Non-Iterative Singular Value Decomposition for Wireless Channel Matrices
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Solution Overview
Problem
Current methods for non-iterative singular-value decomposition (SVD) in wireless communication systems face challenges when processing high-dimensional channel matrices, particularly in beamforming applications, as they require iterative processes for dimension reduction and singular value determination.
Innovation Solution
A method and apparatus for non-iterative SVD in wireless communication systems that involves receiving a signal, determining a channel matrix, reducing its dimension, performing SVD to find singular vectors and coefficients, and outputting results when the dimension is reduced to 2 or less, or by subtracting singular vectors to reduce the rank until the dimension is manageable.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If iterative processes are used for dimension reduction and singular value determination in high-dimensional channel matrices, then processing accuracy can be maintained, but processing complexity and time increase significantly
Solution Approach 1:
The patent segments the high-dimensional channel matrix processing into distinct stages: dimension reduction phase (transforming N×M matrix to min(N,M)×min(N,M)) and singular value decomposition phase. By separating these operations and applying specific algorithms to each stage, the patent avoids the need for iterative processing of the entire high-dimensional matrix, thereby reducing computational complexity while maintaining accuracy.
Solution Approach 2:
The patent applies preliminary dimension reduction operations (using Givens rotations or Householder transformations) before performing singular value decomposition. This preliminary action transforms the original high-dimensional matrix into a reduced-dimension matrix, making the subsequent SVD computation more efficient and avoiding iterative processes that would be required for the full high-dimensional matrix.
2Measurement precision
If iterative processes are used for SVD of high-dimensional matrices, then accurate singular vectors can be obtained, but processing time increases
Solution Approach 1:
The patent performs preliminary dimension reduction using Givens rotations or Householder transformations before executing singular value decomposition. This preliminary action reduces the matrix dimension from N×M to min(N,M)×min(N,M), significantly decreasing the computational burden and processing time required for obtaining accurate singular vectors, especially when N and M are large.
Solution Approach 2:
The patent changes the dimensionality parameter of the channel matrix from high-dimensional (N×M where N and M are large) to reduced-dimension (min(N,M)×min(N,M)) through preliminary transformations. This parameter change enables faster computation of singular vectors while maintaining accuracy, as the reduced dimension directly decreases the number of computational operations required.
3Productivity
If dimension reduction is performed on channel matrices for beamforming feedback, then processing efficiency improves, but system complexity increases
Solution Approach 1:
The patent segments the beamforming feedback processing into distinct functional blocks: channel matrix generation, dimension reduction (Givens rotation or Householder transformation), and singular value decomposition. This segmentation allows each block to be optimized independently and implemented using standard signal processing operations, improving processing efficiency without requiring complex custom hardware for the entire system.
Solution Approach 2:
The patent employs universal linear algebra operations (Givens rotations, Householder transformations, and SVD algorithms) that can be implemented using standard signal processing hardware and software. These multi-functional mathematical operations can handle various matrix dimensions and configurations, improving processing efficiency across different MIMO scenarios without requiring specialized complex system design for each case.
Data Source
AI summary
Method of non-iterative singular-value decomposition (SVD). The method includes receiving, by receiver, a signal; determining, by a channel matrix generator connected to the receiver, a channel matrix for the received signal; reducing, by a singular-value decomposer connected to the channel matrix generator, the dimension of the channel matrix; performing, by the singular-value decomposer, an SVD on the dimension-reduced channel matrix to determine singular vectors and corresponding coefficients that maximize singular values of the singular vectors; and outputting a result of the SVD based on at least one of when the dimension of the dimension-reduced channel matrix is less than or equal to 2 and when two greatest singular values of corresponding singular vectors are determined.