A dual perspective on separable semidefinite programming with applications to optimal beamforming

Consider the downlink beamforming optimization problem with signal-to-interference-plus-noise ratio constraints, null-shaping interference constraints and multiple groups of individual shaping constraints. We propose an efficient algorithm for the problem, which consists of firstly solving the dual of the semidefinite programm (SDP) relaxation, secondly formulating a linear program (LP) and solving it to find a rank-one solution of the SDP relaxation. In contrast to the existing algorithms, the analysis of the proposed algorithm includes neither the rank reduction steps (purification process) nor the Perron-Frobenius theorem.