LCMP Beamformer Bounded Perturbation Regularization
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Solution Overview
Problem
Existing robust adaptive beamforming techniques face challenges in low Signal to Noise Ratio (SNR) environments and are computationally inefficient, particularly when dealing with limited snapshots and sensor mismatches, leading to performance degradation in beamforming applications.
Innovation Solution
A robust linearly constrained minimum power (LCMP) beamformer is developed using a bounded perturbation regularization approach, which reformulates the LCMP problem as an unconstrained least squares problem and automatically adjusts the regularization parameter using a mean squared error criterion, improving the beamforming process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If robust adaptive beamforming techniques are used to handle sensor mismatches and limited snapshots, then reliability is improved, but computational complexity increases and performance degrades in low SNR environments
Solution Approach 1:
The patent transforms the constrained LCMP optimization problem into an unconstrained least squares problem by changing the parameter representation from direct weight optimization to transformation matrix optimization. This parameter transformation simplifies the computational structure while maintaining robustness against mismatches and limited snapshots.
Solution Approach 2:
The patent extracts and removes the linear constraints from the original LCMP formulation by using a transformation matrix approach. The constraints are incorporated into the transformation structure itself, eliminating the need for separate constraint handling and reducing computational complexity.
2Stability of the object's composition
If regularization is applied to the ill-conditioned covariance matrix, then stability is improved, but additional complexity is introduced in selecting the regularization parameter
Solution Approach 1:
The regularization parameter is selected automatically through a self-service mechanism that uses the data itself to determine the optimal parameter value. The method employs a self-consistency criterion where the transformation matrix is computed such that it naturally adapts to the data characteristics, eliminating the need for external parameter tuning.
Solution Approach 2:
The patent implements a feedback mechanism where the transformation matrix computation incorporates information about the data covariance structure to automatically adjust the regularization effect. The solution uses the relationship between the sample covariance matrix and the transformation matrix to self-regulate the regularization strength.
3Ease of operation
If the LCMP problem is reformulated as an unconstrained least squares problem, then ease of operation is improved, but the estimated sample covariance matrix becomes ill-conditioned
Solution Approach 1:
The patent applies regularization as a preemptive measure to counteract the ill-conditioning that would otherwise result from the unconstrained least squares formulation. By incorporating the regularization term beforehand in the transformation matrix computation, the method prevents numerical instability before it occurs.
Data Source
AI summary
Beamformers and beamforming methods are disclosed which involve diagonal loading (regularization). Features may include the automatic determination of the regularization parameter using a linearly constrained minimum power (LCMP) bounded perturbation regularization (BPR) approach.