Joint multi-user detection, channel and impulse noise estimation method of GF-NOMA system

Abstract

The invention discloses a combined multi-user detection, channel and impulse noise estimation method of a GF-NOMA system, and the method comprises the steps: expanding a symbol sent by each active user into an expanded sequence through a unique spread spectrum sequence at a sending end, then transmitting the expanded sequence, and then carrying out the interference of a channel and impulse noise; at a receiving end, a base station receives signals through a plurality of antennas, then constructs a to-be-estimated matrix composed of a plurality of to-be-estimated sparse vectors with the same support set according to the joint sparsity of user sporadic communication and burst impulse noise interference under the receiving of the plurality of antennas, and obtains an estimation problem in combination with a measurement matrix; estimating a to-be-estimated matrix by using a time slot multiple sparse Bayesian learning-least square algorithm, namely jointly estimating a channel and impulse noise; the method has the advantages that active users and prior information of impulse noise are not needed, and good multi-user detection, channel estimation and impulse noise estimation performance can be obtained by fully utilizing receiving information of a plurality of measurement vectors, namely receiving signals of a plurality of antennas.

Description

Technical Field

[0001] The present invention relates to a NOMA (non-orthogonal multiple access) technology, and in particular to a joint multi-user detection, channel and impulse noise estimation method of a GF-NOMA (grant-free non-orthogonal multiple access) system in a large-scale machine type communication application scenario. Background Art

[0002] As one of the three major application scenarios of 5G, massive machine type communication (mMTC) has received extensive attention in the fields of industrial Internet of Things and Internet of Vehicles. Due to the characteristics of massive device access, short data packets, and sporadic transmission, the traditional scheduling-based orthogonal multiple access scheme will cause a large amount of signaling overhead and high transmission delay in the mMTC system, as well as lead to tight spectrum resources, which cannot meet the requirements of mMTC. The emergence of GF-NOMA technology provides a new solution to these problems. GF-NOMA allows different users to transmit data at the same time or spectrum resources without relying on base station scheduling, which can greatly reduce signaling overhead and transmission delay while significantly improving spectrum utilization. However, during the data transmission process, users do not need to be scheduled by the base station and send data to the base station randomly, which results in the base station being unable to obtain the information of active users when users transmit data, and thus unable to correctly decode the data of active users. In addition, in mMTC application scenarios such as industrial Internet of Things and Internet of Vehicles, there is a large amount of impulse noise due to activities such as electrical equipment switching and car ignition. These impulse noises will cause great interference to the mMTC system and seriously damage the communication performance. Therefore, it is of great significance to design a joint multi-user detection, channel estimation and impulse noise estimation method for GF-NOMA system in mMTC application scenarios.

[0003] The existing Gaussian generalized approximate message passing-sparse Bayesian learning algorithm (GGAMP-SBL) uses a single measurement vector to perform joint multi-user detection, channel estimation and impulse noise estimation. Although it can perform joint multi-user detection, channel estimation and impulse noise estimation, it only uses the received information of a single measurement vector and cannot achieve ideal results. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a joint multi-user detection, channel and impulse noise estimation method for a GF-NOMA system in a large-scale machine type communication application scenario, which does not require prior information of active users and impulse noise, and can make full use of the received information of multiple measurement vectors, i.e., the received signals of multiple antennas to achieve good multi-user detection, channel estimation and impulse noise estimation performance.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a joint multi-user detection, channel and impulse noise estimation method of a GF-NOMA system, characterized in that the method assumes that there is 1 base station and K users in the uplink GF-NOMA system, and requires the uplink GF-NOMA system to adopt an overload system, that is, the total number of subcarriers N of the uplink GF-NOMA system is less than K, the base station is configured with R antennas, all users are configured with a single antenna, and it is assumed that only a active users send data, wherein K≥50, the indexes of the K users are 1, 2, ..., K, N>1, R>1, a≥1, a<K, and "<<" is a much less than symbol; the method comprises the following steps:

[0006] Step 1: At the transmitting end of the uplink GF-NOMA system, each symbol sent by each active user in sequence is extended into an N×1 extension sequence after passing through a unique extension sequence of the active user, where all symbols sent by each active user include a pilot symbol and several data symbols; then all active users simultaneously send all the extended sequences obtained by their respective extensions to the base station, and each active user sends all the extended sequences obtained by the extension in the order of the symbols sent, and the extended sequence transmission process will be interfered by the channel and impulse noise;

[0007] Step 2: At the receiving end of the uplink GF-NOMA system, the signal received by the rth antenna of the base station on the pilot is recorded as in, The dimension is N×1, r=1,2,…,R, k=1,2,…,K, represents the channel gain between the kth user and the rth antenna of the base station. The channel gains between active users and the antennas of the base station are independent of each other and obey a complex Gaussian distribution with a mean of 0 and a variance of 1. The channel gain between inactive users and the antennas of the base station is 0. k The dimension is N×1, s k represents the unique spreading sequence of the kth user, s k =[s 1,k ,s 2,k ,…,s N,k ] T , the superscript "T" indicates the transpose operation of a matrix or vector, xp,k represents the pilot symbol sent by the kth user. If the kth user is an active user, then x p,k is 1, if the kth user is an inactive user, then x p,k is 0, and the symbol vector with dimension K×1 formed by the pilot symbols sent by all users is denoted as x p , x p =[x p,1 ,x p,2 ,…,x p,K ] T , F represents the normalized Fourier transform matrix with dimension N×N, The dimension is N×1, represents the burst noise interference received by the rth antenna of the base station in the pilot time slot, The dimension is N×1, represents the background noise vector superimposed by the rth antenna of the base station in the pilot time slot, S represents the sequence matrix of dimension N×K composed of the unique spread spectrum sequences of all users, S=[s1,s2,…,s K ],h r represents the channel coefficient vector with dimension K×1 formed by the channel gain between all users and the rth antenna of the base station, h r and x p have the same support set, h r Except for the support set, the values ​​of the elements in the position other than the support set are all 0, x p The element value corresponding to the active user in h is 1, and the sparsity of active users is reflected in h r middle;

[0008] Step 3: According to the joint sparsity of user sporadic communication and burst impulse noise interference under the reception of R antennas of the base station, that is, block sparsity, a matrix W to be estimated with a dimension of (N+K)×R is constructed, which is composed of R sparse vectors to be estimated with a dimension of (N+K)×1 and the same support set. Let Z denote the background noise matrix of dimension N×R, Let Y represent the pilot segment received signal matrix with dimension N×R consisting of the signals received by the R antennas of the base station on the pilot. Then define the measurement matrix Φ, Φ = [S, F], Rewrite it as Y = ΦW + Z; where, represents the channel matrix of dimension K×R, represents the impulse noise matrix with dimension N×R, The dimension of Φ is N×(N+K);

[0009] Step 4: Based on Y = ΦW + Z, use the TMSBL-LS algorithm to estimate W, that is, joint estimation and

[0010] The specific process of step 4 is as follows:

[0011] Step 4.1: Let l represent the number of iterations of the TMSBL-LS algorithm, and the initial value of l is 1; let l max represents the maximum number of loop iterations using the TMSBL-LS algorithm; let γ j (l＝0) represents the non-negative hyperparameter γ that determines the sparsity of the j-th row of signal blocks in W during the iterative process of the TMSBL-LS algorithm. j The initial value of , where j = 1, 2, ..., N + K; let Γ (l＝0) =diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ), where diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ) represents γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) is a diagonal matrix composed of diagonal elements; let B (l＝0) represents the initial value of the sparse signal block structure correlation matrix B in W during the iterative process of the TMSBL-LS algorithm; let (σ 2 ) (l＝0) represents the variance σ of Z during the iterative process of the TMSBL-LS algorithm 2 The initial value of

[0012] Step 4.2: During the l-th loop iteration, calculate the covariance of W in the l-th loop iteration, denoted as ∑ w (l) , When l = 1, Γ (l-1) Equal to Γ (l＝0) , when l>1,Γ (l-1) represents the value of Γ in the l-1th loop iteration, Γ (l-1) =diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) ), diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K)(l-1) ) represents γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) is a diagonal matrix composed of diagonal elements. When l = 1, γ j (l-1) Equal to γ j (l＝0) , when l>1,γ j (l-1) Indicates that γ in the l-1th loop iteration j The value of Γ=diag(γ1,γ2,…,γ (N+K) ), diag(γ1,γ2,…,γ (N+K) ) represents γ1,γ2,…,γ (N+K) is a diagonal matrix composed of diagonal elements. When l = 1 (σ 2 ) (l-1) Equal to (σ 2 ) (l＝0) , when l>1(σ 2 ) (l-1) represents the variance σ of Z in the l-1th loop iteration 2 The value of , the superscript “H” indicates the conjugate transpose operation of the matrix;

[0013] During the l-th loop iteration, the posterior mean of W in the l-th loop iteration is calculated and recorded as Where I is the identity matrix;

[0014] During the lth loop iteration, calculate γ in the lth loop iteration j ,j=1,2,…,N+K, denoted as γ j (l) ,j=1,2,…,N+K, in, express The row vector of the j-th row elements in B, when l = 1 (l-1) Equal to B (l＝0) , when l>1, B (l-1) represents the value of B in the l-1th loop iteration, (∑ w (l) ) j,j Represents ∑ w (l) The j-th row and j-th column element in ;

[0015] During the lth loop iteration, calculate the value of B in the lth loop iteration, denoted as B (l) , in,"‖·‖ F " represents the F-norm operation of the matrix. is the introduced intermediate variable, η is a constant introduced to enhance the robustness of the TMSBL-LS algorithm, η>0;

[0016] During the l-th loop iteration, calculate the variance σ of Z in the l-th loop iteration 2 The value of (σ 2 ) (l) , Among them, Tr[] means finding the trace of the matrix;

[0017] Step 4.3: Determine whether l is greater than or equal to l max If yes, then end the loop iteration process and get Then continue to execute step 4.4; otherwise, let l=l+1, and return to step 4.2 to continue execution, where the "=" in l=l+1 is an assignment symbol;

[0018] Step 4.4: From Find all values ​​greater than the preset threshold ε, then extract the indexes corresponding to all the found values, and record the set of all the extracted indexes in ascending order as Ω. The set of all indexes less than or equal to K in Ω is the set of indexes of all active users, realizing multi-user detection, where The corresponding indexes are 1, 2, ..., N + K;

[0019] Step 4.5: Order Denotes the estimated value of W, let Indicated by The row index in Ω belongs to the submatrix consisting of all rows, make Indicated by The submatrix consists of all rows whose row indices belong to {1,2,…,N+K}\Ω, Among them, Φ Ω represents the submatrix consisting of all columns in Φ whose column indices belong to Ω, Indicates the pseudo-inverse operation of the matrix, "\" indicates the complement operation; then and All rows in the array are sorted by row index.

[0020] Step 4.6: According to and get and The accurate estimates of each enable channel and impulse noise estimation.

[0021] In step 4.1, γ j(l＝0) =0.001, B (l＝0) =I R ,(σ 2 ) (l＝0) =1, where I R Represents the identity matrix of dimension R×R.

[0022] Compared with the prior art, the advantages of the present invention are:

[0023] 1) The method of the present invention does not require prior information such as the sparsity of active users and impulse noise when detecting active users and estimating impulse noise, making the method of the present invention more suitable for actual multi-user detection, channel estimation and impulse noise estimation scenarios.

[0024] 2) The method of the present invention makes full use of the joint sparsity (i.e., block sparsity) of sporadic user communications and burst impulse noise received by multiple antennas of the base station to perform joint multi-user detection, channel estimation, and impulse noise estimation. Simulation results show that compared with the sparse signal recovery algorithm that only uses a single measurement vector, the method of the present invention has significant advantages in multi-user detection, channel estimation, and impulse noise estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a general implementation block diagram of the method of the present invention;

[0026] Figure 2 It is a performance comparison curve of the method of the present invention (TMSBL-LS algorithm) and the existing GGAMP-SBL algorithm in terms of multi-user detection accuracy under different signal-to-noise ratios;

[0027] Figure 3 Performance comparison curves of the method of the present invention (TMSBL-LS algorithm) and the existing OLS-WINS algorithm, the existing GGAMP-SBL algorithm, and the existing Oracle LS algorithm in channel estimation under different signal-to-noise ratios;

[0028] Figure 4 It is a performance comparison curve of the method of the present invention (TMSBL-LS algorithm) and the existing OLS-WINS algorithm and the existing GGAMP-SBL algorithm in impulse noise estimation under different signal-to-noise ratios. DETAILED DESCRIPTION

[0029] The present invention is further described in detail below with reference to the accompanying drawings.

[0030] The present invention proposes a joint multi-user detection, channel and impulse noise estimation method for the GF-NOMA system in a large-scale machine type communication application scenario. The overall implementation block diagram is as follows: Figure 1As shown, the method assumes that there is 1 base station and K users in the uplink GF-NOMA system, and in order to meet the needs of large-scale connections, the uplink GF-NOMA system is required to adopt an overload system, that is, the total number of subcarriers N in the uplink GF-NOMA system is less than K, the base station is equipped with R antennas, all users are equipped with a single antenna, and it is assumed that only a active users send data, where K≥50, K=200 in this embodiment, the indexes of the K users are 1, 2, ..., K, N>1, N=100 in this embodiment, R>1, R=7 in this embodiment, a≥1, a<<K, "<<" is a much less than symbol, and a=10 in this embodiment. The method includes the following steps:

[0031] Step 1: At the transmitting end of the uplink GF-NOMA system, each symbol sent by each active user in sequence is extended into an extended sequence with a dimension of N×1 after passing through the active user's unique spread spectrum sequence, where all symbols sent by each active user include a pilot symbol and several data symbols, and each user (active user or inactive user) has its own unique spread spectrum sequence; then all active users simultaneously send all their extended sequences to the base station, and each active user sends all extended sequences in the order of the symbols sent. The extended sequence transmission process will be interfered by the channel and pulse noise.

[0032] Step 2: At the receiving end of the uplink GF-NOMA system, the signal received by the rth antenna of the base station on the pilot is recorded as in, The dimension is N×1, r=1,2,…,R, k=1,2,…,K, represents the channel gain between the kth user and the rth antenna of the base station. The channel gains between active users and the antennas of the base station are independent of each other and obey a complex Gaussian distribution with a mean of 0 and a variance of 1. The channel gain between inactive users and the antennas of the base station is 0. k The dimension is N×1, s k represents the unique spreading sequence of the kth user, s k =[s 1,k ,s 2,k ,…,s N,k ] T ,s 1,k Indicates k The first element in s 2,k Indicates k The second element in s N,k Indicates k The Nth element in x, the superscript "T" indicates the transpose operation of the matrix or vector, p,krepresents the pilot symbol sent by the kth user. If the kth user is an active user, then x p,k is 1, if the kth user is an inactive user, then x p,k is 0, and the symbol vector with dimension K×1 formed by the pilot symbols sent by all users is denoted as x p , x p =[x p,1 ,x p,2 ,…,x p,K ] T , x p,1 represents the pilot symbol sent by the first user, x p,2 represents the pilot symbol sent by the second user, x p,K represents the pilot symbol sent by the Kth user, F represents the normalized Fourier transform matrix with dimension N×N, The dimension is N×1, represents the burst noise interference received by the rth antenna of the base station in the pilot time slot, The dimension is N×1, represents the background noise vector superimposed by the rth antenna of the base station in the pilot time slot, S represents the sequence matrix of dimension N×K composed of the unique spread spectrum sequences of all users, S=[s1,s2,…,s K ], s1 represents the unique spreading sequence of the first user, s2 represents the unique spreading sequence of the second user, s K represents the unique spreading sequence of the Kth user, h r Represents the channel coefficient vector with dimension K×1 formed by the channel gain between all users and the rth antenna of the base station, represents the channel gain between the first user and the rth antenna of the base station, represents the channel gain between the second user and the rth antenna of the base station, represents the channel gain between the Kth user and the rth antenna of the base station, h r and x p have the same support set, h r Except for the support set, the values ​​of the elements in the position other than the support set are all 0, x p The element value corresponding to the active user in h is 1, and the sparsity of active users is reflected in h r middle.

[0033] Step 3: According to the joint sparsity of user sporadic communication and burst impulse noise interference under the reception of R antennas of the base station, that is, block sparsity, a matrix W to be estimated with a dimension of (N+K)×R is constructed, which is composed of R sparse vectors to be estimated with a dimension of (N+K)×1 and the same support set. Let Z denote the background noise matrix of dimension N×R, Let Y represent the pilot segment received signal matrix with dimension N×R consisting of the signals received by the R antennas of the base station on the pilot. Then define the measurement matrix Φ, Φ = [S, F], Rewrite it as Y = ΦW + Z as an estimation problem; where, represents the channel matrix of dimension K×R, h 1 The channel gain between all users and the first antenna of the base station is a channel coefficient vector with a dimension of K×1, h 2 The channel gain between all users and the second antenna of the base station is a channel coefficient vector with a dimension of K×1, h R Represents the channel coefficient vector with dimension K×1 formed by the channel gain between all users and the Rth antenna of the base station, represents the impulse noise matrix with dimension N×R, Indicates the burst noise interference received by the first antenna of the base station in the pilot time slot. Indicates the burst noise interference received by the second antenna of the base station in the pilot time slot. It indicates the burst noise interference received by the Rth antenna of the base station in the pilot time slot. represents the background noise vector superimposed by the first antenna of the base station in the pilot time slot, represents the background noise vector superimposed by the second antenna of the base station in the pilot time slot, represents the background noise vector superimposed on the Rth antenna of the base station in the pilot time slot, Indicates the signal received by the first antenna of the base station on the pilot. Indicates the signal received by the second antenna of the base station on the pilot. It represents the signal received by the Rth antenna of the base station on the pilot, and the dimension of Φ is N×(N+K).

[0034] Step 4: Based on Y = ΦW + Z, use the TMSBL-LS (temporally multiple sparsebayesian learning-least squares) algorithm to estimate W, that is, joint estimation and

[0035] In this embodiment, the specific process of step 4 is as follows:

[0036] Step 4.1: Let l represent the number of iterations of the TMSBL-LS algorithm, and the initial value of l is 1; let lmax represents the maximum number of loop iterations using the TMSBL-LS algorithm; let γ j (l＝0) represents the non-negative hyperparameter γ that determines the sparsity of the j-th row of signal blocks in w during the iterative process of the TMSBL-LS algorithm. j The initial value of , where j = 1, 2, ..., N + K; let Γ (l＝0) =diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ), where diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ) represents γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) is a diagonal matrix composed of diagonal elements, γ1 (l＝0) represents the initial value of the non-negative hyperparameter γ1 that determines the sparsity of the first row of signal blocks in W during the iterative process of the TMSBL-LS algorithm, γ2 (l＝0) represents the initial value of the non-negative hyperparameter γ2 that determines the sparsity of the second row of signal blocks in W during the iterative process of the TMSBL-LS algorithm. (N+K) (l＝0) represents the non-negative hyperparameter γ that determines the sparsity of the N+Kth row signal block in W during the iterative process of the TMSBL-LS algorithm. N+k The initial value of B (l＝0) represents the initial value of the sparse signal block structure correlation matrix B in W during the iterative process of the TMSBL-LS algorithm; let (σ 2 ) (l＝0) represents the variance σ of Z during the iterative process of the TMSBL-LS algorithm 2 The initial value of .

[0037] In this embodiment, γ j (l＝0) =0.001, b (l＝0) =I R ,(σ 2 ) (l＝0) =1, where I R Represents the identity matrix of dimension R×R.

[0038] Step 4.2: During the l-th loop iteration, calculate the covariance of W in the l-th loop iteration, denoted as ∑ w (l) , When l = 1, Γ(l-1) Equal to Γ (l＝0) , when l>1,Γ (l-1) represents the value of Γ in the l-1th loop iteration, Γ (l-1) =diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) ), diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) ) represents γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) is a diagonal matrix composed of diagonal elements. When l = 1, γ j (l-1) Equal to γ j (l＝0) , when l>1,γ j (l-1) Indicates that γ in the l-1th loop iteration j The value of Γ=diag(γ1,γ2,…,γ (N+K) ), diag(γ1,γ2,…,γ (N+K) ) represents γ1,γ2,…,γ (N+K) is a diagonal matrix composed of diagonal elements. When l = 1 (σ 2 ) (l-1) Equal to (σ 2 ) (l＝0) , when l>1(σ 2 ) (l-1) represents the variance σ of Z in the l-1th loop iteration 2 The superscript “H” indicates the conjugate transpose operation of the matrix.

[0039] During the l-th loop iteration, the posterior mean of W in the l-th loop iteration is calculated and recorded as Where I is the identity matrix.

[0040] During the lth loop iteration, calculate γ in the lth loop iteration j ,j=1,2,…,N+K, denoted as γ j (l) ,j=1,2,…,N+K, in, express The row vector of the j-th row elements in B, when l = 1 (l-1) Equal to B (l＝0) , when l>1, B (l-1)represents the value of B in the l-1th loop iteration, (∑ w (l) ) j,j Represents ∑ w (l) The j-th row and j-th column element in .

[0041] During the lth loop iteration, calculate the value of B in the lth loop iteration, denoted as B (l) , in,"‖·‖ F " represents the F-norm operation of the matrix. is the introduced intermediate variable, η is a constant introduced to enhance the robustness of the TMSBL-LS algorithm, η>0, and the value of η is 2 in this embodiment.

[0042] During the l-th loop iteration, calculate the variance σ of Z in the l-th loop iteration 2 The value of (σ 2 ) (l) , in,

[0043] Tr[] means finding the trace of a matrix.

[0044] Step 4.3: Determine whether l is greater than or equal to l max If yes, then end the loop iteration process and get Then continue to execute step 4.4; otherwise, let l=l+1, and then return to step 4.2 to continue execution, where the "=" in l=l+1 is an assignment symbol.

[0045] Step 4.4: From Find all values ​​greater than the preset threshold ε, then extract the indexes corresponding to all the found values, and record the set of all the extracted indexes in ascending order as Ω. The set of all indexes less than or equal to K in Ω is the set of indexes of all active users, realizing multi-user detection. The set of all indexes greater than K in Ω is the set of indexes of impulse noise burst positions, where The respective indexes are 1, 2, ..., N+K.

[0046] Step 4.5: Order Denotes the estimated value of W, let Indicated by The row index in Ω belongs to the submatrix consisting of all rows, make Indicated by The submatrix consists of all rows whose row indices belong to {1,2,…,N+K}\Ω, Among them, ΦΩ represents the submatrix consisting of all columns in Φ whose column indices belong to Ω, Indicates the pseudo-inverse operation of the matrix, "\" indicates the complement operation; then and All rows in the array are sorted by row index.

[0047] Step 4.6: According to and get and The accurate estimates of each enable channel and impulse noise estimation.

[0048] In order to verify the feasibility and effectiveness of the method of the present invention, the method of the present invention was simulated by computer using the Monte Carlo cycle method.

[0049] In the computer simulation, the simulation parameters are set as follows: the total number of users K is 200, the number of active users a is 10, the total number of subcarriers N is 100, the number of antennas R of the base station is 7, 4-QAM modulation is used, the unique spread spectrum sequence of each user is a random Gaussian sequence, and the background noise is a mean of 0 and a variance of The Gaussian white noise is used, and the impulse noise model adopts the Gaussian mixture model. If the complex Gaussian random variable u is used to represent the impulse noise, then the probability density function f(u) of u is expressed as in, represents the total number of random variables, The value is 3, β s represents the sth random variable u s The probability of occurrence, f s (u s ) represents the sth random variable u s The probability density function has a mean of 0 and a variance of v s The complex Gaussian distribution of When setting β=[β1, β2, β3]=[0.9, 0.07, 0.03], The signal-to-noise ratio (SNR) is defined as Among them, P singal Represents the signal power, P u represents the pulse noise power, P z Represents the background noise power. The normalized mean square error (NMSE) of channel estimation is defined as Among them, “‖‖2” means taking the binary norm of the matrix. Indicates h r The estimated value of express The estimated value of Indicates h 1 The estimated value of Indicates h 2 The estimated value of Indicates h R The estimated value of Indicates h r The true value of . The mean square error (MSE) of impulse noise estimation is defined as Among them, E{·} represents the mathematical expectation, express The estimated value of express The estimated value of express The estimated value of express The estimated value of express The estimated value of express The true value of .

[0050] In the computer simulation, the comparison files used are: GGAMP-SBL algorithm, OLS-WINS (oracle least squares-with impulsive noise suppression) algorithm with impulse noise suppression, and Oracle LS (oracle least squares) algorithm without impulse noise suppression.

[0051] Figure 2 The performance comparison of the proposed method (TMSBL-LS algorithm) and the existing GGAMP-SBL algorithm in terms of multi-user detection accuracy under different signal-to-noise ratios is given. Figure 2It can be seen that the multi-user detection accuracy of the method of the present invention and the GGAMP-SBL algorithm gradually increases with the increase of the signal-to-noise ratio, and finally approaches 100%. When the signal-to-noise ratio is high, that is, when the impulse noise interference is weak, the multi-user detection accuracy of the two algorithms is not much different, but the multi-user detection accuracy of the method of the present invention is slightly higher than that of the GGAMP-SBL algorithm. However, when the signal-to-noise ratio is low, that is, when the impulse noise interference is strong, the method of the present invention still has a very high multi-user detection accuracy, while the multi-user detection accuracy of the GGAMP-SBL algorithm is significantly lower than that of the method of the present invention, and as the signal-to-noise ratio decreases, this gap becomes more significant. This is because the method of the present invention uses more received information for active user detection compared to the GGAMP-SBL algorithm. Specifically, the GGAMP-SBL algorithm only utilizes the sparsity of the signal to be recovered under a single measurement vector, while the method of the present invention fully utilizes the joint sparsity of sporadic user communications and burst pulse noise under the reception of multiple antennas of the base station, that is, the block sparsity characteristic, which enables the method of the present invention to detect active users more accurately than the GGAMP-SBL algorithm under a lower signal-to-noise ratio.

[0052] Figure 3 The performance comparison of the method of the present invention (TMSBL-LS algorithm) and the existing OLS-WINS algorithm, the existing GGAMP-SBL algorithm, and the existing Oracle LS algorithm in channel estimation under different signal-to-noise ratios is given. Figure 3 In the Oracle LS algorithm, the base station has already known the support set information of active users, but has not considered impulse noise suppression, which can be regarded as the upper limit of the estimation performance without impulse noise suppression. In order to provide an upper limit for the joint estimation of channel and impulse noise, the Oracle LS algorithm is extended to the GF-NOMA system under impulse noise interference, and the OLS-WINS algorithm is proposed. In the OLS-WINS algorithm, the base station has already known the support set of active users and the location of impulse noise bursts, which can be regarded as the upper limit of the joint estimation performance. Figure 3It can be seen that with the increase of signal-to-noise ratio, the channel estimation NMSE of various algorithms is decreasing. Among all the algorithms, the Oracle LS algorithm shows the worst channel estimation performance, which can be regarded as the upper limit of the channel estimation performance without impulse noise suppression. This is because the algorithm has known the support set information of active users in advance, but has not considered the suppression of impulse noise interference, which shows that impulse noise will cause serious damage to the performance of the uplink GF-NOMA system. In all signal-to-noise ratio intervals, the channel estimation NMSE of the method of the present invention is better than that of the GGAMP-SBL algorithm, and this performance advantage becomes more obvious as the signal-to-noise ratio increases. Among various algorithms, the OLS-WINS algorithm shows the best channel estimation performance, because the algorithm can be regarded as the upper limit of the estimation performance. In addition, with the increase of signal-to-noise ratio, the channel estimation NMSE of the method of the present invention gradually approaches that of the OLS-WINS algorithm, which fully reflects the superior performance of the method of the present invention in channel estimation.

[0053] Figure 4 The performance comparison of the proposed method (TMSBL-LS algorithm) and the existing OLS-WINS algorithm and the existing GGAMP-SBL algorithm in impulse noise estimation under different signal-to-noise ratios is given. Figure 4 In the OLS-WINS algorithm, the base station has learned the support set of active users and the location of impulse noise bursts, which can be regarded as the upper limit of the joint estimation performance. Figure 4 It can be seen that with the increase of the signal-to-noise ratio, the MSE of the pulse noise estimation of various algorithms is decreasing. Among all the algorithms, the OLS-WINS algorithm, which can be regarded as the upper limit of the estimation performance, shows the best pulse noise estimation performance. In all signal-to-noise ratio intervals, it can be seen that the MSE of the pulse noise estimation of the method of the present invention is lower than that of the GGAMP-SBL algorithm, and as the signal-to-noise ratio increases, this performance improvement becomes more obvious. This is also because compared with the GGAMP-SBL algorithm, the method of the present invention makes full use of the joint sparsity of the pulse noise presented by multiple antenna reception to accurately obtain the support set of the burst pulse noise, and accurately estimates the pulse noise by using the time slot multiple sparse Bayesian learning-least squares algorithm. In addition, with the increase of the signal-to-noise ratio, the gap between the MSE of the pulse noise estimation of the method of the present invention and the OLS-WINS algorithm is slightly narrowed, which shows that the method of the present invention also has excellent performance in pulse noise estimation.

Claims

1. A joint multi-user detection, channel and impulse noise estimation method for GF-NOMA system, characterized in that The method assumes that there is one base station and K users in the uplink GF-NOMA system, and requires the uplink GF-NOMA system to adopt an overload system, that is, the total number of subcarriers N of the uplink GF-NOMA system is less than K, the base station is configured with R antennas, all users are configured with a single antenna, and it is assumed that only a active users send data, wherein K≥50, the indexes of the K users are 1, 2, ..., K, N>1, R>1, a≥1, a<<K, and "<<" is a much less than symbol; the method comprises the following steps: Step 1: At the transmitting end of the uplink GF-NOMA system, each symbol sent by each active user in sequence is extended into an N×1 extension sequence after passing through a unique extension sequence of the active user, where all symbols sent by each active user include a pilot symbol and several data symbols; then all active users simultaneously send all the extended sequences obtained by their respective extensions to the base station, and each active user sends all the extended sequences obtained by the extension in the order of the symbols sent, and the extended sequence transmission process will be interfered by the channel and impulse noise; Step 2: At the receiving end of the uplink GF-NOMA system, the signal received by the rth antenna of the base station on the pilot is recorded as in, The dimension is N×1, r=1,2,…,R, k=1,2,…,K, represents the channel gain between the kth user and the rth antenna of the base station. The channel gains between active users and the antennas of the base station are independent of each other and obey a complex Gaussian distribution with a mean of 0 and a variance of 1. The channel gain between inactive users and the antennas of the base station is 0. k The dimension is N×1, s k represents the unique spreading sequence of the kth user, s k =[s 1,k ,s 2,k ,…,s N,k ] T , the superscript "T" indicates the transpose operation of a matrix or vector, x p,k represents the pilot symbol sent by the kth user. If the kth user is an active user, then x p,k is 1, if the kth user is an inactive user, then x p,k is 0, and the symbol vector with dimension K×1 formed by the pilot symbols sent by all users is denoted as x p , x p =[x p,1 ,x p,2 ,…,x p,K ] T , F represents the normalized Fourier transform matrix with dimension N×N, The dimension is N×1, represents the burst noise interference received by the rth antenna of the base station in the pilot time slot, The dimension is N×1, represents the background noise vector superimposed by the rth antenna of the base station in the pilot time slot, S represents the sequence matrix of dimension N×K composed of the unique spread spectrum sequences of all users, S=[s1,s2,…,s K ],h r Represents the channel coefficient vector with dimension K×1 formed by the channel gain between all users and the rth antenna of the base station, h r and x p have the same support set, h r Except for the support set, the values ​​of the elements in the position other than the support set are all 0, x p The element value corresponding to the active user in h is 1, and the sparsity of active users is reflected in h r middle; Step 3: According to the joint sparsity of user sporadic communication and burst impulse noise interference under the reception of R antennas of the base station, that is, block sparsity, a matrix W to be estimated with a dimension of (N+K)×R is constructed, which is composed of R sparse vectors to be estimated with a dimension of (N+K)×1 and the same support set. Let Z denote the background noise matrix of dimension N×R, Let Y represent the pilot segment received signal matrix with dimension N×R consisting of the signals received by the R antennas of the base station on the pilot. Then define the measurement matrix Φ, Φ = [S, F], Rewrite it as Y = ΦW + Z; where, represents the channel matrix of dimension K×R, represents the impulse noise matrix with dimension N×R, The dimension of Φ is N×(N+K); Step 4: Based on Y = ΦW + Z, use the TMSBL-LS algorithm to estimate W, that is, joint estimation and 2. The joint multi-user detection, channel and impulse noise estimation method of the GF-NOMA system according to claim 1, characterized in that The specific process of step 4 is as follows: Step 4.1: Let l represent the number of iterations of the TMSBL-LS algorithm, and the initial value of l is 1; let l max represents the maximum number of loop iterations using the TMSBL-LS algorithm; let γ j (l＝0) represents the non-negative hyperparameter γ that determines the sparsity of the j-th row of signal blocks in W during the iterative process of the TMSBL-LS algorithm. j The initial value of , where j = 1, 2, ..., N + K; let Γ (l＝0) =diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ), where diag(γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) ) represents γ1 (l＝0) ,γ2 (l＝0) ,…,γ (N+K) (l＝0) is a diagonal matrix composed of diagonal elements; let B (l＝0) represents the initial value of the sparse signal block structure correlation matrix B in W during the iterative process of the TMSBL-LS algorithm; let (σ 2 ) (l＝0) represents the variance σ of Z during the iterative process of the TMSBL-LS algorithm 2 The initial value of Step 4.2: During the l-th loop iteration, calculate the covariance of W in the l-th loop iteration, denoted as ∑ w (l) , When l = 1, Γ (l-1) Equal to Γ (l＝0) , when l>1,Γ (l-1) represents the value of Γ in the l-1th loop iteration, Γ (l-1) =diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) ), diag(γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) ) represents γ1 (l-1) ,γ2 (l-1) ,…,γ (N+K) (l-1) is a diagonal matrix composed of diagonal elements. When l = 1, γ j (l-1) Equal to γ j (l＝0) , when l>1,γ j (l-1 ) indicates that in the l-1th loop iteration, γ j The value of Γ=diag(γ1,γ2,…,γ (N+K) ), diag(γ1,γ2,…,γ (N+K) ) represents γ1,γ2,…,γ (N+K) is a diagonal matrix composed of diagonal elements. When l = 1 (σ 2 ) (l-1) Equal to (σ 2 ) (l＝0) , when l>1(σ 2 ) (l-1) represents the variance σ of Z in the l-1th loop iteration 2 The value of , the superscript "H" indicates the conjugate transpose operation of the matrix; During the l-th loop iteration, the posterior mean of W in the l-th loop iteration is calculated and recorded as Where I is the identity matrix; During the lth loop iteration, calculate γ in the lth loop iteration j ,j=1,2,…,N+K,denoted as in, express The row vector of the j-th row elements in B, when l = 1 (l-1) Equal to B (l＝0) , when l>1, B (l-1) represents the value of B in the l-1th loop iteration, (∑ w (l) ) j,j Represents ∑ w (l) The j-th row and j-th column element in ; During the lth loop iteration, calculate the value of B in the lth loop iteration, denoted as B (l) , in,"‖·‖ F " represents the F-norm operation of the matrix. is the introduced intermediate variable, η is a constant introduced to enhance the robustness of the TMSBL-LS algorithm, η>0; During the l-th loop iteration, calculate the variance σ of Z in the l-th loop iteration 2 The value of (σ 2 ) (l) , Among them, Tr[ ] means finding the trace of the matrix; Step 4.3: Determine whether l is greater than or equal to l max If yes, then end the loop iteration process and get j=1,2,…,N+K, then continue to execute step 4.4; otherwise, let l=l+1, then return to step 4.2 to continue execution, where "=" in l=l+1 is the assignment symbol; Step 4.4: From Find all values ​​greater than the preset threshold ε, then extract the indexes corresponding to all the found values, and record the set of all the extracted indexes in ascending order as Ω. The set of all indexes less than or equal to K in Ω is the set of indexes of all active users, realizing multi-user detection, where The corresponding indexes are 1, 2, ..., N + K; Step 4.5: Order Denotes the estimated value of W, let Indicated by The row index in Ω belongs to the submatrix consisting of all rows, make Indicated by The submatrix consists of all rows whose row indices belong to {1,2,…,N+K}\Ω, Among them, Φ Ω represents the submatrix consisting of all columns in Φ whose column indices belong to Ω, " " represents the pseudo-inverse operation of the matrix, "\" represents the complement operation; then and All rows in the array are sorted by row index. Step 4.6: According to and get and The accurate estimates of each enable channel and impulse noise estimation.

3. The joint multi-user detection, channel and impulse noise estimation method of the GF-NOMA system according to claim 2, characterized in that In step 4.1, γ j (l＝0) =0.001, B (l＝0) =I R ,(σ 2 ) (l＝0) =1, where I R Represents the identity matrix of dimension R×R.

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