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Robust SINR-constrained MISO downlink beamforming: when is semidefinite programming relaxation tight?

Enbin Song1*, Qingjiang Shi2, Maziar Sanjabi3, Ruo-Yu Sun3 and Zhi-Quan Luo3

Author Affiliations

1 Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China

2 School of Information and Science Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China

3 Department of Electrical and Computer Engineering, University of Minnesota, Twin Cities, MN 55455, USA

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EURASIP Journal on Wireless Communications and Networking 2012, 2012:243  doi:10.1186/1687-1499-2012-243

Published: 6 August 2012


We consider the multiuser beamforming problem for a multi-input single-output downlink channel that takes into account the errors in the channel state information at the transmitter side (CSIT). By modeling the CSIT errors as elliptically bounded uncertainty regions, this problem can be formulated as minimizing the transmission power subject to the worst-case signal-to-interference-plus-noise ratio constraints. Several methods have been proposed to solve this nonconvex optimization problem, but none can guarantee a global optimal solution. In this article, we consider a semidefinite relaxation (SDR) for this multiuser beamforming problem, and prove that the SDR method actually solves the robust beamforming problem to global optimality as long as the channel uncertainty bound is sufficiently small or when the transmitter is equipped with at most two antennas. Numerical examples show that the proposed SDR approach significantly outperforms the existing methods in terms of the average required power consumption at the transmitter.