On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
Mathematics of Operations Research
Complex Matrix Decomposition and Quadratic Programming
Mathematics of Operations Research
Linear precoding via conic optimization for fixed MIMO receivers
IEEE Transactions on Signal Processing
Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel Multicast Groups
IEEE Transactions on Signal Processing
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
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Consider a downlink communication system where multi-antenna base stations transmit independent data streams to decentralized single-antenna users over a common frequency band. The goal of the base stations is to jointly adjust the beamforming vectors so as to minimize the transmission powers while ensuring the signal-to-interference-noise ratio (SINR) requirement of individual users within the system, and keeping lower interference level to other systems which operate in the same frequency band and in the same region. This optimal beamforming problem is a separable homogeneous quadratically constrained quadratical programming (QCQP), and it is difficult to solve in general. In this paper, we give conditions under which strong duality holds, and propose an efficient algorithm for the optimal beamforming problem. First, we study rank-constrained solutions of a general separable semidefinite programming (SDP), and propose a rank reduction procedure to achieve a lower rank solution. Then we show that the SDP relaxation of a class of the optimal beamforming problem has a rank-one solution, which can be obtained by invoking the rank reduction procedure.