Non-Iterative Singular Value Decomposition for Wireless Channel Matrix

Solution Overview

Problem

Current methods for non-iterative singular-value decomposition (SVD) in beamforming, particularly in wireless communication systems, face challenges when dealing with dimensions greater than 2, requiring iterative processes that complicate processing and efficiency.

Innovation Solution

A method and apparatus for non-iterative SVD in wireless communication systems that reduce the dimension of a channel matrix to min(Nrx, Ntx)×min(Nrx, Ntx), perform SVD on the reduced matrix, and iteratively subtract singular vectors to achieve a rank reduction, allowing for efficient computation of singular vectors and coefficients that maximize singular values.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If iterative processes are used for SVD when dimension is greater than 2, then processing completeness is improved, but processing complexity and time consumption increase

Engineering Contradiction:

ImproveSVD processing completenessVSAvoidprocessing complexity

Core Design Contradiction:

Manufacturing precisionVSDevice complexity

Solution Approach 1:

The patent segments the SVD problem into two parts: (1) dimension reduction to min(Ntx, Nrx)×min(Ntx, Nrx) using Givens rotation or Householder transformation, and (2) iterative SVD processing only when the reduced dimension exceeds 2. This segmentation allows most cases to be solved non-iteratively while maintaining completeness for higher dimensions.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary dimension reduction using Givens rotation or Householder transformation before applying iterative SVD. This preliminary action reduces the matrix dimension, so that iterative processing is only needed when min(Ntx, Nrx) > 2, significantly reducing the complexity of the subsequent iterative step.

Inventive Principle:

Principle #10Preliminary action

2Manufacturing precision

If iterative processes are used for SVD when dimension is greater than 2, then processing completeness is improved, but processing time increases

Engineering Contradiction:

ImproveSVD processing completenessVSAvoidprocessing time

Core Design Contradiction:

Manufacturing precisionVSLoss of time

Solution Approach 1:

The patent segments the SVD problem into two parts: (1) dimension reduction to min(Ntx, Nrx)×min(Ntx, Nrx) using Givens rotation or Householder transformation, and (2) iterative SVD processing only when the reduced dimension exceeds 2. This segmentation allows most cases to be solved non-iteratively while maintaining completeness for higher dimensions.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary dimension reduction using Givens rotation or Householder transformation before applying iterative SVD. This preliminary action reduces the matrix dimension, so that iterative processing is only needed when min(Ntx, Nrx) > 2, significantly reducing the complexity of the subsequent iterative step.

Inventive Principle:

Principle #10Preliminary action

3Productivity

If dimension reduction is performed to min(Ntx, Nrx)×min(Ntx, Nrx), then processing efficiency is improved, but processing completeness may be compromised for dimensions greater than 2

Engineering Contradiction:

Improveprocessing efficiencyVSAvoidSVD processing completeness

Core Design Contradiction:

ProductivityVSManufacturing precision

Solution Approach 1:

The patent segments the SVD problem into two parts: (1) dimension reduction to min(Ntx, Nrx)×min(Ntx, Nrx) using Givens rotation or Householder transformation, and (2) iterative SVD processing only when the reduced dimension exceeds 2. This segmentation allows most cases to be solved non-iteratively while maintaining completeness for higher dimensions.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent performs preliminary dimension reduction using Givens rotation or Householder transformation before applying iterative SVD. This preliminary action reduces the matrix dimension, so that iterative processing is only needed when min(Ntx, Nrx) > 2, significantly reducing the complexity of the subsequent iterative step.

Inventive Principle:

Principle #10Preliminary action

Data Source

PatentUS10326511B1Apparatus and method of non-iterative singular-value decomposition

Publication Date: 2019.06.18 SAMSUNG ELECTRONICS CO LTD

AI summary

Method for non-iterative singular-value decomposition (SVD). The method includes receiving, by receiver, signal; determining, by channel matrix generator, channel matrix for received signal, where channel matrix has dimension Nrx×Ntx, Nrx is number of receive antennas, Ntx is integer indicating number of transmit antennas; reducing, by singular-value decomposer, dimension of channel matrix to min(Nrx,Ntx)×min(Nrx,Ntx), where min( ) is function that returns coefficient with minimum value; performing, by singular-value decomposer, SVD on dimension-reduced channel matrix to determine singular vectors and corresponding coefficients that maximize singular values of singular vectors; outputting result of SVD based on at least one of when dimension of dimension-reduced channel matrix is less than or equal to 2 and when two greatest singular values of corresponding singular vectors are determined; when result of SVD not output, subtracting, by singular-value decomposer, singular vectors from dimension-reduced channel matrix to reduce rank and returning to performing SVD.