Robust adaptive beamforming

TLDR

Adaptive beamforming algorithms are highly sensitive to small array characteristic errors; uncorrelated sensor errors act like spatially white noise, so gain against white noise is a key robustness metric. The authors propose a new algorithm that imposes a quadratic inequality constraint on array gain against uncorrelated noise while minimizing output power under multiple linear equality constraints. The algorithm is extended to accommodate a general quadratic constraint, enabling robust adaptive beamforming with exact constraint satisfaction at each step. The authors demonstrate that scaling the projection of tentative weights onto the subspace orthogonal to the linear constraints satisfies the quadratic inequality, equivalent to projecting onto the constraint boundary, yielding a simple, effective, robust adaptive beamforming algorithm that prevents round‑off error accumulation.

Abstract

Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.