A Class of Finitely LMI Representable Worst-Case SINR Maximization Problems of Robust Adaptive Beamforming for General-Rank Signal Models

The robust adaptive beamforming (RAB) problem for general rank signal models is addressed via the worst-case signal-to-interference-plus-noise ratio (SINR) maximization. The worst-case SINR maximization problem is reformulated into a maximin SINR problem. To tackle such nonconvex problem, the uncertainty sets for the parameters in the SINR; the matrix obtained by eigen-decomposition of the high rank desired signal covariance matrix and the interference-plus-noise covariance matrix; need to be convex and closed. Then the corresponding minimax SINR problem is shown to be convex and the maximin and minimax SINR problems are shown to be equivalent to each other in the sense that they enjoy the same set of optimal solutions and the equal optimal value. Further, the minimax SINR problem becomes a semidefinite program (SDP) if the two uncertainty sets are characterized by finite linear matrix inequality constraints. Therefore, a globally optimal RAB solution for the worst-case SINR maximization problem can be obtained by solving the SDP. When the RAB optimization problem for the general rank signal model reduces to the problem for the rank one signal model, the theoretical results established herein are the same as those state-of-the-art results developed earlier, but with a weaker condition. Our results are validated by numerical examples.