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A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints

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Abstract

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.

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Acknowledgments

This work was supported by a grant from the Australia Research Council and a grant from the National Natural Science Foundation of China (No. 11171079).

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Authors and Affiliations

  1. School of Electrical, Electronic and Computer Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia

    Bin Li & Antonio Cantoni

  2. Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Hai Huyen Dam & Kok Lay Teo

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  1. Bin Li
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  2. Hai Huyen Dam
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  3. Antonio Cantoni
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  4. Kok Lay Teo
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Correspondence to Bin Li.

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Li, B., Dam, H.H., Cantoni, A. et al. A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints. Optim Lett 8, 1829–1843 (2014). https://doi.org/10.1007/s11590-013-0673-y

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  • DOI: https://doi.org/10.1007/s11590-013-0673-y

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