Set-Membership Constrained Conjugate Gradient Beamforming Algorithms

TL;DR

This paper introduces a set-membership constrained conjugate gradient algorithm for adaptive beamforming that offers data-selective updates, reduced complexity, and improved convergence and tracking performance.

Contribution

It proposes a novel CG-based adaptive beamforming algorithm with set-membership constraints, variable forgetting factor, and time-varying bounds, enhancing performance over existing methods.

Findings

Enhanced convergence and tracking performance demonstrated in simulations

Reduced computational complexity due to data-selective updates

Effective enforcement of constraints through feasible solution space

Abstract

In this work a constrained adaptive filtering strategy based on conjugate gradient (CG) and set-membership (SM) techniques is presented for adaptive beamforming. A constraint on the magnitude of the array output is imposed to derive an adaptive algorithm that performs data-selective updates when calculating the beamformer's parameters. We consider a linearly constrained minimum variance (LCMV) optimization problem with the bounded constraint based on this strategy and propose a CG type algorithm for implementation. The proposed algorithm has data-selective updates, a variable forgetting factor and performs one iteration per update to reduce the computational complexity. The updated parameters construct a space of feasible solutions that enforce the constraints. We also introduce two time-varying bounding schemes to measure the quality of the parameters that could be included in the parameter space. A comprehensive complexity and performance analysis between the proposed and existing algorithms are provided. Simulations are performed to show the enhanced convergence and tracking performance of the proposed algorithm as compared to existing techniques.