A compressed sensing multi-user detection method based on cross-validation and gradient pursuit

Abstract

The application belongs to the technical field of wireless communication, and discloses a compressed sensing multi-user detection method based on cross-validation and gradient tracking. First, part of active users in a large-scale user send spread spectrum signals to a base station to perform uplink access transmission. Then, the base station receives the uplink signals of multiple users and models the uplink signals as block sparse vectors, and reconstructs a new uplink received signal equation by using the vectors. Then, the base station adopts a structure sparse adaptive matching pursuit algorithm based on cross-validation and gradient tracking to perform active user detection and reconstruct user transmission data. The application is suitable for a large-scale license-free uplink transmission system, and can realize joint and efficient detection of multiple active users and their uplink transmission data.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a compressed sensing multi-user detection method based on cross-validation and gradient tracking. Background Technology

[0002] Massive Machine Type Communication (mMTC), one of the three major application scenarios of 5G mobile networks, is characterized by a large number of access devices, small data packets, predominantly uplink communication, and sparse device activity. Given these characteristics, existing Orthogonal Multiple Access (OMA) technologies suffer from limitations in meeting the demands of large-scale connections, heavy signaling overhead, and significant latency. To address these issues, researchers have proposed unlicensed non-orthogonal multiple access (NOMA) systems. NOMA enables more users to be accommodated on the same resource, facilitating large-scale connections; while grant-free (GF) methods effectively reduce signaling overhead and transmission latency.

[0003] The use of unlicensed NOMA technology solves the problem of massive device access in mMTC scenarios, as well as the problems of signaling overhead and transmission latency. However, it increases the difficulty of detecting user activity and data at the receiver in the uplink. Because the uplink random access signal of users is sparse, it satisfies the basic condition that the original signal must be a sparse signal, which is required by the Compressive Sensing (CS) signal reconstruction algorithm. Therefore, the multi-user detection problem of unlicensed NOMA uplink transmission can be transformed into a sparse signal recovery problem and solved using the Compressive Sensing signal reconstruction algorithm. However, existing multi-user detection algorithms for unlicensed NOMA uplink transmission systems have drawbacks such as low detection performance, poor practicality, and high complexity, such as the Sparsity Adaptive Matching Pursuit (SAMP) algorithm. See the published literature [TTDo, L. Gan, N. Nguyen and TDTran, "Sparsity adaptive matching pursuit algorithm for practical compressed sensing," 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2008, pp. 581-587, doi:10.1109 / ACSSC.2008.5074472. While the Sparse Adaptive Matching Pursuit (SAMP) algorithm does not require known sparsity for recovering sparse signals, it suffers from problems such as low accuracy of the initial support set, difficulty in selecting the algorithm's iteration termination condition, and high computational complexity due to the use of least squares algorithm to estimate sparse signals. How to further improve the algorithm's detection performance and practicality while reducing its complexity, and provide a practical solution for the application of license-free NOMA technology in mMTC scenarios, remains a current challenge. Summary of the Invention

[0004] To address the problems existing in the background technology, this invention proposes a compressed sensing multi-user detection scheme based on cross-validation and gradient pursuit, applicable to large-scale unlicensed uplink transmission systems. This scheme first reorganizes a multi-slot sparse structure model into a block-structure sparse multi-user detection model through matrix operations, utilizing block sparse model CS technology to enhance the estimation of active users. Then, it employs a more practical structure sparse adaptive matching pursuit (CV-GP-SSAMP) algorithm based on cross-validation and gradient pursuit to perform active user detection and reconstruct user transmitted data, effectively improving the detection and reconstruction performance of active user uplink signals while also enhancing the algorithm's running speed and efficiency.

[0005] This invention provides a compressed sensing multi-user detection method based on cross-validation and gradient pursuit, for use in unlicensed NOMA uplink transmission systems in mMTC scenarios. The detection method includes the following steps:

[0006] Step S1: Some active users in the large-scale user base send spread spectrum signals to the base station, and the users and the base station work together to complete the uplink access transmission. It should be noted that the spread spectrum signal specifically refers to the sequence generated by multiplying or XORing the user's original data sequence and the user's unique extended sequence, i.e., the spread spectrum code, also known as the signature code, bit by bit.

[0007] Step S2: The base station receives uplink signals from multiple users, i.e., uplink received signal matrix Y. The uplink signal includes the user's transmitted data matrix X and additive noise matrix V. The transmitted data matrix X is modeled as a row sparse matrix, and the user's transmitted data matrix X is reconstructed into a block sparse vector c∈C through row stacking. KJ×1 A new observation matrix P is constructed by processing the observation matrix G using a diagonal matrix. The uplink received signal matrix Y and the additive noise matrix V are stacked to obtain NJ×1 vectors b and w. The new uplink received signal vector b is reconstructed using block sparse vectors.

[0008] Step S3: Based on the reconstructed new uplink received signal vector b, an active user detection and reconstruction of user transmitted data, i.e., the estimated value of the user's transmitted signal, is performed using a structured sparse adaptive matching pursuit method based on cross-validation and gradient tracking.

[0009] The structure-sparse adaptive matching tracking method based on cross-validation and gradient tracking includes the following steps:

[0010] Step S31: Using ideal channel estimation, input the uplink received signal vector b∈C. NJ×1 Observation matrix P∈C NJ×KJ And the noise vector w, which is used to split the data into training and validation data, the top N t The training data consists of N elements, with the remaining length being N. cv =NJ-N t The data is used as verification data;

[0011] Step S32, initialize parameter settings, specifically, set the initial iteration count n = 0, and the initial active user search step size step. (0) =0, Initial active user support set Initial user sends signal Initial residual signal r (0) =b t Initial cross-validation residual ε (0) =b cv ;

[0012] Step S33, let n = 1, and set the current active user search step size step. (n) =1, using the generalized Jaccard coefficients to calculate the observation matrix training set P t Each column vector The residual signal of the (n-1)th iteration correlation coefficient Let set The correlation coefficient set μ (n) Group the elements in the middle according to k in ascending order, with J elements in each group, and find the group with the largest sum. (n) By examining the user indexes corresponding to each group, we can obtain the initial support set Ψ of active users in the current iteration. (n) The current iteration's active user base will initially support the set Ψ (n) Compared with the final active user support set Γ of the previous iteration (n-1) Merge to obtain the active user candidate support set Λ for the current iteration. (n) ;

[0013] Step S34: Reconstruct the data vector of active users detected in the current iteration based on the LS criterion. By retracing our thinking, we can reconstruct signals. Select the step with the highest energy. (n) By analyzing the user indexes corresponding to each data block, the final active user support set Γ for the current iteration can be obtained. (n) ;

[0014] Step S35: Use a gradient pursuit algorithm based on the steepest descent method to estimate the user's transmitted signal as the reconstructed signal. And calculate the residual signal r of the nth iteration. (n) ;

[0015] Step S36: Validate set P using the observation matrix. cv Received signal verification set b cv and the reconstructed signal Calculate the residual energy of the current iteration of cross-validation ||ε (n) ||2:

[0016] Step S37, compare the cross-validation residual energy ||ε of the current iteration (n) ||2 Cross-validation residual energy with the previous iteration||ε (n-1) ||2 is used to determine whether the current iteration has stopped.

[0017] Step S38, let the output signal vector For vectors Performing reverse stack operations on vectors Arrange each J element into a column to form a matrix and transpose it to obtain an estimate of the original transmitted signal X. Output reconstructed transmission signal The active user index set, i.e., the support set Γ = Γ (n-1) .

[0018] Furthermore, in step S33, the correlation coefficient As shown in equation (11):

[0019]

[0020] Where |·| represents the modulus of the calculated element; the formula for calculating the generalized Jaccard coefficient is shown in equation (12):

[0021]

[0022] Where d and e are two arbitrary m-dimensional vectors.

[0023] The initial support set Ψ of active users in the current iteration (n) As shown in equation (13):

[0024]

[0025] Among them, the function argmax(·,step) (n) ) indicates retrieving step from a set. (n) The index of the largest element;

[0026] The active user candidate support set Λ in the current iteration (n) As shown in equation (14):

[0027] Λ (n) =Ψ (n) ∪Γ (n-1) (14)

[0028] Furthermore, in step S34, the data vector of the active user As shown in equation (15):

[0029]

[0030] in, Training set of observation matrices representing active users The pseudo-inverse matrix;

[0031] The final active user support set Γ of the current iteration (n) As shown in equation (16):

[0032]

[0033] in, Indicates the reconstructed signal The vector corresponding to the (k-1)J to kJ elements corresponds to the data block of user k; ||·||2 represents the 2 norm of the vector, i.e., the energy of the vector.

[0034] Furthermore, in step S35, the gradient pursuit algorithm based on the steepest descent method is used to estimate the user-sent signal. Specifically, it depends on the search direction of the current iteration. and search step size a (n) Estimate the signal sent by the user

[0035]

[0036] The search direction of the current iteration for:

[0037]

[0038] in, Training set of observation matrices representing active users The transpose matrix, r (n-1) This represents the residual signal of the (n-1)th iteration.

[0039] The search step size a in the current iteration (n) for:

[0040]

[0041] in, This represents the square of the 2-norm of a vector;

[0042] The final active user support set Γ obtained using equation (16) (n) Delete reconstructed signal Interference information in the data, even if it does not belong to the final active user support set. (n) The user reconstruction signal is zero, as shown in equation (20):

[0043]

[0044] in, Indicates the reconstructed signal The vector corresponding to the (k-1)J to kJ elements; {1,2,…,K} (n) This indicates that the user does not belong to the final active user support set. (n) The user index set;

[0045] Update the reconstructed signal according to equation (20). The residual signal r of the current iteration is calculated according to equation (21).(n) :

[0046]

[0047] Furthermore, in step S36, the current iteration cross-validation residual energy ||ε (n) The calculation of ||2 is shown in equation (22):

[0048]

[0049] Furthermore, in step S37, the specific condition for determining whether the current iteration should stop is as follows:

[0050] If the cross-validation residual energy of the current iteration is ||ε (n) ||2 is less than the cross-validation residual energy of the previous iteration||ε (n-1) ||2, Determine the active user search step size for the next iteration according to equation (23). (n+1) :

[0051] step (n+1) =step (n) +1 (23)

[0052] The iteration count n = n + 1, return to step 3, and perform the next iteration check;

[0053] If the cross-validation residual energy of the current iteration is ||ε (n) ||2 is greater than the cross-validation residual energy of the previous iteration||ε (n-1) If ||2, then the iteration terminates, and the estimated number of active users in the system, i.e., the sparsity S, is obtained. The expression for is shown in equation (24):

[0054]

[0055] Furthermore, in step S38, the estimated value of the original transmitted signal X...

[0056]

[0057] The beneficial effects of this invention are as follows: This invention fully utilizes the block sparse signal model to improve the performance of multi-user signal detection and reconstruction based on compressed sensing (CS). While inheriting the backtracking idea and sparsity adaptive strategy of the traditional adaptive matching pursuit (SAMP) algorithm, it integrates three optimization strategies: generalized Jaccard coefficients, cross-validation method, and gradient pursuit method based on steepest descent. The generalized Jaccard coefficients are used to select atoms that better match the residual vector, thus optimizing the selection of the initial support set. The cross-validation method is used to accurately estimate the number of active users, solving the overestimation and underestimation problems of the SAMP algorithm, and automatically obtaining the iteration termination condition of the algorithm without needing prior information such as noise power or signal-to-noise ratio, thus improving the practicality of the algorithm. The gradient pursuit method based on steepest descent is used to estimate the user's transmitted signal, avoiding the complex operation of matrix inversion, ensuring accurate and stable signal reconstruction performance with low computational cost, and providing a practical solution for the application of license-free NOMA technology in mMTC scenarios. Attached Figure Description

[0058] Figure 1 This is a system model diagram in an example of the present invention;

[0059] Figure 2 This is the large-scale unlicensed uplink multiple access transmission process in an example of the present invention;

[0060] Figure 3 This is the CV-GP-SSAMP algorithm flow in the example of this invention;

[0061] Figure 4 These are simulation results from examples of this invention. Detailed Implementation

[0062] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0063] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. It should be understood that the term “and / or” as used herein includes any and all combinations of one or more of the associated listed items.

[0064] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0065] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific examples.

[0066] Example

[0067] like Figure 1 The diagram illustrates a sparse MMTC scenario provided by an embodiment of the present invention. This is a typical scenario for a large-scale unlicensed uplink multiple access transmission system, consisting of one base station and K users, each equipped with a single antenna. Users are categorized as active and inactive. Active users are currently transmitting signals to the base station, while inactive users are not transmitting signals. The probability of an individual user being active is very small, indicating that although the total number of users is very large, only a small portion of users are active at any given time. The data transmitted by active users is channel-coded and modulated, then spread using a spreading sequence of length N. Active users transmit uplink data in time frames, each containing J time slots, and the user's active state remains unchanged within a frame. Considering that the uplink data frames of inactive users are equivalent to all-zero frames, the uplink transmission signals of multiple users exhibit frame sparsity characteristics.

[0068] Combination Figure 1 System model, Figure 2 Large-scale unlicensed uplink multiple access transmission process and Figure 3 The specific implementation steps of the CV-GP-SSAMP algorithm in this embodiment are described in detail below:

[0069] The parameters for this embodiment are set as follows: total number of users K = 200, number of active users (sparseness) S = 20, spread spectrum sequence length N = 100; the uplink signal modulation method for users is QPSK, and both the base station and users are configured with a single antenna; the uplink data frame contains 7 time slots, each time slot transmits one data symbol, that is, one frame of data for each user contains 7 data symbols. In the CV-GP-SSAMP algorithm, the length of the training data used to recover the sparse signal is 450, and the length of the validation data used for cross-validation is 250.

[0070] Step 1: In a large-scale unlicensed uplink multiple access transmission system, some active users among the large-scale users send spread spectrum signals to the base station to perform uplink access transmission.

[0071] Step 2: The base station receives uplink signals from multiple users and models them as a block sparse vector, then uses this vector to reconstruct a new uplink received signal equation.

[0072] The specific process of block sparse vector modeling for the received signal is as follows:

[0073] Step 2-1: Model the uplink signal received by the base station as a row sparse matrix;

[0074] Active users transmit uplink data using time frames, with each frame carrying J data symbols, and each symbol corresponding to a transmission time slot. The base station receives the uplink signal y in the j-th time slot. (j) It can be represented as:

[0075]

[0076] Where Φ=[s1,s2,...,s K ]∈C N×K Denotes the spread spectrum sequence matrix, s k ∈C N×1 Let h = [h1, h2, ..., h2] be the spread spectrum sequence for user k. K ] T ∈C K×1 h represents the channel coefficient vector. k Let h represent the channel attenuation coefficient from user k to the base station. It follows a complex Gaussian distribution with mean 0 and variance 1, i.e., h ~ CN(0,1). This represents the data vector transmitted by K users in time slot j. Let X represent the data symbols transmitted by user k in time slot j, and let X represent the complex constellation set of the modulated signal. Inactive users transmit zero data symbols. (j) This represents the additive noise in the channel at the j-th time slot, which follows a mean of 0 and a variance of . The complex Gaussian distribution, i.e.

[0077] A frame of signal Y = [y] received by the base station (1) ,y (2) ,...,y (J) ]∈C N×J It can be represented as:

[0078] Y = GX + V (2)

[0079] Where G=Φ·diag(h)∈C N×K Represents the observation matrix; X = [x (1) ,x (2) ,...,x (J) ]∈C K×J Represents the user's transmitted data matrix; V = [v (1) ,v(2) ,...v (J) ]∈C N×J This represents the additive noise matrix of the channel.

[0080] Since the uplink data frames of inactive users are equivalent to all-zero frames, and the number of active users is much smaller than the total number of users, the data symbol matrix X has row sparsity characteristics.

[0081] Since the user's active state remains unchanged within each frame, the set of active user indices Γ in each frame can be represented as:

[0082] Γ = supp(x (1) ) = supp(x (2) ) = ... = supp(x (j) ) = ... = supp(x (J) (3)

[0083] Among them, supp(x (j) Let Γ represent the set of active user indices in time slot j, also known as the support set of time slot j, where j = 1, 2, ..., J. The 0 norm of Γ is ||Γ||0, which represents the number of active users in a frame, i.e., the sparsity S.

[0084] Step 2-2 reconstructs the received signal matrix of the base station into a block sparse vector;

[0085] The sparse signal matrix X is reconstructed into a block sparse vector using a row stack, as follows:

[0086] The user's sent data matrix X = [x (1) ,x (2) ,...,x (J) Expand as shown in equation (4):

[0087]

[0088] Arrange each row of matrix X sequentially to form a long row vector, and transpose this row vector to obtain the block sparse signal vector c∈C as shown in equation (5). KJ×1 :

[0089]

[0090] in, This represents the data transmitted by user k in time slot j; vec(·) represents the matrix column vectorization function, i.e., the stack function. Vector c consists of K blocks, each block vector has J elements, and the J elements in the k-th block are all zero or non-zero. This represents all data sent by all K users in J time slots. This corresponds to all data sent by the k-th user in the J-th time slot.

[0091] Similarly, stacking the uplink received signal matrix Y and the additive noise matrix V yields NJ×1 dimensional vectors b and w. Vectors b and w are expressed as follows:

[0092] b = vec(Y) T (6)

[0093] w = vec(V T (7)

[0094] Where vec(·) represents the matrix column vectorization function.

[0095] Furthermore, the method for establishing the new uplink received signal equation in step two is as follows:

[0096] A new observation matrix P is constructed using the original observation matrix G, that is, using the element g in the i-th row and j-th column of matrix G. i,j With J×J diagonal matrix I J Replace the element g in the i-th row and j-th column of G with the product of g and g. i,j Generate a new observation matrix P∈C NJ×KJ The new observation matrix P is represented as:

[0097]

[0098] Therefore, the uplink received signal equation described in equation (2) can be rewritten as a new uplink received signal equation:

[0099] b = Pc + w (9)

[0100] Step 3: The base station uses the Structured Sparse Adaptive Matching Pursuit (CV-GP-SSAMP) algorithm based on cross-validation and gradient pursuit to perform active user detection and reconstruct user transmitted data.

[0101] The Structured Sparse Adaptive Matching Pursuit (CV-GP-SSAMP) algorithm based on cross-validation and gradient tracking is as follows:

[0102] Assuming prior knowledge of the channel, the uplink received signal vector b∈C after stacking is... NJ×1 and the new observation matrix P∈C NJ ×KJ User data reconstructed by the base station as input parameters As output.

[0103] Let the sparsity of active users be S; let the search step size for active users in the nth iteration be step. (n) The initial support set and candidate support set of active users in the nth iteration are Ψ (n) and Λ (n)The active user index set, i.e., the support set, in the nth iteration is Γ. (n) The residual signal and cross-validation residual of the nth iteration are r and r, respectively. (n) and ε (n) Based on the above variable definitions, the specific steps for recovering the data signal X from the received signal vector b are described below:

[0104] Step 3-1: Select training and validation data;

[0105] Select the first N of the recombined received signal vector b t The elements constitute a vector. The remaining data, of length N, will be used as training data. cv =NJ-N t vector As verification data; correspondingly, the observation matrix P is divided into and Two sub-matrices; the noise vector w is divided into and As shown in equation (10):

[0106]

[0107] Where, N t +N cv =NJ; Execute step 3-2.

[0108] Step 3-2: Initialize algorithm parameters;

[0109] Initial iteration count n = 0; initial active user search step size step (0) =0; Initial active user support set Initial user sends signal Initial residual signal r (0) =b t Initial cross-validation residual ε (0) =b cv .

[0110] Let n = 1, and let step be the search step size of the active user in the current iteration. (n) =1; Execute step 3-3.

[0111] Step 3-3: Obtain the initial support set Ψ of active users in the current iteration (n) and candidate support set Λ (n) ;

[0112] The observation matrix training set P is calculated using the generalized Jaccard coefficients. t Each column vector The residual signal of the (n-1)th iteration correlation coefficient As shown in equation (11):

[0113]

[0114] Where |·| represents the modulus of the calculated element; the formula for calculating the generalized Jaccard coefficient is shown in equation (12):

[0115]

[0116] Where d and e are two arbitrary m-dimensional vectors.

[0117] Let set The correlation coefficient set μ (n) Group the elements in the middle according to k in ascending order, with J elements in each group, and find the group with the largest sum. (n) By examining the user indexes corresponding to each group, we can obtain the initial support set Ψ of active users in the current iteration. (n) As shown in equation (13):

[0118]

[0119] Among them, the function argmax(·,step) (n) ) indicates retrieving step from a set. (n) The index of the largest element. It should be noted that the set μ... (n) The i-th element of [i] corresponds to the i-th element. One user, symbol This indicates that the integer part is taken.

[0120] The initial support set Ψ for active users in the current iteration (n) Compared with the final active user support set Γ of the previous iteration (n-1) Merge to obtain the active user candidate support set Λ for the current iteration. (n) :

[0121] Λ (n) =Ψ (n) ∪Γ (n-1) (14)

[0122] Perform steps 3-4.

[0123] Steps 3-4: Obtain the final active user support set Γ for the current iteration (n) ;

[0124] Reconstruct the data vector of active users detected in the current iteration based on the LS criterion.

[0125]

[0126] in, Training set of observation matrices representing active users The pseudo-inverse matrix.

[0127] By retracing our thinking, we can reconstruct signals. Select the step with the highest energy. (n) By analyzing the user indexes corresponding to each data block, the final active user support set Γ for the current iteration can be obtained. (n) As shown in equation (16):

[0128]

[0129] in, Indicates the reconstructed signal The vector corresponding to the (k-1)J to kJ elements corresponds to the data block of user k; ||·||2 represents the 2 norm of the vector, which is used to calculate the energy of the vector.

[0130] Perform steps 3-5.

[0131] Steps 3-5: Estimate the user's transmitted signal Calculate the residual signal r of the nth iteration (n) ;

[0132] A gradient pursuit algorithm based on the steepest descent method is used to estimate the user's transmitted signal. Current search direction for:

[0133]

[0134] in, Training set of observation matrices representing active users The transpose matrix, r (n-1) This represents the residual signal of the (n-1)th iteration.

[0135] The search step size a in the current iteration (n) for:

[0136]

[0137] in, It represents the square of the 2-norm of a vector.

[0138] Based on the current search direction and search step size a (n) Estimate the signal sent by the user

[0139]

[0140] The active user support set Γ obtained using equation (16)(n) Delete reconstructed signal Interference information in the data, even if it does not belong to the final active user support set. (n) The user reconstruction signal is zero, as shown in equation (20):

[0141]

[0142] in, Indicates the reconstructed signal The vector corresponding to the (k-1)J to kJ elements; {1,2,…,K} (n) This indicates that the user does not belong to the final active user support set. (n) The user index set.

[0143] Update the reconstructed signal according to equation (20). The residual signal r of the current iteration is calculated according to equation (21). (n) :

[0144]

[0145] Perform steps 3-6.

[0146] Steps 3-6: Calculate the cross-validation residual energy ||ε of the current iteration. (n) ||2;

[0147] Using the observation matrix to validate the set P cv Received signal verification set b cv and the reconstructed signal estimated in steps 3-5 Perform the cross-validation residual energy ||ε of the current iteration (n) The calculation of ||2 is shown in equation (22):

[0148]

[0149] Perform steps 3-7.

[0150] Step 3-7: Determine whether the iteration stopping condition is met;

[0151] Compare the cross-validation residual energy of the current iteration ||ε (n) ||2 Cross-validation residual energy with the previous iteration

[0152] Quantity || ε (n-1) ||2 is used to determine whether the current iteration has stopped;

[0153] 1) If ||ε (n) ||2<||ε (n-1) ||2, which is the cross-validation residual energy of the current iteration||ε (n)||2 is less than the cross-validation residual energy of the previous iteration||ε (n-1) ||2, Determine the active user search step size for the next iteration according to equation (23). (n+1) :

[0154] step (n+1) =step (n) +1 (23)

[0155] The iteration count n = n + 1, return to step 3-3, and perform the next iteration check;

[0156] 2) If ||ε (n) ||2>||ε (n-1) ||2, which is the cross-validation residual energy of the current iteration||ε (n) ||2 is greater than the cross-validation residual energy of the previous iteration||ε (n-1) ||2, terminate the algorithm iteration, the number of active users in the system is the estimated value of sparsity. The expression for is shown in equation (24):

[0157]

[0158] Perform steps 3-8.

[0159] Steps 3-8: Output the reconstructed user-sent signal and end the algorithm;

[0160] Let the output signal vector For vectors Perform the reverse stack operation, that is, the vector Arrange each J element into a column to form a matrix and transpose it, as shown in equation (25), to obtain the estimated value of the original transmitted signal X.

[0161]

[0162] Output reconstructed transmission signal The active user index set, i.e., the support set Γ = Γ (n-1) .

[0163] Based on the same scenario and parameter settings, simulations were performed using MATLAB software, and the performance of this scheme (CV-GP-SSAMP) was compared with that of four other existing CS-MUD schemes. The results are as follows: Figure 4 As shown, under different SNRs, although the bit error rate of the CV-GP-SSAMP algorithm in this scheme is still far from that of the ideal Oracle LS algorithm, its bit error rate is significantly lower than that of the SP-MUD, SAMP-MUD, and DCS-MUD algorithms.

[0164] For specific SP-MUD schemes, please refer to the published literature Wei Dai and Olgica Milenkovic. Subspacepursuit for compressive sensing signal reconstruction. [J]. IEEE Trans. Information Theory, 2009, 55(5): 2230-2249.

[0165] For a detailed scheme of SAMP-MUD, please refer to the published paper TTDo, L. Gan, N. Nguyen and TDTran, "Sparsity adaptive matching pursuit algorithm for practical compressed sensing," 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, 2008, pp. 581-587, doi:10.1109 / ACSSC.2008.5074472.

[0166] For the specific scheme of DCS-MUD, please refer to the public documents Electronics-Electronics and Communications; Researchers at Tsinghua University Report New Data on Electronics and Communications (Dynamic Compressive Sensing-Based Multi-User Detection for Uplink Grant-Free NOMA) [J]. Electronics Newsweekly, 2016.

[0167] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the processes depicted in the drawings are not necessarily essential for implementing the present invention.

[0168] As can be seen from the above description of the embodiments, those skilled in the art can clearly understand that the present invention can be implemented by means of software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0169] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A compressive sensing multi-user detection method based on cross-validation and gradient pursuit, characterized in that, The detection method includes the following steps: Step S1: Some active users among the large-scale users send spread spectrum signals to the base station, and the users and the base station work together to complete the uplink access transmission. Step S2, the base station receives the uplink signals of multiple users, i.e., an uplink received signal matrix Y, the uplink signals including original sending signals X of the users and an additive noise matrix V, the original sending signals X being modeled as a row sparse matrix and reconstructed into a block sparse vector through row stacking , a new observation matrix P is constructed by processing the observation matrix G with a diagonal matrix, and a stacking operation is performed on the uplink received signal matrix Y and the additive noise matrix V to obtain a K-dimensional vector and ; Reconstructing a new uplink received signal vector using block sparse vectors Equation; Step S3, based on vector A structured sparse adaptive matching pursuit method based on cross-validation and gradient pursuit is used to perform active user detection and reconstruct user transmitted data, i.e., the estimated value of the user's transmitted signal. The structure-sparse adaptive matching pursuit method based on cross-validation and gradient tracking includes the following steps: Step S31, using ideal channel estimation, input vector Observation matrix and noise vector For vectors The data is divided into training and validation data. The remaining length is [number] elements constitute the training data. The data is used as verification data; Step S32, set the initial number of iterations. Initial active user search step size Initial active user support set Initial user sends signal Initial residual signal Initial cross-validation residuals ; Step S33, let Current iteration active user search step size The observation matrix training set is calculated using generalized Jaccard coefficients. Each column vector The residual signal of the (n-1)th iteration correlation coefficient Let the set of correlation coefficients ; Set the correlation coefficients Group the elements in the middle according to k in ascending order, with J elements in each group, and find the group with the largest sum. By examining the user indexes corresponding to each group, we can obtain the initial support set of active users for the current iteration. The initial support set of active users in the current iteration Compared with the final active user support set of the previous iteration Merge to obtain the active user candidate support set for the current iteration. ; Step S34: Reconstruct the data vector of active users detected in the current iteration based on the LS criterion. By retracing the thought process, we can reconstruct the signal. Select the one with the highest energy By analyzing the user indexes corresponding to each data block, the final active user support set for the current iteration can be obtained. ; Step S35: Use a gradient pursuit algorithm based on the steepest descent method to estimate the user's transmitted signal as the reconstructed signal. And calculate the residual signal of the nth iteration. ; Step S36: Validate the set using the observation matrix. Received signal verification set and the reconstructed signal Calculate the residual energy of the current iteration of cross-validation. ; Step S37, compare the cross-validation residual energy of the current iteration. Cross-validation residual energy compared to the previous iteration To determine whether the current iteration has stopped; Step S38, let the output signal vector For vectors Performing reverse stack operations on vectors each The elements are arranged in a column to form a matrix, and then transposed to obtain the original transmitted signal. The estimated value Output reconstructed transmission signal The active user index set is the support set. .

2. The compressed sensing multi-user detection method based on cross-validation and gradient pursuit as described in claim 1, characterized in that, In step S33, the correlation coefficient As shown in equation (11): （11） in, This indicates the calculation of the element modulus; the formula for calculating the generalized Jaccard coefficient is shown in equation (12): （12） Where d and e are two arbitrary m-dimensional vectors; The initial support set of active users in the current iteration As shown in equation (13): （13） Among them, the function This means retrieving a certain set. The index of the largest element; The active user candidate support set in the current iteration As shown in equation (14): （14）。 3. The compressed sensing multi-user detection method based on cross-validation and gradient pursuit as described in claim 2, characterized in that, In step S34, the data vector of the active user As shown in equation (15): （15） in, Training set of observation matrices representing active users The pseudo-inverse matrix; The final active user support set of the current iteration As shown in equation (16): （16） in, Indicates the reconstructed signal The to The vector corresponding to each element corresponds to the data block of user k; The 2-norm of a vector is used to calculate the energy of the vector.

4. The compressed sensing multi-user detection method based on cross-validation and gradient pursuit as described in claim 3, characterized in that, In step S35, the gradient pursuit algorithm based on the steepest descent method is used to estimate the user-sent signal. Specifically, it depends on the search direction of the current iteration. and search step size Estimate the signal sent by the user : （19） The search direction of the current iteration for: （17） in, Training set of observation matrices representing active users The transpose of the matrix, This represents the residual signal of the (n-1)th iteration; Search step size in the current iteration for: （18） in, This represents the square of the 2-norm of a vector; The final active user support set obtained using equation (16) Delete reconstructed signal Interference information, even if it does not belong to the final active user support set The user reconstruction signal is zero, as shown in equation (20): （20） in, Indicates the reconstructed signal The to The vector corresponding to each element; This indicates that the user does not belong to the final active user support set. The user index set; Update the reconstructed signal according to equation (20). ; Calculate the residual signal of the current iteration according to equation (21) : （21）。 5. The compressed sensing multi-user detection method based on cross-validation and gradient tracking as described in claim 4, characterized in that, In step S36, the residual energy of the current iteration cross-validation The calculation is shown in equation (22): （22）。 6. The compressed sensing multi-user detection method based on cross-validation and gradient pursuit as described in claim 5, characterized in that, In step S37, the specific condition for determining whether the current iteration should stop is as follows: If the cross-validation residual energy of the current iteration Less than the cross-validation residual energy of the previous iteration The active user search step size for the next iteration is determined according to equation (23). : （23） Number of iterations Return to step 3 and perform the next iteration of detection; If the cross-validation residual energy of the current iteration Greater than the cross-validation residual energy of the previous iteration The iteration terminates when the number of active users in the system, i.e., the estimated sparsity S, is reached. The expression for is shown in equation (24): （24）。 7. The compressed sensing multi-user detection method based on cross-validation and gradient tracking as described in claim 5, characterized in that, In step S38, the original transmitted signal The estimated value : （25）。

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