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

This paper considers the downlink beamforming optimization problem that minimizes the total transmission power subject to global shaping constraints and individual shaping constraints, in addition to the constraints of quality of service (QoS) measured by signal-to-interference-plus-noise ratio (SINR). This beamforming problem is a separable homogeneous quadratically constrained quadratic program (QCQP), which is difficult to solve in general. Herein we propose efficient algorithms for the problem consisting of two main steps: 1) solving the semidefinite programming (SDP) relaxed problem, and 2) formulating a linear program (LP) and solving the LP (with closed-form solution) to find a rank-one optimal solution of the SDP relaxation. Accordingly, the corresponding optimal beamforming problem (OBP) is proven to be "hidden" convex, namely, strong duality holds true under certain mild conditions. In contrast to the existing algorithms based on either the rank reduction steps (the...

• Type: Journal
• Year: 2010
• Where: TSP
• Authors: Yongwei Huang, Daniel Pérez Palomar
• Keywords: Artificial Intelligence, Beamforming Problem, Linear Program, Strong Duality, TSP 2010