A variable step-size algorithm based on modular multiplexing systems

Abstract

A variable step-size algorithm based on a modular division multiplexing (MDM) system, belonging to the field of communication technology, is disclosed. It includes step S1, which calculates the channel crosstalk strength, applies a blind equalization algorithm, and then performs data transmission through signal processing. Step S2 involves using a blind equalization algorithm in the signal processing section, and introducing a sigmoid function to dynamically control the iteration step size, thereby improving the convergence rate and reducing steady-state error. Compared to the traditional CMA algorithm, the improved variable step-size CMA algorithm of this invention effectively solves the contradiction between convergence speed and steady-state error.

Description

Technical Field

[0001] This invention belongs to the field of communication technology and relates to a variable step size algorithm based on a modular division multiplexing system. Background Technology

[0002] Mode-division multiplexing (MDD), as a crucial component of space-division multiplexing (SDM), utilizes orthogonal modes in few-mode fibers as independent channels for signal transmission, significantly increasing transmission capacity and spectral efficiency. Therefore, MMD technology holds great promise in optical communication and has become a hot research topic. However, problems such as mode coupling, differential mode group delay (DMGD), and dispersion arise during transmission, affecting the accuracy of received data.

[0003] Introducing the concept of multiple-input multiple-output (MIMO) equalization from the wireless field into the optical fiber field can eliminate channel interference and loss during transmission, and recover a clear signal.

[0004] At the receiver, an adaptive equalizer is used for channel equalization. This involves dynamically updating the filter tap coefficients based on the transmitted signal using an adaptive algorithm. Common MIMO equalization algorithms include: Linear equalizers (LE), which use linear filters to compensate for linear distortion in the channel. They are suitable for environments with mild distortion and noise, and are characterized by simple implementation and low computational complexity, but their effectiveness is limited for nonlinear distortion and severe interference; and Decision Feedback equalizers (DFE), which compensate for some nonlinear distortion in the channel by feeding back previously decided symbols. They are suitable for environments with moderate distortion and can effectively reduce inter-symbol interference (ISI), but they suffer from error propagation problems. Summary of the Invention

[0005] This invention addresses the problems of existing technologies by providing a variable step-size algorithm based on a modular multiplexing system.

[0006] A variable step-size algorithm based on a modular division multiplexing system includes the following steps:

[0007] Step S1 involves calculating the channel crosstalk strength, applying a blind equalization algorithm, and then transmitting the data through the signal processing section.

[0008] The S2 step and signal processing section use a blind equalization algorithm. By introducing the sigmoid function, the iteration step size is dynamically controlled, which improves the convergence rate and reduces the steady-state error.

[0009] The advantages of this invention are: blind equalization technology, which does not rely on training sequences, but performs adaptive equalization through statistical characteristics and signal structure. Common blind equalization algorithms include Constant Modulus Equalization (CMA) and subspace algorithms, which are suitable for dynamic channel environments. CMA's major advantage is that iteratively updates the equalizer's tap coefficients based on the statistics of the transmitted signal to achieve signal recovery. CMA is widely used for constant modulus signals due to its high efficiency, good real-time performance, and good convergence.

[0010] Compared with the traditional CMA algorithm, the improved variable step size CMA algorithm of this invention effectively solves the problem of the contradiction between convergence speed and steady-state error.

[0011] In simulation experiments, DSP processing was applied to a 700km transmission tri-mode multiplexing system. Compared with the traditional CMA algorithm, the advantages of this invention are:

[0012] 1. By using a nonlinear function relating MSE and channel crosstalk strength to dynamically control the iteration step size, a larger step size is used for rapid convergence in the initial iteration phase; once the system reaches stability, a smaller step size is used for iteration to obtain a smaller iteration error. With the same initial step size, the improved algorithm achieves a 30% faster convergence speed compared to the traditional CMA algorithm.

[0013] 2. By dynamically controlling the step size, the step size is kept small when the MSE is low, thus reducing the steady-state error of the algorithm. In a 700km tri-mode multiplexing system, a step size of 3.8×10⁻⁶ is achieved. -3 The improved algorithm requires a 1.5 dB lower optical signal-to-noise ratio compared to the traditional CMA algorithm under the threshold.

[0014] 3. When DMGD is changed, the bit error rate of the transmitted signal will increase, but the improved CMA is still better than the traditional CMA, indicating that in terms of DMGD, the improved CMA has better equalization performance than CMA. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. As shown in the figures:

[0016] Figure 1 This is a schematic diagram of the algorithm of the present invention.

[0017] Figure 2 This is a graph showing the nonlinear function relationship of the present invention.

[0018] Figure 3 This is a comparison chart of the present invention and the traditional algorithm MSE.

[0019] Figure 4 This is a figure comparing the bit error rate of the present invention with that of traditional algorithms.

[0020] Figure 5 The two figures show a comparison of the bit error rate of the present invention with that of the traditional algorithm. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] Example 1: As Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, a variable step-size algorithm based on a modular multiplexing system and an improved constant modulus equalization algorithm are proposed to address the contradiction between the convergence speed and steady-state error of the constant modulus (CMA) equalization algorithm.

[0023] A variable step-size algorithm based on a modular multiplexing system, such as Figure 1 As shown, x(n) is the transmitted signal, h(n) is the transmission channel impulse response, n(n) is additive white Gaussian noise, y(n) is the received signal, i.e., the equalizer input signal, w(n) is the equalizer tap coefficient, and z(n) is the equalizer output signal. This is the output signal of the decision unit.

[0024] The transmitted signal x(n) reaches the receiver through the channel h(n) to obtain the received signal y(n). The received signal passes through the adaptive filter to obtain the equalizer output signal z(n) = y(n) * w(n), where w(n) is iteratively updated by the CMA algorithm.

[0025] The cost function of the CMA algorithm is J(W) n )=E[(z(n) 2 -R2) 2 ], where R2 is the radius of convergence, which is a positive constant, and can be expressed as: Using gradient descent, the iterative formula for the CMA algorithm can be obtained: W(n+1)=W(n)-μ·z(n)[z(n)] 2 -R2]·Y *(n), where μ is the iteration step size, which is usually chosen as a small positive number, and it determines the convergence accuracy and convergence speed of the equalization algorithm.

[0026] The error function of the CMA algorithm is expressed as: e(n) = z(n)(z(n)) 2 -R2), the iterative formula of the CMA algorithm can be simplified to: W(n+1)=W(n)-μ·e(n)·Y * (n).

[0027] A variable step-size algorithm based on a modular division multiplexing system includes the following steps:

[0028] Step S1 involves calculating the channel crosstalk strength, applying a blind equalization algorithm, and then transmitting the data through the signal processing section.

[0029] The S2 step and signal processing section use a blind equalization algorithm. By introducing the sigmoid function, the iteration step size is dynamically controlled, which improves the convergence rate and reduces the steady-state error.

[0030] It also includes the following steps:

[0031] The formula for calculating the channel crosstalk strength in step S1 is:

[0032] Where s(n) is the received signal of a channel, s io (n) represents the original data of the i-th channel at the transmitter, and M represents the number of digital signals in one transmission period. Since the transmitted signal is a pseudo-random signal, the correlation between the original transmitted signals of different channels is very low. Therefore, there is one and only one unique k1∈[1,M] such that when τ=k1, The maximum value, i.e., the correlation strength between the original signal and the received signal of the i-th channel, is called the correlation peak.

[0033] Similarly, by performing a cross-correlation function on the original signal from the j-th channel and the received signal from the i-th channel, the correlation strength between the j-th original signal and the i-th received signal is obtained, which is called the crosstalk peak. The ratio of the correlation peak to the crosstalk peak is defined as β, representing the crosstalk strength between channels.

[0034] By introducing a sigmoid function relating MSE and β, the iteration step size of the blind equilibrium algorithm is dynamically controlled. The cost function of the CMA algorithm is: J(W n )=E[(|z(n)| 2 -R2) 2 ], where z(n) is the filter output signal; W n Let R2 be the coefficient matrix of the adaptive filter; R2 is the radius of convergence, a positive constant, which can be expressed as: Where y(n) is the filter input signal, the CMA algorithm iterative formula can be obtained using the gradient descent method:

[0035] W(n+1)=W(n)-μ·z(n)[|z(n)| 2 -R2]·Y * (n).

[0036] Where μ is the iteration step size, and by introducing a constant parameter α and the ratio β of the correlation peak to the crosstalk peak, the dynamic iteration step size is obtained: μ i,j (n)=μ0×β i,j ×1 / [1+exp(-α|e(n)×e(n-1)|)], where e(n) is the error function e(n)=z(n)(|z(n)| 2 -R2), μ0 is the initial step size set.

[0037] The cost function of the CMA algorithm is J(W) n )=E[(|z(n)| 2 -R2) 2 ], where R2 is the radius of convergence, which is a positive constant, and can be expressed as: Using gradient descent, the iterative formula for the CMA algorithm can be obtained: W(n+1)=W(n)-μ·z(n)[|z(n)| 2 -R2]·Y * (n), where μ is the iteration step size, usually chosen as a small positive number, which determines the convergence accuracy and convergence speed of the equalization algorithm. Because e(n)=z(n)(|z(n)| 2 -R2), the iterative formula of the CMA algorithm can be simplified to: W(n+1)=W(n)-μ(n)·e(n)·Y * (n).

[0038] The step size function is based on the signal crosstalk intensity and combines the characteristics of few-mode fiber channels to eliminate the randomness error of traditional crosstalk measurement and reduce the convergence time required for channel equalization.

[0039] Example 2: As Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, a variable step-size algorithm based on a modular division multiplexing system is proposed. The signal passes through an adaptive filter to obtain the output signal y(n) = x(n) * w(n), where w(n) is iteratively updated by the CMA algorithm.

[0040] The cost function of the CMA algorithm is J(W) n )=E[(|z(n)| 2 -R2) 2], where R2 is the radius of convergence, which is a positive constant, and can be expressed as: Using gradient descent, the iterative formula for the CMA algorithm can be obtained: W(n+1)=W(n)-μ·z(n)[|z(n)| 2 -R2]·Y * (n), where μ is the iteration step size, which is usually chosen as a small positive number, and it determines the convergence accuracy and convergence speed of the equalization algorithm.

[0041] The error function of the CMA algorithm is expressed as: e(n) = z(n)(|z(n)| 2 -R2), the iterative formula of the CMA algorithm can be simplified to: W(n+1)=W(n)-μ·e(n)·Y * (n).

[0042] Example 3: As Figure 1 , Figure 2 , Figure 3 , Figure 4 and Figure 5 As shown, a variable step-size algorithm based on a modular multiplexing system is presented. The difference between Example 3 and Example 2 is that:

[0043] Introducing a sigmoid function relating MSE and the channel crosstalk strength obtained through S1, the formula for calculating the channel crosstalk strength in S1 is as follows: Where s io (n) represents the original data of the i-th channel at the transmitter, and M represents the number of digital signals in one transmission period. Since the transmitted signal is a pseudo-random signal, the correlation between the original transmitted signals of different channels is very low. Therefore, there is one and only one unique k1∈[1,M] such that when τ=k1, The maximum value, i.e., the correlation strength between the original signal and the received signal of the i-th channel, is called the correlation peak.

[0044] Similarly, by performing a cross-correlation function operation on the original signal of the j-th channel and the received signal of the i-th channel, the correlation strength between the original signal of the j-th channel and the received signal of the i-th channel can be obtained, which is called the crosstalk peak.

[0045] The ratio of the correlation peak to the crosstalk peak is defined as β, which represents the crosstalk intensity between channels:

[0046] The iteration step size of the blind equalization algorithm is dynamically controlled. A sigmoid function, derived from the constant parameter α and β obtained using S1, is introduced to obtain the dynamic iteration step size: μ. i,j (n)=μ0×β i,j ×1 / [1+exp(-α|e(n)×e(n-1)|)], where μ0 is the initial step size set.

[0047] The iterative formula for the improved variable step size CMA algorithm is expressed as: W(n+1)=W(n)-μ(n)·e(n)·Y * (n).

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A variable step-size algorithm based on a modular multiplexing system, characterized in that, Includes the following steps: Step S1: The channel crosstalk strength is calculated, a blind equalization algorithm is applied, and data is transmitted through signal processing. The channel crosstalk strength is represented by the signal correlation peak, and the calculation method is as follows: ,in ,in For the received signal of a channel, Let M be the raw data of the i-th channel at the transmitting end, and M be the number of digital signals in one transmission cycle. Step S2, the signal processing section, uses an adaptive filter based on a blind equalization algorithm. By introducing a sigmoid function to dynamically control the iteration step size, the coefficients of the adaptive filter are updated, improving the convergence rate and reducing steady-state error. The variable step size function is: ; The coefficient update method for adaptive filters is as follows: The cost function of the CMA algorithm is Where R² is the radius of convergence, which is a positive constant, expressed as: Using gradient descent, the iterative formula for the CMA algorithm is obtained: Where μ is the iteration step size, because The iterative formula of the CMA algorithm is ultimately simplified to: , in The output signal of the filter; Let be the coefficient matrix of the adaptive filter; where This is the input signal to the filter.

2. The variable step-size algorithm based on a modular multiplexing system according to claim 1, characterized in that, In step S2, the center value of the initial tap coefficients of the adaptive filter is set to 1, and the rest are 0.

Images