A method suitable for near-field spherical wave ultra-large-scale MIMO uplink signal detection

Abstract

The application relates to the field of wireless communication, in particular to a near-field spherical wave ultra-large-scale MIMO uplink signal detection method. In a near-field spherical wave model system, the uplink signal detection specifically comprises the following steps: dividing a receiving antenna array into C non-intersecting subarrays, taking each array as a factor node and the sending signal of each user as a variable node to construct a factor graph model; according to the factor graph model, the approximate posterior distribution of the sending signal of a user on a subarray is calculated; based on a sorting interference cancellation algorithm, the receiving signal and the channel matrix of each subarray are iteratively updated to complete signal detection. In a multi-user near-field scene, the application can obtain better performance, and in the face of a scene where multiple users arrive at the same angle but have different distances to the array center, the application can still maintain relatively optimal detection performance.

Description

Technical Field

[0001] This invention relates to the field of wireless communication, and in particular to a method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO. Background Technology

[0002] With the continuous development of mobile communication technology, the fifth-generation mobile communication system (5G) has been deployed and applied globally. 5G features low latency, high speed, and high reliability. However, its current performance falls short of ideal specifications. Therefore, researchers have begun research on the sixth-generation mobile communication system (6G).

[0003] Extremely large-scale MIMO (XL-MIMO) can improve data detection rate by leveraging spatial multiplexing gain and enhance detection reliability through spatial diversity gain, enabling the system to serve multiple users simultaneously on the same time and frequency resources. It is considered one of the key technologies for 6G wireless communication. XL-MIMO channels exhibit new characteristics such as spatial non-stationarity and near-field properties. The spatial non-stationarity of the channel indicates that different regions of the array receive signals from different paths with varying power; this difference is referred to as varying "visibility." Existing literature has studied signal detection adapted to non-stationarity using molecular arrays. Because XL-MIMO systems use hundreds or even thousands of antennas to increase the channel size, the Rayleigh distance increases, placing users in the near-field region. This results in a non-negligible difference in the angle of incidence from the user to each antenna element; therefore, channel modeling needs to consider a more general spherical wavefront model.

[0004] In channel modeling using both planar and spherical wavefront assumptions, distance and angle parameters play crucial roles, but some differences remain. In systems modeled using planar wavefronts, the distance parameter only affects the amplitude value. When multiple users are at the same angle but different distances, a high correlation exists between the channels. This means that the channel characteristics of different users are similar, increasing the difficulty of signal detection and impacting system performance. In contrast, in systems modeled using spherical wavefronts, the distance parameter affects both amplitude and phase values. When multiple users are at the same angle but different distances, the channel correlation coefficient decreases as the distance difference between users increases. Therefore, this characteristic can be used to solve the signal detection problem in densely populated scenarios and improve detection performance. However, it is also evident that the channel correlation coefficient remains relatively high in densely populated scenarios, especially when users are at the same angle but have small distance differences. To address the problem of poor signal detection performance caused by high correlation coefficients in densely populated scenarios, a suitable signal detection algorithm is needed to improve detection performance. Summary of the Invention

[0005] To address the signal detection problem in densely populated user scenarios, this invention proposes an uplink signal detection method suitable for near-field spherical wave ultra-large-scale MIMO. In a spherical wave model system, for densely populated user communication scenarios, the uplink signal detection specifically includes the following steps:

[0006] The receiving antenna array is divided into C disjoint subarrays, and a factor graph model is constructed with each array as a factor node and each user's transmitted signal as a variable node.

[0007] Based on the factor graph model, the approximate posterior distribution of the signal transmitted by a user on a subarray is calculated.

[0008] Based on the sorting interference cancellation algorithm, the received signals and channel matrices of each subarray are iteratively updated to complete signal detection.

[0009] Furthermore, in the factor graph model, the process of information transfer between factor nodes and variable nodes is represented as follows:

[0010]

[0011] in, The symbol x sent by the j-th user j The corresponding variable node to the c-th subarray f c The information transmitted by the corresponding factor nodes; The symbol x sent by the j'th user j' The corresponding variable node to the c-th subarray f c The information transmitted by the corresponding factor node is j'∈{1,2,...,K}\j, where K is the number of users; This represents the symbol x sent by the j-th user from the variable node f0 corresponding to the prior information. j The message of the corresponding variable node; It represents the c-th subarray f c The corresponding factor node to the symbol x sent by the j-th user j The information passed by the corresponding variable node; This indicates that the c′-th subarray f c′ The corresponding factor node to the symbol x sent by the j-th user j The information passed by the corresponding variable node is c′∈{1,2,...,C}\c, where {1,2,...,C}\c represents the set of {1,2,...,C} excluding c; x\x j This represents the set of symbols x sent by all users, excluding the symbol x sent by the j-th user. j The combination of symbols; f c (xj ) represents user x in the probabilistic model j The marginal likelihood function.

[0012] Furthermore, the approximate posterior distribution of the j-th detected symbol in the c-th subarray. Represented as:

[0013] Where, b(x) j ) represents the true posterior distribution of the j-th detected symbol; This represents an exponential family distribution; KL[A‖B] is the KL divergence operation, used to characterize the degree of deviation between distributions A and B; The symbol x sent by the j-th user j The corresponding variable node to the c-th subarray f c The information transmitted by the corresponding factor nodes; It represents the c-th subarray f c The corresponding factor node to the symbol x sent by the j-th user j The information passed by the corresponding variable node.

[0014] Furthermore, the approximate posterior distribution b of all detected symbols in the c-th subarray fc The mean and variance of (x) are expressed as:

[0015]

[0016] Where, μ c This represents the approximate posterior distribution of all detected symbols received by the c-th subarray. The mean; Σ c This represents the approximate posterior distribution of all detected symbols in the c-th subarray. The variance; σ represents the noise variance; H represents the channel matrix of the c-th subarray. c The transpose of y; c τ represents the received signal of the c-th subarray; c γ represents the reciprocal of the prior variance of all detected symbols received by the c-th subarray. c Let represent the prior mean of all detected symbols received by the c-th subarray.

[0017] Furthermore, based on the sorting interference cancellation algorithm, the inter-user interference is eliminated by iteratively updating the received signals and channel matrices of each subarray, including the following steps:

[0018] 101. Initialize the iteration count to l = 0, and calculate the approximate posterior distribution b of all detected symbols in the c-th subarray. fc The mean and variance of (x);

[0019] 102. Let l = l + 1, calculate the interference-to-signal ratio (ISR) of each user in each subarray during the l-th iteration, and arrange the user detection order in each subarray according to the ascending sequence of these values ​​to obtain the detection order of the c-th subarray. And let i = 1;

[0020] 103. Select the detection order The i-th user is taken as the user to be estimated, and the received signal of the c-th subarray and the channel matrix of the c-th subarray are reconstructed using the mean of the approximate posterior distribution of all detected symbols of the i-th user in the c-th subarray.

[0021] 104. Determine if i+1 is greater than K. If it is, proceed to step 105; otherwise, set i = i+1 and return to step 103.

[0022] 105. Determine whether the number of iterations l has reached the set maximum number of iterations or whether the algorithm has converged. If so, end the process; otherwise, wait for the central processing unit to return data and repeat steps 102 to 104.

[0023] Furthermore, the reconstruction of the received signal of the c-th subarray and the channel matrix of the c-th subarray using the mean of the approximate posterior distribution of all detected symbols of the i-th user in the c-th subarray includes:

[0024]

[0025] in, This indicates that the signal of the i-th user in the detection sequence has been calculated. The received signal of the c-th subarray obtained after reconstruction has the same value as the received signal of the c-th subarray when i=1, that is... This represents the detection order in the channel matrix of the c-th subarray during the i-th iteration. The element corresponding to the i-th user; This represents the detection order in the c-th subarray during the i-th iteration. The mean of the approximate posterior distribution corresponding to the i-th user.

[0026] Furthermore, the calculation of the interference-to-signal ratio for each user in each subarray includes:

[0027]

[0028] Among them, JSR c,k h represents the interference-to-signal ratio of the k-th user in the c-th subarray; c,i Let |||||| represent the i-th column of the channel matrix of the c-th subarray, ||·|| represent the Euclidean norm, and K represent the number of users.

[0029] This invention considers a base station equipped with a very large-scale array serving multiple single-antenna users, and incorporates a spherical wavefront channel modeling method, thereby introducing a distance parameter. On one hand, this invention utilizes the channel characteristics derived from the distance parameter to divide the channel into multiple sub-arrays and construct a factor map. On the other hand, it combines and adjusts a continuous interference cancellation algorithm with an expectation propagation algorithm, iteratively solving to obtain the final detected symbols for demodulation. This invention achieves better performance in multi-user near-field scenarios, and maintains superior detection performance even when multiple users arrive at the array center at the same angle but at different distances. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of a multi-user near-field scenario according to the present invention;

[0031] Figure 2 This is a schematic diagram of the factor graph model of the present invention;

[0032] Figure 3 This is a schematic diagram of the process for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO according to the present invention;

[0033] Figure 4 This is a simulation diagram showing the performance of signal detection using bit error rate as an indicator in this invention. Detailed Implementation

[0034] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0035] In spherical wave model systems, when users are densely packed in the communication scenario, especially when users are at similar angles and distances, channel correlation is high, meaning the similarity between channels is high. To address this scenario, this invention proposes a method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO, such as... Figure 3 Specifically, it includes the following steps:

[0036] The receiving antenna array is divided into C disjoint subarrays, and a factor graph model is constructed with each array as a factor node and each user's transmitted signal as a variable node.

[0037] Based on the factor graph model, the approximate posterior distribution of the signal transmitted by a user on a subarray is calculated.

[0038] Based on the sorting interference cancellation algorithm, the received signals and channel matrices of each subarray are iteratively updated to complete signal detection.

[0039] like Figure 1 As shown, this embodiment considers K single-antenna users as the transmitting end and a large-scale uniform linear array base station equipped with N antennas as the receiving end to serve the users. For this scenario, based on known channel state information and received signals, the ordered continuous interference cancellation algorithm is combined with the distributed expectation propagation algorithm to complete the uplink signal detection task.

[0040] In this embodiment, the system modulation method is χ-QAM, and the transmitted symbol of the k-th user is represented as x. k x = [x1, x2, ..., x K ] T ∈χ K This refers to the symbol vectors transmitted by K users in the same time slot. For this scenario, the uplink signal detection task is performed. The input / output signal model is as follows:

[0041] y = Hx + n

[0042] in, It is the received signal vector. It is the channel matrix. It is additive white Gaussian noise with a mean of 0 and a variance of σ. 2 I N The distribution is a complex Gaussian distribution, I N Represents an N×N identity matrix.

[0043] Under spherical wave modeling, the near-field channel between the k-th user and the receiver is represented as:

[0044]

[0045] Where, b(θ) k ,r k ) is the guide vector, r k θ represents the distance from the k-th user to the array center along the LoS path. k This represents the angle from the k-th user to the array center along the Loss path, where k is the angle. c =2π / λ c Represented as wave number, λ c =c / f c This represents the wavelength. The steering vector of the assumed spherical wavefront is:

[0046]

[0047] in, β represents the distance from user k to the nth antenna. k This represents the path loss for user k.

[0048] This embodiment considers a near-field channel scenario where two or more users arrive at the array center at the same angle but at different distances, as shown in the diagram below. Figure 1 As shown. Where δ n = (2n-N+1) / 2, n=0,1,...,N-1, antenna spacing d, the distance from the user to the nth antenna is:

[0049]

[0050] in,

[0051] Consider N antennas at the receiver, divided into C disjoint subarray processing units, with each subarray containing N antennas. c ,satisfy Furthermore, considering the non-stationarity of the ultra-large-scale MIMO channel, each subarray element is only visible to a subset of users. The input-output signal model of the c-th subarray is as follows:

[0052] y c =H c x+n c

[0053] Among them, y c This represents the signal vector received by the c-th antenna subarray; Let n represent the independent and identically distributed Rayleigh fading channel matrix, with a certain degree of sparse columns; c It is additive white Gaussian noise in the c-th antenna subarray, which follows a mean of 0 and a variance of . The complex Gaussian distribution, N represents c ×N c The identity matrix.

[0054] This embodiment only considers the signal detection part, and all subsequent work is performed under the condition that the receive vector and channel matrix are known. Given the receive vector and channel matrix, the posterior probability of the transmitted signal x is:

[0055]

[0056] in, The overall array received signal is represented by p(y|x) and p(x), which represent the likelihood function and prior distribution of x, respectively; p(y|x) represents the overall array received signal. c |x) represents the marginal likelihood function on subarray c; p(y) represents the prior information of the received signal y.

[0057] Considering the combination of factor graphs and posterior probabilities, the posterior probability of the transmitted signal x can be expressed as:

[0058]

[0059] Here, f0(x) represents the prior distribution p(x); Let p(y|x) represent the likelihood function; f c (x) can be equivalent to a marginal likelihood p(y). c |x);

[0060] The factor graph model corresponding to this probability model is as follows: Figure 2 As shown in the diagram. Squares represent factor nodes (FN), and circles represent variable nodes (VN). According to the sum-product algorithm, the message passing process between FN and VN can be represented as follows:

[0061]

[0062]

[0063] Among them, symbols Represents the information passed from VN to FN; symbol This represents the information passed from FN to VN.

[0064] By definition, the marginal probability distribution of a variable node is equal to the product of all input messages arriving at that node. Therefore, the transmitted signal x of the j-th user in the c-th subarray... j The actual posterior probability is:

[0065]

[0066] The above equation can be transformed into:

[0067]

[0068] Define confidence level It belongs to the exponential family distribution. It is used to represent the approximate posterior distribution of the j-th detected symbol in the c-th subarray, given by the following formula:

[0069]

[0070] Here, KL[·||·] represents the KL divergence operation, which is used to characterize the degree of deviation between two distributions. Minimizing the KL divergence between two distributions is equivalent to matching the moments between the two distributions. Therefore, by matching the first and second moments between two distributions, the process of approximating the distributions can be completed, thus obtaining an approximate posterior distribution.

[0071] Approximate posterior distribution mean Sum of variance Σ c It can be generated by Bayesian MMSE estimation, that is:

[0072]

[0073] Where, τ c =τ c I k and γ c =[γ 1c ,γ 2c ,…,γ Kc ] T Let b(x) represent the reciprocal of the prior variance and the prior mean of x in the c-th submatrix, respectively. Assume each approximate marginal distribution b(x) j The variances of all () are the same, using The average variance of the approximate marginal distribution is ω. c The c-th subarray represents the approximate marginal distribution b(x) j The reciprocal of the mean variance, ω c Take Σ c The reciprocal of the average diagonal elements, i.e., ω c =((1 / K)tr(Σ) c )) -1 . The mean is μ c The element μ at the corresponding index c,j ,so and Prior confidence provided by factor node f0 Defined as ω0 and μ0, as the fused symbolic variance and symbolic mean of the central processing unit, will be fed back to other factor nodes as prior information. After moment matching is completed, we can obtain:

[0074]

[0075] in, Right now The mean is μ c,j The variance is (v c,j ) -1 Gaussian distribution μ c,j Represents factor node f c Passed to variable node x j The mean, (v c,j ) -1 Represents factor node f c Passed to variable node x j The variance; Right now The mean is μ j,c The variance is (v j,c ) -1 Gaussian distribution μj,c Represents variable node x j Return to factor node f c The prior mean, (v j,c ) -1 Represents variable node x j Return to factor node f c The prior variance can be calculated similarly, and the information transmitted from the factor node f0 to the variable node can be obtained. The factor graph model used in this invention is as follows: Figure 2 As shown, the CPU is used as a factor node, each transmitter is used as a variable node, and each subarray is used as a factor node. The transmission relationship between the variable node and the factor node is obtained through the factor graph model.

[0076] This embodiment considers a multi-user near-field scenario where the channel correlation of spherical wavefront modeling is related to the distance parameter. As the distance difference between users to the array center gradually increases, the correlation shows a decreasing trend and approaches 0. However, this also indicates that even when the distance difference between users is small, it can still be significantly affected by signal interference. To eliminate inter-user interference, the Ordered Successive Interference Cancellation (OSIC) algorithm is combined with the distributed EP algorithm to obtain a factor graph-based EP-OSIC detection algorithm. This mainly involves combining the MMSE estimation part with OSIC. Therefore, the update method for the estimated mean of each subarray is as follows:

[0077] 101. Initialize the number of iterations to l = 0, and calculate the approximate posterior distribution of all detected symbols in the c-th subarray. The mean and variance; according to Update the mean of the confidence level;

[0078] 102. Let l = l + 1, calculate the interference-to-signal ratio (ISR) of each user in each subarray during the l-th iteration, and arrange the user detection order in each subarray according to the ascending sequence of these values ​​to obtain the detection order of the c-th subarray. And let i = 1; specifically:

[0079] Calculate the interference-to-signal ratio for each user in each subarray, including:

[0080]

[0081] Among them, JSR c,k h represents the interference-to-signal ratio of the k-th user in the c-th subarray; c,i Let ||·|| represent the i-th column of the channel matrix of the c-th subarray, and ||·|| represent the Euclidean norm;

[0082] 103. Select the detection order The i-th user is selected as the user to be estimated, and the received signal of the c-th subarray and the channel matrix of the c-th subarray are reconstructed using the mean of the approximate posterior distribution of all detected symbols of the i-th user in the c-th subarray; specifically:

[0083] Calculate the detection order The mean μ of the approximate posterior distribution of all detected symbols for the i-th user in the c-th subarray c,i The channel matrix and received signal of the c-th subarray are reconstructed using this signal, i.e.:

[0084]

[0085] in, This indicates that the signal of the i-th user in the detection sequence has been calculated. The received signal of the c-th subarray obtained after reconstruction has the same value as the received signal of the c-th subarray when i=1, that is... This represents the detection order in the channel matrix of the c-th subarray during the i-th iteration. The element corresponding to the i-th user; This represents the detection order in the c-th subarray during the i-th iteration. The mean of the approximate posterior distribution corresponding to the i-th user;

[0086] 104. Determine if i+1 is greater than K. If it is, proceed to step 105; otherwise, set i = i+1 and return to step 103.

[0087] 105. Determine whether the number of iterations l has reached the set maximum number of iterations or whether the algorithm has converged. If so, end the process; otherwise, wait for the central processing unit to return data and repeat steps 102 to 104.

[0088] After the user signal detection is completed through the above process, the estimated value of the transmitted signal is calculated based on the received signal and the channel matrix. The demodulated signal can then be obtained by demodulating the estimated signal.

[0089] The method of this invention was simulated, with bit error rate as the performance indicator for signal detection. A 16QAM modulation and demodulation scheme was used, and it was assumed that the channel state was known. The entire array was divided into four subarrays, with the number of antennas in each subarray being evenly distributed, i.e., N = C × N. c (C=4), the total number of base station antennas is N=1024, the total number of users at the same angle but different distances is K=12, and considering that the number of non-visible users in each subarray is K / 4, the center frequency is f c=100GHz, the reference angle θ = π / 6 for all users reaching the array center, and the distance from the user to the array center is randomly selected, ranging from r ∈ [1, 20]. The simulation iterations were performed 3 times. PW represents the plane wavefront, and SW represents the spherical wavefront. Performance tests were conducted on the EP-OSIC algorithm with and without distance parameter modeling in a distributed architecture system, and its performance was compared with that of the EP algorithm based on a distributed architecture under distance parameter modeling. The simulation results are as follows: Figure 4 As shown, it can be observed that when the system cannot utilize distance information, i.e., the system is modeled by a planar wavefront, the signal detection performance is extremely poor, causing the system to lose its communication capability. However, in the case of a spherical wavefront system, i.e., considering the influence of distance parameters on the phase, the EP-SIC algorithm based on the distributed architecture is superior to the EP algorithm. This is because when the distance between users is very close, there is interference between users in the system, which causes the performance of the EP algorithm based on the distributed architecture to be worse than that of the EP-OSIC algorithm based on the distributed architecture.

[0090] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO, characterized in that, To address the issue of significant interference between users in densely populated near-field scenarios, uplink signal detection specifically includes the following steps: The receiving antenna array is divided into C disjoint subarrays, and a factor graph model is constructed with each array as a factor node and each user's transmitted signal as a variable node. Based on the factor graph model, the approximate posterior distribution of the signal transmitted by a user in a subarray is calculated, as well as the approximate posterior distribution of the j-th detected symbol in the c-th subarray. Represented as: Where, b(x) j ) represents the true posterior distribution of the j-th detected symbol; This represents an exponential family distribution; KL[A‖B] is the KL divergence operation, used to characterize the degree of deviation between distributions A and B; The symbol x sent by the j-th user j The corresponding variable node to the c-th subarray f c The information transmitted by the corresponding factor nodes; It represents the c-th subarray f c The corresponding factor node to the symbol x sent by the j-th user j The information passed by the corresponding variable node; Based on the sorting interference cancellation algorithm, the received signals and channel matrices of each subarray are iteratively updated to complete signal detection, including the following steps:

101. Initialize the number of iterations to l = 0, and calculate the approximate posterior distribution of all detected symbols in the c-th subarray. The mean and variance; 102. Let l = l + 1, calculate the interference-to-signal ratio (ISR) of each user in each subarray during the l-th iteration, and arrange the user detection order in each subarray according to the ascending sequence of these values ​​to obtain the detection order of the c-th subarray. Let i = 1, where i is the user index; 103. Select the detection order The i-th user is taken as the user to be estimated, and the received signal of the c-th subarray and the channel matrix of the c-th subarray are reconstructed using the mean of the approximate posterior distribution of all detected symbols of the i-th user in the c-th subarray.

104. Determine if i+1 is greater than K, where K is the number of users. If it is greater, proceed to step 105; otherwise, set i = i+1 and return to step 103.

105. Determine whether the number of iterations l has reached the set maximum number of iterations or whether the algorithm has converged. If so, end the process; otherwise, wait for the central processing unit to return data and repeat steps 102 to 104.

2. The method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO according to claim 1, characterized in that, In the factor graph model, the process of information transfer between factor nodes and variable nodes is represented as follows: in, The symbol x sent by the j'th user j' The corresponding variable node to the c-th subarray f c The information passed by the corresponding factor node is j'∈{1,2,...,K}\j; This represents the symbol x sent by the j-th user from the variable node f0 corresponding to the prior information. j The message of the corresponding variable node; This indicates that the c′-th subarray f c′ The corresponding factor node to the symbol x sent by the j-th user j The information passed by the corresponding variable node is c′∈{1,2,...,C}\c, where {1,2,...,C}\c represents the set of {1,2,...,C} excluding c; x\x j This represents the set of symbols x sent by all users, excluding the symbol x sent by the j-th user. j The combination of symbols; f c (x j ) represents user x in the probabilistic model j The marginal likelihood function.

3. The method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO according to claim 1, characterized in that, Approximate posterior distribution of all detected symbols in the c-th subarray The mean and variance are expressed as: Where, μ c This represents the approximate posterior distribution of all detected symbols received by the c-th subarray. The mean; Σ c This represents the approximate posterior distribution of all detected symbols in the c-th subarray. The variance; σ represents the noise variance; H represents the channel matrix of the c-th subarray. c The transpose of y; c τ represents the received signal of the c-th subarray; c γ represents the reciprocal of the prior variance of all detected symbols received by the c-th subarray. c Let represent the prior mean of all detected symbols received by the c-th subarray.

4. The method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO according to claim 1, characterized in that, Reconstructing the received signal of the c-th subarray and the channel matrix of the c-th subarray using the mean of the approximate posterior distribution of all detected symbols of the i-th user in the c-th subarray includes: in, This indicates that the signal of the i-th user in the detection sequence has been calculated. The received signal of the c-th subarray obtained after reconstruction has the same value as the received signal of the c-th subarray when i=1, that is... This represents the detection order in the channel matrix of the c-th subarray during the i-th iteration. The element corresponding to the i-th user; This represents the detection order in the c-th subarray during the i-th iteration. The mean of the approximate posterior distribution corresponding to the i-th user.

5. The method for detecting uplink signals in near-field spherical wave ultra-large-scale MIMO according to claim 4, characterized in that, The calculation of the interference-to-signal ratio for each user in each subarray includes: Among them, JSR c,k h represents the interference-to-signal ratio of the k-th user in the c-th subarray; c,i Let ||·|| represent the i-th column of the channel matrix of the c-th subarray, and ||·|| represent the Euclidean norm.

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