Signal detection method for multi-antenna orthogonal time-frequency-space sparse code division multiple access system

Abstract

The invention provides a signal detection method for a multi-antenna orthogonal time-frequency-space sparse code division multiple access system, which is characterized in that dimensionality reduction is carried out on time domain and time delay Doppler domain signals by utilizing sparsity of a sparse code division multiple access codebook, and prior distribution of the time domain signals is approximated by using Gaussian distribution. Preliminary detection is realized by acquiring cavity distribution of a signal in a time domain, and the posterior probability of the signal is calculated by using a sparse code division multiple access codebook in a time delay Doppler domain. Based on a transformation relation in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system, information exchange between a time domain and a time delay Doppler domain is realized. The sparse structure of the time domain matrix in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system is utilized, and the complexity of matrix inversion in the algorithm is reduced. By using the method, the complexity of algorithm implementation can be reduced while the signal detection performance is ensured by utilizing the dual sparsity of the multi-antenna orthogonal time-frequency-space system and the sparse code division multiple access codebook.

Description

Technical Field

[0001] The present invention relates to the technical field of signal detection, in particular to a signal detection method for a multi-antenna orthogonal time-frequency-space sparse code division multiple access system. Background Art

[0002] Orthogonal Time-Frequency-Space (OTFS) modulation can convert time-varying multipath channels into time-invariant two-dimensional delay-Doppler channels by multiplexing information symbols in the delay-Doppler domain, thereby significantly improving the bit error rate performance in high-speed mobile environments. Multi-Input Multi-Output (MIMO) technology significantly improves system capacity, throughput and link reliability by using multiple antennas for parallel transmission and reception, and is a key technology in modern communication systems. Sparse Code Multiple Access (SCMA) is an efficient multi-user access technology that achieves efficient multiplexing between users and improves spectrum utilization by designing sparse codewords. In multi-user scenarios, SCMA distinguishes multiple users through different sparse codes to support large-scale connection requirements. Combining OTFS with MIMO can further improve spectrum efficiency and transmission reliability, while the introduction of SCMA effectively solves the capacity limitation of OTFS in large-scale connection scenarios.

[0003] In the prior art multi-antenna orthogonal time-frequency-space sparse code division multiple access scheme, multiple users are encoded using different sparse codebooks, and the codeword vector is modulated using OTFS. The modulated transmission signal reaches the receiving end after being transmitted in the channel. The receiving end receives the superimposed signals of multiple users after being transmitted through the channel, and performs joint OTFS and SCMA detection on the signals in the delay-Doppler domain to obtain the transmission codewords of multiple users, thereby completing multi-user detection.

[0004] Existing signal detection mainly includes maximum a posteriori detectors, linear detectors, detection algorithms based on Gaussian message passing GAMP and approximate expected propagation GAEP based on factor graphs, and signal detection algorithms based on expected propagation EP. However, the optimal maximum a posteriori detector is difficult to implement in practice because its complexity grows exponentially with the system dimension. Existing linear detectors, such as zero forcing and linear minimum mean square error detectors, have low computational complexity but can lead to significant performance loss. Although the detection algorithms based on Gaussian message passing GAMP and approximate expected propagation GAEP based on factor graphs can achieve better multi-user detection performance, their computational complexity is still high. In addition, although the signal detection algorithm based on expected propagation EP performs well in performance, due to the high dimensionality of the equivalent channel matrix in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system, the complexity of the matrix inversion operation involved in the processing of the algorithm limits the overall performance of the system. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides a signal detection method for a multi-antenna orthogonal time-frequency-space sparse code division multiple access system. The present invention can utilize the sparsity of the time domain equivalent channel matrix and the sparse code division multiple access codebook in the multi-antenna orthogonal time-frequency-space system to reduce the complexity of the signal detection algorithm.

[0006] The technical solution of the present invention is: a multi-antenna orthogonal time-frequency-space sparse code division multiple access system signal detection method, comprising the following steps:

[0007] S1), initializing the original bit stream of each user to obtain the transmission signal vector, the reception signal vector, the equivalent channel matrix, and the transformation matrix in the delay Doppler domain and the time domain;

[0008] S2), based on the posterior probability, use the non-normalized Gaussian distribution to approximate the prior distribution of the time domain transmission signal vector, set the iteratively updateable parameters, and initialize the parameters;

[0009] S3), based on the first-order moment, the second-order moment parameter, the time-domain received signal vector and the time-domain equivalent channel matrix, obtaining the mean vector and the variance vector of the time-domain cavity distribution;

[0010] S4), transforming the mean vector and variance vector of the time domain cavity distribution to obtain the mean vector and variance vector of the delay Doppler domain cavity distribution;

[0011] S5), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the mean vector and variance vector of the delay-Doppler domain posterior distribution;

[0012] S6), transforming the mean vector and variance vector of the delay-Doppler domain posterior distribution to obtain the mean vector and variance vector of the time domain posterior distribution;

[0013] S7), updating the time domain prior first-order moment and second-order moment parameters based on the moment matching method;

[0014] S8) Repeat steps S3)-S7) until a preset number of iterations is reached to obtain the detection result of the original bit stream.

[0015] Preferably, step S1) specifically includes the following steps:

[0016] S11), modulating and vectorizing the original bit stream of each user to obtain a delay-Doppler domain transmission signal vector;

[0017] S12), performing inverse symplectic finite Fourier transform and Heisenberg transform on the delay Doppler domain transmission signal vector, using a rectangular wave for pulse shaping, and obtaining a time domain transmission signal vector;

[0018] S13), constructing a time domain equivalent channel matrix based on the channel, performing a matrix product operation on the time domain equivalent channel matrix and the time domain transmitted signal vector to obtain a time domain received signal vector;

[0019] S14), using a rectangular wave to perform a receiving matching pulse to perform a Wigner transform and a symplectic finite Fourier transform on a time domain received signal vector to obtain a delay Doppler domain received signal vector;

[0020] S15), based on the sparsity of the sparse code division multiple access codeword, obtain the non-zero position index of the transmitted signal vector and the received signal vector in the original delay Doppler domain and time domain;

[0021] S16), based on the position index of the non-zero elements in the signal, obtain the transmitted signal vector, received signal vector, equivalent channel matrix, and transformation matrix in the delay Doppler domain and the time domain.

[0022] Preferably, in step S11), a corresponding codeword is selected from the SCMA codebook of each user according to the original bit stream for SCMA encoding to obtain SCMA-encoded data symbols; and the SCMA-encoded data symbols are placed on the delay Doppler domain grid along the delay axis to obtain a delay Doppler domain signal matrix.

[0023] Preferably, in step S12), the inverse symplectic finite Fourier transform performs an M-point discrete Fourier transform on the columns of the delay-Doppler domain signal matrix and an N-point discrete inverse Fourier transform on the rows to convert the delay domain to the frequency domain and convert the Doppler domain to the time domain; the Heisenberg transform converts the two-dimensional signal matrix in the time-frequency domain into a time domain vector and applies rectangular pulse shaping.

[0024] Preferably, in step S3), obtaining the mean vector and variance vector of the time domain cavity distribution specifically includes the following steps:

[0025] S31), based on the first-order moment, the second-order moment parameter and the time-domain received signal vector and the equivalent channel matrix after dimensionality reduction, obtaining the time-domain posterior mean vector and the variance matrix;

[0026] S32), based on the time domain posterior variance matrix and the time domain equivalent channel matrix, obtaining the sparse structure of the target inversion matrix;

[0027] S33), based on the sparse structure of the target inversion matrix, sparse reverse Cahir-McGee sorting is performed on the target inversion matrix to obtain a quasi-banded matrix, the quasi-banded matrix is ​​decomposed by Kollerski, the decomposed lower triangular matrix is ​​inverted, and the inversion result of the target inversion matrix is ​​obtained by reordering after multiplication;

[0028] S34), based on the time domain posterior mean vector and variance matrix, obtain the mean vector and variance vector of the time domain cavity distribution.

[0029] Preferably, in step S5), calculating the mean vector and variance vector of the delay-Doppler domain posterior distribution specifically includes the following steps:

[0030] S51), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain;

[0031] S52), based on the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain, obtain the mean vector and variance vector of the delay-Doppler domain posterior distribution.

[0032] The beneficial effects of the present invention are:

[0033] 1. The present invention utilizes the sparsity of the sparse code division multiple access codebook to perform dimensionality reduction processing on time domain and delay Doppler domain signals, adopts Gaussian distribution to approximate the prior distribution of time domain signals, and transmits information only through mean and variance in the time domain and delay Doppler domain, thereby reducing the complexity of the algorithm;

[0034] 2. The present invention realizes preliminary detection in the time domain by acquiring the cavity distribution of the signal; in the delay Doppler domain, the posterior probability of the signal is calculated based on the sparse code division multiple access codebook;

[0035] 3. The present invention realizes information exchange between the time domain and the delay Doppler domain based on the transformation relationship in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system;

[0036] 4. The present invention utilizes the sparse structure of the time domain matrix in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system to reduce the complexity of the matrix inversion required in the iterative algorithm and realize a low-complexity signal detection algorithm based on expected propagation. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the signal detection method of the present invention;

[0038] Figure 2 It is a schematic diagram of the framework of the signal detection method of the present invention. DETAILED DESCRIPTION

[0039] The specific implementation of the present invention will be further described below in conjunction with the accompanying drawings:

[0040] like Figure 1 and 2 As shown, this embodiment provides a multi-antenna orthogonal time-frequency-space sparse code division multiple access system signal detection method. In this embodiment, the multi-antenna orthogonal time-frequency-space sparse code division multiple access system is composed of a single base station and multiple single-antenna user terminals, and is configured as follows:

[0041] In SCMA, the number of users sending signals simultaneously is J = 6, the number of shared orthogonal resources is K = 4, and the number of receiving antennas is N. r =2, the carrier frequency is 4 GHz, the subcarrier spacing is 15 KHz, the number of subcarriers in each OTFS data frame is M = 64, the number of time slots is N = 16, the reduced cyclic prefix type is used, and the maximum delay tap of the channel is l max =3, maximum Doppler tap k max =6, the number of channel paths is P=4, the number of iterations is 10, and the damping factor β is 0.1.

[0042] The steps include:

[0043] S1), initializing the original bit stream of each user to obtain the transmission signal vector, the reception signal vector, the equivalent channel matrix, and the transformation matrix in the delay Doppler domain and the time domain; specifically comprising the following steps:

[0044] S11), modulating and vectorizing the original bit stream of each user to obtain a delay-Doppler domain transmission signal vector;

[0045] In this embodiment, according to the original bit stream, each user has a dimension of K×M modK×1 codewords are selected from the SCMA codebook for SCMA encoding to obtain SCMA-encoded data symbols; then the SCMA-encoded data symbols are placed on a delay-Doppler domain grid of dimension M×N along the delay axis. The purpose of placing SCMA-encoded data symbols along the delay axis is to make the signal have the same sparsity in the delay-Doppler domain and the time domain, so that this sparsity can be used to reduce the dimension of the signal and realize cross-domain message transmission.

[0046] Among them, the delay-Doppler domain signal matrix of the jth user is It is expressed as:

[0047]

[0048] in, represents a complex matrix of dimension M×N, ∈ represents the belonging relation in set operation, X j (·,·) represents the SCMA codeword of dimension K×1;

[0049] Then, the delay-Doppler domain signal matrix X j Vectorization is performed to obtain the transmitted signal vector in the delay-Doppler domain, which is expressed as follows:

[0050]

[0051] Where vec(·) represents the vectorization operation, which stacks the delay-Doppler domain transmission signal vectors of J users to obtain the original total delay-Doppler domain transmission signal vector x dd for:

[0052]

[0053] Where T represents the bias operation.

[0054] S12), performing inverse symplectic finite Fourier transform and Heisenberg transform on the delay Doppler domain transmission signal vector, using a rectangular wave for pulse shaping, and obtaining a time domain transmission signal vector;

[0055] In this embodiment, the inverse symplectic finite Fourier transform is a two-dimensional transform that transforms the delay-Doppler domain signal matrix X j The columns of are subjected to M-point discrete Fourier transform, and the rows are subjected to N-point discrete inverse Fourier transform, thereby converting the delay domain to the frequency domain and converting the Doppler domain to the time domain. The Heisenberg transform converts the two-dimensional signal matrix in the time-frequency domain to a time domain vector and applies rectangular pulse shaping. Thus, the time domain transmitted signal vector s can be obtained from the delay-Doppler domain signal vector td , which is expressed as follows:

[0056]

[0057] In the formula, I J and I M Respectively represent the identity matrix of dimensions J×J, M×M, F N represents the normalized discrete Fourier transform matrix of dimension N×N, (·) H represents the conjugate transpose operation, represents the total transformation matrix; Represents the Kronecker product operation.

[0058] S13), constructing a time domain equivalent channel matrix based on the channel, performing a matrix product operation on the time domain equivalent channel matrix and the time domain transmitted signal vector to obtain a time domain received signal vector;

[0059] Among them, the time domain equivalent channel matrix The expression is:

[0060]

[0061] in, represents the channel matrix between the jth user and the rth antenna of the base station, and its expression is as follows:

[0062]

[0063] Where P represents the number of multipaths between the jth user and the rth receiving antenna at the receiving end; denote the channel gain, delay tap, and Doppler tap of the pth path between the jth user and the rth receiving antenna at the receiving end, respectively; Π denotes the forward cyclic shift matrix; Δ denotes the diagonal Doppler matrix, circ{·} denotes the cyclic shift operation, and diag{·} denotes the operation of creating a diagonal matrix.

[0064] The time domain equivalent channel matrix G td and the time domain transmitted signal vector s td Perform matrix multiplication to obtain the original time domain received signal vector r td , which is expressed as follows:

[0065]

[0066] In the formula, represents a Gaussian white noise vector; Gaussian white noise vector w td Obey Gaussian distribution Represents the noise power at the receiving end.

[0067] S14), using a rectangular wave to receive matching pulses, performing Wigner transform and symplectic finite Fourier transform on the time domain received signal vector, to obtain a delay Doppler domain received signal vector;

[0068] In this embodiment, the time domain received signal vector is processed by rectangular wave matched filtering, and the Wigner transform is completed to obtain the time-frequency domain received signal matrix, and the time-frequency domain received signal matrix is ​​subjected to symplectic finite Fourier transform to complete the conversion from the time-frequency domain to the delay Doppler domain. Thus, the delay Doppler domain received signal vector y td , which is expressed as follows:

[0069]

[0070] In the formula, Indicates that the dimension is N r ×N r The identity matrix of

[0071] S15), based on the sparsity of the sparse code division multiple access codeword, obtain the non-zero position index of the transmitted signal vector and the received signal vector in the original delay Doppler domain and time domain;

[0072] In this embodiment, in SCMA, the data symbol of each user is encoded by a sparse codeword, and the codewords of multiple users share the same resource. The factor matrix describes the mapping relationship between users and resources. Each column of the factor matrix represents a user, and each row represents a resource, showing the transmission of the user on the resource. If the user transmits on the resource, the element at the corresponding position of the factor matrix is ​​1, otherwise it is 0. The factor matrix is ​​represented as a sparse matrix F of dimension J×K, and the number of non-zero elements in each row of the sparse matrix F is d f , the number of non-zero elements in each column of the sparse matrix F is d v According to the sparse matrix F, the sparse structure f of the transmitted signal in the delay-Doppler domain can be obtained, which is expressed as:

[0073]

[0074] In the formula, The dimension is A column vector of all 1s; vec(·) indicates a vectorized operation;

[0075] According to the sparse structure, the position index of the non-zero elements in the signal can be obtained Its expression is as follows:

[0076]

[0077] In the formula, j represents user j.

[0078] S16), based on the position index of the non-zero elements in the signal, obtain the transmitted signal vector, received signal vector, equivalent channel matrix and transformation matrix in the delay Doppler domain and the time domain.

[0079] In this embodiment, based on the position index of the non-zero elements in the signal, the zero elements in the original transmitted signal vector and the received signal vector are deleted, and the columns at the corresponding positions of the time domain equivalent channel matrix are deleted to achieve dimensional compression.

[0080] The transmitted signal vector x in the delay-Doppler domain is expressed as:

[0081]

[0082] In the formula, x dd represents the total delay Doppler domain transmitted signal vector; represents the position index of the non-zero element in the signal; K, M, N, and J represent the codeword dimension of the SCMA codebook, the delay dimension of the OTFS system, the Doppler dimension of the OTFS system, and the number of users in the SCMA codebook, respectively; d v Represents the number of non-zero elements in each column of the sparse matrix F;

[0083] The time domain transmitted signal vector s is expressed as:

[0084]

[0085] In the formula, s td represents the total time domain transmitted signal vector;

[0086] The delay-Doppler domain received signal vector y is expressed as:

[0087]

[0088] In the formula, y dd represents the total delay Doppler domain received signal vector;

[0089] The time domain received signal vector r is expressed as:

[0090]

[0091] In the formula, r td represents the total time domain received signal vector;

[0092] The delay-Doppler domain equivalent channel matrix H is expressed as:

[0093]

[0094] In the formula, H dd represents the total delay Doppler domain equivalent channel matrix; N r Indicates the number of receiving antennas; : indicates the operation of taking all elements of this dimension;

[0095] The time domain equivalent channel matrix G is expressed as:

[0096]

[0097] In the formula, G td represents the total time-domain equivalent channel matrix;

[0098] The transformation matrix D is expressed as:

[0099]

[0100] Where D trans Represents the total transformation matrix.

[0101] S2), based on the posterior probability, use the non-normalized Gaussian distribution to approximate the prior distribution of the time domain transmission signal vector, set the iteratively updateable parameters, and initialize the parameters;

[0102] In this embodiment, a non-normalized Gaussian distribution is used. To approximate the prior distribution of the transmitted signal in the time domain:

[0103]

[0104] In the formula, s i represents the i-th element of the time domain transmitted signal vector; γ i Indicates i The first moment of i Indicates i The second-order moment of i =0,λ i =1, where

[0105] S3), based on the first-order moment, the second-order moment parameter, the time-domain received signal vector and the time-domain equivalent channel matrix, obtaining the mean vector and the variance vector of the time-domain cavity distribution; specifically comprising the following steps:

[0106] S31), based on the first-order moment, the second-order moment parameter and the time-domain received signal vector and the equivalent channel matrix after dimensionality reduction, obtain the time-domain posterior mean vector and variance matrix; its expression is:

[0107]

[0108] Where C represents the variance matrix of the time-domain posterior; μ represents the mean vector of the time-domain posterior; σ w represents the standard deviation of the channel Gaussian white noise; G represents the time domain equivalent channel matrix; (·) H represents the conjugate transpose operation; γ represents the first-order moment parameter; λ represents the second-order moment parameter; diag(·) represents the operation of creating a diagonal matrix; r represents the time domain received signal vector;

[0109]

[0110] S32), based on the time domain posterior variance matrix and the time domain equivalent channel matrix, obtaining the sparse structure of the target inversion matrix;

[0111] In this embodiment, the target inversion matrix Ψ is expressed as:

[0112]

[0113] According to the time domain equivalent channel matrix, the sparse structure S of the target inverse matrix Ψ is expressed as:

[0114]

[0115] In the formula, 1 J×J represents a matrix of all 1s with dimension J×J; represents the Kronecker product operation; Π l represents the matrix of forward circular shift l times; l max represents the maximum delay tap among all possible channel realizations;

[0116] In this embodiment, the sparse structure S is related to the prefix type of the OTFS system and the maximum delay tap in the channel implementation, and has nothing to do with the instantaneous expression of the channel.

[0117] S33), based on the sparse structure of the target inversion matrix, sparse reverse Cahir-McGee sorting is performed on the target inversion matrix to obtain a quasi-banded matrix, the quasi-banded matrix is ​​decomposed by Kollerski, the decomposed lower triangular matrix is ​​inverted, and the inversion result of the target inversion matrix is ​​obtained by reordering after multiplication;

[0118] In this embodiment, based on the sparse structure of the target inverse matrix, a permutation matrix P can be obtained by using sparse reverse Cahill-McGee sorting. The target inverse matrix is ​​reordered by using the permutation matrix P, which is expressed as:

[0119] Φ=PΨP T

[0120] Wherein, Φ represents the quasi-band matrix obtained after reordering, and the bandwidth B of the quasi-band matrix Φ is w For B w ≤2J(2l max +1).

[0121] Performing Kollerski decomposition on the quasi-band matrix Φ, we obtain the lower triangular matrix L, which can be expressed as:

[0122] Φ=LL T

[0123] The decomposed lower triangular matrix L is inverted, multiplied and reordered to obtain the inverse result of the target inversion matrix, that is, the variance matrix C of the time-domain posterior, which is expressed as:

[0124] C=P T ((L -1 ) T L -1 )P.

[0125] S34), based on the time domain posterior mean vector and variance matrix, obtaining the mean vector and variance vector of the time domain cavity distribution;

[0126] In this embodiment, the mean vector κ and variance vector ξ of the time domain cavity distribution are 2 It is expressed as:

[0127]

[0128] In the formula, κ i , are the mean vector κ and variance vector ξ of the cavity distribution in the time domain, respectively. 2 The i-th element of i 2 represents the i-th element on the diagonal of the variance matrix C of the time domain posterior, μ i represents the i-th element of the mean vector μ of the time domain posterior; λ i represents the i-th element of the second-order moment parameter; γ i Represents the i-th element of the first-order moment parameter.

[0129] S4), transforming the mean vector and variance vector of the time domain cavity distribution to obtain the mean vector and variance vector of the delay Doppler domain cavity distribution;

[0130] Based on the transformation matrix D, the mean vector κ and variance vector ξ of the time domain cavity distribution are 2 Transform to obtain the mean vector m and variance vector ε of the delay-Doppler cavity distribution 2 , whose expression is:

[0131] m=D H κ

[0132] ε 2 =[D H diag(ξ 2 )D] diag

[0133] in,[·] diag Indicates the operation of taking the diagonal of the matrix; (·) H Represents the conjugate transpose operation.

[0134] S5), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the mean vector and variance vector of the delay-Doppler domain posterior distribution;

[0135] In this embodiment, the following steps are specifically included:

[0136] S51), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain;

[0137] In this embodiment, the continuous d in the delay-Doppler domain transmission signal vector x and the received signal vector y v The elements are non-zero elements of a specific SCMA codeword of a certain user, and the continuous d v ×1 elements should be considered as a symbol to calculate the posterior probability; for the mean vector m and variance vector ε of the delay-Doppler domain cavity distribution 2 Grouping is performed, expressed as:

[0138]

[0139] In the formula, and Indicates dimension d v ×1 vector, (·) T Represents a transpose operation;

[0140] Therefore, the posterior probability of the SCMA symbol in the delay-Doppler domain is The calculation formula is expressed as:

[0141]

[0142] in, and Indicates rounding up operation; represents the set of non-zero elements in the SCMA codebook of the jth user, a j express One of the v ×1 dimensional codeword; represents the estimated SCMA symbol in the delay-Doppler domain; ∝ represents a proportional relationship; d represents the element index of the codeword.

[0143] S52), based on the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain, obtaining the mean vector and variance vector of the delay-Doppler domain posterior distribution;

[0144] The mean vector χ and variance vector ρ of the posterior distribution in the delay-Doppler domain are 2 Grouping is performed, expressed as:

[0145]

[0146] In the formula, and Indicates dimension d v×1 vector,

[0147] Based on the posterior probability of the SCMA symbol in the delay-Doppler domain, the mean vector χ of the posterior distribution in the delay-Doppler domain is calculated. c and variance vector The d-th element of is expressed as follows:

[0148]

[0149] Among them, 1≤d≤d v , all elements of the mean and variance of the delay-Doppler domain posterior distribution are calculated to obtain:

[0150]

[0151] S6), transforming the mean vector and variance vector of the delay-Doppler domain posterior distribution to obtain the mean vector and variance vector of the time domain posterior distribution;

[0152] Based on the transformation matrix D, the mean vector χ and variance vector ρ of the delay-Doppler domain posterior distribution are 2 Transform to obtain the mean vector μ′ and variance vector σ′ of the time domain posterior distribution 2 , which is expressed as follows:

[0153] μ′=Dχ;

[0154] σ′ 2 =[Ddiag(χ 2 )D H ] diag .

[0155] S7), updating the time domain prior first-order moment and second-order moment parameters based on the moment matching method;

[0156] In this embodiment, the damping factor β is set to update the i-th element of the time domain priori first-order moment and second-order moment parameters, and the expression thereof is as follows:

[0157]

[0158] In the formula, λ i , γ i Respectively represent; μ i ′、σ i ' 2 Represent the mean vector μ′ and variance vector σ′ of the time domain posterior distribution respectively 2 The i-th element of i , are the mean vector κ and variance vector ξ of the cavity distribution in the time domain, respectively. 2 The i-th element of ;

[0159] All elements of the time domain prior first-order moment and second-order moment are updated, completing one iteration of the signal detection algorithm based on expected propagation.

[0160] S8) Repeat steps S3)-S7) until a preset number of iterations is reached to obtain the detection result of the original bit stream.

[0161] In this embodiment, steps S3)-S7) are repeatedly performed until a preset number of iterations is reached, and the algorithm flow is stopped to obtain the final detection result of the SCMA-encoded signal, which is expressed as follows:

[0162]

[0163] The signal detection results after SCMA encoding and the dimension of each user are K×M mod The K×1 codewords in the SCMA codebook are compared to complete SCMA decoding and obtain the detection result of the original bit stream.

[0164] The above embodiments and descriptions are only for illustrating the principles and best embodiments of the present invention. Without departing from the spirit and scope of the present invention, the present invention may be subject to various changes and improvements, all of which fall within the scope of the present invention to be protected.

Claims

1. A signal detection method for a multi-antenna orthogonal time-frequency-space sparse code division multiple access system, characterized in that: The steps include: S1), initializing the original bit stream of each user to obtain the transmission signal vector, the reception signal vector, the equivalent channel matrix, and the transformation matrix in the delay Doppler domain and the time domain; S2), based on the posterior probability, use the non-normalized Gaussian distribution to approximate the prior distribution of the time domain transmission signal vector, set the iteratively updateable parameters, and initialize the parameters; S3), based on the first-order moment, the second-order moment parameter, the time-domain received signal vector and the time-domain equivalent channel matrix, obtaining the mean vector and the variance vector of the time-domain cavity distribution; S4), transforming the mean vector and variance vector of the time domain cavity distribution to obtain the mean vector and variance vector of the delay Doppler domain cavity distribution; S5), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the mean vector and variance vector of the delay-Doppler domain posterior distribution; S6), transforming the mean vector and variance vector of the delay-Doppler domain posterior distribution to obtain the mean vector and variance vector of the time domain posterior distribution; S7), updating the time domain prior first-order moment and second-order moment parameters based on the moment matching method; S8) Repeat steps S3)-S7) until a preset number of iterations is reached to obtain the detection result of the original bit stream.

2. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: Step S1) specifically includes the following steps: S11), modulating and vectorizing the original bit stream of each user to obtain a delay-Doppler domain transmission signal vector; S12), performing inverse symplectic finite Fourier transform and Heisenberg transform on the delay Doppler domain transmission signal vector, using a rectangular wave for pulse shaping, and obtaining a time domain transmission signal vector; S13), constructing a time domain equivalent channel matrix based on the channel, performing a matrix product operation on the time domain equivalent channel matrix and the time domain transmitted signal vector to obtain a time domain received signal vector; S14), using a rectangular wave to perform a receiving matching pulse to perform a Wigner transform and a symplectic finite Fourier transform on a time domain received signal vector to obtain a delay Doppler domain received signal vector; S15), based on the sparsity of the sparse code division multiple access codeword, obtain the non-zero position index of the transmitted signal vector and the received signal vector in the original delay Doppler domain and time domain; S16), based on the position index of the non-zero elements in the signal, obtain the transmitted signal vector, received signal vector, equivalent channel matrix, and transformation matrix in the delay Doppler domain and the time domain.

3. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: In step S3), the mean vector and variance vector of the time domain cavity distribution are obtained, which specifically includes the following steps: S31), based on the first-order moment, the second-order moment parameter and the time-domain received signal vector and the equivalent channel matrix after dimensionality reduction, obtaining the time-domain posterior mean vector and the variance matrix; S32), based on the time domain posterior variance matrix and the time domain equivalent channel matrix, obtaining the sparse structure of the target inversion matrix; S33), based on the sparse structure of the target inversion matrix, sparse reverse Cahir-McGee sorting is performed on the target inversion matrix to obtain a quasi-banded matrix, the quasi-banded matrix is ​​decomposed by Kollerski, the decomposed lower triangular matrix is ​​inverted, and the inversion result of the target inversion matrix is ​​obtained by reordering after multiplication; S34), based on the time domain posterior mean vector and variance matrix, obtain the mean vector and variance vector of the time domain cavity distribution.

4. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 3, characterized in that: In step S32), the target inverse matrix Ψ is expressed as: Where: w represents the standard deviation of the channel Gaussian white noise; G represents the time domain equivalent channel matrix; (·) H represents the conjugate transpose operation; λ represents the second-order moment parameter; diag(·) represents the operation of creating a diagonal matrix; According to the time domain equivalent channel matrix, the sparse structure S of the target inverse matrix Ψ is expressed as: In the formula, 1 J×J represents a matrix of all 1s with dimension J×J; represents the Kronecker product operation; Π l represents the matrix of forward circular shift l times; l max represents the maximum delay tap among all possible channel realizations; Indicates the position index of the non-zero element.

5. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 3, characterized in that: In step S33), based on the sparse structure of the target inverse matrix, the permutation matrix P can be obtained by using the sparse reverse Cahill-McGee sorting; the target inverse matrix is ​​reordered by using the permutation matrix P, which is expressed as: Φ=PΨP T Wherein, Φ represents the quasi-band matrix obtained after reordering, and the bandwidth B of the quasi-band matrix Φ is w For B w ≤2J(2l max +1). Performing Kollerski decomposition on the quasi-band matrix Φ, we obtain the lower triangular matrix L, which can be expressed as: Φ=LL T The decomposed lower triangular matrix L is inverted, multiplied and reordered to obtain the inverse result of the target inversion matrix, that is, the variance matrix C of the time-domain posterior, which is expressed as: C=P T ((L -1 ) T L -1 )P。 6. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 3, characterized in that: In step S34), the mean vector κ and variance vector ξ of the time domain cavity distribution 2 It is expressed as: In the formula, κ i , are the mean vector κ and variance vector ξ of the cavity distribution in the time domain, respectively. 2 The i-th element of ; K, M, N, and J represent the codeword dimension of the SCMA codebook, the delay dimension of the OTFS system, the Doppler dimension of the OTFS system, and the number of users in the SCMA codebook, respectively; d v Represents the number of non-zero elements in each column of the sparse matrix F.

7. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: In step S4), based on the transformation matrix D, the mean vector κ and variance vector ξ of the time domain cavity distribution are transformed. 2 Transform to obtain the mean vector m and variance vector ε of the delay-Doppler cavity distribution 2 , whose expression is: m=D H k ε 2 =[D H diag(ξ 2 )D] diag Where diag(·) represents the operation of creating a diagonal matrix; [·] diag Indicates the operation of taking the diagonal of the matrix; (·) H Represents the conjugate transpose operation.

8. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: In step S5), the mean vector and variance vector of the delay-Doppler domain posterior distribution are calculated, which specifically includes the following steps: S51), based on the mean vector and variance vector of the delay-Doppler domain cavity distribution, obtaining the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain; S52), based on the posterior probability of the sparse code division multiple access symbol in the delay-Doppler domain, obtain the mean vector and variance vector of the delay-Doppler domain posterior distribution.

9. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: In step S51), the a posteriori probability of the sparse code division multiple access symbol in the delay-Doppler domain is The calculation formula is expressed as: in, and Indicates rounding up operation; represents the set of non-zero elements in the SCMA codebook of the jth user, a j express One of the v ×1 dimensional codeword; represents the estimated SCMA symbol in the delay-Doppler domain; ∝ represents a proportional relationship; d represents the element index of the codeword.

10. The method for detecting signals in a multi-antenna orthogonal time-frequency-space sparse code division multiple access system according to claim 1, characterized in that: In step S7), the damping factor β is set, and the i-th element of the time domain priori first-order moment and second-order moment parameters is updated, and the expression is as follows: In the formula, λ i , γ i Represents the i-th element of the time domain prior second-order moment and first-order moment parameter; μ i ′ , Respectively represent the mean vector μ of the posterior distribution in the time domain ′ and the variance vector σ ′2 The i-th element of i , are the mean vector κ and variance vector ξ of the cavity distribution in the time domain, respectively. 2 The i-th element of ; All elements of the time domain prior first-order moment and second-order moment are updated, completing one iteration of the signal detection algorithm based on expected propagation.

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