Set-Membership Conjugate Gradient Constrained Adaptive Filtering Algorithm for Beamforming

TL;DR

This paper presents a novel low-complexity adaptive beamforming algorithm that combines set-membership and conjugate gradient techniques to improve convergence and tracking performance without matrix inversion.

Contribution

It introduces a new CG-based constrained adaptive filtering algorithm that reduces computational complexity and enhances performance in beamforming applications.

Findings

Significantly reduces computational complexity.

Improves convergence and tracking performance.

Avoids matrix inversion in adaptive filtering.

Abstract

We introduce a new linearly constrained minimum variance (LCMV) beamformer that combines the set-membership (SM) technique with the conjugate gradient (CG) method, and develop a low-complexity adaptive filtering algorithm for beamforming. The proposed algorithm utilizes a CG-based vector and a variable forgetting factor to perform the data-selective updates that are controlled by a time-varying bound related to the parameters. For the update, the CG-based vector is calculated iteratively (one iteration per update) to obtain the filter parameters and to avoid the matrix inversion. The resulting iterations construct a space of feasible solutions that satisfy the constraints of the LCMV optimization problem. The proposed algorithm reduces the computational complexity significantly and shows an enhanced convergence and tracking performance over existing algorithms.