Adaptive Signal Weight Updates with Reduced-Dimension Subspace Constraints
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Solution Overview
Problem
Current partial update methods for high-dimensional adaptive signal processors face limitations due to severe misadjustment and increased complexity, particularly when dealing with high-order optimization functions, leading to reduced effectiveness in applications like phased array radar and smart grid networks.
Innovation Solution
The method involves performing a linear transformation to reduce processor parameters from M-dimensions to (M1+L)-dimensions, allowing M1 weights to be updated without constraints and M0 weights to be subjected to soft constraints within an L-dimensional subspace, enabling the same optimization strategy to be applied to reduced-dimensionality weights and data.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If partial update methods are used to reduce computational complexity, then the number of operations per data sample decreases, but misadjustment increases and optimization effectiveness deteriorates
Solution Approach 1:
The patent transforms the weight space from M-dimensions to (M1+L)-dimensions by projecting weights onto a subspace spanned by L orthogonal vectors. This dimensional transformation allows the system to work with fewer effective parameters (M1+L < M) while maintaining optimization effectiveness through the structured subspace constraint, resolving the contradiction between reduced complexity and maintained reliability.
Solution Approach 2:
The patent changes the parameter representation by expressing weights as linear combinations of orthogonal basis vectors rather than independent parameters. This parameter transformation enables the system to achieve the same functional capability with fewer parameters, reducing computational complexity while maintaining optimization performance through the subspace constraint structure.
2Productivity
If high-order optimization functions are used to improve processing capability, then adaptation performance improves, but computational complexity increases significantly
Solution Approach 1:
By transforming to a reduced-dimensional subspace, the patent enables the use of high-order optimization functions with reduced computational burden. The complexity reduction comes from operating in (M1+L)-dimensional space rather than full M-dimensional space, allowing high-order functions to be practically implementable while maintaining their performance benefits.
3Speed
If more weights are updated per adaptation block to improve convergence speed, then adaptation rate increases, but computational load per block increases
Solution Approach 1:
The subspace transformation allows more weights to be effectively updated by utilizing the structured relationship among weights in the reduced-dimensional space. The orthogonal basis vectors provide a framework where updates propagate through the weight set more efficiently, achieving faster convergence without linearly increasing computational load per block.
Data Source
AI summary
A method is explained for any adaptive processor processing digital signals by adjusting signal weights on digital signal(s) it handles, to optimize adaptation criteria responsive to a functional purpose or externalities (transient, temporary, situational, and even permanent) of that processor. Adaptation criteria for the adaptive algorithm may be any combination of a signal or parameter estimation, and measured quality(ies). This method performs a linear transformation adapting parameters from M to (M1+L) dimensions in each adaptation event, such that M1 weights are updated without constraints and M0=M−M1 weights are forced by soft constraints into an L-dimensional subspace they spanned at the beginning of the adaptation period. The same dimensionality reduction, using the same linear transformation, is applied to the input data. The reduced-dimensionality weights are then adapted using the identical optimization strategy employed by the processor, except with input data that has also been reduced in dimensionality.