Worst-Case SINR Maximization Based Robust Adaptive Beamforming Problem with a Nonconvex Uncertainty Set
Yongwei Huang, Hao Fu, Sergiy A. Vorobyov, Zhi-Quan Tom Luo · 2019
The optimal robust adaptive beamforming problem based on worst-case signal-to-noise-plus-interference ratio (SINR) maximization with a nonconvex uncertainty set of the desired steering vectors is considered. The uncertainty set consists of a similarity constraint and a (nonconvex) double-sided ball constraint. The worst-case SINR maximization problem is turned into a quadratic matrix inequality (QMI) problem using the strong duality of semidefinite programs. Then the linear matrix inequality (LMI) relaxation for the QMI problem is formulated, and is further restricted by adding an equivalent representation for the second largest eigenvalue of the positive semidefinite beamforming matrix to be nonnegative. It turns out that the restricted LMI problem is a bilinear matrix inequality (BLMI) relaxation problem. We propose an iterative algorithm to solve the BLMI problem that finds an optimal/suboptimal solution for the original QMI problem for the worst-case SINR maximization problem. To validate our results, simulation examples are presented and demonstrate the improved performance of the proposed robust beamformer in terms of the array output SINR.