Robust Capon Beamforming via ADMM

This paper proposes two methods for robust Capon beamforming. One is for the doubly constrained robust Capon beamforming problem, where the unit modular constraints on the elements of the steering vector of interest are enforced to circumvent the look direction error or phase perturbations of the signal-of-interest; and another addresses robust beamforming in impulsive noise environment, where we consider the l
p
-norm minimization (0 < p < 2) of the output while constraining the mainlobe response ripple term. We apply the splitting technique to simplify the resultant nonconvex optimization problem and solve it using alternating direction method of multipliers. The performance of the proposed methods is demonstrated via numerical examples.