Robust Sparse Beamforming via Minimax and Maximin SINRs for a Radar Receive Array

This paper considers robust sparse beamforming (RSB) designs for a radar receive array via minimax and maximin signal-to-interference-plus-noise ratios (SINRs) criteria (assuming mismatches on the signal-of-interest steering vector and the interference-plus-noise covariance matrices) with a sparsity constraint on the beamvector. We first propose an approximation algorithm for the RSB solution for the minimax SINR problem, where a re-weighted l1-norm regularization method is exploited to account for the sparsity requirement (by means of a tailored penalty term to the objective) and each problem of the underlying sequence of optimizations is recast into a semidefinite programming (SDP) problem by the strong duality theory. We show how to retrieve an optimal beamvector for the regularized minimax problem from the optimal solution to the SDP. For the RSB solution to the maximin SINR problem, an approximation algorithm is established similarly to the previous situation, but with the difference that the regularized maximin problem is transformed into a second-order cone programming problem. The latter approximation algorithm is computationally lighter than the former when the size of the array is sufficiently large. Simulation examples are presented to demonstrate the improved performance of the proposed two RSB solutions in terms of the normalized beampattern and array output SINR, compared to two existing non-robust sparse beamformers.