# American Institute of Mathematical Sciences

2016, 6(3): 297-304. doi: 10.3934/naco.2016012

## A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method

 1 Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA 6845 2 School of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009

Received  March 2015 Revised  September 2016 Published  September 2016

In this paper, we consider the zero-forcing beamforming (ZFBF) under the per-antenna power constraints (PAPC). Our objective is to maximize the minimum user information rate. Traditionally, ZFBF under PAPC with a max-min performance measure can be transformed into a second order cone problem and then solved by applying the interior point method. However, it is expensive to realize this design in practice due to high computational complexity per iteration. An alternative low complexity zero-forcing beamformer design is proposed for MU-MIMO systems by applying a dual gradient method. Different from the step size rule in the literature, a backtracking line search is adopted. A numerical example is provided to show the effectiveness of the proposed method.
Citation: Bin Li, Hai Huyen Dam, Antonio Cantoni. A low-complexity zero-forcing Beamformer design for multiuser MIMO systems via a dual gradient method. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 297-304. doi: 10.3934/naco.2016012
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##### References:
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