A short-distance high-speed optical fiber communication equalization method and system

Abstract

The present invention provides a short-distance high-speed optical fiber communication equalization method and system. A Gaussian mixture model is constructed for an optical signal modulated by a set-order quadrature amplitude modulation. First, the particle swarm optimization algorithm with an initially increasing and then decreasing inertia weight is used to complete the parameter initialization of the Gaussian mixture model. The data features of two dimensions, namely the in-phase component and the quadrature component of the data, are input into the Gaussian mixture model. Then, the expectation-maximization algorithm is used to solve the parameters of the Gaussian mixture model. The membership degree of each data point corresponding to the clustering label of each univariate Gaussian distribution is determined through the parameters, and it is assigned to the corresponding clustering label through the maximum a posteriori probability to complete the nonlinear equalization. The present invention can accurately capture the memory property of signal nonlinear damage, improve the accuracy of nonlinear clustering, and reduce the computational complexity of the nonlinear clustering model under the same clustering effect.

Description

Technical Field

[0001] The present invention relates to the field of optical communication technologies, and particularly to a short-distance high-speed optical fiber communication equalization method and system. Background Art

[0002] In the context of the global information age, the development of information digitization is inseparable from data transmission. As an important part of the transmission network, the optical fiber communication system is facing increasing demands for transmission capacity and transmission distance. As a mature technology, single-mode optical fiber has been widely used in short-distance high-speed communications such as network center interconnection. In short-distance optical fiber communication, the compensation and equalization for various impairments have always been a research hotspot. Various impairments existing in high-speed coherent optical communication systems severely restrict the transmission performance of the systems. Since both optoelectronic devices and optical fiber transmission links have certain nonlinear effects, when there are a large number of devices, the nonlinear effects generated by them are superimposed on each other, which will cause nonlinear phase shift and inter-symbol interference of the transmitted signal, thus seriously affecting the signal quality. How to handle the nonlinear impairments is a major problem that cannot be avoided in the implementation process of high-speed coherent optical communication systems.

[0003] Many nonlinear equalization methods for the digital signal processor (DSP) at the receiving end have been proposed in the prior art, including digital backpropagation (DBP), Volterra series approximation, and perturbation-based nonlinear equalization. The above-mentioned nonlinear equalization methods have been widely studied due to their effectiveness in eliminating the system. However, in high-speed communication systems, the performance of these methods is low while the complexity is huge. With the development of machine learning, the application of a large number of machine learning algorithms provides a new approach for compensating the nonlinear impairments in optical fiber communication systems. Among them, supervised learning algorithms such as support vector machine, support vector regression, and K-means, as well as unsupervised learning algorithms such as k-nearest neighbor and expectation maximization (EM) have attracted much attention due to their good equalization ability. In high-speed communication systems, due to the influence of nonlinearity, pulse broadening occurs during the signal transmission process, and multiple adjacent signals will affect each other, that is, the memory effect appears and becomes a time series. Compared with the algorithms based on Volterra functions and digital backpropagation, machine learning algorithms do not require the parameters of the optical fiber transmission link, and have good flexibility and adaptive ability. In addition, unsupervised learning algorithms do not require training sequence assistance, and have the characteristics of low data redundancy and low computational complexity. The nonlinear equalizer for this algorithm has received great attention.

[0004] Using polarization multiplexing technology in single-mode optical fibers can increase the transmission capacity. However, in short-distance high-speed transmission systems, the superposition of fiber nonlinearity and the nonlinearity of receiving-end devices makes the subsequent compensation much more difficult. Conventional electrical-domain equalization algorithms cannot completely eliminate these mixed interferences. Therefore, for the compensation technology of nonlinear impairments in fiber-optic communication systems, the superposition and temporal correlation of impairments need to be considered to maximize the improvement of system performance, which is also the part ignored in the existing technology. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a short-distance high-speed fiber-optic communication equalization method and system to eliminate or improve one or more defects existing in the prior art, and solve the problem that the superposition of fiber and receiving-end device nonlinearities in short-distance high-speed transmission systems leads to a high complexity of the nonlinear clustering model and makes it difficult to eliminate mixed interferences.

[0006] One aspect of the present invention provides a short-distance high-speed fiber-optic communication equalization method, which is used to be executed at the receiving end in a single-mode fiber-optic communication system. The method includes the following steps:

[0007] Receive the optical signal orthogonally amplitude modulated by the transmitting end with a set order. After performing polarization beam splitting, photoelectric detection, and four-channel digital sampling on the optical signal, perform linear equalization processing using a preset method to obtain complete data sets in two polarization directions; each symbol in the symbol sequence of the data set represents the real part and the imaginary part of the data point based on a two-dimensional vector.

[0008] For the complete data sets, use the particle swarm optimization algorithm to establish the initial parameters of the Gaussian mixture model, where the Gaussian mixture model includes multiple Gaussian distributions, and each Gaussian distribution corresponds to the distribution characteristics of a constellation point in the constellation diagram of the orthogonal amplitude modulation.

[0009] Use the expectation maximization algorithm to iterate the Gaussian mixture model in the state of the initial parameters until the parameters converge.

[0010] Based on the Gaussian mixture model after the parameters converge, calculate the posterior probability of each data point belonging to each Gaussian distribution as the membership degree, and perform clustering to divide into the same clustering clusters according to the membership degree to complete the nonlinear equalization.

[0011] In some embodiments, performing linear equalization processing using a preset method includes:

[0012] Perform I / Q orthogonalization, low-pass filtering, Gardner time synchronization, dispersion compensation, frequency offset compensation, and phase offset compensation on the data obtained after sampling.

[0013] In some embodiments, for the complete data set, the initial parameters of the Gaussian mixture model are established using the particle swarm optimization algorithm, including:

[0014] Initialize the particle swarm, where each particle represents a solution of the Gaussian mixture model parameters;

[0015] In each iteration process, calculate and record the fitness value of each particle; determine the individual extreme value and the global extreme value based on the fitness values of the particles; update the speed and position of each particle itself according to the positions and speeds corresponding to the individual extreme value and the global extreme value;

[0016] When the set number of iterations is reached or the global extreme value reaches the set value, stop the iteration, and output the solution of the particle corresponding to the global extreme value as the initial parameters of the Gaussian mixture model.

[0017] In some embodiments, the fitness value is calculated using the log-likelihood function of the Gaussian mixture model, and the calculation formula is:

[0018]

[0019] where α k represents the mixing coefficient of the k-th Gaussian distribution, μ k represents the mean of the k-th Gaussian distribution, represents the covariance of the k-th Gaussian distribution, represents the probability density of the k-th Gaussian distribution; N represents the number of data points, x i represents the i-th data point; K represents the number of single Gaussian distributions included in the Gaussian mixture model; θ includes the mixing coefficient α k of each Gaussian distribution in the Gaussian mixture model, the mean μ k and the covariance

[0020] In updating the speed and position of each particle itself according to the positions and speeds corresponding to the individual extreme value and the global extreme value, the speed update formula is:

[0021]

[0022] where w is the inertia weight; k is the current iteration number, c1 is the individual learning factor, c2 is the social learning factor; r1 and r2 are random numbers distributed between [0, 1]; represents the position of particle i in the current k-th iteration; represents the individual optimal position of particle i up to the current iteration round; the global optimal position of the entire particle up to the current iteration round; represents the speed of particle i at the (k + 1)-th iteration, Denote the velocity of particle \(i\) at the \(k\)-th iteration;

[0023] The position update formula of the particle is:

[0024]

[0025] Where, Denote the position of particle \(i\) in the next iteration round; is the position of particle \(i\) in the current iteration round, is the velocity of particle \(i\) in the next iteration round.

[0026] In some embodiments, the Gaussian mixture model in the initial parameter state is iterated using the expectation maximization algorithm until the parameters converge, including:

[0027] Define the latent variable \(z\) ik , reflecting that the data point \(x\) i comes from the \(k\)-th Gaussian distribution, and the expression is:

[0028]

[0029] Where, \(i = 1, 2, \ldots, N\); \(k = 1, 2, \ldots, K\); the latent variable and the data point form the complete data, denoted as \((x\) i , \(z\) i1 , \(z\) i2 , \(\ldots\), \(z\) iK ) \(i = 1, 2, \ldots, N\);

[0030] The likelihood function expression of the Gaussian mixture model is:

[0031]

[0032] Where, \(\mu\) k Denote the mean of the \(k\)-th Gaussian distribution, Denote the covariance of the \(k\)-th Gaussian distribution; \(n\) k Denote the number of the \(N\) observation points coming from the \(k\)-th Gaussian distribution;

[0033] Then the log-likelihood function of the Gaussian mixture model is:

[0034]

[0035] In the E step of the expectation maximization algorithm, according to the current parameters, calculate the posterior probability that each data point \(x\) i belongs to the \(k\)-th Gaussian distribution Denote \(\theta\) 0 as the initial value of the iteration parameters, denote \(\theta\) t$\hat{\theta}$ is the estimated value of the parameter $\theta$ in the $t$-th iteration. By taking the expectation of the log-likelihood function, the $Q$ function is obtained as follows:

[0036] $Q(\theta,\hat{\theta}$ t ) = E(log P(x, x|\theta),\hat{\theta}$ t );

[0037]

[0038] where $i = 1, 2, \ldots, N$; $k = 1, 2, \ldots, K$;

[0039] In the M step, find $\theta$ when the $Q$ function reaches its maximum value, and use it as $\hat{\theta}$ t+1 to participate in the next iteration. The expression is:

[0040]

[0041] where $\theta$ includes the mixing coefficients $\alpha$ k of each Gaussian distribution in the Gaussian mixture model, the means $\mu$ k and the covariance The expression is:

[0042] $\theta = (\alpha_1, \alpha_2, \ldots, \alpha$ K ; $\mu_1, \mu_2, \ldots, \mu$ K ; $\sigma_1, \sigma_2, \ldots, \sigma$ K );

[0043] Then the estimates of the mixing coefficient $\alpha$ k , the mean $\mu$ k and the covariance are:

[0044]

[0045]

[0046] Repeat the above E step and M step until the parameters converge.

[0047] In some embodiments, in the method, the transmitter modulates the optical signal using 16-QAM, 64-QAM or 256-QAM.

[0048] On the other hand, the present invention also provides a short-distance high-speed optical fiber communication system, which includes:

[0049] A transmitter, which includes a transmitter digital signal processor, an arbitrary waveform generator, a digital-to-analog converter, and an optical modulator connected in sequence. The optical modulator is provided with a light source by a first local oscillator laser; the transmitter is used to generate an optical signal modulated by a set-order quadrature amplitude modulation;

[0050] An optical amplifier for amplifying the optical signal output by the optical modulator;

[0051] A single-mode optical fiber for conducting the amplified optical signal;

[0052] A receiving end, including an optical mixer, a photodiode, a sampling oscilloscope, and a receiving-end digital signal processor connected in sequence; the optical mixer is connected to a second local oscillator laser; the receiving end executes the above short-distance high-speed optical fiber communication equalization method.

[0053] In some embodiments, the optical fiber amplifier is an erbium-doped optical fiber amplifier.

[0054] On the other hand, the present invention also provides a computer-readable storage medium, on which a computer program / instructions are stored, and when the computer program / instructions are executed by a processor, the steps of the above method are implemented.

[0055] On the other hand, the present invention also provides a computer program product, including a computer program / instructions, and when the computer program / instructions are executed by a processor, the steps of the above method are implemented.

[0056] The beneficial effects of the present invention are at least:

[0057] The short-distance high-speed optical fiber communication equalization method and system of the present invention constructs a Gaussian mixture model for an optical signal modulated by a set-order quadrature amplitude modulation. First, the particle swarm optimization (PSO) algorithm with an inertia weight that first increases and then decreases is used to complete the parameter initialization of the Gaussian mixture model. The data features of two dimensions, namely the in-phase component and the quadrature component of the data, are input into the Gaussian mixture model. Then, the expectation maximization (EM) algorithm is used to solve the parameters of the Gaussian mixture model. The membership degree of each data point corresponding to the clustering label of each univariate Gaussian distribution is determined through the parameters, and it is assigned to the corresponding clustering label through the maximum a posteriori probability, thus completing the nonlinear equalization. The present invention can accurately capture the memory property of signal nonlinear damage, improve the accuracy of nonlinear clustering, and reduce the computational complexity of the nonlinear clustering model under the same clustering effect.

[0058] The additional advantages, objectives, and features of the present invention will be partially described below, and will become partially apparent to those of ordinary skill in the art after studying the following text, or can be learned from the practice of the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structure specifically pointed out in the specification and the drawings.

[0059] Those skilled in the art will understand that the objectives and advantages that can be achieved by the present invention are not limited to the above specifically described, and the above and other objectives that the present invention can achieve will be more clearly understood according to the following detailed description. Description of the Drawings

[0060] The accompanying drawings described herein are used to provide a further understanding of the present invention, form a part of this application, and do not limit the present invention. In the drawings:

[0061] Figure 1 It is a schematic flow chart of the short-distance high-speed optical fiber communication equalization method according to an embodiment of the present invention.

[0062] Figure 2 It is a schematic logic diagram of the short-distance high-speed optical fiber communication equalization method according to another embodiment of the present invention.

[0063] Figure 3 It is a schematic structural diagram of the short-distance high-speed optical fiber communication system according to another embodiment of the present invention.

[0064] Figure 4 It is a diagram showing the change of bit error rate with the received optical power when performing clustering operation on optical signals based on the PSO-GMM model according to an embodiment of the present invention.

[0065] Figure 5 It is a diagram showing the change of quality factor with the received optical power when performing clustering analysis on optical signals based on the PSO-GMM model, K-Means, DBSCAN, and KNN according to an embodiment of the present invention. Detailed implementation manners

[0066] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with the implementation manners and the accompanying drawings. Herein, the illustrative implementation manners of the present invention and their descriptions are used to explain the present invention, but do not limit the present invention.

[0067] Herein, it also needs to be noted that in order to avoid obscuring the present invention due to unnecessary details, only the structures and / or processing steps closely related to the solution of the present invention are shown in the drawings, while other details less related to the present invention are omitted.

[0068] It should be emphasized that the term "including / comprising" when used herein refers to the presence of features, elements, steps, or components, but does not exclude the presence or addition of one or more other features, elements, steps, or components.

[0069] Herein, it also needs to be noted that if not otherwise specified, the term "connection" in this article can not only refer to a direct connection, but also represent an indirect connection with an intermediate.

[0070] During the transmission of optical signals, problems such as non - linear phase shift and inter - symbol interference (ISI) will occur due to non - linear interference in optical fibers and the receiving end, which will affect the quality of the transmitted signals. Especially, the "memory effect" that appears during high - speed and large - capacity transmission exacerbates non - linear distortion. Traditional non - linear equalization methods have limitations in performance or computational complexity and are difficult to meet the requirements of high - speed communication. Therefore, the present invention proposes to use a PSO - GMM clustering model, and uses the particle swarm optimization (PSO) algorithm to improve the convergence speed of the Gaussian mixture model (GMM) to more accurately capture the non - linear characteristics of the signal, achieve efficient non - linear equalization, and thus improve the transmission performance of the system.

[0071] Specifically, one aspect of the present invention provides a short - distance high - speed optical fiber communication equalization method, which is used to be executed at the receiving end in a single - mode optical fiber communication system. As Figure 1 and 2 shown, the method includes the following steps S101 - S104:

[0072] Step S101: Receive the optical signal modulated by the set - order quadrature amplitude modulation from the transmitting end. After performing polarization beam splitting, photoelectric detection, and four - channel digital sampling on the optical signal, perform linear equalization processing using a preset method to obtain complete data sets in two polarization directions; each symbol in the data set symbol sequence is based on a two - dimensional vector to express the real part and the imaginary part of the data point.

[0073] Step S102: For the complete data set, use the particle swarm optimization algorithm to establish the initial parameters of the Gaussian mixture model. The Gaussian mixture model contains multiple Gaussian distributions, and each Gaussian distribution respectively corresponds to the distribution characteristics of a constellation point in the constellation diagram of the quadrature amplitude modulation.

[0074] Step S103: Use the expectation - maximization algorithm to iterate the Gaussian mixture model in the initial parameter state until the parameters converge.

[0075] Step S104: Based on the Gaussian mixture model after the parameters converge, calculate the posterior probability of each data point belonging to each Gaussian distribution as the membership degree, and perform clustering to divide into the same clustering clusters according to the membership degree to complete non - linear equalization.

[0076] In step S101, the optical signal processed by the present invention is based on a set-order quadrature amplitude modulation at the transmitting end. Quadrature Amplitude Modulation (QAM): It is a modulation method that simultaneously uses amplitude modulation and phase modulation. By modulating different information on two orthogonal carriers (one is a cosine wave and the other is a sine wave), more data can be transmitted simultaneously. In QAM, a signal consists of two orthogonal components, usually denoted as I (In-phase) and Q (Quadrature-phase). The I component modulates the amplitude of one carrier, and the Q component modulates the amplitude of another carrier orthogonal to the I component. Specifically, the present invention can process 16-QAM, 64-QAM, or 256-QAM schemes.

[0077] Exemplarily, in 64-QAM, there are 64 possible symbols (signal points), so it can transmit 6 bits of data in each symbol period, 2 6 = 64. These 64 symbols are distributed in a two-dimensional coordinate system, where the horizontal axis represents the I component and the vertical axis represents the Q component. The constellation diagram of 64-QAM consists of 64 points, each point representing a different symbol, and each symbol corresponds to 6 bits of data. The coordinates of each point in the constellation diagram are determined by I (abscissa) and Q (ordinate).

[0078] The transmitting end performs 64-QAM modulation on the original 0-1 bit data. Each constellation point of the signal constellation diagram represents a transmitted symbol, corresponding to 64 categories, numbered from 1 to 64, as the labels for clustering. The data after modulation at the transmitting end is processed by an arbitrary waveform generator (AWG), an electrical amplifier (EA), and a Mach-Zehnder modulator (MZM) to form an optical signal, and then divided into two beams of light to enter a spatial light modulator, and the two beams of light are combined and enter the optical fiber for transmission. At the receiving end of the coherent optical communication system, photoelectric conversion is performed through a polarization beam splitter (PBS) and photodetectors, and a four-channel digital sampling oscilloscope is used to perform digital processing on the signal, and linear equalization processing is performed on the obtained original electrical signal. The linear equalization processing includes row I / Q orthogonality, low-pass filtering, Gardner time synchronization, dispersion compensation, frequency offset compensation, and phase offset compensation.

[0079] I / Q orthogonality decomposes the received signal into two orthogonal components, namely the in-phase (I) component and the quadrature (Q) component. In a modulation system, the I / Q orthogonal components can carry different information respectively. By separating the received signal into I and Q components, the modulation characteristics of each component can be better processed, preparing for subsequent demodulation. Low-pass filtering removes high-frequency noise and interference in the signal. Since various high-frequency noises are introduced during optical signal transmission, low-pass filtering can retain the useful frequency components in the signal while eliminating the unwanted high-frequency noise, thereby improving the signal-to-noise ratio (SNR) of the signal and reducing the impact of noise on signal demodulation. Gardner time synchronization is used to achieve symbol-level time synchronization at the receiving end, ensuring that the sampling moment is aligned with the optimal position of the symbol. Dispersion compensation is used to compensate for the signal broadening or distortion caused by the fiber dispersion effect during transmission. Fiber dispersion causes signals of different frequency components to propagate at different speeds in the fiber, broadening the signal pulse and causing distortion. The dispersion compensation algorithm can correct this distortion and restore the original form of the signal, thereby reducing the inter-symbol interference (ISI) caused by broadening. Frequency offset compensation is used to correct the deviation between the carrier frequency at the receiving end and the carrier frequency at the transmitting end. At the receiving end, the received signal may experience phase and spectrum changes due to frequency offset, resulting in demodulation errors. Frequency offset compensation can correct this deviation, making the carrier frequency at the receiving end consistent with that at the transmitting end and ensuring the accuracy of signal demodulation. Phase offset compensation is used to adjust the signal phase to align it with the phase at the transmitting end. Due to phase noise or other effects during transmission, the phase of the received signal may drift, leading to demodulation errors. Phase offset compensation can eliminate this phase drift, enabling the receiving end to accurately restore the phase information at the transmitting end and thus correctly decode the signal content.

[0080] For an optical signal modulated with 64-QAM at the transmitting end, after linear uniform processing, a 64-QAM symbol sequence s of length N is obtained, s = [s1, s2, …, s N , where the vector s i (i = 1, 2, …, N) represents the i-th symbol of the 64-QAM signal sequence in one polarization direction, and s i = [I i ; Q i is a two-dimensional vector. I i and Q i respectively represent the real and imaginary part data of the M-QAM signal. Taking the real and imaginary part data in one polarization direction as a group of signal points, there are a total of N groups of signal points. The same processing is performed on the data in the other polarization direction to obtain two complete data sets X in and Y in .

[0081] In step S102, the present invention captures the characteristics of non - linear distortion in the optical fiber communication system through statistical modeling and clustering analysis, and classifies and equalizes the signals at the receiving end to counteract the influence of non - linear effects. In step S101, the characteristic data of each data point is extracted through linear equalization processing, such as the in - phase (I) and quadrature (Q) components of a 64 - QAM modulated signal. These data points reflect the distribution of the signal under the current transmission state, but due to non - linear impairments, they deviate from the ideal constellation points. For each constellation point of a QAM with a set order, it forms a unique distribution characteristic during signal transmission. Therefore, by establishing a Gaussian mixture model and performing clustering analysis, signal classification and equalization can be achieved. The present invention processes different polarization directions of the signal separately to obtain a complete non - linear equalization data set. Further, the Gaussian mixture model (GMM) represents the complex signal data distribution as a mixture of multiple Gaussian distributions. Since non - linear distortion makes the signal distribution at the receiving end complex, GMM can approximate these complex distributions through multiple Gaussian components and capture various different patterns in the signal data. Through the GMM model, the signal data can be divided into different clustering labels, which correspond to different signal states (or different non - linear distortion patterns). In this way, according to the actual offset state of the received signal, it can be assigned to the "ideal" distribution state closest to it, thus realizing error correction.

[0082] In step S102, the present invention uses the Particle Swarm Optimization (PSO) algorithm to initialize the GMM parameters. As a global optimization algorithm, PSO finds better parameter values through population search, enabling the GMM model to converge faster and reducing the number of iterations.

[0083] The probability density function (PDF) of a univariate Gaussian distribution is as follows:

[0084]

[0085] where μ and σ 2 are the mean and variance of this Gaussian distribution respectively.

[0086] The Gaussian mixture model is a model composed of multiple univariate Gaussian models and has a probability distribution of the following form:

[0087]

[0088] where K is the number of single - Gaussian models in this mixture model; α k is the weight coefficient of each single - Gaussian model, satisfying α k ≥0 and φ(x|θ k ) represents the probability density of the k - th single - Gaussian model, called the k - th sub - model; θ kDenote the parameters (mean and variance) of the k-th single Gaussian model, i.e.,

[0089] Exemplarily, for 64-QAM modulation, the value of K is 64, and each univariate Gaussian distribution corresponds to the distribution characteristic of a constellation point.

[0090] In some embodiments, for the complete data set, use the particle swarm optimization algorithm to establish the initial parameters of the Gaussian mixture model, including steps S201 to S203:

[0091] Step S201: Initialize the particle swarm (PSO), and each particle represents a solution of the parameters of the Gaussian mixture model.

[0092] Step S202: In each iteration process, calculate and record the fitness value of each particle; determine the individual extreme value and the global extreme value based on the fitness values of each particle; update the velocity and position of each particle itself according to the positions and velocities corresponding to the individual extreme value and the global extreme value.

[0093] Step S203: When the set number of iterations is reached or the global extreme value reaches the set value, stop the iteration, and output the solution of the particle corresponding to the global extreme value as the initial parameters of the Gaussian mixture model.

[0094] In some embodiments, the fitness value in step S202 is calculated using the log-likelihood function of the Gaussian mixture model, and the calculation formula is:

[0095]

[0096] where α k represents the mixing coefficient of the k-th Gaussian distribution, μ k represents the mean of the k-th Gaussian distribution, represents the covariance of the k-th Gaussian distribution, represents the probability density of the k-th Gaussian distribution; N represents the number of data points, x i represents the i-th data point; K represents the number of single Gaussian distributions included in the Gaussian mixture model; θ includes the mixing coefficient α k of each Gaussian distribution in the Gaussian mixture model, the mean μ k and the covariance

[0097] In updating the velocity and position of each particle itself according to the positions and velocities corresponding to the individual extreme value and the global extreme value, the velocity update formula is:

[0098]

[0099] Among them, w is the inertia weight; k is the current iteration number, c1 is the individual learning factor, and c2 is the social learning factor; r1 and r2 are random numbers distributed between [0, 1]; represents the position of particle i at the current k-th iteration; represents the individual optimal position of particle i up to the current iteration round; the global optimal position of the entire particle up to the current iteration round; represents the velocity of particle i at the (k + 1)-th iteration, represents the velocity of particle i at the k-th iteration.

[0100] The position update formula of the particle is:

[0101]

[0102] Among them, represents the position of particle i in the next iteration round; is the position of particle i in the current iteration round, is the velocity of particle i in the next iteration round.

[0103] When the set iteration number is reached or the population extremum reaches the set value, the particle swarm optimization algorithm completes the initialization construction of the Gaussian mixture model parameters.

[0104] In step S103, the main function of the EM algorithm (Expectation-Maximization algorithm) is to optimize and estimate the parameters of the Gaussian mixture model (GMM). Specifically, the EM algorithm is used to iteratively solve the latent variables included in the GMM, and estimate the mean, variance, and weight parameters of the GMM by maximizing the likelihood function, so as to establish an accurate signal data distribution model. After the parameter optimization is completed, the EM algorithm will calculate the posterior probability of each signal point belonging to each Gaussian component according to the calculated Gaussian distribution parameters. Using these posterior probabilities, the signal points are assigned to the clustering label with the highest membership probability to achieve the classification of the signal points and complete the nonlinear equalization.

[0105] In some embodiments, the Gaussian mixture model in the initial parameter state is iterated using the expectation maximization algorithm until the parameters converge, including steps S301 to S306:

[0106] Step S301: Define the latent variable z ik , which reflects that the data point x i comes from the k-th Gaussian distribution, and the expression is:

[0107]

[0108] where \(i = 1, 2, \ldots, N\); \(k = 1, 2, \ldots, K\); the latent variables and the data points form the complete data, denoted as \((x i , z i1 , z i2 , \ldots, z iK ) = 1, 2, \ldots, N\);

[0109] Step S302: The likelihood function expression of the Gaussian mixture model is:

[0110]

[0111] where \(\mu k represents the mean of the \(k\)-th Gaussian distribution, represents the covariance of the \(k\)-th Gaussian distribution; \(n k represents the number of the \(N\) observation points from the \(k\)-th Gaussian distribution.

[0112] Step S303: The log-likelihood function of the Gaussian mixture model is:

[0113]

[0114] Step S304: In the E-step of the expectation-maximization algorithm, according to the current parameters, calculate the posterior probability that each data point \(x i belongs to the \(k\)-th Gaussian distribution Denote \(\theta 0 as the initial value of the iterative parameter, and denote \(\theta t as the estimated value of the parameter \(\theta\) in the \(t\)-th iteration. By taking the expectation of the log-likelihood function, the Q function is obtained:

[0115] \(Q(\theta, \theta t ) = E(\log P(x, x|\theta), \theta t );

[0116]

[0117] where \(i = 1, 2, \ldots, N\); \(k = 1, 2, \ldots, K\);

[0118] Step S305: In the M-step, find \(\theta\) when the Q function reaches its maximum value, and use it as \(\theta t+1 to participate in the next iteration. The expression is:

[0119]

[0120] where \(\theta\) includes the mixing coefficient \(\alpha k of each Gaussian distribution in the Gaussian mixture model, k the mean \(\mu and the covariance, and the expression is:

[0121] θ = (α1, α2, ..., α K ; μ1, μ2, …, μ K ; σ1, σ2, …, σ K );

[0122] Then the estimates of the mixing coefficients α k , the means μ k and the covariance are:

[0123]

[0124] Step S306: Repeat the E-step and the M-step until the parameters converge.

[0125] In step S104, using the Gaussian mixture model with optimized parameters, calculate the posterior probability i that each data point x belongs to the k-th Gaussian distribution as the membership degree for clustering division to complete the non-linear equalization of the signal.

[0126] On the other hand, the present invention also provides a short-distance high-speed optical fiber communication system, as Figure 3 shown, the system includes:

[0127] A transmitting end, which includes a transmitting-end digital signal processor, an arbitrary waveform generator, a digital-to-analog converter, and an optical modulator connected in sequence. The optical modulator is provided with a light source by a first local oscillator laser; the transmitting end is used to generate an optical signal subjected to orthogonal amplitude modulation of a set order.

[0128] An optical amplifier, which is used to amplify the optical signal output by the optical modulator.

[0129] A single-mode optical fiber, which is used to conduct the amplified optical signal.

[0130] A receiving end, which includes an optical mixer, a photodiode, a sampling oscilloscope, and a receiving-end digital signal processor connected in sequence; the optical mixer is connected to a second local oscillator laser; the receiving end executes the short-distance high-speed optical fiber communication equalization method described in the above steps S101 to S104.

[0131] In some embodiments, the optical fiber amplifier is an erbium-doped optical fiber amplifier. A optical power meter is further provided after the optical modulator.

[0132] Exemplarily, the process of the short-distance high-speed optical fiber communication system for non-linearly equalizing the optical signal for 64-QAM modulation includes steps S401 to S403:

[0133] Step S401: At the transmitting end, the original 0-1 bit data is modulated by 64-QAM. Each constellation point of the signal constellation diagram represents a transmitted symbol, corresponding to 64 categories, numbered from 1 to 64 as the labels of the categories. The data passes through an arbitrary waveform generator (AWG), an electrical amplifier (EA), and a Mach-Zehnder modulator (MZM) in sequence to form an optical signal, and then is split into two beams of light and enters the spatial light modulator, and finally merged and transmitted through the optical fiber. At the receiving end of the coherent optical communication system, photoelectric conversion is performed through a polarization beam splitter (PBS) and photodetectors. A four-channel digital sampling oscilloscope is used to digitally process the received signal, and linear equalization processing is performed on the obtained original electrical signal. For the 64-QAM signal at the current moment, two features, namely the in-phase component and the quadrature component of each polarization direction, are selected to construct a data set.

[0134] The high-speed coherent optical communication system is as Figure 3 shown, which represents the basic block diagram of the communication system. It includes an arbitrary waveform generator (AWG) with a rate of 100 Ga / s, a digital-to-analog converter, a 40-GHz high-bandwidth IQ modulator, a 1550-nm laser, an erbium-doped fiber amplifier (EDFA), a G652 standard single-mode fiber (SSMF), an optical mixer, a balanced photodetector, a 256-GS / a digital sampling oscilloscope, and digital signal processing (DSP) modules at the transmitting and receiving ends. In the DSP module at the transmitting end, operations including pseudo-random binary sequence (PRBS), QAM symbol mapping, upsampling, root-raised cosine filter shaping, and resampling are performed; in the DSP module at the receiving end, operations including low-pass filter (LPF), power normalization, IQ orthogonality, clock recovery, chromatic dispersion compensation (CDC), polarization mode dispersion compensation (MCMA), carrier recovery (FOE, CPE), and PSO-GMM nonlinear equalization processing, 64QAM symbol inverse mapping, and bit error rate calculation are performed.

[0135] Step S402: Build a PSO-GMM clustering model for the nonlinear equalization of the high-speed coherent optical communication system. The PSO-GMM algorithm model includes an input layer, a PSO algorithm sub-module, an EM algorithm sub-module, and a linear output layer. The input layer sends the made 64-QAM data set into the PSO algorithm sub-module, and the data set X inIt is a two-dimensional vector with a dimension of N×2, where N represents the length of the dataset and 2 represents the number of data features, including two-dimensional features of the in-phase component and the quadrature component. The PSO algorithm is a heuristic optimization algorithm in the field of intelligent computing. Its core idea is to utilize the sharing of information by individuals in the population to enable the movement of the entire population to evolve from disorder to order in the problem-solving space, thereby quickly obtaining the optimal solution to the problem. It is commonly used in multi-objective optimization to find the global optimal solution. The PSO algorithm sub-module uses the particle swarm optimization algorithm with an initially increasing and then decreasing inertia weight to complete the parameter initialization of the GMM model, so as to accelerate the convergence process and reduce the number of iterations. After the PSO algorithm sub-module completes the parameter initialization, the EM algorithm is used to iterate the parameters to complete the parameter estimation. The EM algorithm is an unsupervised expectation-maximization algorithm mainly used to solve the parameter estimation of a mixture model containing hidden variables. The EM algorithm iteratively solves the maximum likelihood estimation of the parameters. The output layer uses the estimated parameters of the Gaussian mixture model obtained by the EM algorithm iteration to classify the signal points, and selects the maximum membership degree of the current signal point as its final clustering result.

[0136] Step S403: Configure the required parameters for the PSO-GMM algorithm model for nonlinear equalization of the high-speed coherent optical communication system built in Step 2, including the parameters of the PSO algorithm and the parameters of the GMM model. The parameters of the PSO algorithm include the particle swarm size, particle dimension, number of particle iterations, inertia weight, and learning factor; the parameters of the GMM model include the number of single Gaussian models, the mean and variance of each model, and the number of iterations. Use the 64-QAM training dataset made in Step 1 to initialize the parameter values of the GMM model, use the PSO algorithm to initialize the parameter values of the GMM model, then use the GM algorithm to estimate the parameters, and obtain the optimal parameter estimation after iteration. Use the parameters to cluster the data points and divide them into 64 same clusters to complete the nonlinear equalization of the signal.

[0137] In order to find its optimal parameters, parameter control is required. First, determine various parameters of the PSO algorithm sub-module. In this example, set the particle swarm size to 64, the particle dimension to 2, the number of particle iterations to 150, the initial inertia weight to 0.8, which changes linearly with the increase in the number of iterations, the learning factor to 0.01. After the iteration is completed, the inertia weight is 0.443, and at the same time, the initial values of the GMM model parameters are obtained. Subsequently, the optimal values of the GMM model parameters are determined through the EM algorithm iteration. In this example, there are 64 single Gaussian models and their corresponding parameters.

[0138] After determining the initial parameters of the GMM model, iteration begins. When the iteration error remains basically unchanged, the iteration ends, obtaining a complete clustering model. At the same time, the clustering of 64QAM signals is completed, and the bit error rate is calculated to be 0.0187. The PSO-GMM model is used to cluster signals under different received optical powers (ROP) of the receiver. The results are as Figure 4 shown. The PSO-GMM model is compared with traditional GMM, K-mean, and KNN clustering models. Within the range of -15dBm to -5dBm of the system optical transmission power (ROP), the Q factor is used to analyze the clustering effect of different clustering models on 64-QAM signals. The results are as Figure 5 shown.

[0139] The system processes the nonlinear damage of 64-QAM signals at the receiver. For the signal sequence after conventional linear equalization processing, each 64-QAM signal at each moment has four characteristic dimensions, including the real and imaginary part data in two polarization directions. Due to the nonlinear interference of optical fibers and high-speed optical devices, nonlinear effects between symbols are caused. For each 64-QAM symbol at each moment, the PSO-GMM algorithm is used for iteration, and the signal is divided into the clustering cluster with the largest membership degree using the parameters of the GMM model to complete the nonlinear equalization of the signal. The PSO algorithm sub-module is used to initialize the parameters of the GMM model to improve the convergence speed of the GMM model and reduce the number of iterations. At the same time, a dynamic inertia weight is used to make the particle swarm algorithm have strong global convergence ability in the initial stage and strong local convergence ability in the later stage. The EM algorithm is used to perform maximum likelihood estimation on the parameters of the GMM model, and the obtained parameters are used for the clustering division of the signal.

[0140] Corresponding to the above method, the present invention also provides a device / system. The device / system includes a computer device, the computer device includes a processor and a memory, the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the device / system implements the steps of the method described above.

[0141] The embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the steps of the foregoing edge computing server deployment method. The computer-readable storage medium may be a tangible storage medium, such as random access memory (RAM), memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, floppy disks, hard disks, removable storage disks, CD-ROM, or any other form of storage medium well-known in the technical field.

[0142] In summary, for the short-distance high-speed optical fiber communication equalization method and system of the present invention, a Gaussian mixture model is constructed for an optical signal modulated by a set-order quadrature amplitude modulation. First, the particle swarm optimization (PSO) algorithm with an inertia weight that first increases and then decreases is used to complete the parameter initialization of the Gaussian mixture model. The data characteristics of two dimensions, namely the in-phase component and the quadrature component of the data, are input into the Gaussian mixture model. Then, the expectation maximization (EM) algorithm is used to solve the parameters of the Gaussian mixture model. The membership degree of each data point corresponding to the clustering label of each univariate Gaussian distribution is determined through the parameters, and it is assigned to the corresponding clustering label through the maximum a posteriori probability, thereby completing the nonlinear equalization. The present invention can accurately capture the memory property of signal nonlinear damage, improve the accuracy of nonlinear clustering, and reduce the computational complexity of the nonlinear clustering model under the same clustering effect.

[0143] Those of ordinary skill in the art should understand that the various exemplary components, systems, and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software, or a combination of both. Specifically, whether to implement it in hardware or software depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention. When implemented in hardware, it can be, for example, an electronic circuit, an application-specific integrated circuit (ASIC), appropriate firmware, a plug-in, a functional card, and so on. When implemented in software, the elements of the present invention are programs or code segments used to perform the required tasks. The program or code segment can be stored in a machine-readable medium or transmitted through a data signal carried in a carrier wave on a transmission medium or a communication link.

[0144] It should be clear that the present invention is not limited to the specific configurations and processes described above and illustrated in the figures. For the sake of brevity, the detailed description of known methods is omitted here. In the above embodiments, several specific steps are described and illustrated as examples. However, the method process of the present invention is not limited to the specific steps described and illustrated. Those skilled in the art can make various changes, modifications, and additions, or change the order between the steps after understanding the spirit of the present invention.

[0145] In the present invention, the features described and / or illustrated for one embodiment can be used in the same way or in a similar way in one or more other embodiments, and / or combined with the features of other embodiments or replace the features of other embodiments.

[0146] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, various modifications and variations can be made to the embodiments of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A short-distance high-speed fiber optic communication equalization method, characterized in that, The method is used to be executed at the receiving end in a single-mode fiber optic communication system, and the method includes the following steps: Receive the optical signal modulated by the set-order quadrature amplitude modulation at the transmitting end. After performing polarization beam splitting, photoelectric detection, and four-channel digital sampling on the optical signal, perform linear equalization processing using a preset method to obtain complete data sets in two polarization directions; each symbol in the data set symbol sequence represents the real part and the imaginary part of the data point based on a two-dimensional vector. For the complete data set, use the particle swarm optimization algorithm to establish the initial parameters of the Gaussian mixture model. The Gaussian mixture model contains multiple Gaussian distributions, and each Gaussian distribution corresponds to the distribution characteristics of a constellation point in the constellation diagram of the quadrature amplitude modulation. Use the expectation maximization algorithm to iterate the Gaussian mixture model in the state of the initial parameters until the parameters converge. Based on the Gaussian mixture model after the parameters converge, calculate the posterior probability that each data point belongs to each Gaussian distribution as the membership degree, and perform clustering to divide into the same clustering clusters according to the membership degree to complete non-linear equalization.

2. The short-distance high-speed optical fiber communication equalization method according to claim 1, characterized in that, Performing linear equalization processing using a preset method includes: Perform I / Q orthogonality, low-pass filtering, Gardner time synchronization, dispersion compensation, frequency offset compensation, and phase offset compensation on the data obtained after sampling.

3. The short-distance high-speed optical fiber communication equalization method according to claim 2, characterized in that For the complete data set, using the particle swarm optimization algorithm to establish the initial parameters of the Gaussian mixture model includes: Initialize the particle swarm, and each particle represents a solution of the Gaussian mixture model parameters. In each iteration process, calculate and record the fitness value of each particle; determine the individual extreme value and the global extreme value based on the fitness values of each particle; update the speed and position of each particle itself according to the positions and speeds corresponding to the individual extreme value and the global extreme value. When reaching the set number of iterations or the global extreme value reaches the set value, stop the iteration, and output the solution of the particle corresponding to the global extreme value as the initial parameters of the Gaussian mixture model.

4. The short-distance high-speed optical fiber communication equalization method according to claim 3, wherein The fitness value is calculated using the log-likelihood function of the Gaussian mixture model, and the calculation formula is: Among them, α k represents the mixing coefficient of the k-th Gaussian distribution, μ k represents the mean of the k-th Gaussian distribution, represents the covariance of the k-th Gaussian distribution, represents the probability density of the k-th Gaussian distribution; N represents the number of data points, x i represents the i-th data point; K represents the number of single Gaussian distributions included in the Gaussian mixture model; θ includes the mixing coefficient α k of each Gaussian distribution in the Gaussian mixture model, the mean μ k and the covariance In updating the speed and position of each particle itself according to the positions and speeds corresponding to the individual extreme value and the global extreme value, the speed update formula is: Among them, w is the inertia weight; k is the current iteration number, c1 is the individual learning factor, and c2 is the social learning factor; r1 and r2 are random numbers distributed between [0, 1]; represents the position of particle i at the current k-th iteration; represents the individual optimal position of particle i up to the current iteration round; the global optimal position of the entire particle up to the current iteration round; represents the velocity of particle i at the (k + 1)-th iteration, represents the velocity of particle i at the k-th iteration; The position update formula of the particle is: Among them, represents the position of particle i in the next iteration round; is the position of particle i in the current iteration round, is the velocity of particle i in the next iteration round.

5. The short-distance high-speed optical fiber communication equalization method according to claim 4, wherein Using the expectation maximization algorithm to iterate the Gaussian mixture model in the state of the initial parameters until the parameters converge includes: Define the latent variable z ik , which reflects the data point x i from the k-th Gaussian distribution, and the expression is: where \(i = 1, 2, \ldots, N\); \(k = 1, 2, \ldots, K\); the latent variable and the data point form the complete data, denoted as \((x i , z i1 , z i2 , \ldots, z iK )\) for \(i = 1, 2, \ldots, N\); The likelihood function expression of the Gaussian mixture model is: Among them, μk represents the mean of the k-th Gaussian distribution, represents the covariance of the k-th Gaussian distribution; n k represents the number of the N observation points coming from the k-th Gaussian distribution; Then the log-likelihood function of the Gaussian mixture model is: In the E-step of the expectation-maximization algorithm, each data point x is calculated according to the current parameters i the posterior probability belonging to the k-th Gaussian distribution Let θ 0 be the initial value of the iterative parameter, and let θ t be the estimated value of the parameter θ in the t-th iteration. Taking the expectation of the log-likelihood function, the Q function is obtained: Q(θ, θ t ) = E(log P(x, x|θ), θ t ) Where, i = 1, 2,..., N; k = 1, 2,..., K; In step M, find θ when the Q function reaches its maximum value as θ t+1 Participate in the next iteration, and the expression is: where θ includes the mixing coefficient α of each Gaussian distribution in the Gaussian mixture model k , the mean μ k and the covariance The expression is: θ = (α1, α2, …, α K ; μ1, μ2, …, μ K ; σ1, σ2, …, σ K ); Then the estimation of the mixing coefficient α k , the mean μ k and the covariance is as follows: Repeat the E step and the M step until the parameters converge.

6. The short-distance high-speed optical fiber communication equalization method according to claim 1, wherein In the method, the transmitting end modulates the optical signal using 16-QAM, 64-QAM, or 256-QAM.

7. A short-distance high-speed optical fiber communication system, characterized in that, The system includes: A transmitting end, which includes a transmitting end digital signal processor, an arbitrary waveform generator, a digital-to-analog converter, and an optical modulator connected in sequence. The optical modulator is provided with a light source by a first local oscillator laser; the transmitting end is used to generate an optical signal modulated by the set-order quadrature amplitude modulation. An optical amplifier, which is used to amplify the optical signal output by the optical modulator. A single-mode optical fiber for transmitting the amplified optical signal; A receiving end, comprising an optical mixer, a photodiode, a sampling oscilloscope, and a receiving-end digital signal processor connected in sequence; the optical mixer is connected to a second local oscillator laser; the receiving end executes the short-distance high-speed optical fiber communication equalization method according to any one of claims 1 to 6.

8. The short-distance high-speed optical fiber communication system according to claim 7, characterized in that The optical fiber amplifier is an erbium-doped optical fiber amplifier.

9. A computer-readable storage medium having computer programs / instructions stored thereon, characterized in that, When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

10. A computer program product, comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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