Neural network-based Wollaston series nonlinear compensation method

Abstract

The invention discloses a neural network-based Wollaston series nonlinear compensation method, and the method specifically comprises the steps: enabling a Wollaston integral kernel to be used for initializing the weight of a neural network, and achieving the accurate and efficient nonlinear compensation through training; firstly, a transmission experiment is carried out based on an optical fiber transmission experiment platform, and experiment data are collected from a real-time oscilloscope to construct a training set; and then calculating a Wollaston integral kernel according to the link parameters, applying the Wollaston integral kernel to weight initialization of the neural network, and finally performing iterative updating on the weight parameters of the neural network by using the training data so as to improve the nonlinear compensation performance. Compared with a digital back propagation algorithm, a large number of iteration steps are omitted, single-step compensation is achieved, and the calculation efficiency is greatly improved. In a 12,000 km transmission experiment, the compensation performance superior to that of a digital back propagation algorithm is realized with lower calculation complexity and calculation time delay.

Description

Technical Field

[0001] The invention belongs to the technical field of optical fiber communication, and in particular relates to a Volterra series nonlinear compensation method based on a neural network. Background Art

[0002] With the advent of the digital age, multimedia data services such as big data, cloud computing, the Internet of Things, machine-to-machine communication, and remote surgery are developing rapidly, and people's demand for transmission capacity is constantly increasing. Global network traffic has shown explosive growth in the past decade, which makes traditional copper cable communication unable to meet the needs of large data transmission. Compared with copper cables, optical fiber communication has the advantages of high bandwidth and anti-electromagnetic interference, so it has become the first choice for communication and data transmission in modern society. However, in long-distance communication, the complex physical effects of the optical fiber channel (such as attenuation, dispersion effect, Kerr nonlinear effect, etc.) will cause different damages to the signal. At the same time, the optical amplifier will introduce noise while compensating for power loss. The interaction between these physical phenomena makes signal recovery very challenging. In order to compensate for the loss and distortion of the optical signal during transmission, digital signal processing (DSP) technology is usually used at the receiving end to compensate for the signal. At present, the optical transmission system is evolving towards single-fiber 400G×80 waves and higher capacity. On the one hand, as the transmission rate and device bandwidth increase, the signal is more sensitive to nonlinear distortion; on the other hand, the optical system is occupying a wider spectrum (e.g., C+L), which means that the total optical power input to the fiber is larger than that of the C-band optical system, and the resulting signal nonlinear distortion effect will also be stronger. Therefore, the compensation algorithm for nonlinear channels in DSP will be a key factor affecting the further improvement of the capacity of the next generation optical transmission system.

[0003] The most commonly used algorithm for compensating fiber nonlinearity is digital back propagation (DBP). DBP is a serial algorithm whose compensation accuracy increases with the number of steps in each span (StpSP). Limited by the capabilities of digital signal processing (DSP) in actual systems, DBP algorithms with higher StpSP face the problems of high computational complexity and long operation time. On the contrary, if DBP is performed under limited StpSP, the large accumulation of dispersion and nonlinear residuals will reduce system performance as the transmission distance increases. Obviously, nonlinear compensation in this way cannot achieve the co-adaptation of timeliness and accuracy.

[0004] Recently, researchers proposed a nonlinear compensation algorithm based on the Volterra Series (VS). Compared with DBP, the VS algorithm is a single-step algorithm running in a parallel framework, without the need to execute a large number of sub-steps in series. This feature greatly reduces the compensation delay and provides a potential idea for real-time nonlinear compensation. However, the establishment of this parallel computing framework is at the cost of a highly simplified Volterra integral kernel, which makes its compensation performance far lower than that of the DBP algorithm. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to combine the VS algorithm with machine learning, so as to provide a neural network-based Volterra series (NN-VS) nonlinear compensation method.

[0006] The present invention discloses a nonlinear compensation method of Volterra series based on neural network to reduce the computational overhead and computational delay of DSP processing in optical fiber communication. The method mainly uses the Volterra integral kernel to initialize the weight parameters of the neural network (NN) and optimizes it through the gradient descent training strategy. Specifically, the method includes the following steps:

[0007] Step 1: Generate a neural network dataset;

[0008] Step 1.1: Generate a binary bit stream b;

[0009] Step 1.2: Map the bit stream b obtained in step 1.1 to a probability-shaped 16QAM constellation diagram to obtain a symbol stream s, and then upsample the symbol stream s and perform raised cosine pulse shaping to obtain a transmitting end digital signal E = [E x (t,z=0),E y (t, z=0)], convert the digital signal into analog signal by arbitrary waveform generator and modulate it to the channel to be tested by IQ modulator, and finally synthesize the test channel, C-band and L-band stray light channels in 253 channels;

[0010] Step 1.3: Send the wavelength division multiplexed signal into a loop test bench containing ten optical fiber spans for 12057 km transmission;

[0011] Step 1.4: At the receiving end, a programmable optical processor is used to filter out the channel to be tested, and the channel is detected by an integrated coherent receiver, sampled by a real-time digital oscilloscope, and finally the sampled signal E(t,z=L) is processed by offline DSP.

[0012] Step 1.5: In DSP processing, the VS algorithm is first used to perform dispersion and nonlinear compensation on the signal to obtain the signal

[0013] Step 1.6: Use constant modulus, blind phase search and least squares equalization algorithm to Perform polarization demultiplexing, phase recovery, and channel equalization, demap the signal after downsampling, and obtain the demodulated signal

[0014] Step 2: Use the kernel function in the VS algorithm to initialize the weight parameters of the neural network, and optimize and update them through the gradient descent training strategy, and then develop a neural network-assisted Volterra series nonlinear compensation algorithm NN-VS; the original VS is a parallel frequency domain compensation algorithm, which can be written as:

[0015]

[0016] in, It is the frequency domain expression of the transmitted signal E after Fast-Fourier transform (FFT), and ω represents the angular frequency; and Respectively represent the results of linear and nonlinear compensation in frequency domain; L = N PB Δz represents the total transmission distance, Δz is the step length, N PB is the number of parallel branches, β 2 ,γ represent the chromatic dispersion coefficient and nonlinear coefficient respectively; ξ∈[0,1] is an adjustable parameter; i represents the imaginary part of the complex number.

[0017] Step 2.1: Observe the first term of formula (3) K 1 (mΔz) and the last term K 1 (z-mΔz) is similar to the linear transformation in NN, which can be represented by two weight matrices Indicates that N represents the length of the signal; and the second term Corresponding to the activation function in NN, therefore, K 1 (mΔz) and K 1 (z-mΔz) for w 1 ,w 2 Initialization, then update w through gradient descent training 1 ,w 2 The weight parameter of the improved NN-VS algorithm is

[0018]

[0019] in, σ(x)=iξ8 / 9γΔz||x|| 2 , w ones is an all-one matrix, [·] T is the transpose operation.

[0020] Step 2.2: Set the optimizer and training hyperparameters, i.e., maximum number of iterations, batch size, learning rate, and loss function;

[0021] Step 2.3: Perform training, that is, use the transmitted symbol s and the demodulated symbol The network parameters are updated, and the bit error rate in each iteration step is calculated using the validation set data. When it no longer changes significantly, the iteration is terminated, and the NN-VS algorithm training is completed.

[0022] Step 3: Test the nonlinear compensation algorithm modeled by the neural network, specifically: send all subsequences in the test set into the neural network to obtain the compensated signal.

[0023] 2. The Volterra series nonlinear compensation method based on neural network according to claim 1, characterized in that in step 2.2, the gradient optimization function adopts Adma optimizer, the exponential decay factor of the first-order moment estimation is set to 0.9, the exponential decay factor of the second-order moment estimation is set to 0.999, and the weight decay factor is set to 10 -4 ;

[0024] The maximum number of iterations is set to 500 and the batch size is set to 100;

[0025] The initial learning rate is set to 0.05. As the training progresses, the learning rate decreases by 50% every time the number of iterations increases by 50.

[0026] The loss function is defined as:

[0027]

[0028] Among them, ||·|| 1 Represents L 1 Norm.

[0029] Step 2.3: Perform training, that is, use the transmitted symbol s and the demodulated symbol The network parameters are updated, and the bit error rate in each iteration step is calculated using the validation set data. When it no longer changes significantly, the iteration is terminated, and the NN-VS algorithm training is completed.

[0030] Step 3: Test the nonlinear compensation algorithm modeled by the neural network, specifically: send all subsequences in the test set into the neural network to obtain the compensated signal.

[0031] The beneficial technical effects of the present invention compared with the prior art are:

[0032] Compared with DBP and weight filter DBP (W-DBP) algorithms in transoceanic transmission, the method of the present invention achieves superior performance. It also saves a large number of iterative steps and greatly reduces the computational complexity. It can give full play to the advantages of parallel computing and significantly reduce the computational time. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is the block diagram of the ultra-large capacity and ultra-long distance optical fiber transmission experimental system.

[0034] Figure 2 This is a structural diagram of the VS algorithm.

[0035] Figure 3 This is a schematic diagram of the NN-VS algorithm structure adopted by the present invention.

[0036] Figure 4 This is the training process of NN-VS.

[0037] Figure 5 Comparison of the Q factor performance of the signal (H=3.2, H=3.5) after being transmitted 12057km and compensated by DBP, WDBP, VS and NN-VS algorithms respectively.

[0038] Figure 6 This is the curve of the Q factor performance versus time / computational complexity of the NN-VS algorithm and W-DBP algorithm proposed in the present invention under 12075km (H=3.2) transmission. DETAILED DESCRIPTION

[0039] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0040] The present invention proposes a method for nonlinear compensation based on neural networks and Volterra series. First, a training data pair is established based on the VS algorithm. Then, the integral kernel parameters of the VS algorithm are used to initialize the weights of the neural network. The weights are updated through the training pairs, and finally accurate and efficient nonlinear compensation is completed. The NN-VS nonlinear compensation method is mainly divided into the following three steps: 1) Based on the collected data of the ultra-large capacity and ultra-long distance optical fiber transmission experimental system, the demodulated symbols compensated by VS are obtained, and they form training pairs with the transmitted symbols. 2) The calculated VS integral kernel parameters are used to initialize the weight matrix of the neural network 3) Through training, w 1 ,w 2 The weight parameters are iteratively updated to improve the performance.

[0041] like Figure 1 The experimental schematic diagram of the C+L band ultra-high capacity distance product single-mode optical fiber transmission system is shown. At the transmitting end, the test channel uses a tunable laser with a line width of less than 10kHz as the light source (Keysight 81608A). Two pseudo-random bit sequences PRBS_a and PRBS_b, as well as the amplitude probability PA, are input into the constant component distribution matcher (CCDM). The CCDM converts the input bits of the independent Bernoulli (1 / 2) distribution into two probability shaping symbol sequences of I and Q. Finally, the I and Q are combined to obtain the probability shaping 16QAM (PS-16QAM), with 2 samples per symbol. The upsampled digital signal is shaped using a square root raised cosine (SRRC) with a roll-off factor of β = 0.01, and converted into an analog signal with 65GSa / s and 25GHz analog bandwidth through an arbitrary waveform generator (Keysight M8195AAWG). The test channel light source from a tunable external cavity laser (Keysight N7778C) with a linewidth <10kHz is modulated by a 30GHz IQ modulator (EOSPACE) driven by a DAC device to generate 32GBaud PS-16QAM optical signals with different information entropies (H=3.0, 3.2, 3.5). Subsequently, these modulated optical signals are polarization multiplexed (PDM) to obtain 192.0Gb / s PDM-PS-16QAM (H=3.0), 204.8Gb / s PDM-PS-16QAM (H=3.2), 224.0Gb / s PDM-PS-16QAM (H=3.5), and then the test channel, C-band and L-band stray light channels are synthesized in 253 channels and then enter the cyclic loop test bench consisting of ten fiber spans (YOFC, ultra-low loss large effective area fiber). The optical fiber link adopts a loop system. The loop switch is controlled by two acousto-optic modulators (AOMs). The number of turns of the wavelength division multiplexing signal in the loop is controlled by setting the on and off time of the AOM to achieve the target transmission distance. By setting the loop to rotate 16 times, the optical signal transmission distance of 12,000 km can be achieved. Due to the insertion loss of the AOM switch and the coupler, the wavelength division multiplexing signal needs to be amplified by a C / L band EDFA after entering the optical fiber loop, and the attenuator is combined to control the transmission power of the optical fiber loop. The optical fiber attenuation and device insertion loss can be compensated by C-band and L-band EDFA (Accelink, CD-OFA-C / L48). At the receiving end (Rx), the test channel is filtered by C or L band WSS and detected by an integrated coherent receiver, and then the data is collected by a real-time digital oscilloscope (Keysight DSOZ634A) with an electrical bandwidth of 33 GHz and a sampling rate of 80GSa / s.

[0042] Figure 2The figure shows the structure of the VS algorithm. First, the time domain signal is converted to the frequency domain through FFT, and dispersion compensation and nonlinear compensation are performed separately. In nonlinear compensation, the number of parallel branches N is determined according to the adjustable parameter Δz. PB , each parallel branch contains two linear transformations and one nonlinear transformation. Figure 3 The figure shows the structure of the NN-VS algorithm. All parallel branches of the VS algorithm are combined. The linear transformation in nonlinear compensation is represented by two weight matrices w 1 ,w 2 , and its parameters can be obtained by The constructed training pairs are updated.

[0043] Figure 4 The training process of NN-VS. The result of 32GBaud PS-16QAM signal (H=3.0, H=3.2, H=3.5) after 12057km transmission and compensation by DSP algorithm at the receiving end. The training pair is formed with the transmitted symbol s. Then the gradient is back-propagated by establishing the loss function J to update w 1 ,w 2 The weight parameter of .

[0044] Then, NN-VS was compared with DBP, W-DBP and VS. Figure 5 As shown in the figure, the results show that the Q factor performance of all algorithms improves with the increase of the number of steps / parallel branches. The optimal Q factor of the VS algorithm is only slightly better than that of dispersion compensation (CDC); the standard DBP algorithm achieves a small improvement in Q factor when the number of steps is small, and its Q factor improvement is only significant when the number of steps is greater than or equal to the number of fiber spans; the W-DBP algorithm can tolerate fewer steps without seriously degrading system performance. The Q factor of the NN-VS algorithm steadily improves with the increase of parallel branches, and its performance always remains optimal when the step size Δz is the same as that of DBP and W-DBP. And when the entropy values ​​are 3.0 and 3.2, N PB When the entropy value is 3.5, N PB NN-VS with a Q factor of 60 surpasses the optimal Q factor performance of W-DBP.

[0045] Finally, the operating efficiency of the nonlinear compensation algorithm proposed in the present invention is discussed on the same GPU device. The W-DBP algorithm performs serial calculations, and its computational complexity is directly related to the computational delay, in which the choice of step size directly determines its computational accuracy and computational complexity. The present invention is a parallel computing framework, and its total computational complexity is proportional to the number of parallel branches N. PBis directly related to the computational complexity of a single parallel branch, while the computational latency is only related to the computational complexity in a single parallel branch. Figure 6 The curve of Q factor performance versus time / computational complexity of the NN-VS algorithm and W-DBP algorithm proposed in the present invention under 12075km (H=3.2) transmission. PB and the number of steps N of W-DBP step The computational complexity and Q-factor performance can be changed. The dotted line represents the maximum performance improvement that can be achieved using W-DBP. As shown in the figure, the optimal performance of NN-VS is 0.14dB higher than that of WDBP. In addition, NN-V surpasses the maximum achievable performance of W-DBP with about 10% computational complexity. It is worth noting that in terms of time complexity, NN-VS always maintains a fixed value, while the running time of DBP / WDBP increases with the increase of computational complexity. At a transmission distance of 12075km, the time complexity consumed by W-DBP to achieve the maximum Q factor is more than 180 times that of the NN-VS algorithm.

Claims

1. A Volterra series nonlinear compensation method based on neural network, characterized in that: The following steps are involved: Step 1: Generate a neural network dataset; Step 1.1: Generate a binary bit stream b; Step 1.2: Map the bit stream b obtained in step 1.1 to a probability-shaped 16QAM constellation diagram to obtain a symbol stream s, and then upsample the symbol stream s and perform raised cosine pulse shaping to obtain a transmitting end digital signal E = [E x (t,z=0),E y (t, z=0)], convert the digital signal into analog signal by arbitrary waveform generator and modulate it to the channel to be tested by IQ modulator, and finally synthesize the test channel, C-band and L-band stray light channels in 253 channels; Step 1.3: Send the wavelength division multiplexed signal into a loop test bench containing ten optical fiber spans for 12057 km transmission; Step 1.4: At the receiving end, a programmable optical processor is used to filter out the channel to be tested, and the channel is detected by an integrated coherent receiver, sampled by a real-time digital oscilloscope, and finally the sampled signal E(t,z=L) is processed by offline DSP. Step 1.5: In DSP processing, the VS algorithm is first used to perform dispersion and nonlinear compensation on the signal to obtain the signal Step 1.6: Use constant modulus, blind phase search and least squares equalization algorithm to Perform polarization demultiplexing, phase recovery, and channel equalization, demap the signal after downsampling, and obtain the demodulated signal Step 2: Use the kernel function in the VS algorithm to initialize the weight parameters of the neural network, and optimize and update them through the gradient descent training strategy, and then develop a neural network-assisted Volterra series nonlinear compensation algorithm NN-VS; The original VS is a parallel frequency domain compensation algorithm, which can be written as: in, It is the frequency domain expression of the transmitted signal E after fast Fourier transform, and ω represents the angular frequency; and Respectively represent the results of linear and nonlinear compensation in frequency domain; L = N PB Δz represents the total transmission distance, Δz is the step length, N PB is the number of parallel branches, β2,γ represent the chromatic dispersion coefficient and nonlinear coefficient respectively; ξ∈[0,1] is an adjustable parameter; i represents the imaginary component of the complex number; Step 2.1: Observe the first term of formula (3) The K1(mΔz) and the last term K1(z-mΔz) in the above are similar to the linear transformation in NN, which are composed of two weight matrices: Indicates that N represents the length of the signal; and the second term Corresponding to the activation function in NN, K1(mΔz) and K1(z-mΔz) are used to initialize w1 and w2, and then the weight parameters of w1 and w2 are updated by gradient descent training; the improved NN-VS algorithm formula is: in, σ(x)=iξ8 / 9γΔz||x|| 2 , w ones is an all-one matrix, [·] T is the transpose operation; Step 2.2: Set the optimizer and training hyperparameters, i.e., maximum number of iterations, batch size, learning rate, and loss function; Step 2.3: Perform training, that is, use the transmitted symbol s and the demodulated symbol The network parameters are updated, and the bit error rate in each iteration step is calculated using the validation set data. When it no longer changes significantly, the iteration is terminated, and the NN-VS algorithm training is completed. Step 3: Test the nonlinear compensation algorithm modeled by the neural network, specifically: send all subsequences in the test set into the neural network to obtain the compensated signal.

2. The Volterra series nonlinear compensation method based on neural network according to claim 1, characterized in that: In step 2.2, the gradient optimization function uses the Adma optimizer, the exponential decay factor of the first-order moment estimate is set to 0.9, the exponential decay factor of the second-order moment estimate is set to 0.999, and the weight decay factor is set to 10 -4 ; The maximum number of iterations is set to 500 and the batch size is set to 100; The initial learning rate is set to 0.

05. As the training progresses, the learning rate decreases by 50% every time the number of iterations increases by 50. The loss function is defined as: Here, ||·||1 represents the L1 norm.

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