An Inner SOCP Approximate Algorithm for Robust Adaptive Beamforming for General-Rank Signal Model

The worst-case robust adaptive beamforming problem for general-rank signal model is considered. Its formulation is to maximize the worst-case signal-to-interference-plus-noise ratio, incorporating a positive semidefinite constraint on the actual covariance matrix of the desired signal. In the literature, semidefinite program (SDP) techniques, together with others, have been applied to approximately solve this problem. Herein, an inner second-order cone program (SOCP) approximate algorithm is proposed to solve it. In particular, a sequence of SOCPs are constructed and solved, while the SOCPs have the nonincreasing optimal values and converge to a locally optimal value (it is in fact a globally optimal value through our extensive simulations). As a result, our algorithm does not use computationally heavy SDP relaxation technique. To validate our inner approximation results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformer in terms of the averaged cpu-time (indicating how fast the algorithms converge) in a high signal-to-noise region.