Robust Adaptive Beamforming in Uniform Circular Array

Abstract

Phase-mode transformation (PMT) is a commonly used technique to convert a uniform circular array (UCA) into a virtual uniform linear array (ULA). This method restores the Vandemonde structure of the steering vector and makes it easy to apply many existing beamforming algorithms to UCA. One such method is the famous Minimum Variance Distortionless Response (MVDR) algorithm, in which the array gain is equal to unity in the direction of arrival of the desired signal. However, due to the approximation errors of the PMT and signal steering vector mismatches, the performance of these algorithms degrades. To address these two issues, in this paper we develop a robust recursive updating algorithm based on worst-case performance optimization. We show that the proposed algorithm belongs to the class of the diagonal loading technique and the transformation matrix belongs to a certain ellipsoid set. Using the Lagrange multiplier method, we have also derived closed-form solution to the weight vector. Our robust algorithm has low implementation complexity and makes the mean output array SINR consistently close to the optimal one. Numerical experiments have shown that our method outperforms the MVDR algorithm.