Complex Matrix Decomposition and Quadratic Programming
Mathematics of Operations Research
Rank-constrained separable semidefinite programming with applications to optimal beamforming
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel Multicast Groups
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part II
Transmit beamforming for physical-layer multicasting
IEEE Transactions on Signal Processing - Part I
On downlink beamforming with indefinite shaping constraints
IEEE Transactions on Signal Processing
Transmit beamforming and power control for cellular wireless systems
IEEE Journal on Selected Areas in Communications
Hi-index | 35.68 |
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 purification process) or the Perron-Frobenius theorem, the proposed algorithms are based on the linear program strong duality theorem.