Optimum sparse array beamforming for general rank signal models

Abstract

Sparse array design professes several advantages over their uniform array counterparts, including high resolution and ability to deal with large number of sources in the field of view (FOV). In this paper, we examine sparse arrays achieving maximum signal-to-interference plus noise ratio (MaxSINR) for three different cases, namely, single point source, multiple point sources and Gaussianly spread source, operating in an interference active environment. Our approach does not require any apriori knowledge of the source directions of arrival and their respective power. We formulate the problem as quadratically constraint quadratic program (QCQP), where the cost function is penalized with weighted l 1 -norm squared of the beamformer weight vector, and propose an iterative technique to control the desired sparsity. It is shown that the optimum sparse array utilizes the array aperture effectively and provides considerable performance improvement over a compact uniform linear array (ULA). Simulation results are presented to show the effectiveness of proposed algorithm for array configurability in the case of both single and general rank signal correlation matrices.