Hermitian Matrix Inversion via Cholesky Decomposition and Series Approximation
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Solution Overview
Problem
Matrix inversion in physical layer signal processing for wireless communication systems, such as in MMSE-IRC receivers, consumes a large amount of resources and processor cycles, especially for large matrix sizes, leading to increased power consumption and latency.
Innovation Solution
The method involves decomposing a Hermitian matrix into triangular matrices using Cholesky or LDL decomposition, normalizing these matrices, and estimating their inverses using a series approximation, reducing the number of calculations required for matrix inversion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional matrix inversion methods are used in physical layer signal processing, then accurate signal processing can be achieved, but computational resources and processor cycles are consumed excessively
Solution Approach 1:
The patent segments the matrix inversion process into multiple stages: (1) Cholesky decomposition to factorize the Hermitian matrix into triangular matrices, (2) normalization of the triangular matrices, and (3) series approximation to compute the inverse. This segmentation transforms a single computationally intensive operation into a sequence of simpler operations that reduce overall computational resource consumption while maintaining signal processing accuracy.
2Measurement precision
If traditional matrix inversion methods are used, then accurate inverse calculation can be obtained, but processing latency increases
Solution Approach 1:
The patent applies preliminary action by performing Cholesky decomposition and normalization before the actual inverse calculation. These preliminary steps transform the original matrix into a form that is more amenable to efficient inversion through series approximation, thereby reducing the time required for the critical inverse calculation while preserving accuracy.
3Productivity
If standard matrix inversion is performed for large matrix sizes, then complete signal processing can be achieved, but power consumption increases
Solution Approach 1:
The patent changes the parameters of the matrix by transforming it through Cholesky decomposition into triangular matrices with specific structural properties. This parameter transformation allows the use of series approximation methods that converge faster and require fewer computational operations, thereby reducing power consumption while maintaining the ability to process large matrices effectively.
4Measurement precision
If conventional matrix inversion approaches are used, then accurate results can be obtained, but the number of calculations and processor cycles increases
Solution Approach 1:
The patent substitutes the conventional direct matrix inversion method with an alternative computational mechanism based on series approximation. This replacement mechanism uses the structured form obtained from Cholesky decomposition and normalization to compute the inverse through a convergent series, significantly reducing the number of calculations and processor cycles required while maintaining accuracy.
Data Source
AI summary
An apparatus may be configured to obtain one or more of data or at least one signal associated with at least one first matrix, where the at least one first matrix is at least one square matrix; perform a decomposition process on the at least one first matrix to obtain at least one first triangular matrix; estimate an inverse of the at least one first triangular matrix based on the at least one second triangular matrix; calculate an inverse of the at least one first matrix based on at least one of (1) the estimated inverse of the at least one second triangular matrix, or (2) the estimated inverse of the at least one first triangular matrix; and transmit one or more of the data or the at least one signal based on the calculated inverse of the at least one first matrix.