Adaptive Reduced-Rank LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Filters: Design and Analysis

This paper presents reduced-rank linearly constrained minimum variance (LCMV) beamforming algorithms based on joint iterative optimization of filters. The proposed reduced-rank scheme is based on a constrained joint iterative optimization of filters according to the minimum variance criterion. The proposed optimization procedure adjusts the parameters of a projection matrix and an adaptive reducedrank filter that operates at the output of the bank of filters. We describe LCMV expressions for the design of the projection matrix and the reduced-rank filter. We then describe stochastic gradient and develop recursive least-squares adaptive algorithms for their efficient implementation along with automatic rank selection techniques. An analysis of the stability and the convergence properties of the proposed algorithms is presented and semi-analytical expressions are derived for predicting their mean squared error (MSE) performance. Simulations for a beamforming application show that the proposed scheme and algorithms outperform in convergence and tracking the existing full-rank and reduced-rank algorithms while requiring comparable complexity.