A method for detecting signals in a multi-antenna orthogonal time, frequency, space and sparse code division multiple access system

Abstract

The application provides a kind of multi-antenna orthogonal time-frequency-space sparse code division multiple access system signal detection method, the application utilizes the sparsity of sparse code division multiple access codebook to reduce the dimension of time domain and time delay doppler domain signal, and uses Gaussian distribution to approximate the prior distribution of time domain signal.In the time domain, the preliminary detection is realized by obtaining the cavity distribution of signal, and the posterior probability of signal is calculated in the time delay doppler domain by using the sparse code division multiple access codebook.Based on the transformation relationship in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system, the information exchange between the time domain and the time delay doppler domain is realized.The application utilizes the sparse structure of time domain matrix in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system, and reduces the complexity of matrix inversion in the algorithm.By using the application, the double sparsity of multi-antenna orthogonal time-frequency-space system and sparse code division multiple access codebook can be utilized to reduce the complexity of algorithm implementation while ensuring the signal detection performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of signal detection, and particularly relates to a multi-antenna orthogonal time-frequency-space sparse code division multiple access system signal detection method. BACKGROUND

[0002] Orthogonal time-frequency-space (OTFS) modulation can transform a time-varying multipath channel into a time-invariant two-dimensional time-delay-Doppler channel by multiplexing information symbols in the time-delay-Doppler domain, thereby significantly improving the bit error rate performance in a high-speed mobile environment. Multi-input multi-output (MIMO) technology can significantly improve system capacity, throughput and link reliability by utilizing 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 can achieve efficient multiplexing between users by designing sparse code words, thereby improving spectral efficiency. In a multi-user scenario, SCMA can distinguish multiple users by using different sparse codes, thereby supporting large-scale connection requirements. The combination of OTFS and MIMO can further improve spectral efficiency and transmission reliability, and the introduction of SCMA can effectively solve the capacity limitation of OTFS in a large-scale connection scenario.

[0003] In the prior art multi-antenna orthogonal time-frequency-space sparse code division multiple access scheme, multiple users use different sparse codebooks for encoding, and OTFS is used to modulate the code word vector. After the modulated transmission signal is transmitted in the channel, it reaches the receiving end. The receiving end receives the superimposed signal of multiple users after channel transmission, performs joint OTFS and SCMA detection on the signal in the time-delay-Doppler domain, obtains the transmission code word of multiple users, and thus completes multi-user detection.

[0004] The existing signal detection mainly includes maximum a posteriori detector, linear detector, and detection algorithm based on Gaussian message passing (GAMP) and approximate expectation propagation based on factor graph (GAEP), and signal detection algorithm based on expectation propagation (EP). However, the optimal maximum a posteriori detector has an exponential increase in complexity with the system dimension, which is actually difficult to implement. The existing linear detector, such as zero-forcing and linear minimum mean square error detector, although has a low computational complexity, will cause a significant performance loss. The detection algorithm based on GAMP and GAEP, although can achieve a better multi-user detection performance, still has a high computational complexity. In addition, the signal detection algorithm based on EP has a good performance, but due to the high dimension 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 process limits the overall performance of the system. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a multi-antenna orthogonal time-frequency-space sparse code division multiple access system signal detection method, which 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 implementation.

[0006] The technical scheme of the present application is as follows: 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 time delay Doppler domain and time domain transmission signal vector, received signal vector, equivalent channel matrix, and transformation matrix;

[0008] S2), based on the posterior probability, using a non-normalized Gaussian distribution to approximate the prior distribution of the time domain transmission signal vector, setting the parameters that can be iteratively updated, and initializing the parameters;

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

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

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

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

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

[0015] As preferred, in step S1), the following steps are specifically included:

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

[0017] S12), performing inverse symplectic finite Fourier transform and Heisenberg transform on the time-delay Doppler domain sending signal vector, and using a rectangular wave to perform pulse shaping to obtain a time domain sending signal vector;

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

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

[0020] S15), based on the sparsity of a sparse code division multiple access code word, obtaining non-zero position indexes of the sending signal vectors and the receiving signal vectors in the original time-delay Doppler domain and the time domain;

[0021] S16), based on the position indexes of the non-zero elements in the signal, obtaining the sending signal vectors and the receiving signal vectors in the time-delay Doppler domain and the time domain, the equivalent channel matrix, and the transform matrix.

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

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

[0024] As preferred, in step S3), the mean vector and the variance vector of the time-domain cavity distribution are obtained, and the step specifically comprises the following steps:

[0025] S31), based on the first moment, the second moment parameter, the reduced dimension time-domain received signal vector and the equivalent channel matrix, a time-domain posterior mean vector and a variance matrix are obtained;

[0026] S32), based on the time-domain posterior variance matrix and the time-domain equivalent channel matrix, a sparse structure of a target inverse matrix is obtained;

[0027] S33), based on the sparse structure of the target inverse matrix, a quasi-band matrix is obtained by performing sparse reverse Cholesky ordering on the target inverse matrix, Cholesky decomposition is performed on the quasi-band matrix, an inverse result of the target inverse matrix is obtained by performing inversion on the decomposed lower triangular matrix and then multiplying and reordering;

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

[0029] As preferred, in step S5), the mean vector and the variance vector of the time-delay Doppler domain posterior distribution are calculated, and the step specifically comprises the following steps:

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

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

[0032] The beneficial effects of the present application are as follows:

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

[0034] 2. In the time-domain, the present application realizes preliminary detection through obtaining the cavity distribution of the signal; in the time-delay Doppler domain, the present application calculates the posterior probability of the signal based on the sparse code division multiple access codebook;

[0035] 3. The present application realizes information exchange between the time-domain and the time-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 application utilizes the sparse structure of time domain matrix in the multi-antenna orthogonal time-frequency-space sparse code division multiple access system, reduces the complexity of matrix inversion required in the iterative algorithm, and realizes the low-complexity signal detection algorithm based on expectation propagation. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The figure is a flowchart of the signal detection method of the application.

[0038] Figure 2 The figure is a framework diagram of the signal detection method of the application. DETAILED DESCRIPTION

[0039] The specific embodiment of the application will be further described in combination with the accompanying drawings:

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

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

[0042] The method comprises the following steps:

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

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

[0045] In the embodiment, according to the original bit stream, the K modThe Kx1 code word is selected from the SCMA codebook to perform SCMA encoding, and SCMA encoded data symbols are obtained; then the SCMA encoded data symbols are placed on a time delay Doppler domain grid with a dimension of MxN along the time delay axis. The purpose of placing the SCMA encoded data symbols along the time delay axis is to make the signal have the same sparsity in the time delay Doppler domain and the time domain, so that the sparsity can be used to reduce the dimension of the signal and realize cross-domain message passing.

[0046] wherein the time delay Doppler domain signal matrix of the jth user is is expressed as:

[0047]

[0048] wherein, represents a complex matrix with a dimension of MxN, represents the belonging relation in set operation, X j (·,·) represents an SCMA code word with a dimension of Kx1;

[0049] Then, the time delay Doppler domain signal matrix X j is vectorized to obtain a time delay Doppler domain sending signal vector, and the expression is as follows:

[0050]

[0051] wherein, vec(·) represents a vectorization operation, the time delay Doppler domain sending signal vectors of the J users are stacked to obtain an original total time delay Doppler domain sending signal vector x dd is:

[0052]

[0053] In the formula, T represents a bias operation.

[0054] S12), inverse symplectic finite Fourier transform and Heisenberg transform are performed on the time delay Doppler domain sending signal vector, a rectangular wave is used for pulse shaping, and a time domain sending signal vector is obtained;

[0055] In the embodiment, the inverse symplectic finite Fourier transform is a two-dimensional transform, M-point discrete Fourier transform is performed on the columns of the time delay Doppler domain signal matrix X j , and N-point discrete inverse Fourier transform is performed on the rows, so as to convert the time delay domain to the frequency domain and convert the Doppler domain to the time domain. The Heisenberg transform converts the time-frequency domain two-dimensional signal matrix to a time domain vector and applies rectangular pulse shaping. Thus, the time domain sending signal vector s td can be obtained from the time delay Doppler domain signal vector, and the expression is as follows:

[0056]

[0057] wherein I J and I M respectively represent unit matrices of dimensions JxJ, MxM, F N represents a normalized discrete Fourier transform matrix of dimension NxN, (·) H represents a conjugate transpose operation, represents a total transform matrix; represents a Kronecker product operation.

[0058] S13), based on the channel, a time-domain equivalent channel matrix is constructed, and a matrix multiplication operation is performed on the time-domain equivalent channel matrix and a time-domain sending signal vector to obtain a time-domain receiving signal vector;

[0059] wherein the expression of the time-domain equivalent channel matrix is as follows:

[0060]

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

[0062]

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

[0064] The time-domain equivalent channel matrix G td and the time-domain sending signal vector s td are subjected to matrix multiplication to obtain an original time-domain receiving signal vector r td , and its expression is as follows:

[0065]

[0066] wherein represents a Gaussian white noise vector; the Gaussian white noise vector w td obeys a Gaussian distribution represents the noise power of the receiving end.

[0067] S14), a rectangular wave is used to perform receiving matching pulse, and a Wigner transform and a symplectic finite Fourier transform are performed on the time-domain receiving signal vector to obtain a delay-Doppler domain receiving signal vector;

[0068] In this embodiment, the time-domain received signal vector is processed by a rectangular wave matched filter, Wigner transformation is completed to obtain a time-frequency domain received signal matrix, and symplectic finite Fourier transform is performed on the time-frequency domain received signal matrix to complete conversion from the time-frequency domain to the time-delay Doppler domain. Thus, a time-delay Doppler domain received signal vector y td , and its expression is as follows:

[0069]

[0070] In the formula, vec(·) represents vectorization operation. represents a full 1 column vector with a dimension of r ×N r ;

[0071] S15), based on the sparsity of the sparse code division multiple access code word, the non-zero position index of the original time-delay Doppler domain and time-domain transmission signal vector and received signal vector is obtained.

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

[0073]

[0074] In the formula, vec(·) represents vectorization operation. represents a full 1 column vector with a dimension of ;

[0075] According to the sparse structure, the position index of the non-zero element in the signal can be obtained , and 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 element in the signal, the time-delay Doppler domain and time-domain transmission signal vector, received signal vector, equivalent channel matrix and transformation matrix are obtained.

[0079] In this embodiment, the zero elements in the original transmitted signal vector and the received signal vector are deleted based on the position index of the non-zero elements in the signal, and the column corresponding to the position of the time domain equivalent channel matrix is deleted, so as to realize dimension compression. Wherein:

[0080] The time delay Doppler domain transmitted signal vector x is represented as:

[0081]

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

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

[0084]

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

[0086] The time delay Doppler domain received signal vector y is represented as:

[0087]

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

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

[0090]

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

[0092] The time delay Doppler domain equivalent channel matrix H is represented as:

[0093]

[0094] In the formula, H dd represents the total time delay Doppler domain equivalent channel matrix; N r represents the number of receiving antennas; : represents taking all element operations in this dimension;

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

[0096]

[0097] where G td denotes the total time-domain equivalent channel matrix;

[0098] The transformation matrix D is expressed as:

[0099]

[0100] where D trans denotes the total transformation matrix.

[0101] S2), based on the posterior probability, using a non-normalized Gaussian distribution to approximate the prior distribution of the time-domain transmission signal vector, setting the parameters that can be iteratively updated, and performing parameter initialization;

[0102] In this embodiment, the non-normalized Gaussian distribution is used to approximate the prior distribution of the time-domain transmission signal:

[0103]

[0104] where s i denotes the i-th element of the time-domain transmission signal vector; γ i denotes the first moment of s i ; λ i denotes the second moment of s i ; is initialized as γ i = 0, λ i = 1, where

[0105] S3), based on the first moment, the second moment parameter, and 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 including the following steps:

[0106] S31), based on the first moment, the second moment parameter, and the reduced dimension time-domain received signal vector and the equivalent channel matrix, obtaining the time-domain posterior mean vector and the variance matrix; the expression is:

[0107]

[0108] where C denotes the variance matrix of the time-domain posterior; μ denotes the mean vector of the time-domain posterior; σ w denotes the standard deviation of the channel Gaussian white noise; G denotes the time-domain equivalent channel matrix; (·) H denotes the conjugate transpose operation; γ denotes the first moment parameter; λ denotes the second moment parameter; diag(·) denotes the diagonal matrix creation operation; r denotes 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 a sparse structure of the target inverse matrix;

[0111] In the embodiment, the target inverse 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 denotes a full 1 matrix with a dimension of JxJ; denotes a Kronecker product operation; Π l denotes a matrix of forward cyclic shift l times; l max denotes the maximum delay tap in all possible channel implementations;

[0116] In the 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 is irrelevant to the instantaneous expression of the channel.

[0117] S33), based on the sparse structure of the target inverse matrix, sparse reverse Cholesky-McEliece sorting is performed on the target inverse matrix to obtain a quasi-band matrix, Cholesky decomposition is performed on the quasi-band matrix, the inverse of the decomposed lower triangular matrix is obtained, and after multiplication and reordering, the inverse result of the target inverse matrix is obtained;

[0118] In the embodiment, based on the sparse structure of the target inverse matrix, the permutation matrix P can be obtained by using sparse reverse Cholesky-McEliece sorting; the target inverse matrix is reordered by using the permutation matrix P, and is expressed as:

[0119] Φ=PΨP T

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

[0121] Cholesky decomposition is performed on the quasi-band matrix Φ to obtain a lower triangular matrix L, and is expressed as:

[0122] Φ=LL T

[0123] The inverse of the decomposed lower triangular matrix L is obtained, and after multiplication and reordering, the inverse result of the target inverse matrix, i.e., the time-domain posterior variance matrix C, is obtained, and 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, obtain 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 Represented as:

[0127]

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

[0129] S4) Transform the mean vector and variance vector of the time-domain cavity distribution to obtain the mean vector and variance vector of the time-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 The transformation yields the mean vector m and variance vector ε of the cavity distribution in the time-delay Doppler domain. 2 Its expression is:

[0131] m=D H κ

[0132] ε 2 =[D H diag(ξ 2 )D] diag

[0133] in,[·] diag This represents the operation of taking the diagonal of a matrix; (·) H This indicates the conjugate transpose operation.

[0134] S5) Based on the mean vector and variance vector of the cavity distribution in the time-delay Doppler domain, the mean vector and variance vector of the posterior distribution in the time-delay Doppler domain are obtained.

[0135] In this embodiment, the steps include the following:

[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 v elements in the delay-Doppler domain transmitted signal vector x and the received signal vector y are the non-zero elements of a certain specific SCMA code word of a certain user, and the continuous d v ×1 elements should be regarded as a symbol to calculate the posterior probability; the mean vector m and the variance vector ε 2 of the delay-Doppler domain cavity distribution are grouped, and are expressed as:

[0138]

[0139] In the formula, and denote the vector with the dimension of d v ×1, (·) T denotes the transposition operation;

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

[0141]

[0142] In the formula, and denote the upward rounding operation; denotes the set containing the non-zero elements in the SCMA codebook of the jth user, a j denotes a d v ×1-dimensional code word in denotes the estimated SCMA symbol in the delay-Doppler domain; denotes the proportional relationship; d denotes the element index of the code word.

[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 the variance vector ρ 2 of the delay-Doppler domain posterior distribution are grouped, and are expressed as:

[0145]

[0146] In the formula, and denote the vector with the dimension of d va vector χ1,

[0147] Based on the posterior probability of SCMA symbol in delay-Doppler domain, the mean vector χ of delay-Doppler domain posterior distribution is calculated c and the dth element of variance vector , whose expression is as follows:

[0148]

[0149] wherein, 1≤d≤d v , all elements of the mean and variance of delay-Doppler domain posterior distribution are calculated, and

[0150]

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

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

[0153] μ' = Dχ;

[0154] σ' 2 = [Ddiag(χ 2 )D H ] diag .

[0155] S7), the time domain prior first moment and second moment parameters are updated based on the matrix matching method;

[0156] In this embodiment, the damping factor β is set, and the ith element of the time domain prior first moment and second moment parameters is updated, whose expression is as follows:

[0157]

[0158] In the formula, λ i , γ i respectively represent; μ i ', σ i ' 2 respectively represent the ith element of the mean vector μ' and variance vector σ' 2 of time domain posterior distribution; κ i , respectively represent the ith element of the mean vector κ and variance vector ξ 2 of time domain cavity distribution;

[0159] All elements of the time-domain first and second moments are updated, and one iteration of the signal detection algorithm based on expectation propagation is completed.

[0160] S8), repeating steps S3)-S7) until a preset iteration number is reached, and obtaining a detection result of the original bit stream.

[0161] The embodiment repeatedly performs the repeating steps S3)-S7) until the preset iteration number is reached, stops the algorithm process, and obtains a detection result of the final SCMA encoded signal, which is expressed as follows:

[0162]

[0163] Based on the detection result of the SCMA encoded signal, and the Kx1 codeword in the KxM SCMA codebook of each user dimension, SCMA decoding is completed to obtain a detection result of the original bit stream. mod

[0164] The above embodiments and descriptions in the specification are only to illustrate the principles and the best embodiments of the present application, and various changes and improvements can be made without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application.​

Claims

1. A method for signal detection in a multi-antenna orthogonal time, frequency and space spread code division multiple access system, characterized by, Comprising the following steps: S1), initial processing of the original bit stream of each user to obtain time delay Doppler domain and time domain transmission signal vector, received signal vector, equivalent channel matrix, and transformation matrix; specifically comprising the following steps: S11), modulating and vectorizing the original bit stream of each user to obtain a time delay Doppler domain transmission signal vector; S12), inverse symplectic finite Fourier transform and Heisenberg transform are performed on the time delay Doppler domain transmission signal vector, and a rectangular wave is used for pulse shaping to obtain a time domain transmission signal vector; S13), based on the channel, a time domain equivalent channel matrix is constructed, and matrix multiplication operation is performed on the time domain equivalent channel matrix and the time domain transmission signal vector to obtain a time domain received signal vector; S14), using a rectangular wave for receiving matching pulse, a Wigner transform and a symplectic finite Fourier transform are performed on the time domain received signal vector to obtain a time delay Doppler domain received signal vector; S15), based on the sparsity of the sparse code division multiple access code word, the non-zero position index of the original time delay Doppler domain and time domain transmission signal vector and received signal vector is obtained; S16), based on the position index of the non-zero elements in the signal, the time delay Doppler domain and time domain transmission signal vector, received signal vector, equivalent channel matrix, and transformation matrix are obtained; S2), based on the posterior probability, the prior distribution of the time domain transmission signal vector is approximated using a non-normalized Gaussian distribution, the parameters are iteratively updated, and the parameters are initialized; S3), based on the first-order moment, second-order moment parameters, and time domain received signal vector and time domain equivalent channel matrix, the mean vector and variance vector of the time domain cavity distribution are obtained; S4), the mean vector and variance vector of the time domain cavity distribution are transformed to obtain the mean vector and variance vector of the time delay Doppler domain cavity distribution; S5), based on the mean vector and variance vector of the time delay Doppler domain cavity distribution, the mean vector and variance vector of the time delay Doppler domain posterior distribution are obtained; S6), the mean vector and variance vector of the time delay Doppler domain posterior distribution are transformed to obtain the mean vector and variance vector of the time domain posterior distribution; S7), the time domain prior first-order moment and second-order moment parameters are updated based on the moment matching method; S8), steps S3)-S7) are repeated until a preset iteration number is reached to obtain the detection result of the original bit stream.

2. The method of claim 1, wherein the method comprises: In step S3), the mean vector and variance vector of the time domain cavity distribution are obtained, specifically comprising the following steps: S31), based on the first-order moment, second-order moment parameters, and reduced dimension time domain received signal vector and equivalent channel matrix, the time domain posterior mean vector and variance matrix are obtained; S32), based on the time domain posterior variance matrix and the time domain equivalent channel matrix, the sparse structure of the target inverse matrix is obtained; S33), based on the sparse structure of the target inverse matrix, the target inverse matrix is subjected to sparse reverse Cholesky-McKee ordering to obtain a quasi-band matrix, the quasi-band matrix is subjected to Cholesky decomposition, the inverse of the decomposed lower triangular matrix is obtained, and the multiplication is reordered to obtain the inverse result of the target inverse matrix. S34), obtaining the mean vector and variance vector of the time-domain cavity distribution based on the time-domain mean vector and variance matrix of the posterior.

3. The method of claim 2, wherein the method further comprises: In step S32), the target inverse matrix Ψ is expressed as: where σ w denotes the standard deviation of the channel Gaussian white noise; G denotes the time-domain equivalent channel matrix; (·) H denotes the conjugate transpose operation; λ denotes the second moment parameter; diag(·) denotes 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: where 1 J×J denotes an all-one matrix of size J x J; denotes the Kronecker product operation; Π l denotes a matrix that performs a forward cyclic shift of l times; l max denotes the maximum delay tap among all possible channel realizations; denotes the position index of non-zero elements.

4. The method of claim 3, wherein the method further comprises: In step S33), based on the sparse structure of the target inverse matrix, the permutation matrix P is obtained by using sparse reverse Cholesky-McEliece ordering; and the target inverse matrix is reordered by using the permutation matrix P, and is expressed as: Φ = PΨP T In the formula, Φ represents a quasi-band matrix obtained after reordering, a bandwidth B of the quasi-band matrix Φ w is B w ≤ 2J(2l max +1) The Cholesky decomposition is performed on the aligned matrix Φ to obtain a lower triangular matrix L, and is expressed as: Φ = LL T The inverse of the decomposed lower triangular matrix L is obtained, multiplied and reordered to obtain the inverse result of the target inverse matrix, i.e. the time-domain posterior variance matrix C, and is expressed as: C = P T ((L -1 ) T L -1 )P.

5. The method of claim 4, wherein the method further comprises: In step S34), the mean vector K and the variance vector X of the time-domain cavity distribution are calculated 2 is represented as: In the formula, κ i , respectively the mean vector κ and the variance vector ξ of the time domain cavity distribution 2 ; the i-th element; K, M, N, J respectively represent the code word dimension of the SCMA codebook, the time delay dimension of the OTFS system, the Doppler dimension of the OTFS system, and the number of users of the SCMA codebook; d v represent the number of non-zero elements of each column of the sparse matrix F.

6. The method of claim 5, wherein the method further comprises: In step S4), based on the transformation matrix D, the mean vector κ and the variance vector ξ of the time-domain cavity distribution are transformed to obtain the mean vector m and the variance vector ε of the delay-Doppler domain cavity distribution 2 In step S4), based on the transformation matrix D, the mean vector κ and the variance vector ξ of the time-domain cavity distribution are transformed to obtain the mean vector m and the variance vector ε of the delay-Doppler domain cavity distribution 2 The expression is: m = D H K ε 2 = [D H diag(ξ 2 )D] diag where diag(·) denotes the operation of creating a diagonal matrix; [·] diag denotes the operation of taking the diagonal of a matrix; (·) H denotes the conjugate transpose operation.

7. The method of claim 6, wherein the method further comprises: In step S5), the mean vector and variance vector of the time-delay Doppler domain posterior distribution are calculated, and specifically include the following steps: S51), based on the mean vector and variance vector of the time-delay Doppler domain cavity distribution, the posterior probability of the sparse code division multiple access symbol in the time-delay Doppler domain is obtained; S52), based on the posterior probability of the sparse code division multiple access symbol in the time-delay Doppler domain, the mean vector and variance vector of the time-delay Doppler domain posterior distribution are obtained.

8. The method of claim 7, wherein the method further comprises: In step S51), the posterior probability of the sparse code division multiple access symbol in the time-delay Doppler domain is calculated The calculation formula is represented as: wherein, and denotes a rounding up operation; denotes a set containing non-zero elements in the jth user SCMA codebook, a j denotes one d v x 1-dimensional code word; denotes an estimated SCMA symbol in the delay-Doppler domain; denotes a proportional relationship; d denotes an element index of a code word.

9. The method of claim 8, wherein the method further comprises: In step S7), the damping factor β is set, and the i-th element of the time-domain prior first moment and second moment parameter is updated, and the expression is as follows: where λ i , γ i denote the i-th element of the time-domain prior second and first moment parameters, respectively; μ' i , denote the i-th element of the mean vector μ' and variance vector σ' 2 of the time-domain posterior distribution, respectively; κ i , are the i-th element of the mean vector κ and variance vector ξ 2 of the time-domain cavity distribution, respectively; After updating all elements of the time-domain prior first moment and second moment, one iteration of the signal detection algorithm based on expectation propagation is completed.

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