A ROBUST FORMULATION FOR AN OPTIMUM BEAMFORMER SUBJECT TO AMPLITUDE AND PHASE PERTURBATIONS

This paper presents a technique for designing a narrowband beamformer which is robust against array amplitude and phase perturbations. The approach taken in the paper is to constrain the mean-square-error between the desired unity response and the response of the beamformer over variation in amplitude and phase to be less than or equal to a small quantity and obtain a quadratic constraint on the weight vector. The optimal weight is then obtained by minimizing the beamformer mean output power subject to the quadratic constraint. Subsequently, a linear constraint and a norm constraint are used to approximate the effect of the quadratic constraint. Based on the latter approximation, an alternative beamforming structure termed as partitioned beamformer is presented. The equivalent optimal vector for the partitioned beamformer has an interesting geometrical interpretation in the sense that signal suppression and the increase of length of the weighting vector of the beamformer are related. Numerical results are presented to illustrate the performance achievable. © 1990.