Paper Info
Title
A dual perspective on separable semidefinite programming with applications to optimal downlink beamforming
Abstract
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.
Year
DOI
Venue
2010
10.1109/TSP.2010.2049570
IEEE Transactions on Signal Processing
Keywords
Field
DocType
optimization problem,semidefinite programming,signal to interference plus noise ratio,signal to noise ratio,qos,quality of service,linear program,closed form solution,quadratically constrained quadratic program,duality mathematics,base stations,constraint optimization,sinr,duality theorem,linear programming,downlink,strong duality,indexing terms
Mathematical optimization,Quadratically constrained quadratic program,Duality (mathematics),Strong duality,Linear programming,Quadratic programming,Optimization problem,Semidefinite programming,Mathematics,Constrained optimization
Journal
Volume
Issue
ISSN
58
8
1053-587X
Citations 
PageRank 
References 
15
0.81
12
Authors
2
Name
Order
Citations
PageRank
Yongwei Huang181450.83
Daniel Pérez Palomar22146134.10