Adaptive Reduced-Rank Constrained Constant Modulus Beamforming Algorithms Based on Joint Iterative Optimization of Filters

TL;DR

This paper introduces a robust reduced-rank adaptive beamforming scheme based on joint iterative optimization of filters under the constant modulus criterion, improving convergence and tracking performance.

Contribution

It develops a novel joint iterative optimization scheme with automatic rank selection for reduced-rank beamforming, applicable to DFP and GSC structures, with improved performance.

Findings

Outperforms existing methods in convergence speed

Provides better tracking in dynamic environments

Demonstrates effectiveness through simulations

Abstract

This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The novel scheme is designed according to the constant modulus (CM) criterion subject to different constraints, and consists of a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters to estimate the desired signal. We describe the proposed scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithms for its adaptive implementation. The Gram-Schmidt (GS) technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving performance. An automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms. The complexity and convexity analyses are carried out. Simulation results show that the proposed algorithms outperform the existing full-rank and reduced-rank methods in convergence and tracking performance.