Dual iteration sparse minimum mean square error Turbo equilibrium detection method

Abstract

The invention relates to the technical field of wireless communication, in particular to a dual iteration sparse minimum mean square error Turbo equalization detection method, and particularly relates to a dual iteration sparse minimum mean square error Turbo equalization algorithm for performing signal detection on an orthogonal time sequence multiplexing system. According to the detection method, a low-complexity MMSE estimation algorithm is used in a time domain to estimate a time domain posterior mean vector and a posterior covariance matrix, then the time domain posterior mean vector and the posterior covariance matrix are converted to a time delay-sequence domain, and input soft information of a decoder is calculated in the time delay-sequence domain; and calculating a priori mean vector and a priori covariance matrix of a time delay-sequence domain according to output soft information of a decoder, and transforming to the time domain to carry out the next low-complexity MMSE estimation algorithm. And after multiple iterations, carrying out soft decision on the soft information output by the decoder to obtain the bit information of the sending end. The problem that an existing detection method is high in complexity is solved.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and particularly relates to a doubly iterative sparsified minimum mean square error Turbo equalization detection method, and more particularly to a signal detection method for an orthogonal time sequency multiplexing (OTSM) system using a doubly iterative sparsified minimum mean square error (DI-S-MMSE) Turbo equalization algorithm. Background Art

[0002] With the continuous progress of wireless communication technologies, the fifth-generation mobile communication system (5G) has been able to support requirements such as high data rates, low latency, high reliability, and large-scale machine-type communication. However, in high-speed mobile communication scenarios with time-selective fading and frequency-selective fading, the performance of traditional orthogonal frequency division multiplexing (OFDM) modulation technologies will significantly decline. To address this challenge, in recent years, orthogonal time frequency space (OTFS) modulation technologies based on the delay-Doppler domain have become a research hotspot. OTFS modulation places information symbols on the grid in the delay-Doppler domain, thereby converting the time-frequency doubly selective channel into a two-dimensional quasi-time-invariant channel in the delay-Doppler domain, significantly improving the signal transmission performance in high-speed mobile scenarios. However, with the increase in the number of subcarriers and symbols, the implementation complexity of the OTFS system has been greatly improved.

[0003] OTSM modulation technology modulates information symbols in the delay-sequence domain, converting the time-frequency doubly selective channel into a two-dimensional quasi-time-invariant channel in the delay-sequence domain, thereby achieving performance similar to that of the OTFS system. At the same time, the OTSM system performs a Walsh-Hadamard transform (WHT) along the sequence domain, which only involves addition and subtraction compared to the inverse fast Fourier transform (IFFT) performed by the OTFS system along the Doppler domain, providing a low-complexity modulation scheme for reliable communication in high-mobility wireless channels.

[0004] However, due to the large dimensions of the transmitted symbols and the channel matrix in the OTSM system, the dimension of the received signal matrix is also very large, and existing signal detection algorithms have the problem of high complexity. The present invention aims to reduce the complexity of the detection algorithm and realizes a low-complexity detection method for the received signal of the OTSM system.

[0005] In view of this, the present invention is hereby provided. Summary of the Invention

[0006] The object of the present invention is to overcome the above-mentioned disadvantages of the prior art and propose a dual iterative sparse minimum mean square error Turbo equalization detection method.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] On the one hand, the present invention provides an OTSM iterative detection system model based on DI-S-MMSE (dual iterative sparse minimum mean square error) Turbo equalization, characterized in that the OTSM system model includes a transmitter, a wireless channel and a receiver, and the transmitter includes an encoder, an interleaver, a mapping unit, a WHT transformation unit, and a serial-to-parallel conversion unit connected in sequence; the receiver includes a time-domain DI-S-MMSE estimator, a cross-domain message passing unit, an extrinsic information unit, a deinterleaver, a SISO decoder, an adder, an interleaver, a priori information unit, and a cross-domain message passing unit, and the input end of the SISO decoder is also connected to the adder;

[0009] Among them, the DI-S-MMSE estimator includes a DI-S-MMSE estimation algorithm.

[0010] On the other hand, the present invention proposes a dual iterative sparse minimum mean square error Turbo equalization detection method, based on the above-mentioned OTSM iterative detection system model, including the following steps:

[0011] Step 1: After the receiver obtains the time-domain received signal, use the DI-S-MMSE estimation algorithm in the time domain to calculate the posterior mean vector and the posterior covariance matrix, and then transform the time-domain posterior mean vector and the posterior covariance matrix to the delay-sequence domain through the cross-domain message passing unit to obtain the delay-sequence domain posterior mean vector and the posterior covariance matrix;

[0012] Step 2: Calculate the extrinsic information in the delay-sequence domain, deinterleave the extrinsic information and use it as the input soft information of the soft-input soft-output (SISO) decoder;

[0013] Step 3: According to the soft information output after decoding by the SISO decoder, update the priori mean vector and the priori covariance matrix in the time-domain sequence domain, and transform them to the time domain through the cross-domain message passing unit to obtain the time-domain priori mean vector and the priori covariance matrix, and then perform the next iteration. After multiple iterations, the soft information output by the SISO decoder is judged to obtain the transmitter bit information.

[0014] Further, in step 1, the calculation process of the posterior mean vector and the posterior covariance matrix in the time domain includes: performing MMSE estimation through the DI-S-MMSE estimation algorithm based on the time-domain received signal vector, the time-domain channel matrix, and the prior information, and calculating the posterior mean vector and the posterior covariance matrix in the time domain;

[0015] The posterior mean vector in the time domain is expressed as:

[0016]

[0017] where r represents the time-domain received signal vector; represents the prior mean vector; H T represents the time-domain channel matrix; represents the prior covariance matrix; W MMSE represents the time-domain MMSE estimation matrix, as shown below:

[0018]

[0019] It can be seen from equations (1) and (2) that the matrix

[0020] where N0 represents complex Gaussian noise, I MN represents the identity matrix;

[0021] The posterior covariance matrix in the time domain is expressed as:

[0022]

[0023] Among equations (1) and (3), in the initial iteration process, the direct inversion of matrix A is converted into solving two linear equations, and the GMRES algorithm is used to solve the linear equations, and then the posterior mean vector and the posterior covariance matrix in the time domain are calculated according to the solution results; in the remaining iteration processes, first, the matrix A is sparsified based on the graph theory method, and then the FSPAI algorithm is used to obtain A -1 , and finally, it is substituted into equations (1) and (3) to obtain the posterior mean vector and the posterior covariance matrix in the time domain.

[0024] Further, in the initial iteration process, due to the lack of prior information, is a zero vector, is the identity matrix, and the matrix Therefore, the posterior mean vector in the time domain is expressed as:

[0025]

[0026] The posterior covariance matrix in the time domain Expressed as:

[0027]

[0028] The transmitted symbols follow independent and identically distributed, so the posterior covariance matrix in the time domain Only focus on the diagonal elements, specifically expressed as:

[0029]

[0030] where h n is the nth column of H T , 1 ≤ n ≤ MN;

[0031] Let Af1 = r, Af2 = h n , then:

[0032]

[0033]

[0034] Use the GMRES algorithm to solve the linear equations Af1 = r and Af2 = h n to obtain f1 and f2, and then calculate the posterior mean vector and posterior covariance matrix in the time domain.

[0035] Furthermore, in the remaining iterative processes, the sparsification process includes: first sparsifying the matrix A from the edge perspective, and then sparsifying it from the node perspective;

[0036] where the sparsification from the edge perspective includes: normalizing the diagonal elements of the matrix A to obtain the matrix If | |, then ignore this edge, that is, set the corresponding element to 0 to obtain the matrix A1;

[0037] The sparsification from the node perspective includes: when the degree of a certain node of the matrix A1 is lower than the set threshold ε D , then ignore all the edges connecting this node, that is, obtain the sparsified matrix A;

[0038] where J is a diagonal matrix, and its diagonal element J(i, i) = |A(i, i)|, i = 1, 2,..., MN.

[0039] Furthermore, use the Kronecker product operation to transform the posterior mean vector and posterior covariance matrix in the time domain to the delay-sequence domain respectively, to obtain the posterior mean vector and posterior covariance matrix

[0040] Among them, the posterior mean vector in the time delay - sequence domain is expressed as:

[0041]

[0042] The posterior covariance matrix in the time delay - sequence domain is expressed as:

[0043]

[0044] Among them, W N represents the normalized N - point WHT transform matrix, represents the Kronecker product operation, and I M represents the identity matrix.

[0045] Furthermore, in step 2, the process of obtaining the input soft information of the SISO decoder is as follows: First, calculate the extrinsic information log - likelihood ratio, and then, after de - interleaving, it is used as the input soft information of the SISO decoder.

[0046] Furthermore, the formula for calculating the extrinsic information log - likelihood ratio is:

[0047]

[0048]

[0049] Among them, L e (c n,j ) represents the extrinsic information log - likelihood ratio of the j - th bit c n,j of the n - th symbol, s i represents the value of the i - th constellation point in modulation, s i represents the binary bit vector corresponding to the i - th constellation point, s i,j represents the j - th component of s i , c e represents the extrinsic variance, and m e represents the extrinsic mean, as follows:

[0050]

[0051] Among them, represents the n - th element in the prior mean vector in the time delay - sequence domain, represents the n - th element in the posterior mean vector in the time delay - sequence domain, represents the element at the n - th row and n - th column position in the prior covariance matrix in the time delay - sequence domain, represents the element at the n - th row and n - th column position in the posterior covariance matrix in the time delay - sequence domain, 1 ≤ n ≤ MN;

[0052] In the initial iteration process, p(cn,j' = s i,j' ) Using the assumed equiprobable transmission, in the remaining iterations, p(c n,j' = s i,j' ) Solve using the log-likelihood ratio of the prior information.

[0053] Further, in step 3, the process of updating the prior mean vector and the prior covariance matrix in the delay-sequence domain and obtaining the prior mean vector and the prior covariance matrix in the time domain through the cross-domain message passing unit includes: The posterior log-likelihood ratio output by the SISO decoder after decoding is the output soft information of the decoder. According to the idea of Turbo equalization, the soft information is iterated between the DI-S-MMSE estimator and the SISO decoder;

[0054] The iteration of the soft information includes: Subtracting the input prior log-likelihood ratio from the posterior log-likelihood ratio to obtain the extrinsic information, then passing the extrinsic information through the interleaver to obtain the prior log-likelihood ratio in the delay-sequence domain, and then calculating the prior mean vector and the prior covariance matrix according to the prior log-likelihood ratio. Further, transform the prior mean vector and the prior covariance matrix in the delay-sequence domain to the time domain to obtain the prior mean vector and the prior covariance matrix in the time domain, and finally input them into the DI-S-MMSE estimator;

[0055] Among them, the prior log-likelihood ratio L(c n,j ) is expressed as:

[0056]

[0057] For the j-th bit of the n-th transmitted symbol, let the probability that this bit is transmitted as 0 be p j,0 , and the probability that it is transmitted as 1 be p j,1 , which is specifically expressed as follows:

[0058]

[0059] The prior mean vector in the delay-sequence domain is The prior covariance matrix in the delay-sequence domain is

[0060] Among them, represents the mean of the n-th transmitted symbol; c n represents the variance of the n-th transmitted symbol, 1 ≤ n ≤ MN.

[0061] Further, in step 3, use the Kronecker product operation to transform the prior mean vector and the prior covariance matrix in the time-domain sequence domain to the time domain respectively, that is, the prior mean vector and the prior covariance matrix are:

[0062]

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] A dual-iteration sparse minimum mean square error Turbo equalization detection method proposed by the present invention aims to utilize the sparsity characteristic of the time-domain channel matrix of the OTSM system, and adopts the idea of Turbo equalization to iteratively improve the detection performance for multiple times. At the same time, the DI-S-MMSE estimator includes the DI-S-MMSE estimation algorithm. In the initial iteration, this algorithm completes the MMSE estimation by avoiding direct inversion, and realizes low-complexity inversion after sparsifying the matrix in the remaining iterations. Through the above DI-S-MMSE estimation algorithm, the problem of high complexity of the existing detection method is solved. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The drawings here are incorporated into the specification and form a part of this specification, and are used together with the specification to explain the principles of the present invention.

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, for those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0067] Figure 1 It is the OTSM iterative detection system model based on DI-S-MMSE Turbo equalization of the present invention;

[0068] Figure 2 It is the BER performance curve of DI-S-MMSE (Turbo) at P = 4 in Experiment 1 of the embodiment;

[0069] Figure 3 It is the BER performance curve of DI-S-MMSE (Turbo) and I-MMSE (Turbo) at P = 8 in Experiment 1 of the embodiment;

[0070] Figure 4 It is the sparsity of L in the second outer iteration of Experiment 2 of the embodiment

[0071] Figure 5 It is the sparsity of L in Experiment 3 of the embodiment Curve of change with the number of iterations. DETAILED DESCRIPTION OF THE INVENTION

[0072] Exemplary embodiments will be described in detail herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. On the contrary, they are merely examples consistent with some aspects of the present invention detailed in the appended claims.

[0073] This solution belongs to the design of the channel equalization module in an OTSM receiver and can be implemented in hardware on an FPGA.

[0074] On the one hand, please refer to Figure 1 , this embodiment provides an OTSM iterative detection system model based on DI-S-MMSE Turbo equalization. The OTSM system model includes a transmitter, a wireless channel, and a receiver. The transmitter includes an encoder, an interleaver, a mapping unit, a WHT transformation unit, and a serial-to-parallel conversion unit connected in sequence. The receiver includes a time-domain DI-S-MMSE estimator, a cross-domain message passing unit, an extrinsic information unit, a deinterleaver, a SISO decoder, an adder, an interleaver, a priori information unit, and a cross-domain message passing unit. The input end of the SISO decoder is also connected to the adder.

[0075] Among them, the DI-S-MMSE estimator contains the DI-S-MMSE estimation algorithm.

[0076] The system model of the present invention can eliminate inter-symbol interference in the received sequence. The MMSE Turbo equalization detector is composed of a DI-S-MMSE estimator and a SISO decoder. This MMSE Turbo equalization detector performs iteration (hereinafter referred to as outer iteration) between the DI-S-MMSE estimator and the SISO decoder; an internal iteration (hereinafter referred to as inner iteration) is also performed using the DI-S-MMSE estimation algorithm within the DI-S-MMSE estimator to reduce the computational complexity through the inner iteration algorithm.

[0077] This system model is as Figure 1 shown. The specific process is as follows: The bit stream signal at the transmitter is encoded and interleaved, and then constellation mapping is performed in the delay-sequence domain. The present invention uses Quadrature Phase Shift Keying (QPSK), and its constellation points and corresponding bits are shown in Table 1, where j represents the imaginary unit. The modulated MN symbols are subjected to an N-point WHT transformation and placed in a delay-time domain grid of M×N, and then transformed into the time domain through serial-to-parallel conversion and transmitted through the time-domain wireless channel. At the receiver, the time-domain received signal vector r∈C MN×1 is expressed as:

[0078] r = H T z + w (1)

[0079] where, H T ∈ C MN×MN represents the time-domain channel matrix, z ∈ C MN×1 represents the time-domain transmitted symbol vector, w ∈ C MN×1 represents the time-domain noise vector. After obtaining the time-domain received signal, by utilizing the sparsity characteristic of the time-domain channel matrix of the OTSM system, the low-complexity DI-S-MMSE estimation algorithm is used in the time domain to calculate the posterior mean vector and the posterior covariance matrix, and then the posterior mean vector and the posterior covariance matrix are transformed to the delay-sequence domain through cross-domain message passing. The extrinsic information is calculated in the delay-sequence domain, and after deinterleaving the extrinsic information, it is used as the input soft information of the SISO decoder. According to the soft information output by the SISO decoder, the prior mean vector and the prior covariance matrix are calculated in the delay-sequence domain, and are transformed to the time domain through cross-domain message transformation for the next iteration. After multiple iterations, the soft information output by the decoder is judged, and the transmitted-bit information can be obtained.

[0080] Table 1 QPSK constellation diagram

[0081]

[0082] On the other hand, a dual-iteration sparse minimum mean square error Turbo equalization detection method, based on the above-mentioned OTSM iterative detection system model, includes the following steps:

[0083] Step 1: After the receiving end obtains the time-domain received signal, the DI-S-MMSE estimation algorithm is used in the time domain to calculate the posterior mean vector and the posterior covariance matrix, and then the posterior mean vector and the posterior covariance matrix in the time domain are respectively transformed to the delay-sequence domain through the cross-domain message passing unit, obtaining the posterior mean vector and the posterior covariance matrix in the delay-sequence domain;

[0084] Step 2: Calculate the extrinsic information in the delay-sequence domain, and after deinterleaving the extrinsic information, use it as the input soft information of the SISO decoder;

[0085] Step 3: According to the soft information output after decoding by the SISO decoder, update the prior mean vector and the prior covariance matrix in the time-domain sequence domain, and transform them to the time domain through the cross-domain message passing unit, obtaining the prior mean vector and the prior covariance matrix in the time domain, and then perform the next iteration. After multiple iterations, the soft information output by the SISO decoder is judged to obtain the transmitted-bit information; the number of iterations is set in advance manually.

[0086] Furthermore, in step 1, the calculation process of the posterior mean vector and the posterior covariance matrix in the time domain includes: performing MMSE estimation through the DI-S-MMSE estimation algorithm based on the time-domain received signal vector, the time-domain channel matrix, and the prior information, and calculating the posterior mean vector and the posterior covariance matrix in the time domain;

[0087] The posterior mean vector in the time domain is expressed as:

[0088]

[0089] where r represents the time-domain received signal vector; represents the prior mean vector; H T represents the time-domain channel matrix; represents the prior covariance matrix; W MMSE represents the time-domain MMSE estimation matrix, as shown below:

[0090]

[0091] It can be seen from equations (2) and (3) that the matrix

[0092] where N0 represents complex Gaussian noise, and I MN represents the identity matrix;

[0093] The posterior covariance matrix in the time domain is expressed as:

[0094]

[0095] It can be seen from equations (2) and (4) that the high complexity of the equalizer algorithm is mainly due to the inverse operation of A in the MMSE estimation, H T is a random sparse matrix, so A is also a random sparse matrix. However, the sparsity of A does not guarantee that its inverse matrix A -1 is also sparse. To reduce the computational complexity, A is sparsified so that A -1 is also sparse.

[0096] For any random sparse matrix N A = MN, and A is a Hermitian matrix, and the distribution of non-zero elements in the matrix is symmetric. Therefore, A can be represented by an undirected graph G(ξ, ε). This graph consists of a node set ξ and an edge set ε, where the node set ξ contains N Anodes, each node represents a row or a column of matrix A, and the edge set ε represents the connection relationship of non-zero elements. If A(i,j) is non-zero, there will be an edge in the graph connecting node i and node j. The degree of each node refers to the number of edges connected to the node, usually denoted by D. Since A is random, the degrees of its various nodes can be described by the random variable To more intuitively measure the sparsity of the random sparse matrix, the cumulative distribution function (CDF) is usually used to represent it, that is In MMSE estimation, the key factor affecting the computational complexity is the sparsity of the inverse matrix. Therefore, more attention is paid to A -1 -1 Similarly, its node degree can be defined as a random variable and its sparsity is measured by When the value of is smaller, the distribution of is more concentrated in smaller values, which means that A -1 is sparser, and thus the computational complexity is lower.

[0097] Therefore, in this embodiment, in the initial iteration process, directly finding the inverse of matrix A is converted into solving two linear equations, and the GMRES algorithm is used to solve the linear equations, and then the posterior mean vector and posterior covariance matrix in the time domain are calculated according to the solution results; in the remaining iteration processes, first, the matrix A is sparsified based on the graph theory method, and then the FSPAI algorithm is used to obtain A -1 Finally, it is substituted into equations (2) and (4) to obtain the posterior mean vector and posterior covariance matrix in the time domain.

[0098] Specifically, in the initial iteration process, due to the lack of prior information, the prior mean vector is set as an MN×1-dimensional zero vector, and the prior covariance matrix is set as an MN×MN identity matrix.

[0099] Therefore, the matrix The posterior mean vector in the time domain is expressed as:

[0100]

[0101] The posterior covariance matrix in the time domain is expressed as:

[0102]

[0103] The transmitted symbols are independent and identically distributed. Therefore, the posterior covariance matrix in the time domain Only focus on the diagonal elements, specifically expressed as:

[0104]

[0105] where h n is the nth column of H T , 1 ≤ n ≤ MN;

[0106] Let Af1 = r, Af2 = h n , then:

[0107]

[0108]

[0109] Use the GMRES algorithm to solve the linear equations Af1 = r and Af2 = h n to obtain f1 and f2, and then calculate the time-domain posterior mean vector and posterior covariance matrix.

[0110] Specifically, apply the GMRES algorithm in the initial iteration

[0111] From the outer iteration process, A -1 is required when calculating the time-domain posterior mean vector and the posterior covariance matrix . Since there is a lack of prior information in the initial iteration, is a zero vector, is an identity matrix, and at this time So the time-domain posterior mean vector can be expressed as For A -1 r To avoid direct inversion, the inversion problem can be converted into the problem of solving the linear equation Af1 = r. Here, f1 is the unknown to be solved, so And the time-domain posterior covariance matrix can be expressed as: According to the assumption of independent and identically distributed, only care about the diagonal elements, and the diagonal elements are where h n is the nth column of H T , 1 ≤ n ≤ MN, and because all are approximately constant in the initial iteration, it can be calculated once, and it is converted into another linear equation Af2 = h n , so f2 is another unknown. Thus, the matrix inversion can be directly converted into solving two linear equations, thereby greatly reducing the computational amount. The present invention uses the GMRES algorithm to solve the linear equations.

[0112] For a system of linear equations Af = b, where A is an MN×MN matrix. According to the Cayley-Hamilton theorem, there exists a set of coefficients such that:

[0113] f(A)=A MN +a MN-1 A MN-1 +...+a0I = 0 (10)

[0114] Equivalent to:

[0115]

[0116] When solving the system of linear equations, arbitrarily give an initial value f0, and correspondingly generate an initial residual r0 = b - Af0. Then the exact solution of the system of equations can be expressed in the following form f = f0 + A -1 r0, substituting into A -1 , it can be known that theoretically the exact solution of the system of equations can be found in the space {r0, Ar0,..., A MN-1 r0}. However, usually the MN value of the OTSM frame is very large, and the cost of finding the exact solution is too high. Therefore, an approximate solution is searched in a low-dimensional subspace of this space.

[0117] Define the Krylov subspace K of order j j =span{r0, Ar0,..., A j-1 r0}. Assume that r0, Ar0,..., A j-1 r0 are linearly independent, and define the orthogonal basis {p1, p2,..., p j} of the K j subspace. Then any vector u in K j can be expressed as u = P j v j , where P j =[p1, p2,..., p j , and v j is the coefficient of linear representation. Assume that the best approximate solution is f j =f0 + Δf j , where Δf j is a vector obtained from the subspace K j . Therefore, Δf j =P j v j can be obtained. Thus, the solution of f j can be transformed into: one is to find the orthogonal basis, and the other is to solve the coefficient of linear representation v j of Δf j under this set of bases.

[0118] First, use the Gram-Schmidt algorithm to calculate Kj The orthogonal basis of the subspace. Since r0, Ar0, ..., A j-1 r0 are linearly independent, it is only necessary to orthonormalize {r0, Ar0, ..., A j-1 r0}. After obtaining the orthogonal basis, the minimized residual is used to quantify the accuracy of the approximate solution and the exact solution. When ||r j || = ||b - Af j || is smaller, f j is closer to the exact solution.

[0119] When the norm of the residual is less than a certain threshold ε g , the algorithm stops iterating. Otherwise, the current j - order Krylov subspace needs to be extended to the j + 1 - order and a more accurate solution is obtained from it. This iterative process of updating the solution is called an inner iteration of the MMSE estimation. However, as the subspace is continuously extended, the computational complexity increases exponentially. Therefore, a maximum dimension number j of the subspace is usually set before applying this algorithm m .

[0120] The solution of the orthogonal basis and the minimization of the residual will be introduced in detail below. Let ρ = ||r0||, p1 = r0 / ρ. First, calculate z = Ap j ; then, for i = 1, ..., j, calculate t i,j =(z, p i ), where t i,j is the inner product of z and p i , and update z = z - t i, j p i to calculate the t i,j corresponding to the next i value at this j value; finally, let t j+1,j = ||z||, and obtain p j+1 = z / t j+1,j . Also, because:

[0121] t j+1,j p j+1 = Ap j - t 1,j p1 - t 2,j p2 - t 3,j p3 -... - t j,j p j (12)

[0122] That is:

[0123]

[0124] Where:

[0125]

[0126] Therefore, it can be obtained that:

[0127] AP j = [Ap1, Ap2,..., Ap j = P j+1 T j (15)

[0128] To minimize the residual in the current subspace, the following least mean square problem can be obtained:

[0129]

[0130] Substitute Δf j = P j v j into the above formula:

[0131]

[0132] where represents the i-th column of the identity matrix I j+1 . At this time, calculating formula (17) requires less computational effort because T j is a j×(j + 1) matrix, where 1 <= j <= j m , and j is much smaller than MN.

[0133] In the GMRES algorithm, it is the current residual value that determines whether to perform the next inner iteration of the DI-S-MMSE estimator, that is, the least mean square problem in formula (17) needs to be calculated. To avoid calculating formula (17) every time, T j can be transformed into an upper triangular matrix U j column by column with the help of the rotation matrix

[0134]

[0135] where, in the i-th and (i + 1)-th rows, and i = 1,..., j, it is defined as:

[0136]

[0137] It can be obtained that:

[0138]

[0139] Therefore, formula (17) is transformed into:

[0140]

[0141] where Also, because U jThe last row is all zeros, so an appropriate v can be selected j , and the residual w except for the last row j -U j v j can all be made zero. Therefore, no additional calculation is required, and the current residual value is exactly the elements of the last row of w j , that is, ||r j || = |w j (j + 1)|.

[0142] When j m iterations of the DI-S-MMSE estimator are completed, if the norm of the residual still exceeds the threshold ε g , then the current approximate solution is taken as the new initial estimate, that is, let f0' = f jm , and then restart the calculation of the new subspace and start a new round of iteration. Such j m inner iterations are called a restart, and the maximum complexity can be effectively controlled through such algorithm restart.

[0143] Furthermore, during the remaining iterations, the sparsification process includes: first sparsifying the matrix A from the edge perspective, and then sparsifying it from the node perspective;

[0144] Specifically, based on the graph theory method, the further sparsification of the matrix A can be achieved through the following two steps:

[0145] Sparsification from the edge perspective: First, normalize the diagonal elements of the matrix A to obtain a new matrix where J is a diagonal matrix, and its diagonal element J(i, i) = |A(i, i)|, i = 1, 2,..., MN. If the value of an edge is less than the set threshold ε A , that is, satisfying then the edge is ignored, that is, the corresponding element is set to 0; otherwise, the data is retained.

[0146] Sparsification from the node perspective: When the degree of a certain node is lower than the set threshold ε D , that is, D ≤ ε D ,

[0147] then all the edges connecting this node are ignored, otherwise the data is retained.

[0148] Considering the matrix at a lower E b / N0, the matrix A is mainly determined by the second term N0I, so the values of its diagonal elements are significantly larger than those of the non - diagonal elements. In this case, most of the non - diagonal elements can be ignored through sparsification, making the matrix A very sparse. However, when E bWhen / N0 is relatively high, the non - diagonal elements of the matrix may be of the same order of magnitude as the diagonal elements. In this case, the effect of sparsification on increasing the sparsity is limited. However, as the outer iteration progresses, highly reliable prior information can be obtained, and the prior variance it feedbacks gradually approaches zero, making the first term of matrix A also approach zero, so that the diagonal elements are once again much larger than the non - diagonal elements. Therefore, the computational complexity can be further reduced by sparsifying A.

[0149] Specifically, the FSPAI algorithm is applied in the subsequent outer iteration

[0150] After the initial outer iteration, highly reliable means and variances are obtained from the decoder as the inputs of the MMSE detector, making the diagonal elements significantly larger than most non - diagonal elements. Therefore, through sparsification processing, A will become sparse enough, thus greatly reducing the complexity of inversion. The present invention uses the FSPAI algorithm to calculate the approximate value of A -1 of A.

[0151] Since A is a Hermitian positive - definite matrix, it can be expressed as where L A is a lower - triangular matrix. Based on this, solving for A -1 can be transformed into solving the problem of its Cholesky decomposition term L, that is, it is necessary to find a lower - triangular matrix L such that LL H ≈A -1 . By minimizing the Kaporin condition number of L H AL, the best approximate solution of L can be obtained:

[0152]

[0153] where tr(·) and det(·) represent the trace and determinant of the matrix respectively, the condition number K is used to evaluate the quality of the approximation result, and K≥1. Obviously, the more accurate L is, the closer L H AL is to the identity matrix I, and thus the closer K is to 1.

[0154] First, initialize the sparsity property sp(L) of matrix L. If L(i,j) is non - zero, the element in the i - th row and j - th column of sp(L) is 1. Therefore, the position distribution of the non - zero elements of matrix L can be directly obtained through sp(L), and initially sp(L)=I. a k and l k represent the k - th columns of A and L respectively, C k represents the indices of the non - zero elements in l k , and Based on this, we can get:

[0155]

[0156] where \(l\) kk = L(k, k) ∈ ℝ + and \(a\) kk = A(k, k) ∈ ℝ + and ℝ + denotes the set of positive real numbers. For each column, \(l\) kk and can be solved by minimizing the condition number, i.e., and we can obtain:

[0157]

[0158] As can be seen from the above, the calculation of each column of matrix L is independent. Next, the calculation process of one of the columns will be introduced.

[0159] The FSPAI algorithm iteratively improves the approximate result by selecting a new index r and adding it to C k . Each time the index is updated, the process is called an inner iteration. In each iteration, the approximate result is updated by \(l'\) k = \(l\) k + \(l\) rk e r , where \(e\) r represents the r-th column of L and r > k. Therefore, a new condition number \(K\) r ' can be obtained:

[0160]

[0161] To solve the minimum value of the condition number \(K\) r ', we can let So we can obtain:

[0162]

[0163] Since \(l\) k has sparsity, only a small amount of calculation is required to obtain \(l\) rk , and further the minimum value of the condition number \(K\) r ' corresponding to the index r is:

[0164]

[0165] where is used to measure the reduction of the Kaporin condition number after adding r. Due to the sparsity of matrix A, only a small number of indices satisfy \(a\) r (C k ) H l k (C k ) ≠ 0, and these indices form a set:

[0166]

[0167] Next, add the several largest indexes of η rk to set C k to obtain a new set C' k and A more accurate approximate solution can be obtained according to Equations (24) to (26). It should be noted that the computational complexity of the FSPAI algorithm mainly comes from the inversion operation in Equation (24). Therefore, in order to control the computational complexity, should be restricted not to exceed a preset value ζ. This iterative process will continue until one of the following conditions is met: or the maximum value of η rk is less than a threshold ε f , at which point the iteration stops.

[0168] Furthermore, after obtaining the posterior mean vector and posterior covariance matrix in the time domain, since there is no constellation mapping of the OTSM system in the time domain, it is impossible to calculate the extrinsic information in the time domain for signal detection. Therefore, it is necessary to transform to the delay-sequence domain to calculate the extrinsic information, and the extrinsic information is deinterleaved and used as the input soft information of the SISO decoder. In Step 1, the posterior mean vector and posterior covariance matrix in the time domain are respectively transformed to the delay-sequence domain by using the Kronecker product operation to obtain the posterior mean vector and posterior covariance matrix

[0169] where the posterior mean vector in the delay-sequence domain is expressed as:

[0170]

[0171] The posterior covariance matrix in the delay-sequence domain is expressed as:

[0172]

[0173] where W N represents the normalized N-point WHT transform matrix, represents the Kronecker product operation, and I M represents the identity matrix.

[0174] The posterior mean vector in the delay-sequence domain can directly participate in the calculation of the extrinsic information. However, after the posterior covariance matrix is transformed from the time domain to the delay-sequence domain, in addition to the diagonal positions having data, the non-diagonal positions also have data, and it needs to be processed. Since The diagonal elements are the posterior information obtained by MMSE estimation of the time-domain received vector r. According to the independent and identically distributed assumption, only the diagonal elements are concerned, and the non-diagonal elements are discarded. Therefore, the posterior covariance matrix in the delay-sequence domain is a diagonal matrix.

[0175] Furthermore, in step 2, the process of obtaining the input soft information of the SISO decoder is as follows: First, calculate the extrinsic information log-likelihood ratio, and then, after deinterleaving, it is used as the input soft information of the SISO decoder.

[0176] Specifically, after obtaining the posterior mean vector and posterior covariance matrix in the delay-sequence domain, the extrinsic mean m e and extrinsic variance c e are calculated by combining the prior mean vector and prior covariance matrix in the delay-sequence domain:

[0177]

[0178] where, represents the nth element in the prior mean vector, represents the nth element in the posterior mean vector, represents the element at the nth row and nth column position in the prior covariance matrix, represents the element at the nth row and nth column position in the posterior covariance matrix, 1 ≤ n ≤ MN. In the initial iteration process, it is assumed that the prior mean vector in the delay-sequence domain is an MN×1-dimensional zero vector, and the prior covariance matrix is an MN×MN identity matrix. Further, the extrinsic information log-likelihood ratio of the jth bit c n,j of the nth symbol is:

[0179]

[0180] where:

[0181]

[0182] In the above formula (35), s i represents the value of the ith constellation point in modulation, s i represents the binary bit vector corresponding to the ith constellation point, s i,j represents the jth component of s i . p(c n,j' = s i,j' ) uses the assumed equal-probability transmission (equal probability is 1 / 2) in the first iteration, and uses the log-likelihood ratio of the prior information to solve in the remaining iteration processes. After solving the extrinsic information log-likelihood ratio, it is deinterleaved and then used as the input soft information of the SISO decoder.

[0183] Further, in step 3, the prior mean vector and the prior covariance matrix in the time-delay sequence domain are updated, and the prior mean vector and the prior covariance matrix in the time domain are obtained through the cross-domain message passing unit transformation, including: the posterior log-likelihood ratio output after decoding by the SISO decoder is the output soft information of the decoder. According to the idea of Turbo equalization, the soft information is iterated between the DI-S-MMSE estimator and the SISO decoder;

[0184] Specifically, the iteration of the soft information includes: subtracting the input prior log-likelihood ratio from the posterior log-likelihood ratio to obtain the extrinsic information, then passing the extrinsic information through an interleaver to obtain the prior log-likelihood ratio in the time-delay sequence domain, and then calculating the prior mean vector and the prior covariance matrix according to the prior log-likelihood ratio. Further, the prior mean vector and the prior covariance matrix in the time-delay sequence domain are transformed to the time domain to obtain the prior mean vector and the prior covariance matrix in the time domain, and finally they are input into the DI-S-MMSE estimator;

[0185] Among them, the prior log-likelihood ratio L(c n,j ) in the time-delay sequence domain can be expressed as:

[0186]

[0187] For the j-th bit of the n-th transmitted symbol, let the probability that this bit is transmitted as 0 be p j,0 , and the probability that it is transmitted as 1 be p j,1 :

[0188]

[0189] Therefore, the prior probability of the n-th transmitted symbol is the product of the probabilities of transmitting 0 or 1 at each bit position. Next, calculate the prior mean and the prior variance of each transmitted symbol in the time-delay sequence domain as:

[0190]

[0191] Among them, represents the mean of the n-th transmitted symbol, c n represents the variance of the n-th transmitted symbol, 1 ≤ n ≤ MN, the prior mean vector in the time-delay sequence domain, and the prior covariance matrix

[0192] Further, in step 3, the prior mean vector and the prior covariance matrix in the time-domain sequence domain are respectively transformed to the time domain by using the Kronecker product operation, that is, the prior mean vector and the prior covariance matrix are:

[0193]

[0194]

[0195] After the prior covariance matrix is transformed from the time-delay sequence domain to the time domain, in addition to the data at the diagonal positions, there is also data at the non-diagonal positions. According to the assumption of independent and identically distributed, only the diagonal elements are concerned, and the non-diagonal elements are discarded.

[0196] Next, the complexity of the signal detection algorithm is analyzed.

[0197] For the GMRES algorithm, the complexity is O(n cyc (j m +κ)j m MN), where n cyc represents the number of times to restart GMRES, κ represents the number of non-zero elements in each column of A. Considering that usually j m <<κ, so the complexity is approximately O(n cyc κj m MN). For the FSPAI algorithm, its complexity mainly depends on the inversion operation in Equation (24). Considering that after obtaining L, due to the sparsity of L, only a small amount of operations are required to obtain A -1 , therefore, only the sparsity of L is concerned. If the degree of a certain column of L is D, the computational complexity of this column is O(D 4 ). However, D depends on A, and A is a random matrix, so only the average computational complexity can be given through its statistical characteristics. From it can be seen that the average complexity is n p is the number of parallel processors. Therefore, even in the worst case, the complexity of the FSPAI algorithm is O(ζ 4 MN / n p ).

[0198] For the iterative detection algorithm proposed by the present invention, assuming that Turbo equalization needs to be iterated n iter times, then the complexity required by the equalizer of the present invention is while the complexity of the direct-inversion I-MMSE Turbo equalization is O(n iter (MN) 3 ). The complexity of the LMMSE equalization is O((MN) 3 ). By comparison, it can be seen that the detection algorithm proposed by the present invention achieves excellent BER performance with a smaller complexity.

[0199] To prove the efficacy of the present invention, the following experiments are conducted by the present invention:

[0200] The performance of the OTSM signal detection algorithm using DI-S-MMSE Turbo equalization is verified through simulation experiments, and the performance of other equalization detection algorithms is compared. For the sake of easy distinction here, if the receiver detector does not require a decoder, the output of the MMSE estimator is directly used as the extrinsic information and fed back to the MMSE estimator, and this detector is called the DI-S-MMSE equalization detector. Considering that the matrix L largely determines the complexity of the FSAPI algorithm, the simulation results regarding the sparsity of L will be given, and the complexity of the detection algorithm proposed in the present invention will be given. Therefore, three groups of simulation experiments are set up to compare the algorithm complexities. The three groups of simulation experiments are as follows:

[0201] 1. Under the condition that other conditions are the same, compare the Bit Error Rate (BER) performance of the DI-S-MMSE (Turbo) equalization detector and other equalization detectors;

[0202] 2. The sparsity of the matrix L in the second extrinsic iteration of the DI-S-MMSE (Turbo) equalization detector under the conditions of E b / N0 being 6 dB and 10 dB;

[0203] 3. The variation of the sparsity of the matrix L of the DI-S-MMSE (Turbo) equalization detector with the number of extrinsic iterations under the conditions of E b / N0 being 6 dB and 10 dB.

[0204] The simulation parameters are shown in Table 2

[0205] Table 2 Simulation parameter settings

[0206]

[0207] Experiment 1

[0208] The first simulation experiment compares the BER performance of different detection algorithms. The parameter settings are shown in Table 2, and the simulation results are as shown in Figure 2 and Figure 3 shown, Figure 2 and Figure 3 where the number of paths P is 4 and 8 respectively.

[0209] From Figure 2It can be seen that in the first iteration, the DI-S-MMSE equalizer using GMRES has the same BER performance as the traditional LMMSE equalizer. After 5 outer iterations, when BER = 1e-3, the DI-S-MMSE equalizer has a 3dB performance improvement compared to the LMMSE equalizer. When an encoder is added to the system, the DI-S-MMSE Turbo equalizer shows better BER performance. When BER = 1e-4, the DI-S-MMSE Turbo equalizer has an encoding gain of approximately 1.5dB compared to the DI-S-MMSE equalizer.

[0210] Figure 3 The algorithm performance of DI-S-MMSE(Turbo) equalization when P = 8 is given. To compare the performance loss caused by using GMRES and FSPAI, the algorithm performance of directly inverting without using these two approximation algorithms is also given. For distinction, according to whether an encoder is added, it is divided into iterative MMSE (I-MMSE) equalization and I-MMSE Turbo equalization. These two algorithms are used as the lower bounds of the DI-S-MMSE(Turbo) equalization algorithm respectively. It can be seen from the figure that neither the GMRES algorithm used in the first outer iteration nor the FSPAI algorithm used in subsequent iterations causes performance loss. Therefore, the detection method proposed in the present invention greatly reduces the complexity without performance loss.

[0211] Experiment Two

[0212] The second simulation experiment analyzes the sparsity of L in the second outer iteration of the DI-S-MMSE(Turbo) equalization detector under the conditions of E b / N0 being 6dB and 10dB. This sparsity is measured by . The simulation parameters are shown in Table 2, where P = 8, and the simulation results are as shown in Figure 4 .

[0213] It can be seen from Figure 4 that under E b / N0 = 6dB, the corresponding to DI-S-MMSE Turbo, that is, the degrees of approximately 33% of the nodes are 0. Under E b / N0 = 10dB, the corresponding to DI-S-MMSE Turbo, that is, the vast majority of is 0, and L is almost a diagonal matrix. This is because as E b / N0 increases, the extrinsic information generated by the decoder is more reliable. Therefore, the new variance is closer to zero. Coupled with the sparsification policy applied to A, L becomes sparser. On the other hand, under the same Eb Under / N0, the is strictly greater than that of the DI-S-MMSE receiver L is sparser and requires less computation. Therefore, it is verified that the FSPAI algorithm can indeed significantly reduce the complexity, and with the help of the decoder, this reduction is more obvious.

[0214] Experiment 3

[0215] The third simulation experiment analyzes the variation of the L sparsity of the DI-S-MMSE (Turbo) equalization detector with the number of outer iterations under the conditions of E b / N0 of 6 dB and 10 dB. The simulation parameters are shown in Table 2, where P = 8 and D is set to 0 and P / 2 respectively. The simulation results are as Figure 5 shown.

[0216] From Figure 5 it can be seen that, the same as the conclusion of Experiment 2, under the same E b / N0, the is strictly greater than that of the DI-S-MMSE equalization This shows that the encoder reduces the complexity of the detector. And it can be seen that, as E b increases with the increase of / N0. As the number of outer iterations increases, the overall complexity of the FSPAI algorithm is mainly due to the second outer iteration. As the outer iteration progresses, the prior information fed back from the decoder becomes more and more reliable, so the prior variance gets closer and closer to 0, resulting in L being sparser. From Figure 2 and Figure 5 it can be seen that adopting the Turbo structure not only improves the BER performance but also greatly reduces the complexity.

[0217] The above are only specific implementation manners of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention.

[0218] It should be understood that the present invention is not limited to the above-described content and can be modified and changed without departing from its scope. The scope of the present invention is only limited by the appended claims.

Claims

1. An OTSM iterative detection system model based on DI-S-MMSE Turbo equalization, characterized in that, The OTSM system model includes a transmitter, a wireless channel, and a receiver. The transmitter includes an encoder, an interleaver, a mapping unit, a WHT transformation unit, and a serial-to-parallel conversion unit connected in sequence. The receiver includes a time-domain DI-S-MMSE estimator, a cross-domain message passing unit, an extrinsic information unit, a deinterleaver, a SISO decoder, an adder, an interleaver, a priori information unit, and a cross-domain message passing unit. The input end of the SISO decoder is also connected to the adder. Among them, the DI-S-MMSE estimator contains the DI-S-MMSE estimation algorithm.

2. A dual-iteration sparse minimum mean square error Turbo equalization detection method, characterized in that The OTSM iterative detection system model according to claim 1 includes the following steps: Step 1: After the receiver obtains the time-domain received signal, use the DI-S-MMSE estimation algorithm in the time domain to calculate the posterior mean vector and posterior covariance matrix, and then transform the time-domain posterior mean vector and posterior covariance matrix to the delay-sequence domain through the cross-domain message passing unit to obtain the delay-sequence domain posterior mean vector and posterior covariance matrix. Step 2: Calculate the extrinsic information in the delay-sequence domain, and use the deinterleaved extrinsic information as the input soft information of the SISO decoder. Step 3: According to the soft information output after decoding by the SISO decoder, update the priori mean vector and priori covariance matrix in the time-domain sequence domain, and transform them to the time domain through the cross-domain message passing unit to obtain the time-domain priori mean vector and priori covariance matrix, and then perform the next iteration. After multiple iterations, judge the soft information output by the SISO decoder to obtain the transmitter bit information.

3. The detection method according to claim 2, wherein In step 1, the calculation process of the time-domain posterior mean vector and posterior covariance matrix includes: performing MMSE estimation on the time-domain received signal vector, time-domain channel matrix, and priori information through the DI-S-MMSE estimation algorithm to calculate the time-domain posterior mean vector and posterior covariance matrix. The posterior mean vector in the time domain is expressed as: where r represents the time-domain received signal vector; represents the prior mean vector; H T represents the time-domain channel matrix; represents the prior covariance matrix; W MMSE represents the time-domain MMSE estimation matrix, as shown below: As can be seen from equations (1) and (2), the matrix where N0 represents complex Gaussian noise, and I MN represents the identity matrix; The posterior covariance matrix in the time domain is expressed as: In equations (1) and (3), during the initial iteration process, the direct inversion of matrix A is converted into solving two linear equations, and the GMRES algorithm is used to solve the linear equations. Then, based on the solution results, the posterior mean vector and posterior covariance matrix in the time domain are calculated. In the remaining iteration processes, first, matrix A is sparsified based on the graph theory method, and then the FSPAI algorithm is used to obtain A -1 , and finally, they are substituted into equations (1) and (3) to obtain the posterior mean vector and posterior covariance matrix in the time domain.

4. The detection method according to claim 3, wherein In the initial iteration process, due to the lack of prior information, is a zero vector, is an identity matrix, and the matrix Therefore, the posterior mean vector in the time domain is expressed as: The posterior covariance matrix in the time domain is expressed as: The transmitted symbols are independent and identically distributed, so the posterior covariance matrix in the time domain only needs to focus on the diagonal elements, which are specifically expressed as: where h n is the n-th column of H T with 1 ≤ n ≤ MN; Let Af1 = r and Af2 = h n , then: The GMRES algorithm is used to solve the linear equations Af1 = r and Af2 = h n to obtain f1 and f2, and then the posterior mean vector and posterior covariance matrix in the time domain are calculated.

5. The detection method according to claim 3, characterized in that, In the remaining iteration processes, the sparsification process includes: first sparsifying the matrix A from the edge perspective, and then sparsifying it from the node perspective. Among them, the edge-based sparsification process includes: normalizing the diagonal elements of matrix A to obtain matrix If at this time, then ignore this edge, that is, set the element at the corresponding position to 0 to obtain matrix A1; The sparsification process from the perspective of nodes includes: when the degree of a certain node in the matrix A1 is lower than the set threshold ε D then all the edges connecting this node are ignored, that is, the matrix A after sparsification processing is obtained; Among them, J is a diagonal matrix, and its diagonal element J(i, i) = |A(i, i)|, where i = 1, 2,..., MN.

6. The detection method according to claim 3, wherein In Step 1, the posterior mean vector and the posterior covariance matrix in the time domain are respectively transformed into the delay-sequence domain by using Kronecker product operation, and the posterior mean vector in the delay-sequence domain is obtained and the posterior covariance matrix Among them, the posterior mean vector in the time delay-sequence domain is expressed as: Posterior covariance matrix in the time-delay sequence domain It is expressed as: Among them, W N represents the normalized N-point WHT transform matrix, represents the Kronecker product operation, and I M represents the identity matrix.

7. The detection method according to claim 3, wherein In step 2, the process of obtaining the input soft information of the SISO decoder is: first calculate the extrinsic information log-likelihood ratio, and then use the deinterleaved result as the input soft information of the SISO decoder.

8. The detection method according to claim 7, characterized in that The formula for calculating the extrinsic information log-likelihood ratio is: Among them, L e (c n,j ) represents the extrinsic information log-likelihood ratio of the j-th bit c of the n-th symbol, s n,j represents the value of the i-th constellation point in modulation, s i represents the binary bit vector corresponding to the i-th constellation point, s i represents the j-th component of s i,j represents s i 's j-th component, c e represents the extrinsic variance, m e represents the extrinsic mean, as follows: Among them, represents the nth element in the prior mean vector in the time-delay sequence domain, represents the nth element in the posterior mean vector in the time-delay sequence domain, represents the element at the nth row and nth column position in the prior covariance matrix in the time-delay sequence domain, represents the element at the nth row and nth column position in the posterior covariance matrix in the time-delay sequence domain, 1≤n≤MN; In the initial iteration process, p(c n,j' = s i,j' ) uses the assumed equiprobable transmission. In the remaining iteration processes, p(c n,j' = s i,j' ) is solved using the log-likelihood ratio of the prior information.

9. The detection method according to claim 2, wherein In step 3, the process of updating the priori mean vector and priori covariance matrix in the delay-sequence domain and transforming them through the cross-domain message passing unit to obtain the time-domain priori mean vector and priori covariance matrix includes: the posterior log-likelihood ratio output after decoding by the SISO decoder is the output soft information of the decoder. According to the idea of Turbo equalization, perform iterative soft information between the DI-S-MMSE estimator and the SISO decoder. The iteration of the soft information includes: subtracting the input prior log-likelihood ratio from the posterior log-likelihood ratio to obtain extrinsic information, then passing the extrinsic information through an interleaver to obtain the prior log-likelihood ratio in the time-delay sequence domain, calculating the prior mean vector and the prior covariance matrix based on the prior log-likelihood ratio, further transforming the prior mean vector and the prior covariance matrix in the time-delay sequence domain to the time domain to obtain the prior mean vector and the prior covariance matrix in the time domain, and finally inputting them into the DI-S-MMSE estimator; Among them, the prior log-likelihood ratio L(c n,j ) in the time-delay sequence domain is expressed as: For the j-th bit of the n-th transmitted symbol, let the probability that this bit is transmitted as 0 be p j,0 , and the probability that it is transmitted as 1 be p j,1 , which is specifically expressed as follows: The prior mean vector in the time-delay sequence domain is The prior covariance matrix in the time-delay sequence domain is Among them, represents the mean of the nth transmitted symbol; c n represents the variance of the n-th transmitted symbol, where 1 ≤ n ≤ MN.

10. The detection method according to claim 2, wherein In step 3, the prior mean vector and the prior covariance matrix in the time domain-sequence domain are respectively transformed to the time domain by using the Kronecker product operation, that is, the prior mean vector and the prior covariance matrix in the time domain are:

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