Pearson correlation coefficient-based PSO decision feedback equalizer optimization method

Abstract

This invention proposes a Pearson correlation coefficient-based PSO decision feedback equalizer optimization method, primarily addressing the existing problem of eliminating intersymbol interference (ISI) between signal symbols after transmission over a nonlinear high-speed link. Its implementation involves: performing channel simulation in ADS software to obtain the pre-equalization impulse response waveform and the pre-equalization output response waveform, and saving their text; reading the pre-equalization impulse response text to determine its starting point, and extracting data of length l from the starting point as input data for the channel simulation; inputting this data into a decision feedback equalizer, optimizing the decision feedback equalizer tap coefficients using an improved PSO algorithm; and using the optimized feedback equalizer to equalize the input signal at the receiving end, obtaining a worst-case eye diagram representative of the quality of high-speed signal transmission. Simulation results demonstrate that this invention improves equalization effectiveness and effectively reduces ISI, making it suitable for signal equalization processing at the receiving end of high-speed links.

Description

Technical Field

[0001] The present invention belongs to the field of signal processing technology, and in particular relates to a PSO decision feedback equalizer optimization method, which can be used for signal equalization processing at the receiving end of a high-speed link, thereby reducing inter-symbol interference and improving data such as the eye height and eye width of the worst-case eye diagram as much as possible, thereby reducing the bit error rate of the high-speed transmission system. Background Art

[0002] In high-speed links, the channel's signal attenuation varies across frequency bands, with higher attenuation for high-frequency signals than for low-frequency signals. This results in undesirable signals being generated at the receiver after the transmitted code pattern passes through the channel, increasing the eye closure bit error rate (BER). Therefore, equalization of the transmitted signal at the receiver is necessary. Decision feedback equalization (DFE) is a widely used equalizer technology for mitigating intersymbol interference (ISI) and improving signal quality. Many communication systems employ DFE equalization to compensate for channel loss, and DFE relies heavily on optimizing its tap coefficients to achieve optimal performance.

[0003] The current mainstream DFE equalization algorithms include the zero-forcing algorithm ZF, the recursive least squares algorithm RLS, and the minimum mean square error algorithm LMS, among which:

[0004] The basic principle of the zero-forcing algorithm (ZF) is to ensure that the equalizer output waveform has a sample value of 1 only for the current bit and 0 for all other bits, thereby minimizing the impact of ISI. This method is simple in principle and easy to implement. However, because additive channel noise is omitted in the analysis, the solution obtained by this algorithm may not be optimal in the presence of actual noise. Specifically, when the channel frequency response is relatively flat and the resulting intersymbol interference (ISI) is not severe, this algorithm can achieve channel equalization. However, when interference is severe, this algorithm is less effective and cannot achieve equalization.

[0005] The recursive least squares algorithm (RLS) is an adaptive filtering algorithm based on the least squares method. Its basic principle is to use existing observation data to estimate the required filter coefficients and optimize the filtering effect by minimizing the mean square error of the prediction error. The algorithm has a complex structure and is not easy to implement.

[0006] The LMS algorithm is a gradient descent algorithm based on the Wiener filter. It is an optimized extension of the Wiener filter theory using the fast descent method. This algorithm does not require the statistical characteristics of the input and desired signals. The current weight coefficient is calculated by adding a proportional term to the previous weight coefficient plus the negative mean square error gradient, where the error is the difference between the filter output signal and the desired signal. However, the LMS equalization adaptive algorithm has a slow convergence speed and relies on gradient descent, which can lead to gradient vanishing and gradient exploding problems.

[0007] To address these issues, the IEEE article "Wiener filter equalization for higher data rates over 100m large-core 1mm SI-POF" proposes an algorithm that uses the MMSE criterion for DFE equalization. While this algorithm addresses the complex structure of the RLS algorithm and achieves good equalization, it suffers from high computational complexity, poor applicability, and some residual inter-symbol interference.

[0008] Article in SCI database: "Bayesian Optimization for High-Speed ​​Channel Equalization"

[0009] It uses a Bayesian machine learning network to replace the LMS algorithm in the approximation process of the Wiener solution. Although this method solves the problems of gradient disappearance and gradient explosion, and also solves the defect of the ZF algorithm that does not consider additive noise, it is sensitive to the input signal. When encountering different input signals, a certain network needs to be trained before balancing operations can be performed. In addition, the number of neurons in the hidden layer of the network is too large to be physically realized, and there is still obvious inter-code interference after processing. Summary of the Invention

[0010] The purpose of the present invention is to address the shortcomings of the above-mentioned prior art and propose a Pearson correlation coefficient-based PSO decision feedback equalizer optimization method to further eliminate inter-symbol interference at the receiving end, avoid gradient explosion and gradient vanishing, reduce the amount of calculation, simplify the equalizer structure, and meet the processing requirements of high-speed signal equalizers with loss and noise.

[0011] The technical idea for achieving the purpose of the present invention is to optimize the tap coefficients of the decision feedback equalizer through the particle swarm algorithm of nonlinear chaotic mapping, so as to design the decision feedback equalizer using the optimized tap coefficients, reduce inter-symbol interference, and simplify the structure of the receiving end equalization module.

[0012] According to the above ideas, the implementation steps of the present invention include the following:

[0013] (1) Generate the impulse response waveform before equalization:

[0014] Set the receiving end RX to the unbalanced mode, set the input PRBS code frequency f and code length m,

[0015] Using the code as the input of channel simulation, channel simulation is performed in a bit-by-bit manner to obtain the pulse waveform before equalization, and the pulse waveform is saved as an impulse response text before equalization;

[0016] (2) Generate the output response waveform before equalization:

[0017] Set the receiver RX to the mode that cancels decision feedback equalization, and set the frequency f and length n of the randomly generated PRBS code as input;

[0018] Using the code as the input of the channel simulation, the channel simulation is performed in a bit-by-bit manner to obtain the output response waveform before equalization, and the pulse waveform is saved as an output response text before equalization;

[0019] (3) reading the impulse response text before equalization in step (1) and determining its starting point using a hula hoop algorithm, which is the starting point of the waveform corresponding to the output response text before equalization in step (2);

[0020] (4) Read the output response text before equalization in step (2), and take data of length l from the starting point obtained in step (3) as the input data of the particle swarm optimization algorithm PSO.

[0021] (5) Optimize the decision feedback equalizer based on the particle swarm optimization algorithm PSO:

[0022] 5a) Set the number of iterations Nstep for initializing the particle swarm algorithm, the number of individuals N in the population, and the maximum value of the particle position x max and the minimum value x min , the maximum value of the particle velocity v max and the minimum value v min , the dimension D of the particle, the maximum weight coefficient ω of the particle update max and the minimum value ω min , the upper limits of the uniform distribution of self-learning factor and social learning factor are and

[0023] 5b) The normalized parameter of the Pearson correlation coefficient PLCC between the desired signal and the equalized signal is selected as the fitness function of the PSO optimization function, which is expressed as follows:

[0024]

[0025] where x i (t+1) is the position of the i-th particle in the t+1-th iteration, It represents the Pearson correlation coefficient PLCC between the equalized signal and the expected signal, y is the equalized signal, is the mean of y, y d is the expected signal;

[0026] 5c) Use the improved velocity update formula to update each particle and obtain the updated particle velocity vector v i (t+1)

[0027] 5d) Update the positions of all particles in the population according to the updated velocity vector of the particle to obtain the updated position x of each particle i (t+1):

[0028] 5e) Repeat steps 5b) to 5d) until the maximum number of iterations is reached, and the final updated positions of all particles are obtained;

[0029] 5f) According to the fitness function f(x(t)) of each particle, the optimal position g(t) of all particles is selected as the optimal tap coefficient of the decision feedback equalizer to obtain the optimized feedback equalizer;

[0030] 6) Use the optimized feedback equalizer to equalize the signal at the receiving end RX to obtain the worst eye diagram that can represent the quality of high-speed signal transmission.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] 1. Since the present invention constructs a fitness function for the decision feedback equalizer (DFE), it can reflect the degree and direction of adjustment of the equalizer tap coefficient to the leading bit that causes ISI. By calculating the correlation coefficient between the expected level value and the equalized signal value in each iteration, the range of random vibration of particles can be adjusted in a timely manner, and the robustness is strong.

[0033] 2. The present invention uses an improved speed update formula to update each particle, that is, adopts chaotic mapping to obtain the weight coefficient in the speed update formula, which can reflect the diversity of the population, so that it can balance the global search ability and local search ability according to the change of the number of iterations, and can make the global search ability stronger in the early stage of iteration and the local search ability stronger in the later stage of iteration, so as to jump out of the local optimal solution and improve the ability to find the global optimal solution.

[0034] 3. The principle of the present invention is simple, easy to implement, and requires few hyperparameters, which can effectively avoid the adverse effects and instability caused by artificial settings of hyperparameters.

[0035] Simulation results show that under the interference factors of additive noise, reflection, and jitter, different types of links are selected for testing. The worst-case eye diagram data obtained by the present invention is better than the traditional worst-case eye diagram data, that is, the eye height and eye width are 4% to 5% better than those of the traditional algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is an implementation flow chart of the present invention;

[0037] Figure 2 is a differential microstrip line link diagram for channel simulation according to the present invention;

[0038] Figure 3 It is the particle convergence oscillation diagram of the present invention;

[0039] Figure 4 This is the worst eye diagram obtained by simulation of the present invention. Specific implementation plan

[0040] The embodiments and effects of the present invention are described in further detail below with reference to the accompanying drawings.

[0041] Reference Figure 1 , the implementation steps for this example include the following:

[0042] Step 1: Generate the impulse response waveform before equalization:

[0043] 1.1) Set the receiver RX to unbalanced mode and set the input PRBS code frequency f and code length m;

[0044] In this example, it is assumed but not limited to that the first 600 bits of the PRBS code have a level value of 0, the 601st bit has a level value of 1, and the last 600 bits have a level value of 0; the rising and falling edges of the code are 10 ps, ​​the frequency f of the code is 10 GHz, and the length m of the code is 1201.

[0045] 1.2) Reference Figure 2 , establish a differential microstrip line link in ADS software;

[0046] 1.3) Use the PRBS code set in step 1.1) as the input of the link. Use bit-by-bit simulation to calculate the impulse response of a single bit of data in the PRBS code. Then, superimpose the impulse responses of all bits to obtain the final response waveform.

[0047] Step 2: Generate the output response waveform before equalization.

[0048] 2.1) Set the receiver RX to the mode of canceling decision feedback equalization, and set the frequency f and length n of the randomly generated PRBS code as follows:

[0049] In this example, it is assumed, but not limited to, that the frequency of the PRBS code is f 10 GHz and the length n is 12000, and the rising and falling edges of the code are 10 ps;

[0050] 2.2) Reference Figure 2, using the code as the input of the link, a bit-by-bit method is used to perform channel simulation, and the impulse response of a single bit data in the PRBS code is calculated by bit-by-bit simulation. Then, the impulse responses of all bits are superimposed to obtain the output response waveform before equalization, and the pulse waveform is saved as an output response text before equalization.

[0051] Step 3: Read the impulse response text before equalization and use the hula hoop algorithm to determine its starting point.

[0052] 3.1) Subtract the influence of DC level from the rising and falling edges of the output response waveform before equalization, and obtain an impulse response through shifting and superposition. The sampling point data corresponding to the maximum value of the impulse response peak is recorded as (x m ,y m );

[0053] 3.2) Set the time interval UI will collect data from the sampling point (x m ,y m ) to the left of the corresponding position to find 0.5 times the time interval UI, and record the corresponding data as (x l ,y l ), and then from the sampling point data (x m ,y m ) to the right of the corresponding position to find 0.5 times the time interval UI, and record the corresponding data as (x r ,y r ); In this example, the time interval UI is set to, but not limited to, 32, i.e., the waveform of one bit period is sampled at 32 points;

[0054] 3.3) Set the sampling point position x r and x l In x m The left side of the range is moved right by 1 bit at the same time, and the data point |y is calculated during the movement. r -y l | minimum value, and the x corresponding to the minimum value at this time l and x r The mean of is used as the starting point of the impulse response waveform before equalization. In this example, the starting point is equal to 190342. This starting point is the starting point of the waveform corresponding to the output response text before equalization in step 2.

[0055] Step 4: Starting from the starting point, the decision feedback equalizer is optimized using the particle swarm algorithm (PSO).

[0056] 4.1) Read the output response text before equalization, and take a data segment of length l from the starting point obtained in step 3 as the input data of the particle swarm optimization algorithm PSO. In this example, the data length l is set to 5000, but not limited to it;

[0057] 4.2) Set the parameters for initializing the particle swarm algorithm:

[0058] In this example, it is assumed but not limited to the number of population iterations Nstep = 100, the number of individuals in the population N = 100, and the maximum value of the particle position x max =1 and minimum value x min =-1, the maximum value of particle velocity v max =2 and minimum value v min = -1, particle dimension D = 4, maximum weight coefficient of particle update ω max =0.9 and minimum value ω min =0.4, the upper limit values ​​of the uniform distribution of self-learning factor and social learning factor are and

[0059] 4.3) Set the fitness function of the swarm optimization algorithm PSO:

[0060] 4.3.1) Calculate the Pearson correlation coefficient between the equalized signal and the expected signal

[0061] Where y is the equalized signal, is the mean of y, y d is the expected signal;

[0062] 4.3.2) According to the Pearson correlation coefficient Select the normalized parameter as the fitness function f(x i (t+1)):

[0063] where x i (t+1) is the position of the i-th particle in the t+1-th iteration;

[0064] 4.4) Use the velocity update formula to perform a preliminary update on each particle:

[0065] 4.4.1) Compare the fitness functions of all particles in the current iteration with their own historical fitness functions to obtain the optimal position p of a single particle with a better fitness function. i (t) is:

[0066] p i (t)=[p i,1 (t),p i,2 (t),…,p i,j (t),…,p i,D (t)]

[0067] where p i,j(t) is the position value of the jth dimension of the i-th particle in the population, j = 1, 2, 3, ..., D;

[0068] 4.4.2) Compare the fitness functions of all individual particles in the population to obtain the best individual of all particles in the current iteration, that is, the global extreme value: g(t) = p j (t)=[p j,1 (t),p j,2 (t),…,p j,s (t),…,p N,D (t)];

[0069] 4.4.3) Define the particle diversity function S(t):

[0070]

[0071] Where, f(x i (t)) is the fitness value of the i-th particle after the current iteration; f min (x(t)) and f max (x(t)) are the minimum and maximum fitness of all particles in the population after the current iteration, respectively. The diversity function S(t) characterizes the motion characteristics of the particles;

[0072] 4.4.4) Substitute the diversity function into the Logistic one-dimensional chaotic map to obtain the adjustment factor:

[0073] r t+1 =(LS(t))r t (1-r t ), r t ∈(0,1)

[0074] Among them, r t Indicates the adjustment factor of the current iteration, r t+1 is the adjustment factor for the next iteration, L is a non-negative constant, L≤4;

[0075] 4.4.5) Use the adjustment factor to calculate the updated weight of the velocity vector of the i-th particle in the population:

[0076]

[0077] Among them, t represents the number of current iterations, ω i (t) is the velocity vector update weight coefficient of the current iteration;

[0078] 4.4.6) Substitute the above weights into the particle velocity update formula to obtain the initial updated velocity of the current i-th particle:

[0079] v i(t+1)=ω i (t)v i (t)+c 1i (p i (t)-x i (t))+c 2i (g(t)-x i (t));

[0080] Among them, ω i (t) is the velocity vector update weight coefficient of the current iteration, p i (t) is the historical optimal position of each individual in the population, g(t) is the global optimal position in the population, c 1i and c 2i are the self-learning factor and social learning factor updated by the i-th particle in the population, and are non-negative random constants, v i (t+1) is the velocity vector after the initial update of the current iteration, v i (t) is the velocity vector of the current iteration;

[0081] 4.5) To prevent the velocity update from exceeding the boundary value, a penalty term is introduced after the initial velocity update, and the final updated velocity vector is obtained as follows:

[0082]

[0083] 4.6) Using the updated velocity vector v i (t+1) Initial update of particle position:

[0084] x i (t+1)=x i (t)+v i (t+1)

[0085] Among them, x i (t+1) is the particle position after the initial update of the current iteration, x i (t) is the particle position at the current iteration;

[0086] 4.6.1) To prevent the initial updated position from exceeding the boundary value, a penalty term is introduced after the initial update of the particle position. The final updated position is as follows:

[0087]

[0088] 4.7) Repeat steps 4.2) to 4.6) until the maximum number of iterations is reached, and the final updated positions of all particles are obtained;

[0089] 4.8) Based on the fitness function f(x(t)) of each particle, the optimal position g(t) of all particles is selected as the optimal tap coefficient of the decision feedback equalizer, and the optimized feedback equalizer is obtained:

[0090] 4.8.1) Use the fitness function f(x(t)) to calculate the fitness of each particle;

[0091] 4.8.2) From the positions of all particles p(t) = [p1(t), p2(t), ..., p j (t),…,p N (t)], pick out a position with the minimum corresponding fitness function and get the D-dimensional matrix g(t), which is the optimal position of all particles;

[0092] 4.8.3) Use the values ​​of each dimension in g(t) as the tap coefficients of the decision feedback equalizer.

[0093] Step 5: Use the optimized feedback equalizer to equalize the signal at the receiver RX to obtain the worst-case eye diagram that represents the quality of high-speed signal transmission. The worst-case eye diagram focuses on three indicators: maximum eye height, center eye height, and eye width. The specific implementation of equalization is as follows:

[0094] 5.1.1) The decision feedback equalizer at the receiver (RX) inputs the pre-equalized signal x(n). Each signal then passes through D-1 delay units, resulting in a total of D signal values ​​x(n), x(n-1), …, x(n-D+1).

[0095] 5.1.2) Based on these D signal values, obtain decision signals d(n), d(n-1), …, d(n-D+1);

[0096] 5.1.3) Multiply the D signal values ​​by the decision signals d(n), d(n-1), …, d(n-D+1) of the decision detector, and then multiply them by the corresponding optimal tap coefficients g(1,1), g(1,2), …, g(1,D), and accumulate the resulting products.

[0097] 5.1.4) Add the accumulated value calculated in step 5.1.3) to the pre-equalization signal x(n) to obtain the equalized signal y(n):

[0098]

[0099] At this point, the optimization of the PSO decision feedback equalizer is completed.

[0100] The effects of the present invention are further described below in conjunction with simulation experiments:

[0101] 1. Conditions of simulation experiment:

[0102] The hardware platform of the simulation experiment of the present invention is: the processor is Intel(R) Core(TM) i7-11700KF, the main frequency is 3.6GHz, and the memory is 32GB.

[0103] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system, Matlab 2022a software and ADS 2022 software.

[0104] The parameters of the differential microstrip line in the simulation experiment are shown in Table 1:

[0105] Table 1 Experimental parameters

[0106]

[0107] W1 and W2 represent the wire widths of differential line 1 and differential line 2, respectively. S1 and S2 represent the wire spacing between the two differential lines, respectively. Length1 and Length2 represent the lengths of differential line 1 and differential line 2, respectively.

[0108] 2. Simulation content and result analysis of simulation experiment:

[0109] Simulation 1: Under the above experimental conditions, the equalizer tap coefficients are iteratively optimized using the present invention to obtain the oscillation diagram of the particles during the iterative process, as shown in Figure 3 As shown. Among them:

[0110] Figure 3 (a) shows the oscillation of the four dimensions of the particle obtained during the test of experimental group 1;

[0111] Figure 3 (b) shows the oscillation of the four dimensions of the particles obtained during the test of experimental group 2;

[0112] Figure 3 (c) shows the oscillation of the four dimensions of the particles obtained during the test of experimental group 3;

[0113] Figure 3 (d) shows the oscillation of the four dimensions of the particles obtained during the test of experimental group 4;

[0114] from Figure 3 It can be seen that particles can oscillate and converge to stable values ​​within the convergence domain, indicating that the method of the present invention has good robustness.

[0115] Simulation 2: Under the above experimental conditions, for the signal transmitted from the high-speed link, the eye height of the worst eye diagram under the unbalanced, adaptively equalized and the method of the present invention is plotted as a function of the input signal frequency. Figure 4 As shown. Among them:

[0116] Figure 4(a) is a graph showing the changes in the output signal eye height versus the input signal frequency for the three cases in experimental group 1;

[0117] Figure 4 (b) is a graph showing the changes in the output signal eye height versus the input signal frequency for the three conditions in experimental group 2;

[0118] Figure 4 (c) is a graph showing the changes in the output signal eye height versus the input signal frequency for the three conditions in experimental group 3;

[0119] Figure 4 (d) is a graph showing the change of output signal eye height with input signal frequency for the three cases in experimental group 4.

[0120] from Figure 4 It can be seen that when the input signal frequency changes from 30 MHz to 30 GHz, the eye height of the worst eye diagram after adaptive equalization is higher than that of the worst eye diagram without equalization. The difference is not significant at low frequencies, but the effect is obvious at high frequencies. The eye height of the worst eye diagram obtained by the method of the present invention is higher than that of adaptive equalization, and there is a stable improvement in the entire frequency band.

Claims

1. A Pearson correlation coefficient-based PSO decision feedback equalizer optimization method, characterized in that: The steps include: (1) Generate the impulse response waveform before equalization: Set the receiver RX to unbalanced mode and set the input PRBS code frequency f and code length m; Using the code as the input of the channel simulation, the channel simulation is performed in a bit-by-bit manner to obtain the pulse waveform before equalization, and the pulse waveform is saved as an impulse response text before equalization; (2) Generate the output response waveform before equalization: Set the receiver RX to a mode that cancels decision feedback equalization, and input a randomly generated PRBS code with a frequency f and length n. Use this code as the input for channel simulation, perform channel simulation in a bit-by-bit manner, obtain the output response waveform before equalization, and save this pulse waveform as an output response text before equalization. (3) reading the impulse response text before equalization in step (1) and determining its starting point using a hula hoop algorithm, which is the starting point of the waveform corresponding to the output response text before equalization in step (2); (4) Read the output response text before equalization in step (2), and take data of length l from the starting point obtained in step (3) as the input data of the particle swarm optimization algorithm PSO. (5) Optimize the decision feedback equalizer based on the particle swarm optimization algorithm PSO: 5a) Set the number of iterations Nstep for initializing the particle swarm algorithm, the number of individuals N in the population, and the maximum value of the particle position x max and the minimum value x min , the maximum value of the particle velocity v max and the minimum value v min , the dimension D of the particle, the maximum weight coefficient ω of the particle update max and the minimum value ω min , the upper limits of the uniform distribution of self-learning factor and social learning factor are and 5b) The normalized parameter of the Pearson correlation coefficient PLCC between the desired signal and the equalized signal is selected as the fitness function of the PSO optimization function, which is expressed as follows: Among them, x i (t+1) is the position of the i-th particle in the t+1-th iteration, It represents the Pearson correlation coefficient PLCC between the equalized signal and the expected signal, y is the equalized signal, is the mean of y, y d is the expected signal; 5c) Update each particle to obtain the updated particle velocity vector v i (t+1): 5c1) Compare the fitness functions of all particles in the current iteration with their own historical fitness functions to obtain the optimal position p of a single particle with a better fitness function. i (t) is: p i (t)=[p i,1 (t),p i,2 (t),…,p i,j (t),…,p i,D (t)], where p i,j (t) is the position value of the jth dimension of the i-th particle in the population, j = 1, 2, 3, ..., D; 5c2) Compare the fitness functions of all individual particles in the population to obtain the best individual of all particles in the population in the current iteration, that is, the global extreme value g(t); 5c3) Define the particle diversity function S(t): in, The diversity function S(t) characterizes the motion characteristics of the particle, f min (x(t)) and f max (x(t)) are the minimum and maximum fitness of all particles in the population after the current iteration, f(x i (t)) is the fitness value of the i-th particle after the current iteration; 5c4) Substitute the diversity function into the Logistic one-dimensional chaotic map to obtain the adjustment factor r t+1 =(LS(t))r t (1-r t ), r t ∈(0,1), where r t+1 is the adjustment factor for the next iteration, L is a non-negative constant, L≤4, r t Indicates the adjustment factor of the current iteration; 5c5) Using the adjustment factor, calculate the updated weight of the velocity vector of the i-th particle in the population: Among them, t is the number of current iterations, ω i (t) is the updated weight of the velocity vector of the i-th particle in the population after the current iteration; 5c6) Substitute the updated weight into the particle velocity update formula to obtain the initial updated velocity of the current i-th particle: v i (t+1)=ω i (t)v i (t)+c 1i (p i (t)-x i (t))+c 2i (g(t)-x i (t)); Among them, v i (t+1) is the velocity vector of the i-th particle after the initial update of the current iteration, ω i (t) is the velocity vector update weight coefficient for the current iteration, v i (t) is the velocity vector of the current iteration, c 1i and c 2i are the self-learning factor and social learning factor updated by the i-th particle in the population, and are non-negative random constants, p i (t) is the historical optimal position of each individual in the population, g(t) is the global optimal position in the population, and x i (t) is the position of the i-th particle in the current iteration; 5c7) To prevent the velocity update from exceeding the boundary value, a penalty term is introduced after the initial velocity update. The final updated velocity vector is as follows: 5d) Update the positions of all particles in the population according to the updated velocity vector of the particle to obtain the updated position x of each particle i (t+1): 5d1) Using the updated velocity vector v i (t+1) Initial update of particle position: x i (t+1)=x i (t)+v i (t+1) Among them, x i (t+1) is the particle position after the initial update of the current iteration; 5d2) To prevent the initial updated position from exceeding the boundary value, a penalty term is introduced after the initial update of the particle position. The final updated position is as follows: 5e) Repeat steps 5b) to 5d) until the maximum number of iterations is reached, and the final updated positions of all particles are obtained; 5f) According to the fitness function f(x(t)) of each particle, the optimal position g(t) of all particles is selected as the optimal tap coefficient of the decision feedback equalizer to obtain the optimized feedback equalizer; 5f1) Using the fitness function f(x(t)), calculate the fitness of each particle; 5f2) From the positions of all particles p(t) = [p1(t), p2(t), ..., p N (t)], pick out a position with the minimum corresponding fitness function and get the D-dimensional matrix g(t), which is the optimal position of all particles; 5f3) using the value of each dimension in g(t) as the tap coefficient of the decision feedback equalizer; (6) The optimized feedback equalizer is used to equalize the signal at the receiving end RX to obtain the worst eye diagram that can represent the quality of high-speed signal transmission.

2. The method according to claim 1, characterized in that In step (1), channel simulation is performed in a bit-by-bit manner, which is implemented as follows: 1a) Set up a linear time-invariant channel (LTI), use the PRBS code in step (1) as the input of the channel simulation, and calculate the impulse response of a single bit of data in the PRBS code; 1b) Superimpose the impulse responses of all data to obtain the final response waveform.

3. The method according to claim 1, characterized in that Step (3) uses the hula hoop algorithm to determine the starting point of the impulse response text before equalization, and the implementation steps are as follows: 3a) Subtract the influence of DC level from the rising and falling edges of the output response waveform before equalization, and obtain an impulse response through shifting and superposition. The sampling point data corresponding to the maximum value of the impulse response peak is recorded as (x m ,y m ); 3b) will be obtained from the sampling point data (x m ,y m ) to the left of the corresponding position to find 0.5 times the time interval UI, and record the corresponding data as (x l ,y l ), from the sampling point data (x m ,y m ) to the right of the corresponding position to find 0.5 times the time interval UI, and record the corresponding data as (x r ,y r ), the UI size can be set arbitrarily, usually a multiple of 32. Here, UI=32 is set, that is, the waveform of one bit period is sampled at 32 points; 3c) Set the sampling point position x r and x l In x m The left side of the range is moved right by 1 bit at the same time, and the data point |y is calculated during the movement. r -y l | minimum value, and the x corresponding to the minimum value at this time l and x r The mean of the impulse response waveform is used as the starting point before equalization.

4. The method according to claim 1, wherein The steps of equalizing the signal at the receiving end RX using the optimized feedback equalizer in step (6) are as follows: 6a) The decision feedback equalizer at the receiving end (RX) inputs each bit of the signal before equalization, x(n). Each bit of the signal then passes through D-1 delay units, resulting in a total of D signal values ​​x(n), x(n-1), …, x(n-D+1). 6b) Based on the D signal values, decision signals d(n), d(n-1), ..., d(n-D+1) are obtained; 6c) Multiplying the D signal values ​​by the decision signals d(n), d(n-1), ..., d(n-D+1) of the decision device, and then multiplying them by the corresponding optimal tap coefficients g(1,1), g(1,2), ..., g(1,D), respectively, and accumulating the resulting product values; 6d) Add the accumulated value calculated in step 6c) to the signal before equalization x(n) to obtain the equalized signal y(n):

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