Low-complexity robust precoding method and system for massive MIMO based on stochastic optimization
By employing a stochastically optimized, low-complexity robust precoding method in large-scale MIMO systems and utilizing a dimension-reduced channel to update precoding variables, the high computational complexity of existing algorithms is solved, achieving efficient computation and storage optimization, and making it suitable for 5G and future 6G networks.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- TONGJI UNIV
- Filing Date
- 2026-06-12
- Publication Date
- 2026-07-21
AI Technical Summary
In existing large-scale MIMO systems, existing precoding algorithms such as SWMMSE and SPWMMSE have high computational complexity, resulting in extremely high computational latency and hardware costs, making it difficult to meet the real-time requirements of 5G and future 6G networks, and also incurring large storage overhead.
A low-complexity robust precoding method based on stochastic optimization is adopted. By obtaining the long-term statistical channel covariance matrix and performing singular value decomposition, low-dimensional precoding variables are generated. The equivalent channel after dimensionality reduction is used for iterative updates, avoiding full-dimensional matrix inversion and requiring only matrix multiplication with linear complexity.
It reduces computational complexity, improves computational efficiency, reduces storage overhead, and maintains performance comparable to high-complexity algorithms under different channel models, making it suitable for large-scale MIMO systems.
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Abstract
Description
Technical Field
[0001] This invention relates to the field of wireless communication signal processing technology, and specifically to a low-complexity robust precoding method and system for large-scale MIMO based on stochastic optimization. Background Technology
[0002] In massive MIMO (multiple-in multiple-out) systems, base stations are equipped with large-scale antenna arrays to serve multiple users, significantly improving spectral and energy efficiency. Due to the difficulty in obtaining instantaneous channel state information (CSI), maximizing the ergodic weighted sum rate (WSR) based on statistical CSI has become an important precoding design criterion. Existing algorithms for maximizing ergodic WSR, such as the stochastic weighted minimum mean square error (SWMMSE) algorithm or the stochastic near-end WMMSE (SPWMMSE) algorithm, while achieving good performance, suffer from severe computational complexity issues. Specifically, these algorithms require high-dimensional matrix inversion operations in each iteration of the precoding matrix update, with complexity proportional to the cube of the number of base station antennas M (O(M^3)). As antenna size increases to a maximum (e.g., M=1024 or more), this cubically growing complexity leads to extremely high computational latency and hardware costs, making it difficult to meet the real-time requirements of 5G and future 6G networks. In addition, some algorithms (such as SWMMSE) also need to store a large number of historical channel samples or substitution functions, resulting in huge storage overhead. Summary of the Invention
[0003] This invention is made to solve the above-mentioned problems, and aims to provide a low-complexity robust precoding method and system for large-scale MIMO based on random optimization.
[0004] This invention provides a low-complexity robust precoding method for large-scale MIMO based on stochastic optimization, characterized by the following steps: Step S1, obtaining the long-term statistical channel covariance matrix for each user, performing singular value decomposition on each long-term statistical channel covariance matrix, extracting principal eigenvectors to form a principal eigenvector matrix, and concatenating the user's principal eigenvector matrices along the column direction to obtain a global low-dimensional projection matrix; Step S2, randomly generating initial low-dimensional precoding variables and initializing them according to the maximum transmit power of the base station; Step S3, in the r-th iteration, obtaining the current time... The instantaneous channel sample matrix is used to calculate the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix. In step S4, using the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration, the receiving filter, weighting matrix, and low-dimensional precoding vector of the rth iteration are updated sequentially based on the weighted minimum mean square error criterion. In step S5, steps S3 to S4 are repeated until the convergence condition is met or the preset maximum number of iterations is reached. In step S6, the full-dimensional precoding matrix is calculated based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix.
[0005] The low-complexity robust precoding method for large-scale MIMO based on random optimization provided by this invention may also have the following feature: in step S1, the number of principal feature vectors is determined by the energy ratio threshold to be retained, such that the number of principal feature vectors is much smaller than the number of antennas.
[0006] The low-complexity robust precoding method for large-scale MIMO based on random optimization provided by this invention may also have the following feature: wherein, in step S4, the update formula for the receiving filter for each user is:
[0007]
[0008] in, For users noise power, For users In the Dimensionality reduction channel in the next iteration For users In the Low-dimensional precoded variables for the next iteration.
[0009] The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization provided by this invention may also have the following feature: wherein, in step S4, the update formula for the weighting matrix for each user is:
[0010]
[0011] in, It is the identity matrix. For users In the Low-dimensional precoded variables for the next iteration.
[0012] The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization provided by this invention may also have the following feature: wherein, in step S4, the update formula for the low-dimensional precoding vector for each user is:
[0013]
[0014] in, , It is the receive beamforming matrix for user j. It is the weighted matrix of user j. yes The conjugate transpose of the matrix. For user j, the dimension-reduced channel in the r-th iteration, Let j be the noise power. This is the maximum transmit power of the base station. The trace of the matrix, Global low-dimensional projection matrix The conjugate transpose of . It is a global low-dimensional projection matrix. This is the regularization step size parameter.
[0015] The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization provided by this invention also has the following feature: In step S6, the formula for calculating the full-dimensional precoding matrix is:
[0016]
[0017] in, The power normalization factor, It is a global low-dimensional projection matrix. These are low-dimensional precoded variables.
[0018] The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization provided in this invention also has the following feature: the power normalization factor is calculated using the following formula:
[0019]
[0020] in, For full-dimensional precoding matrix Its conjugate transpose The trace of the product of .
[0021] This invention provides a low-complexity robust precoding system for large-scale MIMO based on stochastic optimization, characterized by the following features: a subspace construction module, used to obtain the long-term statistical channel covariance matrix of each user, perform singular value decomposition on each long-term statistical channel covariance matrix, extract principal eigenvectors to form a principal eigenvector matrix, and concatenate the user's principal eigenvector matrices along the column direction to obtain a global low-dimensional projection matrix; an initialization module, used to randomly generate initial low-dimensional precoding variables and initialize them according to the maximum transmit power of the base station; and a dimensionality reduction calculation module, used to obtain the instantaneous value of the current time in the r-th iteration. The system comprises: a time-channel sample matrix, which calculates the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix; a variable update module, which uses the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration to sequentially update the receiving filter, weighting matrix, and low-dimensional precoding vector in the rth iteration based on the weighted minimum mean square error criterion; a convergence determination module, which repeats steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached; and a precoding output module, which calculates the full-dimensional precoding matrix based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix.
[0022] The role and effect of invention
[0023] The present invention relates to a low-complexity robust precoding method and system for large-scale MIMO based on stochastic optimization, comprising: Step S1, obtaining the long-term statistical channel covariance matrix of each user, performing singular value decomposition on each long-term statistical channel covariance matrix, extracting principal eigenvectors to form a principal eigenvector matrix, and concatenating the user's principal eigenvector matrices along the column direction to obtain a global low-dimensional projection matrix; Step S2, randomly generating initial low-dimensional precoding variables and initializing them according to the maximum transmit power of the base station; Step S3, in the r-th iteration, obtaining the instantaneous channel sample matrix at the current moment, and calculating the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix; Step S4, utilizing the dimensionality reduction... The equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration are used to update the receiving filter, weighting matrix, and low-dimensional precoding vector in the r-th iteration sequentially based on the weighted minimum mean square error criterion. Step S5 repeats steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached. Step S6 calculates the full-dimensional precoding matrix based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix. Therefore, the low-complexity robust precoding method and system for large-scale MIMO based on stochastic optimization of this invention avoids full-dimensional matrix inversion through dimensionality reduction. Only the complexity of matrix multiplication in the algorithm is related to the number of base station antennas, and its complexity is linearly related to the number of base station antennas. Therefore, the total complexity of the algorithm is reduced from... Reduce to This greatly improves computational efficiency. Attached Figure Description
[0024] Figure 1 This is a flowchart illustrating a low-complexity robust precoding method for large-scale MIMO based on random optimization, as described in an embodiment of the present invention.
[0025] Figure 2 This is a comparison chart of the algorithm convergence performance under a Gaussian channel in an embodiment of the present invention.
[0026] Figure 3 This is a comparison chart of algorithm convergence performance under the Urban Macro Cell (UMA) channel model in the embodiments of the present invention.
[0027] Figure 4 This is a comparison chart of the average CPU execution time of the algorithms in the embodiments of the present invention.
[0028] Figure 5 This is a schematic diagram of a module of a low-complexity robust precoding system for large-scale MIMO based on random optimization in an embodiment of the present invention.
[0029] The specific system's module Siish method
[0030] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, provide a detailed description of the low-complexity robust precoding method and system for large-scale MIMO based on random optimization. Example
[0031] Figure 1 This is a flowchart illustrating a low-complexity robust precoding method for large-scale MIMO based on random optimization, as described in an embodiment of the present invention.
[0032] like Figure 1 As shown, this embodiment provides a low-complexity robust precoding method for large-scale MIMO based on stochastic optimization, including:
[0033] Step S1: Obtain the long-term statistical channel covariance matrix for each user. Singular value decomposition (SVD) is performed on each long-term statistical channel covariance matrix to extract principal eigenvectors and construct a principal eigenvector matrix. The user's main feature vector matrix is then concatenated along the column direction to obtain the global low-dimensional projection matrix. .
[0034] In step S1, the number of principal feature vectors The number of principal eigenvectors is determined by the energy ratio threshold, making it much smaller than the number of antennas. .
[0035] Step S2: Randomly generate initial low-dimensional precoding variables and initialize them according to the maximum transmit power of the base station.
[0036] Step S3: In the r-th iteration, obtain the instantaneous channel sample matrix at the current time. The dimensionality-reduced equivalent channel is calculated based on the global low-dimensional projection matrix and the instantaneous channel sample matrix. The channel dimension is reduced from... Reduced to .
[0037] Step S4: Using the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration, based on the weighted minimum mean square error criterion, update the receiving filter, weighting matrix, and low-dimensional precoding vector of the rth iteration in sequence.
[0038] In step S4, the update formula for the receiving filter for each user is:
[0039]
[0040] in, For users noise power, For users In the Dimensionality reduction channel in the next iteration For users In the The low-dimensional precoded variables of the next iteration. This calculation only involves... Finding the inverse of a dimension.
[0041] In step S4, the formula for updating the weighted matrix for each user is:
[0042]
[0043] in, It is the identity matrix. For users In the Low-dimensional precoded variables for the next iteration.
[0044] In step S4, the update formula for the low-dimensional precoding vector for each user is:
[0045]
[0046] in , It is the receive beamforming matrix for user j. It is the weighted matrix of user j. yes The conjugate transpose of the matrix. For user j, the dimension-reduced channel in the r-th iteration, Let j be the noise power. This is the maximum transmit power of the base station. The trace of the matrix, Global low-dimensional projection matrix The conjugate transpose of . It is a global low-dimensional projection matrix. This is the regularization step size parameter. The calculation involves... The complexity of finding the inverse of the dimension is independent of the number of antennas.
[0047] Step S5: Repeat steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached.
[0048] Step S6: Calculate the full-dimensional precoding matrix based on the converged low-dimensional precoding variables.
[0049] In step S6, the formula for calculating the full-dimensional precoding matrix is:
[0050]
[0051] in, The power normalization factor, It is a global low-dimensional projection matrix. These are low-dimensional precoded variables.
[0052] The formula for calculating the power normalization factor is as follows:
[0053]
[0054] in, For full-dimensional precoding matrix Its conjugate transpose The trace of the product of .
[0055] After obtaining the full-dimensional precoding matrix, the output is performed, avoiding the need for matrix inversion across all dimensions.
[0056] Figure 2 This is a comparison chart of the algorithm convergence performance under a Gaussian channel in an embodiment of the present invention.
[0057] Figure 3 This is a comparison chart of algorithm convergence performance under the Urban Macro Cell (UMA) channel model in the embodiments of the present invention.
[0058] Figure 4 This is a comparison chart of the average CPU execution time of the algorithms in the embodiments of the present invention.
[0059] like Figure 2 , Figure 3 , Figure 4 As shown, in a scenario with M=1024 antennas serving K=8 users (32 streams in total), the average CPU execution time of the SLWMMSE algorithm proposed in this embodiment is only 1.40% of the traditional SPWMMSE algorithm and only 0.08% of the SWMMSE algorithm, while achieving the same traversal and rate performance. This fully demonstrates the efficiency and practicality of this invention in large-scale antenna systems.
[0060] Figure 5 This is a schematic diagram of a module of a low-complexity robust precoding system for large-scale MIMO based on random optimization in an embodiment of the present invention.
[0061] like Figure 5 As shown, this embodiment also provides a low-complexity robust precoding system 100 for large-scale MIMO based on stochastic optimization, including:
[0062] The subspace construction module 1 uses the above step S1 to obtain the long-term statistical channel covariance matrix of each user, performs singular value decomposition on each long-term statistical channel covariance matrix, extracts the principal eigenvectors to form the principal eigenvector matrix, and concatenates the user's principal eigenvector matrix along the column direction to obtain the global low-dimensional projection matrix.
[0063] The initialization module 2 uses step S2 described above to randomly generate initial low-dimensional precoding variables and initialize them according to the maximum transmit power of the base station.
[0064] The dimensionality reduction calculation module 3 uses the above step S3 to obtain the instantaneous channel sample matrix at the current moment in the r-th iteration and calculate the equivalent channel after dimensionality reduction.
[0065] The variable update module 4 uses the above step S4 to update the receiving filter, weighting matrix and low-dimensional precoding vector of the r-th iteration sequentially based on the weighted minimum mean square error criterion using the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration.
[0066] The convergence determination module 5 uses the above step S5 to repeat steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached.
[0067] The precoding output module 6 uses the above step S6 to calculate the full-dimensional precoding matrix based on the converged low-dimensional precoding variables.
[0068] The role and effect of the embodiments
[0069] The method and system for low-complexity robust precoding of large-scale MIMO based on stochastic optimization involved in this embodiment includes: Step S1, obtaining the long-term statistical channel covariance matrix of each user, performing singular value decomposition on each long-term statistical channel covariance matrix, extracting principal eigenvectors to form a principal eigenvector matrix, and concatenating the user's principal eigenvector matrices along the column direction to obtain a global low-dimensional projection matrix; Step S2, randomly generating initial low-dimensional precoding variables and initializing them according to the maximum transmit power of the base station; Step S3, in the r-th iteration, obtaining the instantaneous channel sample matrix at the current moment, and calculating the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix; Step S4, utilizing dimensionality reduction... The equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration are used to update the receiving filter, weighting matrix, and low-dimensional precoding vector in the r-th iteration sequentially based on the weighted minimum mean square error criterion. Step S5 repeats steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached. Step S6 calculates the full-dimensional precoding matrix based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix. Therefore, the low-complexity robust precoding method and system for large-scale MIMO based on stochastic optimization of this invention avoids full-dimensional matrix inversion through dimensionality reduction. Only the complexity of matrix multiplication in the algorithm is related to the number of base station antennas, and its complexity is linearly related to the number of base station antennas. Therefore, the total complexity of the algorithm is reduced from... Reduce to This greatly improves computational efficiency.
[0070] The stochastic optimization framework used in this embodiment only needs to be updated using the current channel samples, without storing historical channel samples or substitution functions, which significantly reduces storage overhead.
[0071] This embodiment also introduces a regularization step size parameter, which ensures the convergence of the algorithm in a random sampling environment and maintains a sum rate performance comparable to high-complexity algorithms under different channel models.
[0072] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.
Claims
1. A low-complexity robust precoding method for large-scale MIMO based on stochastic optimization, characterized in that, include: Step S1: Obtain the long-term statistical channel covariance matrix of each user, perform singular value decomposition on each long-term statistical channel covariance matrix, extract the principal eigenvectors to form a principal eigenvector matrix, and concatenate the user's principal eigenvector matrix along the column direction to obtain a global low-dimensional projection matrix. Step S2: Randomly generate initial low-dimensional precoding variables and initialize them according to the maximum transmit power of the base station; Step S3: In the r-th iteration, obtain the instantaneous channel sample matrix at the current moment, and calculate the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix; Step S4: Using the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration, based on the weighted minimum mean square error criterion, update the receiving filter, weighting matrix, and low-dimensional precoding vector of the rth iteration in sequence. Step S5: Repeat steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached. Step S6: Calculate the full-dimensional precoding matrix based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix.
2. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 1, characterized in that: in, In step S1, the number of principal feature vectors is determined by the energy ratio threshold to ensure that the number of principal feature vectors is much smaller than the number of antennas.
3. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 1, characterized in that: in, In step S4, for each user, the update formula for the receiving filter is: in, For users noise power, For users In the Dimensionality reduction channel in the next iteration For users In the Low-dimensional precoded variables for the next iteration.
4. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 1, characterized in that: in, In step S4, for each user, the update formula for the weighting matrix is: in, It is the identity matrix. For users In the Low-dimensional precoded variables for the next iteration.
5. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 1, characterized in that: in, In step S4, for each user, the update formula for the low-dimensional precoding vector is: in, , It is the receive beamforming matrix for user j. It is the weighted matrix of user j. yes The conjugate transpose of the matrix. For user j, the dimension-reduced channel in the r-th iteration, Let j be the noise power. This is the maximum transmit power of the base station. The trace of the matrix, Global low-dimensional projection matrix The conjugate transpose of . It is a global low-dimensional projection matrix. This is the regularization step size parameter.
6. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 1, characterized in that: In step S6, the formula for calculating the full-dimensional precoding matrix is: in, The power normalization factor, It is a global low-dimensional projection matrix. These are low-dimensional precoded variables.
7. The low-complexity robust precoding method for large-scale MIMO based on stochastic optimization according to claim 6, characterized in that: in, The formula for calculating the power normalization factor is as follows: in, For full-dimensional precoding matrix Its conjugate transpose The trace of the product of .
8. A low-complexity robust precoding system for large-scale MIMO based on stochastic optimization, characterized in that, include: The subspace construction module is used to obtain the long-term statistical channel covariance matrix of each user, perform singular value decomposition on each long-term statistical channel covariance matrix, extract the principal feature vector to form the principal feature vector matrix, and concatenate the user's principal feature vector matrix along the column direction to obtain the global low-dimensional projection matrix. The initialization module is used to randomly generate initial low-dimensional precoding variables and initialize them according to the maximum transmit power of the base station. The dimensionality reduction calculation module is used to obtain the instantaneous channel sample matrix at the current moment in the r-th iteration, and calculate the dimensionality-reduced equivalent channel based on the global low-dimensional projection matrix and the instantaneous channel sample matrix; The variable update module is used to update the receiving filter, weighting matrix, and low-dimensional precoding vector of the r-th iteration sequentially using the dimensionality-reduced equivalent channel and the low-dimensional precoding variables obtained in the (r-1)th iteration, based on the weighted minimum mean square error criterion. The convergence determination module is used to repeat steps S3 to S4 until the convergence condition is met or the preset maximum number of iterations is reached. The precoding output module is used to calculate the full-dimensional precoding matrix based on the converged low-dimensional precoding variables and the global low-dimensional projection matrix.