Analysis and Design of Optimum Sparse Array Configurations for Adaptive Beamforming

In this paper, we analyze the effect of nonuniform array configurations on adaptive beamforming for enhanced signal-to-interference-plus-noise ratio (SINR). The array is configured using a given number of antennas or through a selection of subset of antennas from a larger available set, leading to a sparse array in both cases. The bounds on the highest achievable SINR for a given number of antennas are formulated and used to offer new insights into open-loop adaptive beamforming. The upper and lower bounds underscore the role of array configurations in optimizing performance for interference-free and interference-active environments, respectively. This paper considers the general case of multiple sources and interferences in the field of view. We formulate three angles, namely eigenspace angle, conventional angle, and minimum canonical angle for characterizing spatial separation between the source and interference subspaces, which represent performance loss incurred by interference nulling. Three sparse array design methods, incorporating these angles, are proposed. Simulation examples confirm the role of subspace angles in optimum beamforming and validate the utility of antenna selection algorithms for sparse array design.