Low rank modified matrix inversion method and system for wireless communication precoding computation

Abstract

The application discloses a low-rank correction matrix inversion method and system for wireless communication precoding calculation, and comprises: obtaining a to-be-inverted correlation matrix, the obtaining mode being: in a multi-user downlink transmission process, acquiring channel matrices of each user on different subcarriers according to a base station to construct a to-be-inverted correlation matrix for precoding calculation; inputting the to-be-inverted correlation matrix into a structured correction expansion network based on Newton-Schulz for iterative inversion, and outputting a final inverse matrix approximation; wherein, before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the amplitude of the target residual in the early iteration. The application can reduce the residual amplitude in the early iteration under the premise of ensuring the accuracy of the matrix inversion approximation, make the inversion process enter the stable convergence stage faster, and then reduce the number of iterations required to reach the target accuracy.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication technology and matrix inversion technology, specifically to a method and system for inverting low-rank modified matrices for wireless communication precoding computation. Background Technology

[0002] Wireless communication technology is a crucial component of the next generation of information technology. In high-throughput, low-latency service scenarios such as 5G mobile communication, VMI (Very Large Scale) antenna arrays for 6G mobile communication, industrial internet, vehicle-to-everything (V2X) communication, low-altitude communication, satellite internet, and smart IoT, base stations need to complete a large number of baseband signal processing operations within a limited time. Among these, the calculation of precoding matrices or beamforming matrices in downlink multi-user transmission scenarios is a key technical step in achieving directional transmission, suppressing inter-user interference, and improving spectral efficiency and energy efficiency. In multi-user multiple-input multiple-output (MIMO) communication systems, base stations typically need to construct downlink precoding matrices based on the channel state information of each user. With the continuous increase in the number of base station antennas, the number of served users, and transmission bandwidth, the dimension of the channel matrix continues to increase, and the calculation frequency of the precoding matrix also increases significantly. Especially in high-speed mobile, low-latency services and dynamic wireless environments, the channel state changes rapidly over time, requiring base stations to frequently update the precoding matrix. Therefore, the real-time performance of precoding calculations has become a significant factor affecting the throughput, link reliability, and baseband processing capabilities of wireless communication systems.

[0003] In existing technologies, when base stations perform downlink beamforming or precoding calculations, they typically need to first obtain the channel matrix, construct a correlation matrix based on the channel matrix, and then perform inversion or inverse approximation calculations on the correlation matrix. For example, in methods such as regularized zero-forcible precoding and minimum mean square error precoding, it is often necessary to calculate the matrix inverse of the following form:

[0004]

[0005] in, Represents the channel matrix. Represents the regularization parameter. This represents the identity matrix. Furthermore, the precoding weight matrix can be calculated based on the obtained inverse matrix and used for subsequent downlink transmission signal weighting processing. Therefore, the computational efficiency of matrix inversion directly affects the update speed of the precoding matrix and the real-time processing capability of wireless communication devices.

[0006] To address the aforementioned matrix inversion requirements, existing technologies typically employ two types of solutions. The first type is direct inversion schemes, such as those based on LU decomposition, QR decomposition, and Cholesky decomposition. These methods achieve high accuracy when the matrix size is small or in offline computation scenarios. However, when the channel matrix dimension is large, the number of users is large, and the precoding matrix needs frequent updates, direct inversion schemes usually require significant computational resources and long processing times, easily becoming a computational bottleneck in baseband processing and failing to meet the real-time requirements of wireless communication systems. The second type is iterative inversion schemes. For example, the Newton-Schulz (NS) iterative method is a common matrix inversion method, and its update form can be expressed as:

[0007]

[0008] in Let be the matrix whose inverse is to be found. For the first The inverse matrix approximation is obtained through iteration. This type of method mainly completes the iterative update through matrix multiplication. It has the characteristics of relatively regular implementation and easy hardware deployment, and is therefore used in matrix inverse approximation calculation tasks.

[0009] However, in wireless communication precoding applications for next-generation information technology, existing technologies still have the following shortcomings: First, in large-scale multiple-input multiple-output or multi-user high-dimensional channel scenarios, the dimension of the inverse matrix to be constructed from the channel matrix is ​​large, and in some cases, it has a large condition number. For traditional Newton-Schulz iteration and its common improvements, when the condition of the inverse matrix to be calculated is poor, more iteration steps are often required to achieve the predetermined accuracy, which leads to an increase in the precoding matrix update delay and affects the real-time computational efficiency of downlink beamforming.

[0010] Secondly, most existing improvement methods employ methods such as overall scaling, preconditioning, or scalar parameter adjustment to improve the matrix iterative inversion process. These methods primarily provide uniform adjustment to the overall iterative process, lacking the ability to fine-grained correct the error in the dominant direction. In wireless communication scenarios, due to the statistical characteristics and structural features of the channel matrix, iterative errors are often not uniformly distributed but may be concentrated in a few dominant directions. Existing technologies struggle to utilize this type of error structure information for targeted correction, thus failing to effectively reduce the number of iterations while maintaining accuracy.

[0011] In summary, existing technologies have at least the following shortcomings: First, in the process of downlink beamforming or precoding calculation in wireless communication, traditional matrix inversion methods are not very efficient in high-dimensional and high-condition-number scenarios, making it difficult to meet the requirements for rapid updating of precoding matrices; second, most existing iterative inversion methods lack effective utilization of error structure information, resulting in a large number of iterations required to achieve the target accuracy; and third, existing solutions are unable to further reduce baseband processing latency and computational resource consumption while ensuring precoding calculation accuracy.

[0012] In view of the above, this application is hereby submitted. Summary of the Invention

[0013] The technical problem this invention aims to solve is how to reduce the computational complexity, number of iterations, and precoding matrix update time in the process of inverting high-dimensional correlation matrices in wireless communication downlink beamforming or precoding computation scenarios, while ensuring matrix inversion accuracy and precoding performance. This, in turn, improves the real-time signal processing capabilities of wireless communication devices in multi-user, high-dimensional channel environments. This invention provides a low-rank modified matrix inversion method and system for wireless communication precoding computation. This invention applies a low-rank modified expansion iterative structure to the solution of downlink beamforming or precoding matrices in wireless communication. When performing inverse approximation calculation on the correlation matrix to be inverted obtained from the channel matrix, the current inverse matrix approximation is first structurally modified before Newton-Schulz iterative updates are performed, thereby compensating for the dominant components in the iteration error. This technical solution reduces the residual amplitude in the early stages of iteration while ensuring the accuracy of the matrix inverse approximation, allowing the inversion process to enter a stable convergence phase more quickly, thus reducing the number of iterations required to achieve the target accuracy.

[0014] This invention is achieved through the following technical solution:

[0015] In a first aspect, this invention provides a method for inverting a low-rank modified matrix for precoding computation in wireless communication. This method is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems. The method includes:

[0016] The method for obtaining the inverse correlation matrix to be calculated is as follows: during multi-user downlink transmission, the inverse correlation matrix to be calculated is constructed based on the channel matrix of each user on different subcarriers obtained by the base station.

[0017] The correlation matrix to be inverted is input into a structured modified expansion network based on Newton-Schulz for iterative inversion, and the final approximate inverse matrix is ​​output.

[0018] The iterative inversion process of the structured correction expansion network based on Newton-Schulz is as follows: before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual in the early stage of the iteration.

[0019] Furthermore, the inverse correlation matrix to be determined Corresponding to the The precoding correlation matrix on each subcarrier is expressed as follows:

[0020] ;

[0021] in, Indicates the subcarrier index; Indicates the first Channel matrix on subcarriers; express The conjugate transpose of; This represents a regularization parameter or a noise-related parameter. Represents the identity matrix.

[0022] Furthermore, the Newton-Schulz-based structured correction unfolding network includes a multi-layer unfolding structure, with each layer including a structured correction step and a Newton-Schulz iterative update step.

[0023] Furthermore, the correlation matrix to be inverted is input into a structured modified expansion network based on Newton-Schulz for iterative inversion, including:

[0024] Construct an initial inverse approximation of the inverse correlation matrix to be determined;

[0025] The initial inverse approximation input is expanded into a structured modified network based on Newton-Schulz. The process is repeated layer by layer until the preset total number of iterations is reached or the accuracy requirement is met, to obtain the final approximation of the inverse matrix.

[0026] Among them, in the first In the layer iteration, the current inverse matrix approximation is corrected by low rank to obtain the corrected intermediate variable matrix; and the corrected intermediate variable matrix is ​​updated by Newton-Schulz iteration to obtain the inverse matrix approximation.

[0027] Furthermore, the formula for the low-rank correction is:

[0028] ;

[0029] in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Denotes a low-rank dimension, and typically satisfies ; Here, the inverse correlation matrix is ​​represented. The dimension, that is .

[0030] Furthermore, the formula for the Newton-Schultz iterative update is:

[0031] ;

[0032] in, Indicates the first The inverse matrix approximation obtained by layer iteration; Representation and matrix A dimensionally consistent identity matrix; This indicates the problem of finding the inverse correlation matrix. The normalized matrix obtained by performing normalization processing; This represents the intermediate variable matrix.

[0033] Secondly, this invention provides a low-rank modified matrix inversion system for precoding computation in wireless communication. This system is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems. The system includes:

[0034] The unit for obtaining the inverse correlation matrix is ​​used to obtain the inverse correlation matrix to be obtained. The method for obtaining the inverse correlation matrix to be obtained is as follows: during the multi-user downlink transmission process, the inverse correlation matrix to be obtained is constructed for precoding calculation based on the channel matrix of each user on different subcarriers obtained by the base station.

[0035] An improved iterative solution unit is used to input the correlation matrix to be inverted into a Newton-Schulz-based structured correction expansion network for iterative inversion, and output the final approximation of the inverse matrix. The iterative inversion process of the Newton-Schulz-based structured correction expansion network is as follows: before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual in the early stage of iteration.

[0036] Furthermore, the Newton-Schulz-based structured correction expansion network includes a multi-layer expansion structure, each layer of which includes a structured correction sub-unit and a Newton-Schulz iterative update sub-unit;

[0037] The structured correction subunit is used to perform low-rank correction on the current inverse matrix approximation of the input, to obtain the corrected intermediate variable matrix;

[0038] The Newton-Schulz iterative update sub-unit is used to perform Newton-Schulz iterative updates on the corrected intermediate variable matrix to obtain an approximate inverse matrix.

[0039] Furthermore, the formula for the low-rank correction is:

[0040] ;

[0041] in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Denotes a low-rank dimension, and typically satisfies ; Here, the inverse correlation matrix is ​​represented. The dimension, that is .

[0042] Thirdly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for inverting a low-rank modified matrix for precoding computation in wireless communication.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] This invention relates to a low-rank correction matrix inversion method and system for wireless communication precoding computation. It applies a low-rank correction expansion iterative structure to wireless communication downlink beamforming or precoding matrix solving scenarios to improve the efficiency of correlation matrix inversion. Specifically, after constructing the channel matrix and correlation matrix based on user channel state information, this invention employs a multi-layer expansion structure of low-rank correction and Newton-Schulz iterative updates to perform inverse approximation of the correlation matrix. In each iteration, low-rank correction is first used to compensate for the dominant error direction in the current inverse matrix approximation, followed by Newton-Schulz iterative updates, thereby reducing the number of iterations required to achieve the target accuracy. By combining low-rank correction and iterative inversion hierarchically, this invention improves the computational efficiency of high-dimensional correlation matrix inversion while maintaining the stability of the original iterative framework. The inversion results are further used to generate precoding matrices or beamforming weight matrices, enhancing the real-time signal processing capabilities of wireless communication devices. This invention can reduce the residual amplitude in the early stages of iteration while ensuring the accuracy of the matrix inverse approximation, allowing the inversion process to enter a stable convergence phase more quickly, thus reducing the number of iterations required to achieve the target accuracy. Attached Figure Description

[0045] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0046] Figure 1 This is a diagram of the classic Newton-Schultz iterative method;

[0047] Figure 2 This is the structured modified unfolded network diagram based on Newton-Schulz in this invention;

[0048] Figure 3 This is a flowchart of the low-rank modified matrix inversion method for precoding computation in wireless communication according to the present invention;

[0049] Figure 4 This is a comparison of the residual descent process of the method of this invention and the classic Newton-Schultz iteration method under different condition number matrices.

[0050] Figure 5 This is a block diagram of the low-rank modified matrix inversion system for wireless communication precoding computation according to the present invention. Detailed Implementation

[0051] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0052] To address the high throughput, low latency, and real-time processing requirements of downlink beamforming or precoding computation in next-generation wireless communication systems, existing matrix inversion methods still suffer from high computational complexity, numerous iterations, and significant precoding matrix update delays in high-dimensional, multi-user, and large condition number channel scenarios. Particularly in applications such as 5G mobile communication, VMI (Very Large Scale Infrared) communication for 6G mobile communication, millimeter-wave communication, vehicle-to-everything (V2X) communication, industrial internet, and smart IoT, base stations need to frequently update the precoding matrix based on rapidly changing channel state information. Therefore, the efficiency of matrix inversion directly impacts the real-time baseband processing capabilities of wireless communication equipment.

[0053] like Figure 1 As shown, Figure 1 This is a diagram of the classic Newton-Schulz iterative method. While traditional direct inversion methods can achieve high accuracy, they suffer from significant computational overhead in scenarios with large matrix dimensions and frequent channel state changes, making it difficult to meet low-latency processing requirements. Existing iterative inversion methods, although possessing advantages such as regular computational structure, ease of parallel implementation, and hardware deployment, often employ fixed update strategies. They typically only adjust the iterative process holistically, making it difficult to utilize the dominant direction, low-dimensional subspace, or channel structure information in the iterative residuals for targeted corrections. Therefore, while maintaining the accuracy of matrix inverse approximation and precoding performance, existing schemes still struggle to further reduce computational latency and resource consumption.

[0054] like Figure 2 As shown, Figure 2 This invention presents a structured correction expansion network diagram based on Newton-Schulz. It applies a low-rank correction expansion iterative structure to the process of downlink beamforming or precoding matrix solving in wireless communication. When performing inverse approximation calculation on the inverse correlation matrix obtained from the channel matrix, the current inverse matrix approximation is first structurally corrected before Newton-Schulz iterative updates are performed, thereby compensating for the dominant components in the iteration error. This technical solution reduces the target residual amplitude in the early stages of iteration while ensuring the accuracy of the matrix inverse approximation, allowing the inversion process to enter a stable convergence phase more quickly, thus reducing the number of iterations required to achieve the target accuracy.

[0055] First, in the technical solution of this invention, before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term. This correction process can compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual in the early stages of iteration. Since the convergence speed of the Newton-Schulz iteration is closely related to the current residual size, the above correction mechanism can enable the iteration process to enter the fast convergence stage more quickly, thereby reducing the number of iterations required to achieve the same accuracy requirements.

[0056] Secondly, the correction mechanism proposed in this invention is introduced in a structured form: a low-rank correction form, which enables adjustments to the dominant errors concentrated in a few spectral directions in the error matrix. Compared to existing methods that rely solely on global scaling or scalar parameter adjustment, this approach more effectively improves the iterative update process, allowing iterative processes to more efficiently approximate the target inverse matrix.

[0057] Furthermore, this invention retains the basic update structure of the classic Newton-Schultz iteration, adding only a structured correction operation before each iteration, thus preserving the fundamental stability characteristics of the original iterative method. Simultaneously, since the main computational process still primarily involves matrix multiplication, the method of this invention maintains a relatively good computational structure in its implementation.

[0058] In summary, by introducing a structured correction mechanism into the classical Newton-Schulz iterative framework, this invention can improve the error evolution process while maintaining the original iterative stability, thereby reducing the number of iteration steps and improving the efficiency of matrix inversion calculation.

[0059] The following is a derivation of how this invention reduces the number of iterations by decreasing the target residual through low-rank correction:

[0060] 1. Classical Newton-Schultz Iteration

[0061] set up Given an invertible matrix, the goal is to find its inverse matrix. The Newton-Schultz iteration format is as follows:

[0062]

[0063] in, Let be the matrix whose inverse is to be found. The target inverse matrix, For the first The approximation of the inverse matrix obtained by step iteration, It is the identity matrix;

[0064] Definition of the first The step residual matrix is:

[0065]

[0066] Then there is the first Step residual matrix:

[0067]

[0068] therefore:

[0069]

[0070] This demonstrates that the Newton-Schultz iteration has a quadratic convergence property.

[0071] 2. The residual change introduced in this invention after low-rank correction

[0072] To accelerate early convergence, a low-rank correction is introduced before updating the standard NS:

[0073]

[0074] in, The intermediate iteration variables are the low-rank corrected variables, i.e., the intermediate variable matrix; To adjust the step size; It is a low-rank correction matrix;

[0075] The low-rank correction term is defined as follows:

[0076]

[0077] in, All are low-rank corrected basis matrices; For the correction coefficient vector; For the reason The diagonal matrix formed;

[0078] Corrected residuals for:

[0079]

[0080] Substitution We can obtain:

[0081]

[0082] Subsequently, the revised Perform NS update:

[0083]

[0084] Therefore, the new residual satisfies:

[0085]

[0086] Therefore:

[0087]

[0088] If the low-rank correction can effectively suppress the dominant residual component, then:

[0089]

[0090] in, Let be the residual compression factor, satisfying 0 ≤ <1;

[0091] Then we have:

[0092]

[0093] Compared to the classic Newton-Schultz iteration:

[0094]

[0095] Low-rank correction introduces a smaller contraction factor. Therefore, the residuals decrease faster.

[0096] 3. The reason why the low-rank correction of this invention reduces the number of iterations compared to the classical Newton-Schultz iteration.

[0097] Classical Newton-Schultz iteration satisfies:

[0098]

[0099] If required:

[0100]

[0101] in, For target error accuracy;

[0102] Then it is necessary to:

[0103]

[0104] After the low-rank correction, we have:

[0105]

[0106] The corresponding number of iterations can be expressed as:

[0107]

[0108] because:

[0109]

[0110] Therefore, the effective residual after low-rank correction is smaller, and fewer iterations are required to achieve the same accuracy.

[0111] Therefore, the core mechanism of the classical Newton-Schultz iteration is the residual square: This mechanism ensures that the algorithm exhibits fast quadratic convergence when the residuals are sufficiently small. However, for ill-conditioned matrices with large condition numbers, the initial residuals are often close to 1, leading to slow convergence in the early stages. The core idea of ​​the low-rank correction method in this invention is to compensate for the dominant residual direction using a low-rank structure before performing residual squaring, thus changing the residual direction from... Reduce to Then, a Newton-Schultz update is performed, which squares the smaller residuals, thus significantly amplifying the residual compression effect. Therefore, the acceleration mechanism of this method can be summarized as follows: That is, first suppress the dominant residual component by low-rank correction, and then use the quadratic convergence mechanism of NS iteration to further amplify the acceleration effect, thereby reducing the number of iterations required to reach the target accuracy.

[0112] Example 1

[0113] like Figure 3 As shown, this invention provides a low-rank modified matrix inversion method for precoding computation in wireless communication. This method is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems. The method includes:

[0114] The method for obtaining the inverse correlation matrix to be calculated is as follows: during multi-user downlink transmission, the inverse correlation matrix to be calculated is constructed based on the channel matrix of each user on different subcarriers obtained by the base station.

[0115] The correlation matrix to be inverted is input into a structured modified expansion network based on Newton-Schulz for iterative inversion, and the final approximate inverse matrix is ​​output.

[0116] The iterative inversion process of the structured correction expansion network based on Newton-Schulz is as follows: before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual in the early stage of the iteration.

[0117] like Figure 2 As shown, the structured correction expansion network based on Newton-Schulz in this invention includes a multi-layer expansion structure, with each layer comprising a structured correction step and a Newton-Schulz iterative update step. A low-rank correction is added before each Newton-Schulz iteration to perform a structured correction on the current inverse matrix approximation, obtaining corrected intermediate variables, before the Newton-Schulz iterative update is performed. By repeating the above process in the multi-layer structure, the dominant error components in the error matrix can be gradually reduced, thereby obtaining a high-accuracy matrix inverse approximation with fewer iterations.

[0118] This invention proposes a low-rank modified expansion iterative matrix inversion method and applies it to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems. During multi-user downlink transmission, the base station first acquires the channel matrix of each user on different subcarriers. And further construct the inverse matrix to be calculated for precoding computation: ,in, Indicates the subcarrier index; Indicates the first Channel matrix on subcarriers Indicates the number of base station transmitting antennas. This indicates the number of receiving antennas on the user side or the equivalent user dimension in a multi-user scenario. Indicates the first Channel matrix on each subcarrier The conjugate transpose of; This represents a regularization parameter or a noise-related parameter. Representation and matrix An identity matrix with consistent dimensions. Therefore, the matrix Indicates the first The inverse correlation matrix to be calculated for precoding on each subcarrier. For ease of explanation, the following explanation uses the inverse matrix corresponding to a single subcarrier as an example, denoted as... The objective of this invention is to improve the matrix. A fast inversion or inverse approximation calculation is performed for the generation of subsequent precoding matrices or beamforming weight matrices. Based on this, the proposed method uses the classical Newton-Schulz matrix inversion iteration as its foundation, introducing a low-rank correction module before each iteration update to structurally adjust the current inverse matrix approximation, thus constructing an expanded network structure composed of multiple "low-rank correction + Newton-Schul iterative updates". Through this approach, the dominant error components in the error matrix can be specifically corrected while retaining the original iterative framework, thereby reducing the number of iterations required to achieve the target accuracy, improving the convergence efficiency of the matrix inversion process, and further enhancing the real-time computational efficiency of the precoding matrix.

[0119] The method in this embodiment includes the following steps:

[0120] Step 1: Matrix normalization.

[0121] To ensure the stability of the Newton-Schultz iteration, the input quasi-matrix to be solved is first... Normalization is performed to obtain the normalized matrix. :

[0122]

[0123] in, Let the matrix be the inverse matrix to be found. This is a normalization factor used to ensure the matrix satisfies the convergence condition of the Newton-Schulz iteration. In this embodiment, the inverse correlation matrix to be calculated... Corresponding to the The precoding correlation matrix on each subcarrier is as follows:

[0124]

[0125] in, Indicates the subcarrier index; Indicates the first Channel matrix on subcarriers; express The conjugate transpose of; This represents a regularization parameter or a noise-related parameter. Represents the identity matrix.

[0126] Step 2: Initialize the inverse matrix approximation.

[0127] Construct the inverse correlation matrix to be determined Initial inverse approximation For example, the following initialization method can be used:

[0128]

[0129] in, Indicates the first Initial approximation of the inverse matrix before the start of layer iteration; Representation matrix The transpose of . In some implementations, when the matrix When the matrix is ​​a complex Hermitian matrix, it can also be used. This represents its conjugate transpose, and the initial inverse approximation can then be written as:

[0130]

[0131] Step 3: Construct the low-rank correction module.

[0132] The initial inverse approximation input is expanded into a structured modified network based on Newton-Schulz. Layer iteration, at the 1st In the layer iteration, the current inverse matrix is ​​first approximated. Perform low-rank correction to obtain the corrected intermediate variable matrix:

[0133]

[0134] in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Denotes a low-rank dimension, and typically satisfies ; Here, the inverse correlation matrix is ​​represented. The dimension, that is .

[0135] The above is achieved through a matrix The product constructs a low-rank correction term, which can compensate for the dominant error direction in the error matrix, thereby improving the subsequent iteration process.

[0136] Step 4: Newton-Schultz iterative update.

[0137] For the corrected intermediate variable matrix Perform Newton-Schultz iterative updates:

[0138]

[0139] in, Indicates the first The inverse matrix approximation obtained by layer iteration; Representation and matrix A dimensionally consistent identity matrix; This represents the normalized matrix obtained in step 1; This represents the intermediate variable matrix obtained in step 3. This step is used to further approximate the matrix based on the current low-rank correction. The inverse matrix.

[0140] Step 5: Multi-level iterative calculation.

[0141] Repeat steps 3 and 4 for a total of [number] times. Layer-by-layer iterative computation results in a hierarchical computational structure composed of multiple "low-rank corrections + Newton-Schultz updates". This indicates the preset total number of iterations. Through multiple iterations, the error in the inverse matrix approximation can be gradually reduced, improving the accuracy of approximating the target inverse matrix.

[0142] Step 6: Output matrix inverse approximation.

[0143] When the preset number of iterations is reached Or, when the accuracy requirements are met, the final inverse matrix is ​​output as an approximation.

[0144]

[0145] in, Indicates the process The final approximate result of the inverse matrix obtained after low-rank layer correction and Newton-Schultz iterative update; Represents the matrix to be inverted The inverse matrix. In wireless communication precoding scenarios, the approximate result of the inverse matrix can be further used to generate the... The precoding matrix or beamforming weight matrix on each subcarrier.

[0146] By following the steps above, a high-precision matrix inverse approximation result can be obtained with fewer iterations, thereby improving the real-time computation efficiency of precoding matrices in wireless communication systems.

[0147] Figure 4 This is a comparison of the residual descent process of the method of this invention and the classical Newton-Schulz iteration method under different condition number matrices. Figure 4 (a) is the matrix condition number. Condition, Figure 4 (b) is the matrix condition number. Condition, Figure 4 (c) represents the matrix condition number. Condition, Figure 4 The horizontal axis represents the number of iterations, and the vertical axis represents the approximation error of the inverse matrix. Figure 4 As can be observed, under different condition number settings, the method of this invention can achieve a rapid decrease in residuals with fewer iterations compared to the classic Newton-Schultz iteration method. For example, when the condition numbers are respectively... , and In contrast, the classic Newton-Schulz iteration method requires approximately 19, 25, and 35 iterations respectively to achieve the given accuracy, while the method of this invention requires only approximately 5, 6, and 10 iterations to achieve the same level of accuracy. Furthermore, the residual descent curves reveal that the method of this invention rapidly reduces the residual value in the early stages of iteration, allowing the algorithm to enter the fast convergence phase earlier. In contrast, the classic Newton-Schulz iteration method experiences a slower residual descent in the initial stages, requiring more iterations to achieve the same accuracy. Therefore, it can be seen that this invention effectively reduces the number of iterations required for matrix inversion while maintaining convergence stability, thereby improving the efficiency of matrix inversion calculations.

[0148] In addition to comparing the residual descent process, a comprehensive performance comparison was also conducted between the method of this invention and several existing matrix inversion methods. The comparison methods include the Neumann iteration method, the Newton-Schulz method, the Jacobi preconditioned Newton-Schulz method, and the scaled Newton-Schulz method. Table 1 shows the performance of the method at different matrix sizes (…). , and ) and different condition numbers ( , , and The performance of each method in terms of iteration count, computation time, and relative error is compared under different matrix sizes and condition numbers. Table 1 shows that, under different matrix sizes and condition numbers, the present invention requires significantly fewer iterations than the traditional Newton-Schulz method and its improvements. For example, when the condition number is... and In cases where the Newton-Schulz method typically requires approximately 25 to 35 iterations, this invention requires only about 6 to 12 iterations to achieve a similar error level. Furthermore, computational time metrics show that, because this invention can complete matrix inversion calculations with fewer iterations, its overall computation time is generally lower than existing methods. While maintaining similar relative error accuracy, this invention demonstrates higher computational efficiency in most test cases. Therefore, experimental results show that this invention effectively reduces iteration steps and overall computation time while ensuring inversion accuracy, thereby improving the efficiency of the matrix inversion calculation process.

[0149] Table 1: Performance comparison of matrix inversion under different condition numbers and matrix sizes

[0150]

[0151] Example 2

[0152] This embodiment applies the method of Embodiment 1 to a downlink beamforming task in a wireless communication system. In this task, two sets of channel matrices with different dimensions are selected respectively. and It comprises 31 channel matrix subcarriers. The first subcarrier is selected for model parameter training, and the remaining 30 subcarriers are used for testing and evaluation. During beamforming, the transmit weight matrix is ​​calculated as follows:

[0153]

[0154] in, This is represented by the channel matrix. For parameters, Let be the identity matrix. The above formula involves matrix inversion, therefore the method of this invention can be used for efficient approximation of the matrix inverse. Comparison metrics include the number of iterations, running time, and the approximation error of the related matrix inverse (…). ) and precoding matrix error ( )

[0155] As shown in Table 2, under two sets of real channel data of different scales, the method of the present invention requires significantly fewer iterations than existing methods while ensuring the accuracy of the inverse approximation of the correlation matrix and the accuracy of the precoding matrix. For example, when At that time, the classic NS (Newton-Schultz iteration) method, the preconditioning NS method, and the NNI (Neural Newton iteration) method all require 33 iterations, the Scaled-NS method requires 24 iterations, while the method of this invention only requires 11 iterations; when Existing methods typically require 26 to 36 iterations, while the method of this invention requires only 15 iterations. Furthermore, the runtime metrics show that the method of this invention has a shorter computation time for both sets of data. At that time, the running time of the method of the present invention is 3.268ms, which is lower than the 6.420ms of the NS method and the 6.267ms of the Scaled-NS method; when At that time, the running time of the method of the present invention was 5.332ms, which is significantly lower than the 12.119ms of the NS method and the 10.601ms of the Scaled-NS method. On the other hand, the method of the present invention... and The performance metrics remain on the same order of magnitude as existing high-precision methods, indicating that the present invention does not significantly reduce inversion accuracy and precoding performance despite the reduction in the number of iterations. In summary, the method of the present invention can effectively reduce the number of iterations and computation time while maintaining inversion accuracy in downlink beamforming tasks in wireless communication, thereby improving overall computational efficiency.

[0156] Table 2: Performance Comparison of Different Methods in Wireless Communication Tasks

[0157]

[0158] Example 3

[0159] like Figure 5 As shown, the difference between this embodiment and Embodiment 1 is that this embodiment provides a low-rank modified matrix inversion system for wireless communication precoding computation. This system corresponds one-to-one with the low-rank modified matrix inversion method for wireless communication precoding computation in Embodiment 1. This system is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems. The system includes:

[0160] The unit for obtaining the inverse correlation matrix is ​​used to obtain the inverse correlation matrix to be obtained. The method for obtaining the inverse correlation matrix to be obtained is as follows: during the multi-user downlink transmission process, the inverse correlation matrix to be obtained is constructed for precoding calculation based on the channel matrix of each user on different subcarriers obtained by the base station.

[0161] An improved iterative solution unit is used to input the correlation matrix to be inverted into a Newton-Schulz-based structured correction expansion network for iterative inversion, and output the final approximation of the inverse matrix. The iterative inversion process of the Newton-Schulz-based structured correction expansion network is as follows: before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual in the early stage of iteration.

[0162] In this embodiment, the Newton-Schulz-based structured correction unfolding network includes a multi-layer unfolding structure, and each layer of the unfolding structure includes a structured correction sub-unit and a Newton-Schulz iterative update sub-unit.

[0163] The structured correction subunit is used to perform low-rank correction on the current inverse matrix approximation of the input, to obtain the corrected intermediate variable matrix;

[0164] The Newton-Schulz iterative update sub-unit is used to perform Newton-Schulz iterative updates on the corrected intermediate variable matrix to obtain an approximate inverse matrix.

[0165] In this embodiment, the formula for low-rank correction is:

[0166] ;

[0167] in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Denotes a low-rank dimension, and typically satisfies ; Here, the inverse correlation matrix is ​​represented. The dimension, that is .

[0168] The execution process of each unit can be carried out according to the steps of the low-rank modified matrix inversion method for wireless communication precoding computation in Example 1, and will not be described in detail in this example.

[0169] This invention introduces a structured correction sub-unit before each iterative update in the Newton-Shull matrix inversion iterative process. This sub-unit corrects the current inverse matrix approximation before executing the overall computational framework of the Newton-Shull iterative update. The structured correction sub-unit adopts a low-rank correction form, constructing a low-rank matrix to compensate for the current inverse matrix approximation, thereby adjusting the dominant error direction in the error matrix. Furthermore, the matrix inversion iterative process is represented as a multi-layered expansion structure, with each layer containing both structured correction steps and Newton-Shull iterative update steps. The matrix inversion computation constructed based on this structure can be used for various matrix inversion or inverse approximation computation tasks.

[0170] It should be noted that the parameters in the structured correction sub-unit can be adaptively adjusted according to the current matrix characteristics or error structure, thereby improving the convergence efficiency of the iterative process.

[0171] Furthermore, the structured correction subunit is not limited to the low-rank matrix form; other structured correction methods can also be used, such as block correction, sparse correction, or other forms of structured update mechanisms. At the same time, the Newton-Shull iterative update step can also be replaced by other matrix iterative inversion frameworks. All of these fall within the scope of protection of this invention while maintaining the overall idea of ​​"structured correction + iterative update".

[0172] Meanwhile, the present invention also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-described method for inverting a low-rank modified matrix for precoding computation in wireless communication.

[0173] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0177] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for inverting a low-rank modified matrix for precoding computation in wireless communication, characterized in that, This method is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems; the method includes: The method for obtaining the inverse correlation matrix to be calculated is as follows: during multi-user downlink transmission, the inverse correlation matrix to be calculated is constructed based on the channel matrix of each user on different subcarriers obtained by the base station for precoding calculation. The correlation matrix to be inverted is input into a structured modified expansion network based on Newton-Schulz for iterative inversion, and the final inverse matrix approximation is output. The iterative inversion process of the structured correction expansion network based on Newton-Schulz is as follows: before each Newton-Schulz iteration update, the current inverse matrix is ​​approximated by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual during the iteration process.

2. The method for inverting a low-rank modified matrix for precoding computation in wireless communication according to claim 1, characterized in that, The inverse correlation matrix to be determined Corresponding to the The precoding correlation matrix on each subcarrier is expressed as follows: ； in, Indicates the subcarrier index; Indicates the first Channel matrix on subcarriers; express The conjugate transpose of; This represents a regularization parameter or a noise-related parameter. Represents the identity matrix.

3. The method for inverting a low-rank modified matrix for precoding computation in wireless communication according to claim 1, characterized in that, The Newton-Schulz-based structured correction unfolding network includes a multi-layer unfolding structure, and each layer includes a structured correction step and a Newton-Schulz iterative update step.

4. The method for inverting a low-rank modified matrix for precoding computation in wireless communication according to claim 3, characterized in that, The correlation matrix to be inverted is input into a structured modified expansion network based on Newton-Schulz for iterative inversion, including: Construct an initial inverse approximation of the inverse correlation matrix to be determined; The initial inverse approximation input is then processed using a Newton-Schulz structured correction expansion network. The process is repeated layer by layer until the preset total number of iterations is reached or the accuracy requirement is met, to obtain the final approximation of the inverse matrix. Among them, in the first In the layer iteration, the current inverse matrix approximation is corrected by low rank to obtain the corrected intermediate variable matrix; and the corrected intermediate variable matrix is ​​updated by Newton-Schulz iteration to obtain the inverse matrix approximation.

5. The method for inverting a low-rank modified matrix for precoding computation in wireless communication according to claim 4, characterized in that, The formula for the low-rank correction is: ； in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Describes a low-rank dimension, and satisfies ; Here, the inverse correlation matrix to be determined is represented as... The dimension, that is .

6. The method for inverting a low-rank modified matrix for precoding computation in wireless communication according to claim 4, characterized in that, The formula for the Newton-Schultz iterative update is: ； in, Indicates the first The inverse matrix approximation obtained by layer iteration; Representation and matrix A dimensionally consistent identity matrix; This indicates that the inverse correlation matrix to be determined... The normalized matrix obtained by performing normalization processing; This represents the intermediate variable matrix.

7. A low-rank modified matrix inversion system for precoding computation in wireless communication, characterized in that, This system is applied to multi-user downlink beamforming or precoding matrix solving scenarios in wireless communication systems; the system includes: The unit for obtaining the inverse correlation matrix is ​​used to obtain the inverse correlation matrix to be obtained. The method for obtaining the inverse correlation matrix to be obtained is as follows: during multi-user downlink transmission, the inverse correlation matrix to be obtained is constructed for precoding calculation based on the channel matrix of each user on different subcarriers obtained by the base station. An improved iterative solution unit is used to input the correlation matrix to be inverted into a Newton-Schulz-based structured correction expansion network for iterative inversion, and output the final inverse matrix approximation. The iterative inversion process of the Newton-Schulz-based structured correction expansion network is as follows: before each Newton-Schulz iteration update, the current inverse matrix approximation is adjusted by constructing a structured low-rank correction term to compensate for the dominant error components in the error matrix, thereby reducing the magnitude of the target residual during the iteration process.

8. The low-rank modified matrix inversion system for precoding computation in wireless communication according to claim 7, characterized in that, The Newton-Schulz-based structured correction unfolding network includes a multi-layer unfolding structure, and each layer of the unfolding structure includes a structured correction sub-unit and a Newton-Schulz iterative update sub-unit. The structured correction subunit is used to perform low-rank correction on the current inverse matrix approximation of the input, to obtain the corrected intermediate variable matrix; The Newton-Schulz iterative update subunit is used to perform Newton-Schulz iterative updates on the corrected intermediate variable matrix to obtain an approximate inverse matrix.

9. The low-rank modified matrix inversion system for precoding computation in wireless communication according to claim 8, characterized in that, The formula for the low-rank correction is: ； in, Indicates the iterative layer index; Indicates the first The current inverse matrix is ​​approximated during layer iteration; This represents the intermediate variable matrix after low-rank correction. Indicates the first The correction factor or correction step size of the layer; and They represent the first Two correction matrices in a low-rank correction layer; Denotes a low-rank dimension, and typically satisfies ; Here, the inverse correlation matrix to be determined is represented as... The dimension, that is .

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the low-rank modified matrix inversion method for precoding computation in wireless communication as described in any one of claims 1 to 7.

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