A block sparse Bayesian multi-slot data detection method

Abstract

The present invention discloses a block sparse Bayesian multi-slot data detection method, the main steps of which are: step S1: through matrix vec operation, the MMV model is expressed as a block SMV model; step S2: assuming that the transmitted signal satisfies the Gaussian prior of zero mean, the variance is determined by variables γ and C, and the prior distribution of the transmitted signal is obtained; step S3: assuming that the matrix noise satisfies the complex Gaussian distribution, the variance is λ, the variable y is used as the observed variable, b is used as the hidden variable, the likelihood function of the variable y is obtained, and the posterior distribution of the transmitted signal is obtained by combining the likelihood function and the prior distribution; step S4: in order to estimate three hyperparameters, an iterative EM algorithm is used, and the maximum likelihood function is calculated by the hidden variables; step S5: by updating the three hyperparameters, iterating continuously, and finally outputting the three hyperparameters and the signal b. The method of the present invention utilizes the sparse structural characteristics of the transmitted signal and the intra-block coherence to improve the accuracy of multi-user detection.

Description

Technical Field

[0001] The invention relates to a multi-user detection method for a non-authorized non-orthogonal multiple access system, and in particular to a block sparse Bayesian multi-time slot data detection method. Background Art

[0002] Massive Machine Type Communication (mMTC) is an important application of future wireless communications, which supports large-scale connections from a huge number of devices to the base station (BS). However, mMTC devices are usually activated sporadically and their behavior is completely different from human-centric communications. In order to improve the spectrum efficiency of mMTC, unlicensed non-orthogonal multiple access (GF-NOMA) is advocated. At the current stage of development, there are still several important issues to be solved. One challenge is to design an effective multi-user detection (MUD) scheme that can recover information sent simultaneously from multiple devices.

[0003] Designing efficient and high-performance multi-user detection (MUD) schemes is one of the research issues in GF-NOMA systems. In the future 6G communications, the main feature of mMTC is that a large number of devices are connected to the BS, and only a portion of them are active. This inherent sparsity paves the way for adopting compressed sensing (CS) techniques to recover the transmitted information.

[0004] In traditional multi-user detection, linear detectors such as linear minimum mean square error (MMSE) detectors are usually used. However, when the number of users increases, the computational complexity of this method increases dramatically. The performance of RD and LD detectors is better than that of traditional MMSE methods, but it is necessary to assume that the active user factors are known. However, the present invention combines the theories and methods of block sparsity, Bayesian learning and multi-user detection to achieve more accurate and efficient multi-user detection. The core idea is to assume that the user's signal is sparse, that is, the signal has fewer non-zero elements. By using a sparse representation method, the signal recovery problem can be converted into a sparse optimization problem. Specifically, the present invention performs signal recovery by probabilistically modeling the sparse coefficients of the user signal. Summary of the invention

[0005] The purpose of the present invention is to provide a block sparse Bayesian multi-time slot data detection method, which utilizes the sparse structural characteristics of the transmitted signal and the intra-block coherence to improve the accuracy of multi-user detection.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a block sparse Bayesian multi-time slot data detection method, for an uplink unlicensed non-orthogonal multiple access system including a single-antenna base station and K single-antenna users, wherein the K single-antenna users randomly transmit data to the single-antenna base station, in L consecutive time slots, only some active users continue to transmit signals, inactive users do not transmit signals, and the information of active user k is transmitted after spreading, and the length of the spreading sequence is N; the base station receiving signal is equivalent to a multiple measurement vector model, that is, an MMV model:

[0007] Y=HB+W,

[0008] in, is the equivalent measurement matrix composed of the spreading sequence and the channel coefficients. Assuming that the frame length is less than the channel coherence time, H remains unchanged throughout the frame time. b l is the transmitted signal of all users in the lth time slot, l = 1, 2, ..., L, y l is the received signal of the base station in the lth time slot, w l is zero-mean and has a covariance matrix of σ 2 Complex Gaussian noise of Ι;

[0009] The method comprises the following steps:

[0010] Step S1: Through matrix vec operation, the MMV model is expressed as a block SMV model, the observation signal Y is converted into y, the transmission signal B is converted into b, and the noise variable W is converted into w. The specific operations are as follows:

[0011]

[0012] Step S2: Since the transmitted signal b vector is mostly zero, it is assumed that the transmitted signal b satisfies the Gaussian prior with zero mean, and the variance is determined by variables γ and C, where γ is a non-negative hyperparameter that determines the row sparsity of signal b, and C is a positive definite matrix of size L×L that controls the column coherence of signal b, and the prior distribution of signal b is obtained;

[0013] Step S3: Assume that the matrix noise w satisfies the complex Gaussian distribution with a variance of λ, take the variable y as the observed variable and b as the hidden variable, obtain the likelihood function of the variable y, and obtain the posterior distribution of the transmitted signal by combining the likelihood function and the prior distribution;

[0014] Step S4: In order to estimate the parameters {γ, C, λ}, an iterative EM algorithm is used. The update of γ determines the convergence speed and recovery performance of the algorithm of the present invention. C is a positive definite matrix that controls the consistency of the columns. The learning rule of C affects the recovery performance and prevents overfitting. The maximum likelihood function is calculated through hidden variables, denoted as Q function, and the partial derivatives of the three parameters are calculated to be zero to obtain the update rule. Then the three parameters are continuously updated until the preset value conditions are reached, and the three parameters and signal b are output;

[0015] The beneficial effects of the method of the present invention are:

[0016] (1) Utilize row correlation and column correlation

[0017] The present invention decomposes the user signal into multiple blocks for processing. This block structure can capture the correlation of the transmitted signal in time or frequency. Compared with the traditional processing of a single sampling point or a continuous time series, it is more suitable for signals with correlation structures. In addition, two parameters γ and C are introduced to control the row sparsity and column coherence of the transmitted signal respectively.

[0018] (2) No need to know user activity factors

[0019] The RD and LD detection methods utilize the sparse characteristics of the transmitted signal, but they need to assume that the actual number of active users is known. However, in large-scale machine-type communications, the number of active users cannot be accurately known. The present invention updates the posterior distribution and hyperparameters of the transmitted signal, and does not need to know the actual number of users during the iteration process.

[0020] (3) Introducing hyperparameters to improve recovery performance

[0021] In order to recover the signal transmitted by the user more quickly, three parameters {γ, C, λ} are introduced, among which the learning rule of C affects the recovery performance and prevents overfitting; λ directly affects the recovery of the signal by controlling the observation matrix y; the update of γ determines the convergence speed and recovery performance of the method of the present invention; when γ approaches 0, b also approaches 0. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of a block sparse Bayesian multi-slot data detection method of the present invention;

[0023] Figure 2 It is a symbol error rate analysis diagram of various multi-user detection methods under flat fading channels. DETAILED DESCRIPTION

[0024] The present invention considers an uplink unlicensed non-orthogonal multiple access system with a single-antenna base station and K single-antenna users, wherein the K single-antenna users randomly transmit data to the single-antenna base station. In L consecutive time slots, only some active users continue to transmit signals, and inactive users always remain silent. The information of the active user k is transmitted after spreading, and the length of the spreading sequence is N; the base station receiving signal is equivalent to a multiple measurement vector model, that is, an MMV model:

[0025] Y=HB+W,

[0026] in, is the equivalent measurement matrix composed of the spreading sequence and the channel coefficients. Assuming that the frame length is less than the channel coherence time, H remains unchanged throughout the frame time. b l is the transmitted signal of all users in the lth time slot, l = 1, 2, ..., L, y l is the received signal of the base station in the lth time slot, w l is zero-mean and has a covariance matrix of σ 2 Complex Gaussian noise of Ι;

[0027] like Figure 1 As shown, the method comprises the following steps:

[0028] Step S1: Considering the joint sparsity of user activities in multiple consecutive time slots, the present invention converts the MMV model into a single measurement vector (SMV) model with blocks as units.

[0029]

[0030] in, vec(·) represents the vectorization operation of the matrix. represents the Kronecker product matrix of size m×n, where m=NL and n=KL.

[0031] Step S2: Since the transmitted signal vector is mostly zero, it is assumed that the transmitted signal satisfies the zero Gaussian prior, and the variance is composed of γ and C, and the prior distribution of signal b is obtained (where The specific steps are as follows:

[0032]

[0033] Where γ is a non-negative hyperparameter that determines the row sparsity of signal b, C is a positive definite matrix of size L×L that controls the column coherence of signal b, and γ i , C i are the i-th column hyperparameters and the positive definite matrix ∑0 is a diagonal matrix with the following formula:

[0034]

[0035] Step S3: Assuming that the matrix noise w satisfies the complex Gaussian distribution, taking the variable y as the observed variable and b as the hidden variable, the likelihood function of y can be obtained. The specific steps are as follows:

[0036]

[0037]

[0038] The Bayesian learning-based algorithm calculates the posterior distribution of the transmitted signal b. By combining the likelihood function and the prior distribution, the posterior distribution of the transmitted signal b is obtained:

[0039]

[0040] μ and ∑ are the mean and covariance values ​​of the signal respectively, and the results are as follows:

[0041] μ=∑0 A H (λI+A∑0 A H ) -1 y (7)

[0042] ∑=(∑0+λ -1 Alpha H Α) -1 (8)

[0043] Therefore, the estimated transmitted signal is:

[0044] x←∑0A H (λI+A∑0A H ) -1 y (9)

[0045] Step S4: In order to estimate the three hyperparameters {γ, C, λ}, the iterative EM algorithm is used to calculate the maximum likelihood function through the hidden variables, denoted as the Q function, where Q (t) (y, b; γ, C, λ) represents the maximum likelihood function at the current moment; the t in the upper right corner of the letter represents the parameters at the current moment, Tool The body formula is as follows:

[0046]

[0047] Where const is a constant, Γ is a diagonal matrix of size K×K, and the specific formula is as follows:

[0048] Γ=diag(γ1,γ2,...,γ K ) (11)

[0049] In order to obtain the new rules with three parameters, we need to maximize the Q function and calculate the parameters. (t) (y, b; γ, C, λ) calculates the partial derivatives of γ, C, and λ and sets them to zero. The specific steps are as follows:

[0050]

[0051]

[0052]

[0053] So we get the specific update rule:

[0054]

[0055]

[0056]

[0057] in is the ith block of μ, is the ith block of ∑, Q (t) (y, b; γ, C, λ) represents the maximum likelihood function at the current moment; the t in the upper right corner of the letter represents the parameters at the current moment. According to the above formula, the three parameters γ, C, and λ are updated. The specific update iteration rules are as follows:

[0058] (1) Let t = 0, initialize γ (0) ,C (0) and λ (0) , and then estimate the posterior distribution parameter μ according to (6) to (8) (0) and∑ (0) ;

[0059] (2) Let t+1→t, and use μ according to (15) to (17) (t-1) and∑ (t-1) Deriving hyperparameters γ (t) ,C (t) and λ (t) ;

[0060] (3) Use γ (t) ,C (t) , (t) And (6) to (8) to get μ (t) and∑ (t) ;

[0061] (4) If ||μ (t) -μ (t-1) ||2 is greater than the preset value 10 -6 , then return to (2), otherwise end the loop.

[0062] In the embodiments of the present application, the feasibility of a block sparse Bayesian multi-slot data detection method is verified through simulation experiments.

[0063] Simulation parameters: The method of the present invention considers a flat fading channel, the modulation scheme is binary phase shift keying (BPSK), the total number of users is K = 20, and the user activity factor is P a =0.2, the spreading factor is N=32, the frame structure length is L=6, the maximum number of iterations is RPT=100, the average signal-to-noise ratio (SNR) of active users is 3dB to 15dB, and the symbol error rate (SER) calculation method is:

[0064]

[0065] Where err represents the number of symbol detection errors.

[0066] Simulation results: Simulated multi-user detection performance in multiple time slots with a fixed user activity factor P a =0.2, and the symbol error rate (SER) performance analysis of ZF, MMSE, RD, LD, OMP, SBL and the method of the present invention is studied. Figure 2 As shown, it can be seen that the method of the present invention is superior to the traditional LS, MMSE, RD, LD and OMP detection methods. Since ZF and MMSE do not consider the sparse characteristics; RD, LD, and OMP use the sparse characteristics but do not consider the time correlation, that is, the row correlation; the present invention considers both the row correlation and the column correlation at the same time, and does not need to understand the user activity factor, the performance is optimal, and not only that, the method of the present invention achieves better recovery performance than SBL, and is an efficient and flexible method for reconstructing structural sparse signals.

[0067] The above are specific implementation methods and simulation verifications of the method of the present invention. It should be pointed out that those skilled in the art can clearly understand that the above embodiments and simulations of the block sparse Bayesian multi-slot data detection method of the present invention are only used to illustrate and verify the rationality and feasibility of the method, and are not used to limit the method of the present invention. Although the present invention can be effectively illustrated and described through the embodiments, there are many changes in the present invention without departing from the spirit of the present invention. Without departing from the spirit and essence of the method of the present invention, those skilled in the art can make various corresponding changes or deformations according to the method of the present invention, but these corresponding changes or deformations all belong to the protection scope required by the method of the present invention.

Claims

1. A block sparse Bayesian multi-slot data detection method, characterized in that: For an uplink unlicensed non-orthogonal multiple access system including a single-antenna base station and K single-antenna users, the K single-antenna users randomly transmit data to the single-antenna base station. In L consecutive time slots, only some active users continue to transmit signals, and inactive users do not transmit signals. The information of active user k is transmitted after spreading, and the length of the spreading sequence is N; The base station receiving signal is equivalent to a multi-measurement vector model, namely the MMV model: Y=HB+W, in, is the equivalent measurement matrix composed of the spreading sequence and the channel coefficients. Assuming that the frame length is less than the channel coherence time, H remains unchanged throughout the frame time. b l is the transmitted signal of all users in the lth time slot, l = 1, 2, ..., L, y l is the received signal of the base station in the lth time slot, w l is zero-mean and has a covariance matrix of σ 2 Complex Gaussian noise of Ι; The method comprises: Step S1: Through matrix vec operation, the MMV model is represented as a block SMV model, the observation signal Y is converted into y, the transmission signal B is converted into b, and the noise variable W is converted into w; Step S2: Since the transmitted signal b vector is mostly zero, it is assumed that the transmitted signal b satisfies the Gaussian prior with zero mean, and the variance is determined by variables γ and C, where γ is a non-negative hyperparameter that determines the row sparsity of signal b, and C is a positive definite matrix of size L×L that controls the column coherence of signal b, and the prior distribution of signal b is obtained; Step S3: Assume that the matrix noise w satisfies the complex Gaussian distribution with a variance of λ, take the variable y as the observed variable and b as the hidden variable, obtain the likelihood function of the variable y, and obtain the posterior distribution of the transmitted signal by combining the likelihood function and the prior distribution; Step S4: In order to estimate the parameters {γ, C, λ}, an iterative EM algorithm is used. The update of γ determines the convergence speed and recovery performance of the algorithm of the present invention. C is a positive definite matrix that controls column consistency. The learning rule of C affects the recovery performance and prevents overfitting. The maximum likelihood function is calculated through hidden variables, which is recorded as Q function. Step S5: Calculate partial derivatives of the three parameters respectively to make them zero, obtain update rules, and then continue to update the three parameters until the preset value conditions are reached, and output the three parameters and signal b; In step S1, the joint sparsity of user activities in multiple consecutive time slots is considered, and the MMV model is converted into a single measurement vector model in blocks, that is, an SMV model: in, vec(·) represents the vectorization operation of the matrix. represents the Kronecker product matrix of size m×n, m=NL, n=KL; In step S2, it is assumed that the transmitted signal satisfies the Gaussian prior of zero mean, and the variance is composed of γ and C. The specific steps of obtaining the prior distribution of the signal b are as follows: Among them, p(b;γ i ,C i ) represents the prior distribution of the transmitted signal b, represents a zero-mean Gaussian distribution, γ is a non-negative hyperparameter that determines the row sparsity of signal b, C is a positive definite matrix of size L×L that controls the column coherence of signal b, and γ i , C i are the i-th column hyperparameters and positive definite matrices, ∑0 is a diagonal matrix, and the formula is as follows: In step S3, it is assumed that the matrix noise w satisfies the complex Gaussian distribution, and the variable y is used as the observed variable and b is used as the hidden variable to obtain the likelihood function of y. The specific steps are as follows: Among them, p(w) represents the distribution of noise, λ represents the variance, I represents the identity matrix, λI represents the covariance matrix; p(y|b; λ) represents the likelihood function of y; The Bayesian learning algorithm combines the likelihood function of y and the prior distribution of the transmitted signal b to obtain the posterior distribution of the transmitted signal b: μ and ∑ are the mean and covariance values ​​of the signal respectively, and the results are as follows: μ=Σ0A H (λI+A∑0 A H ) -1 y (7) ∑=(Σ0+λ -1 A H A) -1 (8) The estimated transmitted signal is therefore: x←∑0 A H (λI+A∑0A H )- 1 (9) In step S4, in order to estimate the three parameters {γ, C, λ}, an iterative EM algorithm is used to calculate the maximum likelihood function through hidden variables, which is denoted as Q function, as follows: Where const is a constant, Γ is a diagonal matrix of size K×K, and the specific formula is as follows: Γ=diag(γ1,γ2,...,γ K ) (11) In order to obtain a new rule with three parameters, we need to maximize the Q function and calculate the parameters. ( t ) (y, b; γ, C, λ) calculates the partial derivatives of γ, C, and λ and sets them to zero. The specific steps are as follows: Get the specific update rules: in is the ith block of μ, is the ith block of ∑, Q ( t ) (y, b; γ, C, λ) represents the maximum likelihood function at the current moment. The t in the upper right corner of the letter represents the parameters at the current moment. According to the above formula, the three parameters γ, C, and λ are iteratively updated.

Images