A low-complexity signal detection method for massive MIMO based on extrapolation principle

Abstract

The present invention provides a large-scale MIMO low-complexity signal detection method based on the extrapolation principle, comprising the following steps: constructing a large-scale MIMO system uplink transmission model to obtain relevant parameters of the MIMO system; obtaining initial data of a transmitted signal according to the relevant parameters of the MIMO system; using a signal detection method based on EISOR iteration to detect a received signal to obtain a signal detection result; the present invention proposes a novel linear detector based on the EISOR method for a large-scale MIMO uplink, thereby achieving performance improvement while taking into account the complexity requirements, and overcoming the problem that the detection algorithm in the prior art requires multiple iterations and has high complexity.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a large-scale MIMO low-complexity signal detection method based on an extrapolation principle. Background Art

[0002] Massive multiple-input multiple-output (massive MIMO) technology has become a breakthrough in wireless communication systems and has been successfully implemented in 5G networks. Due to its inherent advantages and potential for further development, it is expected to continue to play a core role in communications after 5G. A massive MIMO system refers to the configuration of dozens or even hundreds of antenna arrays at the base station to simultaneously serve multiple single-antenna clients. Its advantage is that it improves data throughput and diversity gain, thereby improving link reliability.

[0003] In a massive MIMO system, the complexity is closely related to the number of antennas. As the number of antennas increases, the complexity of the algorithm increases. Therefore, a signal detection algorithm with low complexity and high detection performance is required at the receiving end.

[0004] There are two main categories of detection techniques for MIMO systems, linear detection algorithms and nonlinear detection algorithms. Maximum likelihood detection (ML) is the best detection technique for MIMO systems. However, its complexity grows exponentially with the increase in the modulation order and the number of transmit antennas, and it is not applicable even when the number of antennas is small. Compared with ML, linear zero forcing (ZF) and minimum mean square error (MMSE) detectors are considered to have lower complexity. However, they require matrix inversion, and in large-scale MIMO systems, the dimensions of the matrix can be very large, which becomes challenging when the number of antennas and users increases.

[0005] In order to avoid the complexity problem of linear detection, simplified algorithms have emerged. Generally speaking, there are two major categories of methods to overcome the complexity of the inverse matrix. The first category is based on methods for approximate matrix inversion, including Neumann series (NS), truncated polynomial expansion (TPE), and Newton iteration (NI). The second category of detection techniques for massive MIMO is based on iterative methods, in which the transmission vector can be approximated without the need for matrix inversion. In general, iterative methods achieve a balance between complexity and performance over approximate inverse matrix methods. Examples of these methods include Jacobi (JA), Gauss-Seidel (GS), continuous over-relaxation (SOR), accelerated over-relaxation (AOR), Richardson iteration (RI), and conjugate gradient (CG).

[0006] However, the above iterative algorithms require multiple iterations to approach the optimal performance, and the complexity of the algorithm increases with the number of iterations. Therefore, it is necessary to propose an algorithm with low complexity and only a small number of iterations to achieve near-optimal performance. Summary of the invention

[0007] Purpose of the invention: The technical problem to be solved by the present invention is to address the deficiencies of the prior art and to provide a large-scale MIMO low-complexity signal detection method based on the extrapolation principle, which only requires a small number of iterations to approach the optimal performance and has low complexity, thus overcoming the problem that the detection algorithm of the prior art requires multiple iterations and has high complexity.

[0008] In order to achieve the above object, the present invention is implemented by adopting the following technical solutions:

[0009] The present invention discloses a large-scale MIMO low-complexity signal detection method based on extrapolation principle, comprising the following steps:

[0010] Step 1, constructing a massive MIMO (multiple-in multipleout, MIMO) system uplink transmission model, and obtaining relevant parameters of the MIMO system, wherein the relevant parameters include a channel response matrix, the number of transmitting antennas, the number of receiving antennas, a received signal vector, and a noise variance;

[0011] Step 2: construct an MMSE (minimum mean square error, Minimum Mean Square Error, MMSE) detection matrix according to the relevant parameters of the MIMO system, and obtain a matched filter signal, and obtain the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix according to the number of transmitting antennas and the number of receiving antennas;

[0012] Step 3, decompose the matched filter matrix to obtain the traces of the diagonal elements in the filter matrix and the iterative initial values ​​of the number of transmitting antennas and users; optimize and calculate the over-relaxation parameters and the acceleration parameters according to the initial data of the transmitted signal, so as to calculate the extrapolation parameters, and use the EISOR (extrapolation improved successive overrelaxation, EISOR) iterative signal detection method based on the extrapolation principle combined with optimization improved according to the optimized over-relaxation parameters and extrapolation parameters to detect the received signal and obtain the signal detection result.

[0013] In step 1, the uplink transmission model of the massive MIMO system includes a massive MIMO system, the massive MIMO system includes a base station and a user terminal, the base station includes single antenna users and Root antenna communication, where , the channel in the massive MIMO system is a Rayleigh flat channel, and the channel state information of the base stations is synchronized, then The signal vector x sent independently by each user is expressed as , the symbol vector y received by the base station is expressed as , then the relationship between x and y is expressed as ;in, Indicates The signal transmitted by a user, Indicates The symbols received by the base station are is the channel response matrix, is additive white Gaussian noise, It is a plural set.

[0014] Step 2 includes: constructing an MMSE detection matrix according to the channel response matrix, and obtaining a matched filter signal;

[0015] According to the number of transmitting antennas and the number of receiving antennas, the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix are obtained.

[0016] In step 2, the expression of the MMSE detection matrix is:

[0017]

[0018] Where A is the MMSE detection matrix, is the symmetric transposed matrix of the channel response matrix H, is the noise variance, I is The identity matrix of

[0019] The expression of the matched filter signal is:

[0020]

[0021] in, is the matched filter signal.

[0022] In step 2, the maximum eigenvalue expression of the MMSE detection matrix is:

[0023]

[0024] in, is the maximum eigenvalue of the MMSE detection matrix;

[0025] The minimum eigenvalue expression of the MMSE detection matrix is:

[0026]

[0027] in, is the minimum eigenvalue of the MMSE detection matrix.

[0028] Step 3 includes the following steps:

[0029] Step 3-1, decomposing the MMSE filter matrix to obtain a diagonal component matrix; decomposing the filter matrix by extracting matrix elements to obtain a band matrix, an upper triangular matrix, and a lower triangular matrix with a matrix bandwidth parameter of 1;

[0030] Step 3-2, according to the initial data of the transmission signal, the relaxation parameter and the acceleration parameter are calculated, and then the extrapolation parameter is calculated;

[0031] Step 3-3, calculating an initial value according to the diagonal component, the number of transmitting antennas, and the number of receiving antennas;

[0032] Step 3-4, iterating according to the initial value obtained in step 3-3, using an algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm for iterative calculation.

[0033] In step 3-1, the MMSE filter matrix is ​​diagonally decomposed using the following formula:

[0034]

[0035] Where D is the diagonal component matrix, L is a strictly lower triangular matrix, and U is a strictly upper triangular matrix;

[0036] The matched filter matrix is ​​decomposed by extracting matrix elements to obtain a band matrix with a bandwidth parameter of 1, an upper triangular matrix, and a lower triangular matrix:

[0037]

[0038] in, is a banded matrix with a matrix bandwidth parameter of 1, and They are the lower triangular matrix and upper triangular matrix of the matched filter matrix respectively.

[0039] In step 3-2, the expression of the over-relaxation parameter is:

[0040]

[0041] in, is the over-relaxation parameter;

[0042] The expression of the acceleration parameter is:

[0043]

[0044] in, is the acceleration parameter.

[0045] In step 3-2, the expression of the extrapolated parameter is,

[0046]

[0047] in, is the extrapolated parameter.

[0048] In step 3-3, the initial value calculation formula is:

[0049]

[0050] in, is the initial value, is the trace of the diagonal component matrix;

[0051] In step 3-4, the continuous over-relaxation algorithm is linearly optimized using the difference vector to obtain an improved continuous over-relaxation algorithm, the formula is:

[0052]

[0053] in, , K is the total number of iterations, is the relaxation factor; is the estimated value of the transmitted signal for the i-th iteration;

[0054] In step 3-4, an algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm is used for iterative calculation, and the formula is:

[0055]

[0056] in, is the estimated value of the transmitted signal for the i+1th iteration.

[0057] Compared with the prior art, the beneficial effects of the present invention include: the present invention uses an iterative algorithm that combines a generalized extrapolation method and an improved efficient continuous over-relaxation iteration method to estimate the process of inverting the MMSE detection matrix, and converts the matrix inversion process into matrix multiplication and addition, which greatly reduces the complexity.

[0058] The present invention adopts an iterative algorithm combining a generalized extrapolation method and an improved efficient continuous over-relaxation iterative method. By using a difference vector, the iterative formula of the traditional SOR is linearly optimized, the dependence of the SOR algorithm on the relaxation parameter is reduced to improve robustness, and the convergence speed of the SOR is accelerated. At the same time, combined with the extrapolation technology, the convergence speed is accelerated, and the estimation accuracy of the transmission symbol in the large-scale MIMO system is improved. This method uses the advantages of the extrapolation method to optimize the iterative process and obtain more accurate signal detection results. It is possible to approach the optimal performance with a smaller number of iterations, thereby improving the detection capability.

[0059] The over-relaxation parameters involved in the present invention and acceleration parameters is the number of transmitting antennas and the number of receiving antennas Direct calculation approximation saves the process of finding the eigenvalue of the MMSE detection matrix, greatly reducing the complexity.

[0060] The initial value of the transmitted signal in the present invention uses an approximate value that only depends on the trace of the diagonal elements in the MMSE filter matrix and the number of transmitting antennas and users, avoiding the calculation of the MMSE detection matrix, the diagonal matrix of the MMSE detection matrix and the inverse matrix of the diagonal matrix, further reducing the complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 is a flow chart of the method of the present invention.

[0062] Figure 2 It is a comparison chart of the bit error performance of the method of the present invention and other existing iterative algorithms under 64QAM modulation under 16×128 antenna array.

[0063] Figure 3 It is a comparison chart of the bit error performance of the method of the present invention and other existing iterative algorithms under 64QAM modulation under 16×64 antenna array.

[0064] Figure 4 This is a comparison diagram of the bit error performance of the method of the present invention with different numbers of receiving antennas. DETAILED DESCRIPTION

[0065] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0066] This embodiment provides a large-scale MIMO low-complexity signal detection method based on the extrapolation principle, comprising the following steps:

[0067] Step 1, constructing a massive MIMO (multiple-in multipleout, MIMO) system uplink transmission model, and obtaining relevant parameters of the MIMO system, wherein the relevant parameters include a channel response matrix, the number of transmitting antennas, the number of receiving antennas, a received signal vector, and a noise variance;

[0068] Step 2: construct an MMSE (minimum mean square error, Minimum Mean Square Error, MMSE) detection matrix according to the relevant parameters of the MIMO system, and obtain a matched filter signal, and obtain the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix according to the number of transmitting antennas and the number of receiving antennas;

[0069] Step 3, decompose the matched filter matrix to obtain the traces of the diagonal elements in the filter matrix and the iterative initial values ​​of the number of transmitting antennas and users; optimize and calculate the over-relaxation parameters and the acceleration parameters according to the initial data of the transmitted signal, so as to calculate the extrapolation parameters, and use the EISOR (extrapolation improved successive overrelaxation, EISOR) iterative signal detection method based on the extrapolation principle combined with optimization improved according to the optimized over-relaxation parameters and extrapolation parameters to detect the received signal and obtain the signal detection result.

[0070] The technical concept of the present invention is, on the one hand, to use an iterative algorithm that combines a generalized extrapolation method with an improved efficient continuous over-relaxation iterative method to estimate the process of inverting the MMSE detection matrix, and convert the matrix inversion process into matrix multiplication and addition, thereby reducing the complexity; on the other hand, to use an iterative algorithm that combines a generalized extrapolation method with an improved efficient continuous over-relaxation iterative method to estimate, the algorithm converges faster, can approach the optimal performance with a smaller number of iterations, and improves the detection performance.

[0071] In step 1, the uplink transmission model of the massive MIMO system includes a massive MIMO system, the massive MIMO system includes a base station and a user terminal, the base station includes single antenna users and Root antenna communication, where , the channel in the massive MIMO system is a Rayleigh flat channel, and the channel state information of the base stations is synchronized, then The signal vector x sent independently by each user is expressed as , the symbol vector y received by the base station is expressed as , then the relationship between x and y is expressed as ;in, Indicates The signal transmitted by a user, Indicates The symbols received by the base station are is the channel response matrix, is additive white Gaussian noise, It is a plural set.

[0072] Step 2 includes: constructing an MMSE detection matrix according to the channel response matrix, and obtaining a matched filter signal;

[0073] According to the number of transmitting antennas and the number of receiving antennas, the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix are obtained.

[0074] In step 2, the expression of the MMSE detection matrix is:

[0075]

[0076] Where A is the MMSE detection matrix, is the symmetric transposed matrix of the channel response matrix H, is the noise variance, I is The unit matrix of the present invention; it is worth noting here that, although the present invention theoretically includes this step, since the part of the matrix A involved in the method later uses A to participate in large-scale matrix multiplication and addition operations, the computational complexity is very high, and therefore this step can be omitted, that is, only the expression is constructed, but no operation is performed. When the operation part of the matrix A is involved later, the associative law of multiplication is used to simplify the operation, thereby further reducing the complexity of the method.

[0077] The expression of the matched filter signal is:

[0078]

[0079] in, is the matched filter signal.

[0080] In step 2, the maximum eigenvalue expression of the MMSE detection matrix is:

[0081]

[0082] in, is the maximum eigenvalue of the MMSE detection matrix;

[0083] The minimum eigenvalue expression of the MMSE detection matrix is:

[0084]

[0085] in, is the minimum eigenvalue of the MMSE detection matrix. This step is based on random matrix theory. In this embodiment, it is assumed that all users are single-antenna users, so the number of users is the number of transmitting antennas. That is, when the number of receiving antennas and the number of transmitting antennas on the base station side grow to infinity, the minimum eigenvalue and maximum eigenvalue of the MMSE detection matrix A will be stable and converge to the minimum eigenvalue expression and the maximum eigenvalue expression respectively. Therefore, the acceleration parameter and over-relaxation parameter It can be directly calculated and approximated by the number of receiving antennas and the number of transmitting antennas at the base station side, eliminating the process of calculating the eigenvalue of the MMSE detection matrix A and greatly reducing the complexity of the algorithm.

[0086] Step 3 includes the following steps:

[0087] Step 3-1, decomposing the MMSE filter matrix to obtain a diagonal component matrix; decomposing the filter matrix by extracting matrix elements to obtain a band matrix, an upper triangular matrix, and a lower triangular matrix with a matrix bandwidth parameter of 1;

[0088] Step 3-2, according to the initial data of the transmission signal, the relaxation parameter and the acceleration parameter are calculated, and then the extrapolation parameter is calculated;

[0089] Step 3-3, calculating an initial value according to the diagonal component, the number of transmitting antennas, and the number of receiving antennas;

[0090] Step 3-4, iterating according to the initial value obtained in step 3-3, using an algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm for iterative calculation.

[0091] In step 3-1, the MMSE filter matrix is ​​diagonally decomposed using the following formula:

[0092]

[0093] Where D is the diagonal component matrix, L is a strictly lower triangular matrix, and U is a strictly upper triangular matrix;

[0094] The matched filter matrix is ​​decomposed by extracting matrix elements to obtain a band matrix with a bandwidth parameter of 1, an upper triangular matrix, and a lower triangular matrix:

[0095]

[0096] in, is a banded matrix with a matrix bandwidth parameter of 1, and They are the lower triangular matrix and upper triangular matrix of the matched filter matrix respectively.

[0097] In step 3-2, the expression of the over-relaxation parameter is:

[0098]

[0099] in, is the over-relaxation parameter;

[0100] The expression of the acceleration parameter is:

[0101]

[0102] in, is the acceleration parameter.

[0103] In step 3-2, the expression of the extrapolated parameter is,

[0104]

[0105] in, is the extrapolated parameter.

[0106] In step 3-3, the initial value calculation formula is:

[0107]

[0108] in, is the initial value, is the trace of the diagonal component matrix; this step avoids directly calculating the MMSE detection matrix, the diagonal matrix of the MMSE detection matrix, and the inverse matrix of the diagonal matrix, further reducing the complexity.

[0109] In step 3-4, the continuous over-relaxation algorithm is linearly optimized using the difference vector to obtain an improved continuous over-relaxation algorithm, the formula is:

[0110]

[0111] in, , K is the total number of iterations, is the relaxation factor; is the estimated value of the transmitted signal for the i-th iteration; have:

[0112]

[0113] in, is the relaxation factor of the SOR iterative algorithm, for and difference;

[0114] In step 3-4, the improved efficient SOR algorithm is also a first-order stationary iterative method:

[0115]

[0116] Among them, S is the iteration matrix and c is the constant vector.

[0117] Use extrapolated values:

[0118]

[0119] replace , we can get:

[0120]

[0121] in, is the real matrix that controls the extrapolation behavior, is the estimated value of the transmitted signal for the i-th iteration.

[0122] matrix The specific choice of will affect the convergence and performance of the algorithm. In the case of iterative solution of the MMSE equation, careful selection and optimization of the extrapolation matrix It can speed up the convergence.

[0123] Set the extrapolation iteration matrix to:

[0124]

[0125] in, is the extrapolation iteration matrix.

[0126] According to the generalized extrapolation method, the extrapolation technique combined with the iterative algorithm is calculated:

[0127]

[0128] Combine the above formula with the improved efficient SOR algorithm and set:

[0129]

[0130] set up:

[0131]

[0132] An algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm is used for iterative calculation. The formula is:

[0133]

[0134] in, is the estimated value of the transmitted signal for the i+1th iteration. After the iteration of this step is completed, the final estimated value of the transmitted signal is obtained. In this step, the iterative formula of the traditional SOR is linearly optimized by using the difference vector, which reduces the dependence of the SOR algorithm on the relaxation parameter to improve the robustness and speeds up the convergence of the SOR. At the same time, it is combined with the extrapolation technology to speed up the convergence speed and improve the estimation accuracy of the transmission symbols in the large-scale MIMO system. This method uses the advantages of the extrapolation method to optimize the iteration process and obtain more accurate signal detection results.

[0135] In this embodiment, the experimental results are as follows: Figure 2 , 3 As shown in , MMSE represents the minimum mean square error method, SOR represents the continuous over-relaxation method, and EISOR represents the method of this embodiment.

[0136] In this embodiment, it is assumed that all users are single-antenna users, so the number of users is the number of transmitting antennas. Figure 2 As shown, the number of receiving antennas on the base station side is 128, the number of users is 16, the modulation mode is 64QAM, the channel is a Rayleigh fading channel, and k represents the number of iterations. It can be seen from the figure that with the increase of the signal-to-noise ratio, the bit error rate gradually decreases, and each algorithm requires several iterations to obtain performance close to that of the MMSE detection algorithm. Under the same number of iterations, the EISOR algorithm has better detection performance than the SOR algorithm. The method proposed in this embodiment is almost the same as the traditional MMSE detection algorithm after 4 iterations; among them, the higher the signal-to-noise ratio, the more obvious the effect. For example, when the number of iterations is 4, the bit error rate is close to When , the EISOR algorithm has a 1.5dB advantage.

[0137] like Figure 3 As shown, at the base station side, there are 64 receiving antennas, 16 users, 64QAM modulation mode, and Rayleigh fading channel. It can be seen from the figure that under the same number of iterations, the method proposed in this embodiment is better than the SOR algorithm, and the 4th iteration is close to the traditional MMSE detection algorithm. Among them, the effect of 3 detections is almost similar to the performance of the SOR algorithm with 4 detections.

[0138] like Figure 4 As shown in the figure, under the premise that the number of user antennas is 16, as the number of base station antennas increases, the detection performance of the EISOR algorithm also improves. When SNR = 14dB, under the 256×16 antenna configuration, the bit error rate reaches the order of 10^(-7). In contrast, under the 128×16 antenna configuration, the bit error rate is the order of 10^(-3), under the 64×16 antenna configuration, the bit error rate is the order of 10^(-2), and under the 32×16 antenna configuration, the bit error rate is only the order of 10^(-1). It can be seen that as the number of base station antennas increases, the spatial degrees of freedom also increase, and the signal transmission efficiency and system capacity are improved.

[0139] This embodiment studies the signal detection algorithm in the large-scale MIMO uplink transmission system. A signal detection method based on EISOR iteration is proposed. By using the difference vector to linearly optimize the iterative formula of the traditional SOR, the SOR algorithm reduces the dependence on the relaxation parameter to improve the robustness, and accelerates the convergence speed of the SOR. At the same time, combined with the extrapolation technology, the convergence speed is accelerated, the estimation accuracy of the transmission symbols in the large-scale MIMO system is improved, the convergence speed is accelerated, and the detection performance is improved. The simulation results show that the method of this embodiment is universal in communication systems with different antenna numbers, and has better detection performance than the SOR detection method.

[0140] The present invention provides a large-scale MIMO low-complexity signal detection method based on the extrapolation principle. There are many methods and ways to implement the technical solution. The above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented using existing technologies.

Claims

1. A low-complexity signal detection method for large-scale MIMO based on extrapolation principle, characterized in that: The following steps are involved: Step 1, constructing a large-scale MIMO system uplink transmission model, and obtaining relevant parameters of the MIMO system, wherein the relevant parameters include a channel response matrix, the number of transmitting antennas, the number of receiving antennas, a received signal vector, and a noise variance; In step 1, the uplink transmission model of the massive MIMO system includes a massive MIMO system, the massive MIMO system includes a base station and a user terminal, the base station includes N T single-antenna users and N R In the massive MIMO system, the channel is a Rayleigh flat channel, and the channel state information of the base stations is synchronized, then N T The signal vector x sent independently by each user is expressed as The symbol vector y received by the base station is expressed as Then the relationship between x and y is expressed as y=Hx+n; where, Indicates the Nth T The signal transmitted by a user, Indicates the Nth R The symbols received by the base station are is the channel response matrix, is additive white Gaussian noise, is a plural set; Step 2: construct an MMSE detection matrix according to the relevant parameters of the MIMO system, and obtain a matched filter signal, and obtain the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix according to the number of transmitting antennas and the number of receiving antennas; Step 2 includes: constructing an MMSE detection matrix according to the channel response matrix, and obtaining a matched filter signal; According to the number of transmitting antennas and the number of receiving antennas, the minimum eigenvalue and the maximum eigenvalue of the MMSE detection matrix are obtained; In step 2, the expression of the MMSE detection matrix is: A=H H H+σ 2 I, Where A is the MMSE detection matrix, H H is the symmetric transposed matrix of the channel response matrix H, σ 2 is the noise variance, I is N T ×N T The identity matrix of The expression of the matched filter signal is: in, is the matched filter signal; In step 2, the maximum eigenvalue expression of the MMSE detection matrix is: Among them, λ max is the maximum eigenvalue of the MMSE detection matrix; The minimum eigenvalue expression of the MMSE detection matrix is: Among them, λ min is the minimum eigenvalue of the MMSE detection matrix; Step 3, decomposing the matched filter matrix to obtain the trace of the diagonal elements in the filter matrix and the iterative initial values ​​of the number of transmitting antennas and users; optimizing and calculating the over-relaxation parameter and the acceleration parameter according to the initial data of the transmitted signal, thereby calculating the extrapolation parameter, and using the signal detection method based on the extrapolation principle combined with the optimized EISOR iteration improved according to the optimized over-relaxation parameter and the extrapolation parameter to detect the received signal, and obtain the signal detection result; Step 3 includes the following steps: Step 3-1, decomposing the MMSE filter matrix to obtain a diagonal component matrix; decomposing the filter matrix by extracting matrix elements to obtain a band matrix, an upper triangular matrix, and a lower triangular matrix with a matrix bandwidth parameter of 1; Step 3-2, according to the initial data of the transmission signal, the relaxation parameter and the acceleration parameter are calculated, and then the extrapolation parameter is calculated; Step 3-3, calculating an initial value according to the diagonal component, the number of transmitting antennas, and the number of receiving antennas; Step 3-4, iterating according to the initial value obtained in step 3-3, using an algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm to perform iterative calculation; In step 3-1, the MMSE filter matrix is ​​diagonally decomposed using the following formula: A=D+L+U, Where D is the diagonal component matrix, L is a strictly lower triangular matrix, and U is a strictly upper triangular matrix; The matched filter matrix is ​​decomposed by extracting matrix elements to obtain a band matrix with a bandwidth parameter of 1, an upper triangular matrix, and a lower triangular matrix: A=D1+L1+U1, Wherein, D1 is a band matrix with a matrix bandwidth parameter of 1, L1 and U1 are the lower triangular matrix and upper triangular matrix of the matched filter matrix respectively; In step 3-2, the expression of the over-relaxation parameter is: Among them, β is the over-relaxation parameter; The expression of the acceleration parameter is: Among them, α is the acceleration parameter; In step 3-2, the expression of the extrapolated parameter is, Among them, γ is the extrapolation parameter; In step 3-3, the initial value calculation formula is: Among them, x 0 is the initial value, trace(D) is the trace of the diagonal component matrix; In step 3-4, the continuous over-relaxation algorithm is linearly optimized using the difference vector to obtain an improved continuous over-relaxation algorithm, the formula is: Where i = 0, 1, ..., K, K is the total number of iterations, ω is the relaxation factor; x i is the estimated value of the transmitted signal for the i-th iteration; In step 3-4, an algorithm combining the extrapolation technique with the improved continuous over-relaxation algorithm is used for iterative calculation, and the formula is: Among them, x i+1 is the estimated value of the transmitted signal for the i+1th iteration.

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