Robust Reduced-Rank Adaptive LCMV Beamforming Algorithms Based on Joint Iterative Optimization of Parameters - Advances in Heuristic Signal Processing and Applications - page 17

Chapter 2
Robust Reduced-Rank Adaptive LCMV
Beamforming Algorithms Based on Joint
Iterative Optimization of Parameters

Rodrigo C. de Lamare

Abstract This chapter presents robust reduced-rank linearly constrained minimum
variance (LCMV) beamforming algorithms based on the concept of joint iterative
optimization of parameters. The proposed robust reduced-rank scheme is based on
a constrained robust joint iterative optimization (RJIO) of parameters according to
the minimum variance criterion. The robust optimization procedure adjusts the pa-
rameters of a rank-reduction matrix, a reduced-rank beamformer, and the diagonal
loading in an alternating manner. LCMV expressions are developed for the design
of the rank-reduction matrix and the reduced-rank beamformer. Stochastic gradient
and recursive least-squares adaptive algorithms are then devised for an efficient im-
plementation of the RJIO robust beamforming technique. Simulations for a beam-
forming application in the presence of uncertainties show that the RJIO scheme
and algorithms outperform existing algorithms in convergence and tracking perfor-
mances while they require a comparable computational complexity.

2.1 Introduction

In the last decade, adaptive beamforming techniques have attracted significant inter-
est from researchers and engineers, and found applications in radar, sonar, wireless
communications, and seismology [ 1 , 2 ]. The optimal linearly constrained minimum
variance (LCMV) beamformer is designed in such a way that it minimizes the array
output power while maintaining a constant response in the direction of a signal of in-
terest (SoI) [ 1 - 3 ]. However, this technique requires the computation of the inverse
of the input data covariance matrix and the knowledge of the array steering vec-
tor. Adaptive versions of the LCMV beamformer were subsequently reported with
stochastic gradient (SG) [ 4 , 5 ] and recursive least-squares (RLS) [ 6 ] algorithms.
A key problem with adaptive beamforming techniques is the impact of uncertainties
which can result in a considerable performance degradation. These mismatches are

B

R.C. de Lamare ( )

Communications Research Group, Department of Electronics, University of York,
York Y010 5DD, UK
e-mail: [e-mail]