Robust Adaptive Beamforming Based on Steering Vector Estimation via Semidefinite Programming Relaxation

TL;DR

This paper introduces a robust adaptive beamforming method that estimates the signal steering vector using semidefinite programming relaxation, improving performance under steering vector errors without requiring parameter tuning.

Contribution

It proposes a novel SDP-based approach for steering vector estimation in robust beamforming, with a proof of strong duality and efficient solution methods.

Findings

Outperforms existing robust beamforming methods in simulations

Provides closed-form solutions in special cases

Demonstrates effectiveness under various steering vector errors

Abstract

We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the actual steering vector, which then is used for obtaining the optimal beamforming weight vector. The objective for finding such an estimate of the actual signal steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate of the steering vector does not converge to an interference steering vector. Our objective and constraints are free of any design parameters of non-unique choice. The resulting optimization problem is a non-convex quadratically constrained quadratic program, which is NP hard in general. However, for our problem we show that an efficient solution can be found using the semi-definite relaxation technique. Moreover, the strong duality holds for the proposed problem and can also be used for finding the optimal solution efficiently and at low complexity. In some special cases, the solution can be even found in closed-form. Our simulation results demonstrate the superiority of the proposed method over other previously developed robust adaptive beamforming methods for several frequently encountered types of signal steering vector errors.