A geometric method for downlink precoding information in ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation.

Abstract

This invention discloses an information geometry method for downlink precoding in ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal partitioning. This invention transforms the calculation of intermediate results in RZF precoding into a Gaussian distribution mean-finding problem, introduces a user reordering mechanism based on channel spatial correlation, making the strip-shaped diagonal of the channel Gram matrix dominant, and introduces a novel partitioning strategy to split the reordered Gram matrix into a strip-shaped matrix and several cross-shaped matrix components. Based on the partitioning results, within the information geometry framework, iterative calculations using local inverse-free algebraic operations and strip-shaped matrix inversion are performed to achieve low-complexity matrix inverse multiplication into vector approximation. This invention utilizes a matrix partitioning method of strip-shaped and cross-shaped matrices to fully exploit the local correlations between users, significantly accelerating the algorithm's convergence speed while maintaining near-optimal RZF precoding performance, making it suitable for ultra-large-scale MIMO practical communication systems with extremely low latency.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, specifically relating to a precoding method for reducing baseband processing complexity in downlink transmission of ultra-large-scale MIMO (XL-MIMO) systems, and particularly to a geometric method for XL-MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation. Background Technology

[0002] The evolution of wireless networks for sixth-generation (6G) communication has established Ultra-Large-Scale Multiple-Input Multiple-Output (XL-MIMO) as a transformative technology. By equipping base stations with massive antenna arrays, XL-MIMO offers unprecedented spatial freedom, enabling simultaneous service to a large number of users. However, as the scale of multiplexing increases, the system bottleneck shifts from air interface capacity to baseband processing. The enormous dimension of the XL-MIMO channel introduces significant computational overhead, making efficient multi-user interference (MUI) suppression extremely complex.

[0003] Linear regularized zero-forcing (RZF) precoders are widely used because they balance multi-user interference cancellation and noise amplification. However, RZF requires... Individual users execute Find the inverse of a 3D Gram matrix. The complexity of this leads to unacceptable latency and power consumption, making direct inversion impractical in dense 6G networks.

[0004] While existing low-complexity approximate precoding methods avoid direct matrix inversion, they face significant obstacles. Polynomial expansions (such as Neumann series) require higher-order terms, potentially exceeding the complexity of exact inversion. Iterative solvers (such as conjugate gradients and Jacobi algorithms) converge slowly due to the ill-conditioned nature of XL-MIMO channels. Recent research has proposed a block cross-segmentation-based information geometry method (BCS-IGA), but its diagonal block segmentation structure struggles to fully capture the continuous spatial correlations across block boundaries in dense XL-MIMO channels. Furthermore, increasing the block size to accelerate convergence leads to higher-dimensional strip matrix inversions, increasing computational costs. Summary of the Invention

[0005] Purpose of the invention: To address the shortcomings of existing RZF precoding methods, such as high complexity of direct inversion and slow convergence and high overhead of matrix inversion, this invention aims to provide an information geometry method based on cross-shaped and striped diagonal segmentation (CBS-IGA). This method can accelerate convergence and approach the optimal system and speed performance with low computational cost by utilizing low-complexity scalar operations and striped matrix inversion.

[0006] Technical Solution: To achieve the above objectives, this invention provides a geometric method for downlink precoding information in ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation, comprising the following steps:

[0007] Obtain the downlink channel matrix from the base station to all scheduled user terminals, and obtain the data vector to be transmitted;

[0008] The Gram matrix of the channel matrix is ​​calculated, and the Gram matrix and the data vector to be transmitted are reordered according to spatial correlation to enhance the strip diagonal dominance of the Gram matrix.

[0009] The reordered Gram matrix is ​​split into a strip matrix, and The residual multi-user interference cross-shaped matrix components, while simultaneously splitting the data vector to be transmitted into... _ inter-term vectors, where Number of users;

[0010] Based on the decomposition results, the target manifold is constructed within the information geometry framework. The parameters of the auxiliary manifold and the additional auxiliary manifold used to process the banded matrix are updated iteratively through scalar operations based on the sparsity of the cross-shaped matrix components and Woodbury's lemma and the inversion of the banded matrix until the preset number of iterations is reached.

[0011] Based on the converged target manifold parameters, the intermediate result vector of regularized zero-forcible (RZF) precoding is calculated, restored to the original user order, and multiplied with the channel matrix to obtain the final downlink transmission signal.

[0012] As a preferred option, the specific steps for reordering users based on spatial relevance include:

[0013] Calculate the normalized spatial correlation matrix Its elements are ,in The channel Gram matrix;

[0014] Set threshold Construct a sparse adjacency matrix ,when and hour, Otherwise, it is 0;

[0015] Bandwidth reduction algorithm is used to process sparse adjacency matrices This causes the non-zero elements to converge towards the main diagonal to extract the permutation vector, which is then used to reorder the channel Gram matrix and the data vector.

[0016] As a preferred method, the reordered Gram matrix is ​​split, specifically as follows:

[0017] Introducing a mask matrix When the absolute value of the difference between the row index and the column index is less than or equal to the one-sided bandwidth When the mask matrix is ​​active, its elements are 1; otherwise, they are 0. Calculate the strip matrix. ,in It represents the Hadamah accumulation. This is the reordered channel Gram matrix. For regularization parameters, for 1-order identity matrix; calculate the residual multi-user interference matrix. Define a selection matrix with rank 1. ,in The first unit of the identity matrix The column utilizes the selection matrix from the residual multi-user interference matrix. Extract the corresponding row and column vectors, divide them by two and reconstruct them to obtain the split-off first... Each cross-shaped matrix component And simultaneously extract the corresponding first Inter-term vectors The specific splitting formula is as follows: , ,in This is the reordered data vector to be sent.

[0018] Preferably, the target manifold, additional auxiliary manifold, and [other manifolds] are constructed within the information geometry framework. An auxiliary manifold is used for parameter iterative updates via scalar operations and banded matrix inversion, including:

[0019] Based on the split structure design Auxiliary probability distributions , , Additional auxiliary probability distributions used to handle banded matrices , , ; and target probability distribution , , ;in Let be a complex Gaussian random vector. and The split of the first Each cross term vector and negative definite cross-shaped matrix component for An identity matrix of order 1. It is a strip matrix. , , For vectors, , , Set the parameters to scalars, and initialize the manifold vector and the scalar parameters;

[0020] according to Calculate vectors sum matrix Alternative transmission belief vector and the transmission of belief scalar Make the auxiliary probability distribution The traces of the mean and covariance matrices remain unchanged before and after projection; according to the vector and scalar Update additional auxiliary manifold parameters and Target manifold parameters and and auxiliary manifold parameters and Repeat until the preset number of iterations is reached; the update method is as follows:

[0021] ,

[0022] ,

[0023] ,

[0024] ,

[0025] ,

[0026] ,

[0027] in For damping factor, superscript Mark the number of iterations.

[0028] Preferably, the invariance of the trace of the mean and covariance matrix means that:

[0029] probability distribution With probability distribution The mean and trace of the covariance matrix are equal, where , Additional auxiliary probability distribution With the target probability distribution The mean and the trace of the covariance matrix are equal.

[0030] As a preferred option, according to the first The covariance matrix of the auxiliary probability distributions and mean vector Calculate the scalar of transmitted beliefs and the transmission of belief vectors for:

[0031] ,

[0032] ,

[0033] Based on the fact that the mean of the target probability distribution and the trace of the covariance matrix are equal, and combined with the covariance matrix of the additional auxiliary probability distribution... and mean vector Calculate the target probability distribution parameters:

[0034] ,

[0035] .

[0036] As a preferred option, since the negative definite matrix The cross-shaped structure constructed from the rank-1 choice matrix determines that it can be decomposed into a rank-2 matrix product. Based on Woodbury's matrix inversion lemma and algebraic simplification, matrix inversion is completely avoided, and the trace of the covariance matrix is ​​obtained. and mean The solution is simplified to scalar form, specifically:

[0037] Define local variables and Calculate local scalars , , , Trace of the covariance matrix and local mean The calculation is as follows:

[0038] ,

[0039] .

[0040] Preferably, the intermediate result vector of the regularized zero-forced (RZF) precoding is calculated, restored to the original user order, and then multiplied with the channel matrix to obtain the final downlink transmission signal, specifically including:

[0041] Extracting scalar parameters of the target manifold after iterative convergence and vector parameters The approximate precoding intermediate result vector is calculated. , pre-encoded intermediate result vector The elements in the array are rearranged in reverse order to restore the original user index order, resulting in an intermediate result vector after restoration and sorting. ; Restore the sorted intermediate result vector Conjugate transpose of the original downlink channel matrix of the base station Multiplying them yields the final downlink transmission signal vector. .

[0042] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation.

[0043] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation.

[0044] Beneficial Effects: Compared with existing technologies, this invention proposes an information geometry method for downlink precoding in ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation. This method transforms the calculation of intermediate precoding results into a Gaussian distribution mean-finding problem. First, it introduces a user reordering mechanism based on channel spatial correlation, making the channel Gram matrix strip-shaped diagonal dominant. Then, it introduces a novel splitting strategy, dividing the reordered Gram matrix into a strip-shaped matrix and several cross-shaped matrix components. Next, based on the information geometry framework, iterative calculations using local inverse-free algebra and strip-shaped matrix inversion are performed to achieve low-complexity matrix inverse multiplication into vector approximation, obtaining the intermediate precoding result vector. Finally, the intermediate result vector is multiplied by the channel matrix to obtain the approximate RZF precoding result. This invention utilizes a matrix segmentation method of strip-shaped and cross-shaped matrices to fully exploit the local correlations between users. While maintaining near-optimal RZF precoding performance, it reduces detection complexity and improves convergence performance, effectively supporting the implementation of ultra-large-scale MIMO system transmission methods and solving the implementation complexity problem of ultra-large-scale MIMO systems. Attached Figure Description

[0045] Figure 1 The flowchart shows a geometric method for downlink precoding information in ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation.

[0046] Figure 2 A flowchart for cross-shaped and strip-shaped diagonal segmentation of an ultra-large-scale MIMO matrix;

[0047] Figure 3The diagram illustrates a cross-shaped and striped diagonal segmentation. Taking a 16×16 dimension as an example, Figure (a) shows that after reordering users based on spatial correlation in the Gram matrix, strong interference energy is highly concentrated near the main diagonal. The dark-filled area in the figure represents the main block of the striped matrix extracted by masking. Figure (b) shows the residual multi-user interference matrix outside the main block and its... The energy splitting logic involves dividing each non-zero grid of the residual multi-user interference matrix into two triangles diagonally: the upper left triangle is filled with column indices (such as the first...). The exclusive linear identifier of the column represents Energy is attributed to the column dimension components of the user's cross-shaped structure; the lower right half-triangle fills the row index (such as the first...). The exclusive logo of (line) represents another Energy is allocated to the user's row dimension component;

[0048] Figure 4 A comparison of the channel spatial correlation matrix of an ultra-large-scale MIMO system before and after reordering using the reverse Cuthill-McKee (RCM) algorithm;

[0049] Figure 5 The figure shows the system and rate performance comparison results of the cross-and-strip diagonal segmentation method and other iterative methods in the downlink precoding scenario of ultra-large-scale MIMO.

[0050] Figure 6 The figure shows the comparison of the convergence performance of the cross-plus-strip diagonal segmentation method and other iterative methods in the downlink precoding scenario of ultra-large-scale MIMO. Detailed Implementation

[0051] The technical solutions provided by the present invention will be described in detail below with reference to specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention.

[0052] like Figure 1 As shown, the geometric method for downlink precoding information of ultra-large-scale MIMO based on cross-shaped plus strip diagonal segmentation disclosed in this embodiment of the invention includes: obtaining the downlink channel matrix from the base station to all scheduled user terminals, and obtaining the data vector to be transmitted; calculating the Gram matrix of the channel matrix, and reordering the Gram matrix and the data vector to be transmitted according to spatial correlation to enhance the strip diagonal dominance characteristic of the Gram matrix; splitting the reordered Gram matrix into a strip matrix, and The residual multi-user interference cross-shaped matrix components, while simultaneously splitting the data vector to be transmitted into... There are _ inter-term vectors, where For the number of users; based on the splitting results, construct the target manifold within the information geometry framework. The parameters of the auxiliary manifold and the additional auxiliary manifold used to process the strip matrix are iteratively updated through scalar operations based on the sparsity of the cross-shaped matrix components and Woodbury's lemma and the inversion of the strip matrix until the preset number of iterations is reached. Based on the converged target manifold parameters, the intermediate result vector of regularized zero-forcible (RZF) precoding is calculated, restored to the original user sorting, and multiplied with the channel matrix to obtain the final downlink transmission signal.

[0053] like Figure 2 As shown, the matrix cross-segmentation method with striped diagonal elements in this embodiment of the invention includes: introducing a mask matrix, where the mask matrix element is 1 when the absolute value of the difference between the row index and the column index is less than or equal to the single-sided bandwidth, and 0 otherwise; splitting the reordered Gram matrix into a striped matrix and the sum of the residual multi-user interference matrix without striped diagonal elements; after extracting the striped matrix, constructing a rank-1 selection matrix based on the user sequence number, extracting the corresponding row and column vectors from the residual multi-user interference matrix, dividing them by 2 and reconstructing them to obtain the split... Each cross-shaped matrix component and its corresponding Each cross term vector component.

[0054] The user terminal in the above embodiments can be a mobile terminal such as a mobile phone, in-vehicle device, or smart equipment, or a fixed terminal. The method of this invention is mainly applicable to systems where the base station is equipped with a very large-scale antenna array to simultaneously serve multiple users. The specific implementation process of the downlink precoding method involved in this invention will be described in detail below with reference to a specific communication system example.

[0055] I. System Model

[0056] Consider a single-cell downlink ultra-large-scale multiple-input multiple-output (XL-MIMO) system using time-division duplex (TDD) mode, consisting of a base station equipped with an ultra-large-scale uniform planar array (UPA) antenna and... It consists of a single-antenna user terminal (UE); the base station's UPA has a total of Root transmitting antenna, These represent the number of antennas in the horizontal and vertical directions, respectively. Assume the base station has ideal downlink channel state information (CSI). The downlink transmission signal model can be represented as follows:

[0057] (1)

[0058] in, For the received signal vector, This is the downlink channel matrix. It is a linear precoding matrix. The normalized data vector to be sent satisfies , It is an additive white Gaussian noise vector. for An identity matrix of order 1. This represents the noise variance.

[0059] This embodiment uses Regularized Zero-Forcible (RZF) precoding, and its precoding matrix is ​​in the form of:

[0060] (2)

[0061] in For regularization parameters, To satisfy the normalization factor of the base station transmit power constraint, the core computational bottleneck of RZF precoding lies in solving the intermediate linear system, i.e., the intermediate result vector.

[0062] (3)

[0063] Direct matrix inversion has extremely high computational complexity. This invention avoids matrix inversion by using information geometry methods, and approximates the vector calculation with low complexity. .

[0064] II. User Reordering Based on Channel Spatial Correlation

[0065] Before performing the information geometry derivation of the precoder, in order to make full use of the spatial topology characteristics of the ultra-large-scale MIMO channel, this invention introduces a user reordering mechanism based on channel spatial correlation to maximize the banded diagonal dominance of the enhanced channel Gram matrix.

[0066] First, calculate the normalized spatial correlation matrix. Its matrix elements are defined as:

[0067] (4)

[0068] in, This is the original channel Gram matrix calculated from the original downlink channel matrix.

[0069] Next, set the correlation threshold. Construct a sparse adjacency matrix that reflects strong interference relationships between users. .when and season Otherwise Subsequently, a bandwidth reduction algorithm (such as the reverse Cuthill-McKee algorithm, i.e., the RCM algorithm, or the CM algorithm, AMD algorithm, etc.) is used to process the sparse adjacency matrix. The purpose of this type of algorithm is to extract a permutation vector by renumbering the nodes (i.e., users) to reduce the bandwidth of the matrix. .

[0070] Finally, using the extracted permutation vector For the original channel Gram matrix and the raw data vector to be sent Perform synchronized consistency replacement and reordering. Specifically, for By simultaneously performing symmetric row and column permutations on this permutation vector, the reordered channel Gram matrix is ​​obtained. ; data vector to be sent Perform one-dimensional positional permutations of the elements to obtain the reordered data vector. .

[0071] After the above reordering process, the strong interference energy that was originally randomly distributed in multi-user communication is highly concentrated near the main diagonal, making the reordered... It possesses extremely strong diagonal dominance characteristics in the strip structure. This not only ensures strict alignment of the data stream and the channel on the user index, but also lays the core structural foundation for subsequent low-complexity extraction of the strip matrix and separation of the cross-shaped residual multi-user interference matrix.

[0072] III. Design of a Preencoder Based on a Geometric Method for Cross-shaped and Strip-shaped Diagonal Segmentation Information

[0073] Information geometry methods often decompose the original probability distribution and approximate the optimal solution by solving for several low-dimensional marginal distributions. This approach aims to avoid directly dealing with high-dimensional matrices using information geometry methods. Find the reverse. Let be the channel Gram matrix. The algebraic solution problem needs to be transformed into a statistical inference problem of finding the mean of the probability distribution. Specifically, we construct a virtual complex Gaussian random vector. probability distribution

[0074] (5)

[0075] Within the framework of information geometry, this complex Gaussian probability distribution can be derived from natural parameters. Represented as

[0076] (6)

[0077] Among them, the original natural parameters are

[0078] (7)

[0079] According to natural parameters With expected parameter (mean) Mapping relationship between ) The mean of this distribution is It can be seen that the mean of this complex Gaussian distribution is exactly equal to the intermediate result vector obtained by precoding. .

[0080] Define the target probability distribution

[0081] (8)

[0082] in for 3D diagonal matrix for dimensional vector, is a scalar parameter. The purpose of this method is to find a target probability distribution whose mean approximates the mean of the true original distribution through iterative projection of information geometry.

[0083] Precoding based on cross-shaped and strip-shaped diagonal segmentation requires processing the reordered Gram matrix. Perform structured decomposition. Introduce a mask matrix. ,when ( When the bandwidth is unilateral Otherwise First, define a strip matrix. and residual multi-user interference matrix

[0084] (9)

[0085] in The symbol represents the Hadamard product. A choice matrix with rank 1 is defined. ,in For the unit array The original natural parameters can then be broken down into columns.

[0086] (10)

[0087] in For the first A vector of intersection terms, For the first Each negative definite cross-shaped structure matrix component.

[0088] Based on the information geometry framework, construct There are one auxiliary probability distribution manifold and one additional auxiliary probability distribution manifold. The natural parameters of an auxiliary probability distribution manifold can be written as:

[0089] (11)

[0090] in and Let be the free variables, and the auxiliary probability distribution in the manifold be... Then the first The expected parameters (covariance matrix) of the auxiliary probability distribution manifold and mean )for

[0091] (12)

[0092] because It has a special cross-shaped structure with rank 2 (due to the negative definite matrix). The cross-shaped structure constructed from the rank-1 selection matrix determines that it can be decomposed into a rank-2 matrix product. According to Woodbury's matrix inversion lemma and algebraic simplification, the calculation of the above expected parameters can completely avoid matrix inversion, simplifying to the following scalar form. Define local variables. and and local scalars , , , Then the trace and mean of the covariance matrix can be simplified to:

[0093] (13)

[0094] Next, it is necessary to calculate the projection of each auxiliary probability distribution manifold and the transit value of each auxiliary probability distribution manifold. The result of projecting an auxiliary probability distribution manifold onto a target auxiliary probability distribution manifold must satisfy the condition that the mean and the trace of the covariance matrix are equal.

[0095] (14)

[0096] After mapping the expected parameters back to the natural parameters, the first... Transmitted Belief Scalar of an Auxiliary Probability Distribution Manifold sum vector It can be represented as

[0097] (15)

[0098] The natural parameters of the extra auxiliary manifold (EAM) are: , Therefore, its expected parameter (mean) can be obtained. Covariance Matrix )for:

[0099] (16)

[0100] Desired parameters of the target manifold It is necessary to strictly match the corresponding features of the additional auxiliary manifold, i.e., the means are equal and the traces of the covariance matrix are uniformly distributed:

[0101] (17)

[0102] Given that the natural parameters of the target manifold are set as follows: Therefore, it can be deduced that:

[0103] (18)

[0104] contrast The definition allows direct retrieval of the target manifold scalar parameters. Update function:

[0105] (19)

[0106] Furthermore, based on the condition that the means are equal... ,because The vector parameters of the target manifold can be derived. Update function:

[0107] (20)

[0108] The parameters of the auxiliary and target manifolds are updated by passing on beliefs until the algorithm converges. A damping factor is needed when updating the parameters. To ensure the convergence of the algorithm, the specific parameter update expression is as follows:

[0109] (twenty one)

[0110] in For the number of iterations, This is the damping factor. After the algorithm converges, an approximate value of the precoded intermediate result vector can be obtained by calculating the mean of the target manifold.

[0111] (twenty two)

[0112] The intermediate result vector is rearranged in reverse order and then multiplied by the channel matrix to obtain the final precoded signal used for downlink transmission at the physical layer.

[0113] In summary, the design steps of the preencoder based on the cross-shaped plus strip diagonal segmentation information geometry method can be summarized as follows:

[0114] Step S101: The base station obtains the data vector to be transmitted. Downlink channel matrix Calculate the regularization parameter and the initial channel Gram matrix ;

[0115] Step S102: Calculate the normalized spatial correlation matrix and construct a sparse adjacency matrix reflecting strong interference relationships between users by combining it with a set correlation threshold. A bandwidth reduction algorithm (such as the reverse Cuthill-McKee (RCM) algorithm, the forward Cuthill-McKee (CM) algorithm, or the approximate minimum degree (AMD) algorithm) is used to process this sparse adjacency matrix. Through the above algorithm processing, a permutation vector is extracted. This permutation vector aims to reduce the matrix bandwidth, so that the strong interference energy that was originally randomly scattered in the matrix is ​​highly concentrated near the main diagonal. Subsequently, the permutation vector is used to uniformly reorder the channel Gram matrix and the data vector to be transmitted. Specifically, for the channel Gram matrix, the permutation vector is used to simultaneously perform symmetrical row and column permutations to maintain the conjugate symmetry of the matrix; for the original data vector to be transmitted... By performing a one-dimensional permutation of elements using the same permutation vector, a reordered data vector can be obtained. .

[0116] The above-mentioned synchronous permutation enhances the strip diagonal dominance of the Gram matrix while ensuring that the data stream and channel are strictly aligned on the user index.

[0117] Step S103: Split the rearranged Gram matrix into strip matrices. and the residual multi-user interference matrix without striped diagonal elements sum. Will Perform cross-section splitting into Each negative definite cross-shaped structure matrix component And the rearranged data vector is correspondingly split into Inter-term vectors Specifically:

[0118] (twenty three)

[0119] Step S104, based on the split structure design Auxiliary probability distributions , , ,in For vectors, We initialize the diagonal scalar parameters and design additional auxiliary and target probability distributions.

[0120] Step S105, according to Calculate the first Inter-term vectors and negative definite matrix Alternative transmission belief vector and the transmission of belief scalar Make the auxiliary probability distribution The traces of the mean and covariance matrices remain unchanged before and after projection onto the target manifold;

[0121] Step S106, based on the transmitted belief vector and scalar Aggregate updates of additional auxiliary manifold parameters and Solve the linear band system to update the target manifold parameters. and And update the parameters of each auxiliary manifold. and :

[0122] (twenty four)

[0123] Repeat steps S105 to S106 until the preset number of iterations is reached or the convergence condition is met.

[0124] Step S107, based on the vector of the target manifold and scalar Calculate the mean of the intermediate result vector:

[0125] (25)

[0126] Will After reversing the order, the signal is multiplied by the conjugate transpose of the original channel matrix to output the final downlink precoded transmission signal.

[0127] IV. Implementation Results

[0128] To enable those skilled in the art to better understand the present invention, a performance comparison of the cross-plus-strip diagonal segmentation information geometry method and existing iterative methods is provided below in this embodiment under a specific system configuration.

[0129] Consider a massively multi-channel MIMO system with a total number of base station antennas. (Using a 32x16 array), the total number of users in the cell is 800, and users are scheduled according to the least correlation among them. Downlink transmission is performed by a single-antenna user terminal. The channel is generated using the 3GPP UMa_NLOS scenario. Figure 4 A comparison of normalized spatial correlation matrix heatmaps before and after channel reordering using a bandwidth reduction algorithm (in this embodiment, the reverse Cuthill-McKee (RCM) algorithm is used as an example, but in other implementations, the CM algorithm or Sloan algorithm, etc., can also be used). Before reordering (e.g. Figure 4 As shown in (a), the multi-user interference energy is randomly distributed in the matrix; while using a correlation threshold... After performing RCM algorithm rearrangement (such as) Figure 4 As shown in b), the strong interference energy is highly concentrated near the main diagonal, giving the Gram matrix a very strong banded diagonal dominance characteristic. This optimization allows the method of this invention to work even with extremely small single-sided bandwidth (such as...). Even under these conditions, the extracted strip matrix can still capture about 86% of the interference energy, thus laying a structural foundation for subsequent elimination of large-scale matrix inversion. Figure 5 The proposed cross-shaped diagonal segmentation information geometry method (CBS-IGA) is presented under different signal-to-noise ratios (SNR), with a set single-sided bandwidth. This invention compares the system and sum-rate performance with other mainstream iterative algorithms such as conjugate gradient CG, block Jacobi (block size 8), and block cross-splitting based BCS-IGA (block size 1). The advantages of this invention are particularly significant in high signal-to-noise ratio (SNR) scenarios requiring precise suppression of multi-user interference (e.g., 20dB). With the same 4 iterations, the system and sum-rate loss of this invention is only 4.3% compared to the ideal RZF precoding, while the existing BCS-IGA method suffers a loss of 12%. In contrast, even with 5 iterations, the Jacobi and CG algorithms still suffer performance losses as high as 20% and 14%, respectively. The system and sum-rate achieved by this invention in only 3 iterations already comprehensively surpasses the performance of block Jacobi and CG algorithms after 5 iterations, approaching the ideal system capacity limit with fewer iterations. Figure 6 This paper presents a comparison of the convergence performance of different algorithms with varying iteration numbers, based on the normalized mean square error (NMSE) at a signal-to-noise ratio of 20 dB. Figure 6 As can be seen, this invention (CBS-IGA, The convergence curve of ) almost perfectly matches that of computationally more expensive, large-block-dimensional ( The BCS-IGA algorithm curve. To achieve... To achieve the target NMSE accuracy, this invention requires only 3 iterations, while the conventional BCS-IGA ( The traditional method requires 4 iterations, while the CG algorithm requires nearly 5 iterations. This demonstrates that the present invention utilizes the continuous spatial correlation between users more efficiently through a strip structure, completely eliminating the computational burden of inverting high-dimensional block-level matrices in traditional block-based methods, and reducing the computational complexity of each iteration to a minimum. While ensuring extremely high convergence accuracy, the computational complexity of a single iteration is significantly reduced, achieving an excellent balance between convergence speed and extremely low computational overhead.

[0130] This invention also discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation.

[0131] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation.

[0132] In the embodiments provided in this application, it should be understood that the disclosed methods can be implemented in other ways without departing from the spirit and scope of this application. The current embodiments are merely exemplary examples and should not be considered limiting, nor should the specific content given limit the purpose of this application. For example, some features may be omitted or not performed. All content not described in detail in this application is prior art.

[0133] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications are also considered within the scope of protection of this invention.

Claims

1. A geometric method for downlink precoding information of ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation, characterized in that, Includes the following steps: Obtain the downlink channel matrix from the base station to all scheduled user terminals, and obtain the data vector to be transmitted; The Gram matrix of the channel matrix is ​​calculated, and the Gram matrix and the data vector to be transmitted are reordered according to spatial correlation to enhance the strip diagonal dominance of the Gram matrix. The reordered Gram matrix is ​​split into a strip matrix, and The residual multi-user interference cross-shaped matrix components, while simultaneously splitting the data vector to be transmitted into... _ inter-term vectors, where Number of users; Based on the decomposition results, the target manifold is constructed within the information geometry framework. The parameters of the auxiliary manifold and the additional auxiliary manifold used to process the banded matrix are updated iteratively through scalar operations based on the sparsity of the cross-shaped matrix components and Woodbury's lemma and the inversion of the banded matrix until the preset number of iterations is reached. Based on the converged target manifold parameters, the intermediate result vector of regularized zero-forcible (RZF) precoding is calculated, restored to the original user order, and multiplied with the channel matrix to obtain the final downlink transmission signal.

2. The geometric method for downlink precoding information of ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation according to claim 1, characterized in that, The specific steps for reordering users based on spatial relevance include: Calculate the normalized spatial correlation matrix Its elements are ,in The channel Gram matrix; Set threshold Construct a sparse adjacency matrix ,when and hour, Otherwise, it is 0; Bandwidth reduction algorithm is used to process sparse adjacency matrices This causes the non-zero elements to converge towards the main diagonal to extract the permutation vector, which is then used to reorder the channel Gram matrix and the data vector.

3. The geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation according to claim 1, characterized in that, The reordered Gram matrix is ​​then split as follows: Introducing a mask matrix When the absolute value of the difference between the row index and the column index is less than or equal to the one-sided bandwidth When the mask matrix is ​​active, its elements are 1; otherwise, they are 0. Calculate the strip matrix. ,in It represents the Hadamah accumulation. This is the reordered channel Gram matrix. For regularization parameters, for An identity matrix of order 1; Calculate the residual multi-user interference matrix Define a selection matrix with rank 1. ,in The first unit of the identity matrix The column utilizes the selection matrix from the residual multi-user interference matrix. Extract the corresponding row and column vectors, divide them by two and reconstruct them to obtain the split-off first... Each cross-shaped matrix component And simultaneously extract the corresponding first Inter-term vectors The specific splitting formula is as follows: , ,in This is the reordered data vector to be sent.

4. The geometric method for downlink precoding information of ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation according to claim 1, characterized in that, Constructing target manifolds, additional auxiliary manifolds, and... within the information geometry framework An auxiliary manifold is used for iterative parameter updates via scalar operations and banded matrix inversion, including: Based on the split structure design Auxiliary probability distributions , , Additional auxiliary probability distributions used to handle banded matrices , , ; and target probability distribution , , ;in Let be a complex Gaussian random vector. and The split of the first Each cross-term vector and negative definite cross-shaped matrix component for An identity matrix of order 1. It is a strip matrix. , , For vectors, , , Set the parameters to scalars and initialize the manifold vector and scalar parameters; according to Calculate vectors sum matrix Alternative transmission belief vector and the transmission of belief scalar , making the auxiliary probability distribution The traces of the mean and covariance matrices remain unchanged before and after projection; according to the vector and scalar Update additional auxiliary manifold parameters and Target manifold parameters and and auxiliary manifold parameters and Repeat until the preset number of iterations is reached; the update method is as follows: ， ， ， ， ， ， in For damping factor, superscript Mark the number of iterations.

5. The geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation according to claim 4, characterized in that, The invariance of the traces of the mean and covariance matrices means that: probability distribution With probability distribution The mean and trace of the covariance matrix are equal, where , Additional auxiliary probability distribution With the target probability distribution The mean and the trace of the covariance matrix are equal.

6. The geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation according to claim 4, characterized in that, According to the The covariance matrix of the auxiliary probability distributions and mean vector Calculate the scalar of transmitted beliefs and the transmission of belief vectors for: ， ， Based on the fact that the mean of the target probability distribution and the trace of the covariance matrix are equal, and combined with the covariance matrix of the additional auxiliary probability distribution... and mean vector Calculate the target probability distribution parameters: ， 。 7. The geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip-shaped diagonal segmentation according to claim 4, characterized in that, Based on Woodbury's matrix inversion lemma and algebraic simplification, matrix inversion is completely avoided, and the trace of the covariance matrix is ​​obtained. and mean The solution is simplified to scalar form, specifically: Define local variables and Calculate local scalars , , , Trace of the covariance matrix and local mean The calculation is as follows: ， 。 8. The geometric method for downlink precoding information of ultra-large-scale MIMO based on cross-shaped and strip-shaped diagonal segmentation according to claim 1, characterized in that, The calculation yields an intermediate result vector of Regularized Zero-Force (RZF) precoding. After restoring this vector to the original user ordering, it is multiplied by the channel matrix to obtain the final downlink transmission signal. Specifically, this includes: Extracting scalar parameters of the target manifold after iterative convergence and vector parameters The approximate precoding intermediate result vector is calculated. , pre-encoded intermediate result vector The elements in the array are rearranged in reverse order to restore the original user index order, resulting in an intermediate result vector after restoration and sorting. ; Restore the sorted intermediate result vector Conjugate transpose of the original downlink channel matrix of the base station Multiplying them yields the final downlink transmission signal vector. .

9. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip diagonal segmentation as described in any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the geometric method for ultra-large-scale MIMO downlink precoding information based on cross-shaped and strip diagonal segmentation as described in any one of claims 1-8.

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