Robust Adaptive Beamforming with Multiple Signal Mismatch Constraints: A Sequential Convex Approximation Method

A robust adaptive beamforming (RAB) problem of maximizing the worst-case (the minimal) signal-to-interference-plus-noise ratio (SINR) over the union of small uncertainty sets of the desired signal steering vector is formulated and recast into a quadratic minimization problem with nonconvex constraints. In existing works, the semidefinite programming relaxation technique is applied to approximately solve the quadratic problem, incurring heavy computational burden or low array output SINR. Herein, a sequential convex second-order cone programming (SOCP) approximation algorithm is proposed. In particular, an SOCP problem is constructed and solved in each step, and it is shown that the sequence of the optimal values of the SOCPs is nonincreasing and bounded, and the optimal solutions of the SOCPs are feasible for the quadratic problem and converge to a locally optimal solution. Example simulations are performed to demonstrate the improved performance of the proposed algorithm in terms of the beamformer output SINR, as well as the average CPU time and average number of iterations of the algorithm.