristic matrix A in step three is: Obtaining a singular value matrix ∑, selecting the first r singular values from the singular value matrix ∑ to form an r×r diagonal matrix ∑ r where the elements on the diagonal are the selected singular values, and other elements are zero; At the same time, the first r columns of the left singular matrix U are selected to form a Lxr matrix U r , the column vector is called the eigenvector, and L represents the length of the input signal; the first r rows of the right singular matrix V are selected to form a rxL matrix V r ; According to The characteristic matrix A is solved.

5. The method of claim 1, wherein the nonlinear impairment compensation is performed for each of the subcarriers of the subcarrier groups. The specific method for optimizing the Kuppmann probabilistic neural network in step three is: Randomly initialize the weight parameters and bias parameters of the neural network; Determine the hyperparameters of the Adam algorithm, including the learning rate, the batch size, the weight initialization method, the optimization method and the number of iterations; Repeat the iterative training until the pre-set number of iterations is reached or the loss function converges.

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