Applications of Robust Optimization in Signal Processing: Beamforming and Power Control

In this presentation, we study the applications of robust optimization in signal processing: robust beamforming in array and power control in wireless networks. First, the background of beamforming and the traditional diagonal loading (DL) method are introduced. Then, the robust beamforming designs are proposed by considering the worst-case distortionless and probabilistic constraints of the steering vector, respectively. It is shown that the robust beamforming design can be formulated as a seconder order cone programming (SOCP) problem or a semidefinite programming (SDP) problem, and then can be solved efficiently. In the last, the robust power control problem in cognitive radio networks can be formulated as a SOCP problem by considering the worst-case uncertainties in the wireless channel gains.