Convex optimization and its applications in robust adaptive beamforming

Convex optimization plays an important role in science and engineering research. In many signal processing applications, convex optimization is one of the critical mathematical tools. For example, robust adaptive beamformer is always formulated as quadratic optimization problem with some linear or quadratic constraints. In this paper, we review some of the progresses of our group on using Constraints on Magnitude Response (CMRs) for robust adaptive beamforming. Some mathematical skills on how to transform the beamformer with CMRs into convex programming problems are introduced. With proper convex formulations, the proposed beamformers posses simple implementation, flexible performance control, as well as significant SINR enhancement.