Unraveling the Rank-One Solution Mystery of Robust MISO Downlink Transmit Optimization: A Verifiable Sufficient Condition via a New Duality Result
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AbstractThis paper concentrates on a robust transmit optimization problem for the multiuser multi-input single-output (MISO) downlink scenario and under inaccurate channel state information (CSI). This robust problem deals with a general-rank transmit covariance design and follows a safe rate-constrained formulation under spherically bounded CSI uncertainties. Curiously, simulation results in previous works suggested that the robust problem admits rank-one optimal transmit covariances in most cases. Such a numerical finding is appealing because transmission with rank-one covariances can be easily realized by single-stream transmit beamforming. This gives rise to a fundamentally important question, namely, whether we can theoretically identify conditions under which the robust problem admits a rank-one solution. In this paper, we identify one such condition. Simply speaking, we show that the robust problem is guaranteed to admit a rank-one solution if the CSI uncertainties are not too large and the multiuser channel is not too poorly conditioned. To establish the aforementioned condition, we develop a novel duality framework, through which an intimate relationship between the robust problem and a related maximin problem is revealed. Our condition involves only a simple expression with respect to the multiuser channel and other system parameters. In particular, unlike other sufficient rank-one conditions that have appeared in the literature, ours is verifiable. The application of our analysis framework to several other CSI uncertainty models is also discussed.
All Author(s) ListWing-Kin Ma, Jiaxian Pan, Anthony Man-Cho So, Tsung-Hui Chang
Journal nameIEEE Transactions on Signal Processing
Volume Number65
Issue Number7
Pages1909 - 1924
LanguagesEnglish-United States
KeywordsMultiuser MIMO, transmit optimization, robust optimization, semidefinite program, rank-one solution

Last updated on 2020-21-11 at 02:05