Several worst-case performance optimization-based broadband adaptive beamforming techniques with an improved robustness against array manifold errors are developed. The proposed beamformers differ from the existing broadband robust techniques in that their robustness is directly matched to the amount of uncertainty in the array manifold, and the suboptimal subband decomposition step is avoided. Convex formulations of the proposed beamformer designs are derived based on second-order cone programming (SOCP) and semidefinite programming (SDP). Simulation results validate an improved robustness of the proposed robust beamformers relative to several state-of-the-art robust broadband techniques.

Introduction

Adaptive array processing has received considerable attention during the last four decades, particularly in the fields of sonar, radar, speech acquisition and, more recently, wireless communications [1,2]. The main objective of adaptive beamforming algorithms is to suppress the interference and noise while preserving the desired signal components. One of the early adaptive beamforming algorithms for broadband signals is the linearly constrained minimum variance (LCMV) algorithm developed by Frost in [3] and extensively studied in the follow-up literature [1, 4, 5]. Frost's broadband array processor includes a presteering delay front-end whose function is to steer the array towards the desired signal so that each of its frequency components appears in-phase across the array after the presteering delays. Each presteering delay is then followed by a finite impulse response (FIR) adaptive filter and the outputs of all these filters are summed together to obtain the array output.