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
Code design for radar STAP via optimization theory
IEEE Transactions on Signal Processing
Doubly Constrained Robust Capon Beamformer With Ellipsoidal Uncertainty Sets
IEEE Transactions on Signal Processing
Quality of Service and Max-Min Fair Transmit Beamforming to Multiple Cochannel Multicast Groups
IEEE Transactions on Signal Processing
Far-Field Multicast Beamforming for Uniform Linear Antenna Arrays
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part II
On downlink beamforming with indefinite shaping constraints
IEEE Transactions on Signal Processing
Iterative multiuser uplink and downlink beamforming under SINR constraints
IEEE Transactions on Signal Processing
Transmit beamforming and power control for cellular wireless systems
IEEE Journal on Selected Areas in Communications
IEEE Transactions on Signal Processing
IEEE Transactions on Wireless Communications
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Consider a downlink communication system where multiantenna 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 to minimize the transmission powers while ensuring the signal-to-interference-noise ratio requirement of each user within the system. At the same time, it may be necessary to keep the interference generated on other coexisting systems under a certain tolerable level. In addition, one may want to include general individual shaping constraints on the beamforming vectors. This beamforming problem is a separable homogeneous quadratically constrained quadratic program, and it is difficult to solve in general. In this paper, we give conditions under which strong duality holds and propose efficient algorithms for the optimal beamforming problem. First, we study rank-constrained solutions of general separable semidefinite programs (SDPs) and propose rank reduction procedures to achieve a lower rank solution. Then we show that the SDP relaxation of three classes of optimal beamforming problem always has a rank-one solution, which can be obtained by invoking the rank reduction procedures.