Robust Minimum Variance Beamforming with Sidelobe-Level Control Using the Alternating Direction Method of Multipliers

Adaptive beamforming with sidelobe-level control in the presence of signal steering vector uncertainty is investigated. Unlike the traditional multiconstrained optimization strategy using the interior point method, iterative optimization algorithms with the aid of the alternating direction method of multipliers (ADMM) framework are proposed. The uncertainty set constraint and the sidelobe constraint are formulated into two optimization subproblems and handled with the Lagrange multiplier method. By introducing matrix decomposition techniques, subproblem 1 is transformed into a polynomial root-finding problem that can be solved with low computational complexity. For subproblem 2, a closed-form solution can be obtained directly. Furthermore, for the continuously receiving snapshots case, iterative gradient minimization is introduced and embedded into the ADMM iterations to give an approximate solution free from matrix decompositions. Theoretical analyses and simulations verify the low complexities and performance advantages of the proposed algorithms in the low sample support, steering vector mismatch, and real-time snapshot update scenarios.