ISAC system signal detection method based on block diagonal expected propagation

Abstract

The invention provides an ISAC system signal detection method based on block diagonal expected propagation, and the method comprises the steps: obtaining a communication signal and a target echo signal transmitted by multi-antenna user equipment through a receiving end, carrying out the whitening of the received signal and noise, and minimizing the interference of a radar to communication; converting the optimized complex signal into a real value system model; initializing a mean vector and a covariance matrix parameter of the expectation propagation algorithm, and setting the number of iterations; calculating diagonal elements of the covariance matrix by adopting a block diagonal Neumann series approximation method; updating a mean vector and adjusting an iteration step length through a dynamic residual factor; and after a preset number of iterations, outputting a final detection signal. According to the method, the complexity is reduced by calculating the diagonal elements of the matrix inversion instead of directly solving the matrix inversion, and a special averaging method is designed for the diagonalization characteristic of the matrix with the similar channel hardening characteristic to optimize the precision.

Description

Technical Field

[0001] The present invention relates to the field of wireless communications, and in particular to an ISAC system signal detection method based on block diagonal expected propagation. Background Art

[0002] With the development of 6G technology, integrated sensing and communication (ISAC) systems have become a research hotspot. However, existing ISAC signal detection technologies still face significant challenges. Traditional methods typically simply model radar target echoes as additive white Gaussian noise. This simplification can lead to significant performance losses in practical applications. Research has shown that in typical application scenarios, this processing method can result in a 5-8dB signal-to-noise ratio loss, increasing the system bit error rate by more than an order of magnitude.

[0003] Signal detection in multi-antenna user equipment (MAUE) scenarios presents even greater technical challenges. Due to device size limitations, antenna spacing is often compressed to 0.3-0.5 wavelengths, resulting in spatial correlation coefficients between antennas as high as 0.6-0.8. This strong correlation significantly weakens the channel hardening effect, causing a sharp decline in the performance of traditional detection algorithms based on the independent and identically distributed channel assumption. Field measurements show that under strongly correlated channel conditions, the bit error rate of existing detection algorithms can deteriorate by 10-100 times.

[0004] Furthermore, computational complexity also hinders the practical deployment of ISAC systems. Traditional precise matrix inversion computations have a computational complexity as high as O(N³), and in a 64-antenna system, single-detection latency exceeds 10ms, making it difficult to meet real-time requirements. Although various approximate algorithms have been proposed, these methods suffer from significant accuracy loss or unstable performance under relevant channel conditions. In edge computing scenarios, in particular, the computational resources required by existing algorithms often exceed the processing capabilities of terminal devices, severely limiting the widespread application of ISAC technology. Summary of the Invention

[0005] To address the high algorithmic complexity, this paper proposes a signal detection method for ISAC systems based on block diagonal expectation propagation. This solution reduces complexity by calculating the diagonal elements of the matrix inverse instead of directly solving the matrix inverse. Furthermore, a specialized averaging method is designed to optimize accuracy for matrix diagonalization characteristics similar to channel hardening. The technical solutions provided by this paper are as follows:

[0006] A signal detection method for an ISAC system based on block diagonal expected propagation comprises the following steps:

[0007] Step 1: The receiving end obtains the communication signal and target echo signal sent by the multi-antenna user equipment, and whitens the received signal and noise to minimize radar interference with communication.

[0008] Step 2, converting the optimized complex signal into a real-valued system model;

[0009] Step 3: Initialize the mean vector and covariance matrix parameters of the expectation propagation algorithm and set the number of iterations;

[0010] Step 4: During the first iteration, the channel matrix is ​​subjected to singular value decomposition (SVD) to convert the complex matrix inversion operation into eigenvalue operation to reduce computational complexity.

[0011] Step 5: In subsequent iterations, the diagonal elements of the covariance matrix are calculated using the block diagonal Neumann series approximation method.

[0012] Step 6: Update the mean vector and adjust the iteration step size by the dynamic residual factor;

[0013] Step 7: After a preset number of iterations, the final detection signal is output.

[0014] Preferably, a whitening matrix is ​​constructed using the Sherman-Morrison formula and the eigendecomposition method to perform whitening processing on the received signal. The whitening matrix Q is expressed as:

[0015] ,

[0016] in is the identity matrix, is the standard deviation of the Gaussian distribution, is the radar channel response matrix, is the transmit beamforming vector, .

[0017] Preferably, through joint optimization Minimize radar interference with communications:

[0018]

[0019] in, is the complex domain communication channel response, is the steering vector, P max is the maximum transmit power, is the minimum radar gain threshold.

[0020] Preferably, the real-valued expression of the received vector is:

[0021]

[0022] in is zero in mean and has a variance of The additive white Gaussian noise vector of and is the spatial correlation matrix between the receiver and transmitter, , , , and They are the base station receiving signal and communication transmitting signal in the complex domain respectively. represents the real part, Represents the imaginary part.

[0023] Preferably, the initialization parameters in step 3 are: and ,in represents the average symbol energy, and are the parameters that determine the characteristics of the alternative Gaussian function in each dimension.

[0024] Preferably, the large-scale channel matrix is ​​divided into several sub-block matrices of the same size according to the user antenna grouping, and each sub-block corresponds to the antenna set of a user device; the diagonal elements of each sub-block matrix are extracted to form a diagonal matrix, and the inverse matrix of the diagonal matrix is ​​calculated as an initial approximation; the Neumann series expansion method is used to gradually approximate the true inverse matrix of each sub-block matrix through a finite number of matrix multiplication and addition operations, wherein the number of terms in the series expansion is dynamically adjusted according to the required accuracy; after obtaining the approximate inverse matrix of each sub-block matrix, the approximate inverse matrix is ​​recombined according to the block structure of the original matrix to form a complete approximate covariance matrix.

[0025] Preferably, the update optimization method of the mean vector specifically includes: in each iteration, first using the currently estimated covariance matrix and the received signal vector to construct a linear equation group; then using the pre-processed Jacobi iteration method to solve the equation group, by decomposing the coefficient matrix into two parts, a diagonal matrix and a non-diagonal matrix, and retaining only the inverse matrix of the diagonal matrix to participate in the calculation; in the iterative solution process, dynamically adjusting the relaxation factor according to the degree of channel hardening to accelerate the convergence speed; at the same time, introducing the statistical characteristics of the channel state information, and performing weighted averaging processing on each dimension of the mean vector, where the weight coefficient is proportional to the quality of the corresponding antenna channel.

[0026] Preferably, the dynamic residual factor adjustment mechanism includes the following process: in the algorithm initialization stage, the residual factors of all iterative layers are set to a unified empirical value; in each iteration process, the residual factor size of each layer is dynamically updated according to the condition number and signal-to-noise ratio parameters of the current channel matrix through preset adjustment rules; a momentum term is introduced during the update process to smooth parameter changes; at the same time, the upper and lower limit thresholds of the residual factor are set, and truncation processing is performed when the calculated update value exceeds the range.

[0027] Compared with the existing technology, the beneficial effects achieved by the present invention are: improving the block matrix Neumann method, replacing the original calculation of the matrix inverse with the calculation of the diagonal elements of the matrix inverse to reduce the complexity; designing a method for calculating the average value for constructing the matrix diagonalization characteristics similar to channel hardening; and optimizing the method to solve the accuracy problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0029] Figure 1 It is a system model diagram of the present invention;

[0030] Figure 2 Schematic diagram of using the block diagonal method to solve the matrix C in the embodiment;

[0031] Figure 3 Schematic diagram of using the improved block diagonal method to solve the matrix D in the embodiment;

[0032] Figure 4 It is a network structure diagram of the improved block diagonal expectation propagation algorithm of the present invention. DETAILED DESCRIPTION

[0033] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0034] In order to make the above-mentioned objects, features and effects of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Example 1: A signal detection method for an ISAC system based on block diagonal expected propagation. The present invention is based on an ISAC system, such as Figure 1 As shown, one of the multi-antenna base stations receives communication signals from multiple users and simultaneously performs sensing target detection. The present invention specifically includes the following steps.

[0036] Step 1: The receiving end obtains the communication signal and target echo signal sent by the multi-antenna user equipment, and whitens the received signal and noise to minimize the interference of radar on communication.

[0037] In the ISAC system, the received signal can be expressed as:

[0038]

[0039] in, 、 、 、 、 and are the base station received signal, communication channel response, communication transmit signal, radar channel response matrix, transmit beamforming vector and system noise in the complex domain, respectively. and Indicates that it has not been whitened. , is the guiding vector. is the reflection coefficient of the target, and s is the radar signal transmitted by the base station. and They correspond to the number of antennas at the base station receiving end and the communication user transmitting end respectively.

[0040] Following the Swerling II target model, it is assumed that the reflection coefficient of the target varies with the pulse with a Rayleigh / exponential distribution. In this case, The inner diameter follows a complex Gaussian distribution. For ease of notation and without loss of generality, the noise power To normalize The variance of .

[0041] In order to detect the communication signal, other signals including the target echo and noise are regarded as unwanted signals. Therefore, the signal model can be expressed as:

[0042]

[0043] in Since the random variable and vector are all white Gaussian distributed and independent of each other, so their linear combination is also a Gaussian distribution with zero mean. Its covariance matrix is:

[0044]

[0045] This shows It obeys the complex Gaussian distribution, which leads to correlation between the communication sub-channels. With this known covariance matrix, the received signal can be whitened and the communication channel can be decomposed into several independent sub-channels:

[0046]

[0047] in is the whitening matrix.

[0048] Calculate R using the Sherman-Morrison formula -1 , due to R -1 It is the identity matrix plus a rank-1 matrix, whose inverse matrix can be expressed analytically as:

[0049]

[0050] make ,but .

[0051] The whitening matrix Q must satisfy, Right now , using eigendecomposition to solve , the eigenvalue decomposition of R is: ,in , ,the remaining (because is a rank-1 matrix, contributing only one non-zero eigenvalue), and U is a unitary matrix.

[0052] calculate ,in , so the whitening matrix Q is expressed as:

[0053] .

[0054] in It can be expressed through joint optimization, that is, minimizing the interference of radar on communication while ensuring basic perception:

[0055]

[0056] Among them, P max is the maximum transmit power, is the minimum radar gain threshold. The problem can be solved by Lagrange multiplier method or semi-definite programming (SDP).

[0057] Step 2: Convert the optimized complex signal into a real-valued system model.

[0058] At this point, the system model formula can be expressed as: ,in represents the complex domain base station received signal after whitening processing, represents the whitened complex domain communication channel response, is the standard Gaussian white noise matrix.

[0059] To facilitate the implementation of the signal detection algorithm, the system model in the complex domain is converted into an equivalent real domain expression as follows:

[0060] in, , , .

[0061] like Figure 1 As shown, the present invention considers an ISAC system, in which the base station BS is configured with N r antennas communicate with m multi-antenna users, each user is equipped with m UE antennas, and a radar for target perception. Under this architecture: the transmitting antennas within the same user show significant spatial correlation due to the spacing, while the antenna channel correlation between different user devices can usually be ignored. The total number of antennas at the transmitting end of the system is , the transmission vector is expressed as , where the elements for , , millimeter wave channel matrix , . Denotes the uplink from the jth antenna of the i-th UE to the BS. Let N = 2N r , M=2N t , the vector received by BS , then the real-valued expression of the receiving vector is:

[0062]

[0063] in is zero in mean and has a variance of The spatial correlation matrices of the receiver and transmitter are and .

[0064]

[0065]

[0066] in is the value in the pth row and qth column of the receive antenna correlation matrix, is the value in the pth row and qth column of the transmit antenna correlation matrix, and represents its complex conjugate, and are defined as the correlation factors of the receiving antenna and transmitting antenna from the same terminal respectively.

[0067] In a multi-antenna user equipment system, multiple antennas of the same user equipment are usually arranged in a uniform linear array, with the spacing between adjacent antennas being d iDue to UE size limitations, antenna spacing is usually less than half a wavelength. , resulting in enhanced spatial correlation. Assume that the antenna spacing of the i-th UE is d i , its transmitter spatial correlation matrix The element in row m and column n of can be modeled as: ;

[0068] in is the inter-antenna correlation factor, which is inversely proportional to the antenna spacing. hour, , then the antennas are approximately independent; when hour, The value increases with decreasing spacing, which has two main effects: the off-diagonal elements of the channel matrix are significantly enhanced and the channel hardening phenomenon is weakened.

[0069] Based on the constructed system model, the posterior probability distribution of the transmission symbol vector can be expressed as:

[0070]

[0071] in is an indicator function, if Returns 1 if yes, otherwise returns 0.

[0072] Step 3: Initialize the mean vector and covariance matrix of the expectation propagation algorithm and set the number of iterations.

[0073] The expectation propagation algorithm is a technique in Bayesian machine learning that is used to approximate the posterior belief with an exponential family distribution. When applied to signal detection, the first step is to construct a Gaussian approximation. Instead of the posterior distribution of the transmitted symbol vector . Then the mean of the Gaussian approximation is iteratively updated with polynomial time complexity and variance The formula for EP iterative detection is given in detail below.

[0074] Given the posterior distribution, decompose it into Gaussian and non-Gaussian parts:

[0075]

[0076] in and is the parameter that determines the characteristics of the alternative Gaussian function in each dimension. Let For any vector and , the covariance matrix and the mean vector The calculation is as follows:

[0077]

[0078]

[0079] Obviously, recursive update Equivalent to refreshing the Gaussian function The average vector and the covariance matrix As the number of iterations increases, the approximation accuracy gradually improves. Set the initial solution and ,in represents the average symbol energy. The iterative update process is as follows:

[0080] Compute the cavity edges: ;

[0081] in, , ;

[0082] The exact non-Gaussian factor Introduction In the equation, we get:

[0083]

[0084]

[0085]

[0086] Update , which makes the following non-normalized Gaussian distribution: With mean and variance , the calculation formula is as follows:

[0087]

[0088]

[0089] At this point, one iteration has been basically completed.

[0090] After the refinement and Substitute the covariance matrix and mean vector into the calculation, and proceed to the next iteration, gradually improving the approximation accuracy until the required number of iterations is reached. In each iteration, all All on the corresponding input dimensions Updated in parallel.

[0091] In order to further improve the convergence speed of the EP algorithm, the commonly used strategies in message passing are:

[0092]

[0093]

[0094] in The high complexity of the expected propagation algorithm detection is mainly caused by the calculation of the matrix covariance and the calculation of the mean vector. In particular, the matrix inverse operation of the covariance has a computational complexity of , which will lead to excessively high computational overhead in signal detection in high-dimensional MIMO systems.

[0095] Step 4: During the first iteration, singular value decomposition is performed on the channel matrix to convert the complex matrix inversion operation into eigenvalue operation to reduce the computational complexity.

[0096] Step 5: In subsequent iterations, the block diagonal Neumann series approximation method is used to calculate the diagonal elements of the covariance matrix.

[0097] The large-scale channel matrix is ​​divided into several sub-block matrices of equal size according to user antenna groups, with each sub-block corresponding to a set of antennas of a user device. The diagonal elements of each sub-block matrix are extracted to form a diagonal matrix, and the inverse matrix of the diagonal matrix is ​​calculated as an initial approximation. The Neumann series expansion method is used to gradually approximate the true inverse matrix of each sub-block matrix through a finite number of matrix multiplication and addition operations, where the number of terms in the series expansion is dynamically adjusted according to the required accuracy. After obtaining the approximate inverse matrices of each sub-block matrix, these approximate inverse matrices are recombined according to the block structure of the original matrix to form a complete approximate covariance matrix.

[0098] Specifically, first transform the matrix Divided into 4 matrix blocks, where the upper left and lower right matrices are set to Then the matrix The approximate diagonal elements of small matrices, the size of each small matrix is , set them in order In order to ensure the convergence of the Neumann method, the parameter , for all small matrix operations . Find the inverse of each small matrix . The complexity of direct solution is , there are both diagonal elements and off-diagonal elements. To reduce the complexity of the inversion, the block matrix Neumann method is used to make the following approximation:

[0099] ,

[0100] take out in : , ;

[0101] For block matrices Subblock Matrix Neumann Method Iteration ;

[0102] Same as above , then and Put it together: ;

[0103] Get what you need Repeat the above method: , , ;

[0104] For block matrices Second block matrix Neumann method iteration: ,get .

[0105] Just need The diagonal elements of .according to , , rewritten as follows: ;

[0106] After calculation:

[0107]

[0108]

[0109] Found multiple Multiplying them together reveals a pattern of off-diagonal and diagonal lines with a period of 2. So we get:

[0110]

[0111]

[0112] Since the above formula does not contain diagonal elements, there is no need to calculate , only need to calculate and :

[0113] .

[0114] From this formula we can see and , so we only need to calculate and . Observe again and find that it only needs to be requested once and matrix multiplication.

[0115] As the correlation level increases, the channel hardening phenomenon of the first layer becomes worse and worse, so instead of approximating the first layer, we adopt the following method (i.e., for the first iteration): first Perform singular value decomposition: , U is the left singular matrix, V is the right singular matrix, is the singular value matrix;

[0116] get , because the first time I brought For a diagonal matrix with the same values, the following simplification is performed:

[0117]

[0118] .

[0119] Step 6: Update the mean vector and adjust the iteration step size by the dynamic residual factor.

[0120] In each iteration, a linear system of equations is first constructed using the currently estimated covariance matrix and the received signal vector. The preconditioned Jacobi iteration method is then used to solve the system of equations by decomposing the coefficient matrix into two parts: a diagonal matrix D and a non-diagonal matrix L. Only the inverse matrix of the diagonal matrix is ​​retained for calculation. During the iterative solution process, the relaxation factor is dynamically adjusted according to the degree of channel hardening to accelerate the convergence speed. At the same time, the statistical characteristics of the channel state information are introduced to perform weighted averaging on each dimension of the mean vector, where the weight coefficient is proportional to the quality of the corresponding antenna channel.

[0121] The dynamic residual factor adjustment mechanism includes the following processing flow: in the algorithm initialization phase, the residual factors of all iterative layers are set to a unified empirical value; in each iteration, the residual factor size of each layer is dynamically updated according to the condition number and signal-to-noise ratio parameters of the current channel matrix through preset adjustment rules; in the specific update process, a momentum term is introduced to smooth parameter changes and prevent parameter oscillations caused by channel mutations; at the same time, the upper and lower limit thresholds of the residual factor are set, and when the calculated update value exceeds this range, it is truncated to ensure numerical stability.

[0122] Step 7: After a preset number of iterations, the final detection signal is output.

[0123] Steps 3 to 7 constitute the improved block diagonal expectation propagation algorithm proposed in this invention. The algorithm network is as follows: When the first layer of the network (t=1), the initialization process is different from the subsequent layers. The parameters are initialized according to the input received signal vector, channel matrix, noise power and signal average energy. and , calculate the approximate covariance matrix and the initial mean estimate .

[0124] The input of the second layer to the tth layer (t>=2) of the network is the mean vector from the previous layer and parameters 、 , first calculate the covariance matrix , the intermediate variable b uses the Jacobi method to update the mean estimate , then extract the diagonal to calculate the error method And calculate the mean without nonlinear mapping , nonlinear mapping and residual factor Link , output the updated variance And update the parameters and Finally, after iterative optimization of the T-layer network, the mean value of the last layer output is This is the final estimated value of the transmitted signal detected.

[0125] The above network structure is as follows Figure 4 As shown in Table 1, the algorithm pseudo code is shown in Table 1.

[0126] Table 1 Improved expectation propagation algorithm

[0127]

[0128] Embodiment 2 The computer-readable storage medium of this embodiment stores a computer program, which, when executed by a processor, implements the steps of the ISAC system signal detection method based on block diagonal expected propagation in embodiment 1.

[0129] The computer-readable storage medium of this embodiment may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal; the computer-readable storage medium of this embodiment may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card, a secure digital card, a flash memory card, etc. equipped on the terminal; further, the computer-readable storage medium may also include both an internal storage unit of the terminal and an external storage device.

[0130] The computer-readable storage medium of this embodiment is used to store computer programs and other programs and data required by the terminal. The computer-readable storage medium can also be used to temporarily store data that has been output or is to be output.

[0131] Example 3 The computer device of this embodiment includes a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the ISAC system signal detection method based on block diagonal expected propagation in Example 1 are implemented.

[0132] In this embodiment, the processor can be a central processing unit, or other general-purpose processors, digital signal processors, application-specific integrated circuits, off-the-shelf programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The memory can include read-only memory and random access memory, and provide instructions and data to the processor. A part of the memory can also include non-volatile random access memory. For example, the memory can also store information about the device type.

[0133] Those skilled in the art will clearly understand that each embodiment can be implemented using software plus a necessary general-purpose hardware platform, or of course, hardware. Based on this understanding, the essence of the above-mentioned technical solution, or the portion 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 computer-readable storage medium, such as ROM / RAM, a magnetic disk, or an optical disk, and includes a number of instructions for causing a computer device (such as a personal computer, server, or network device) to execute the methods described in various embodiments or certain portions of the embodiments.

[0134] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A signal detection method for an ISAC system based on block diagonal expected propagation, characterized in that: The following steps are involved: Step 1: The receiving end obtains the communication signal and target echo signal sent by the multi-antenna user equipment, and whitens the received signal and noise to minimize radar interference with communication. Step 2, converting the optimized complex signal into a real-valued system model; Step 3: Initialize the mean vector and covariance matrix parameters of the expectation propagation algorithm and set the number of iterations; Step 4: During the first iteration, the channel matrix is ​​subjected to singular value decomposition (SVD) to convert the complex matrix inversion operation into eigenvalue operation to reduce computational complexity. Step 5: In subsequent iterations, the diagonal elements of the covariance matrix are calculated using the block diagonal Neumann series approximation method. Step 6: Update the mean vector and adjust the iteration step size by the dynamic residual factor; Step 7: After a preset number of iterations, the final detection signal is output.

2. The ISAC system signal detection method based on block diagonal expected propagation according to claim 1, characterized in that: The whitening matrix is ​​constructed using the Sherman-Morrison formula and the eigendecomposition method to whiten the received signal. The whitening matrix Q is expressed as: ， in is the identity matrix, is the standard deviation of the Gaussian distribution, is the radar channel response matrix, is the transmit beamforming vector, H represents the conjugate transpose of the matrix, .

3. The ISAC system signal detection method based on block diagonal expected propagation according to claim 2, characterized in that: Through joint optimization Minimize radar interference with communications: ； in, is the complex domain communication channel response, is the orientation vector, is the direction of the signal wave, P max is the maximum transmit power, is the minimum radar gain threshold, min is the minimum function, and st represents the constraint condition.

4. The ISAC system signal detection method based on block diagonal expected propagation according to claim 3, characterized in that: The real-valued expression for the received vector is: ； in is zero in mean and has a variance of The additive white Gaussian noise vector of and is the spatial correlation matrix between the receiver and transmitter, , , , and They are the base station receiving signal and communication transmitting signal in the complex domain respectively. represents the real part, Represents the imaginary part.

5. The ISAC system signal detection method based on block diagonal expected propagation according to claim 1, characterized in that: Step 3: Initialization parameters: and ,in represents the average symbol energy, and are the parameters that determine the characteristics of the alternative Gaussian function in each dimension.

6. The ISAC system signal detection method based on block diagonal expected propagation according to claim 5, characterized in that: The large-scale channel matrix is ​​divided into several sub-block matrices of equal size according to the user antenna grouping. Each sub-block corresponds to a set of antennas of a user device. The diagonal elements of each sub-block matrix are extracted to form a diagonal matrix, and the inverse matrix of the diagonal matrix is ​​calculated as the initial approximation. The Neumann series expansion method is used to gradually approximate the true inverse matrix of each sub-block matrix through a finite number of matrix multiplication and addition operations, where the number of terms in the series expansion is dynamically adjusted according to the required accuracy. After obtaining the approximate inverse matrix of each sub-block matrix, the approximate inverse matrix is ​​reassembled according to the block structure of the original matrix to form a complete approximate covariance matrix.

7. The ISAC system signal detection method based on block diagonal expected propagation according to claim 1, characterized in that: The specific update optimization method of the mean vector includes: in each iteration, first, using the current estimated covariance matrix and the received signal vector to construct a linear equation system; then using the pre-processed Jacobi iteration method to solve the equation system, by decomposing the coefficient matrix into two parts: a diagonal matrix and an off-diagonal matrix, and retaining only the inverse matrix of the diagonal matrix for calculation; during the iterative solution process, the relaxation factor is dynamically adjusted according to the degree of channel hardening to accelerate the convergence speed; at the same time, the statistical characteristics of the channel state information are introduced, and each dimension of the mean vector is weighted averaged, where the weight coefficient is proportional to the quality of the corresponding antenna channel.

8. The ISAC system signal detection method based on block diagonal expected propagation according to claim 7, characterized in that: The dynamic residual factor adjustment mechanism includes the following process: In the initialization phase of the algorithm, the residual factors of all iterative layers are set to a unified empirical value; In each iteration, the residual factor of each layer is dynamically updated according to the condition number and signal-to-noise ratio parameters of the current channel matrix through the preset adjustment rules; A momentum term is introduced during the update process to smooth parameter changes; at the same time, upper and lower thresholds of the residual factor are set, and truncation is performed when the calculated update value exceeds the range.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the ISAC system signal detection method based on block diagonal expected propagation are implemented as described in any one of claims 1 to 8.

10. A computer device comprising a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the ISAC system signal detection method based on block diagonal expected propagation are implemented as described in any one of claims 1 to 8.

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