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On Gaussian MIMO BC-MAC Duality With Multiple Transmit Covariance Constraints

Author(s): Zhang, Lan; Zhang, Rui; Liang, Ying-Chang; Xin, Yan; Poor, H Vincent

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Abstract: Owing to the special structure of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC), the associated capacity region computation and beamforming optimization problems are typically non-convex, and thus cannot be solved directly. One feasible approach is to consider the respective dual multiple-access channel (MAC) problems, which are easier to deal with due to their convexity properties. The conventional BC-MAC duality has been established via BC-MAC signal transformation, and is applicable only for the case in which the MIMO BC is subject to a single transmit sum-power constraint. An alternative approach is based on minimax duality, which can be applied to the case of the sum-power constraint or per-antenna power constraint. In this paper, the conventional BC-MAC duality is extended to the general linear transmit covariance constraint (LTCC) case, which includes sum-power and per-antenna power constraints as special cases. The obtained general BC-MAC duality is applied to solve the capacity region computation for the MIMO BC and beamforming optimization for the multiple-input single-output (MISO) BC, respectively, with multiple LTCCs. The relationship between this new general BC-MAC duality and the minimax duality is also discussed, and it is shown that the general BC-MAC duality leads to simpler problem formulations. Moreover, the general BC-MAC duality is extended to deal with the case of nonlinear transmit covariance constraints in the MIMO BC.
Publication Date: 15-Mar-2012
Citation: Zhang, Lan, Zhang, Rui, Liang, Ying-Chang, Xin, Yan, Poor, H Vincent. (2012). On Gaussian MIMO BC-MAC Duality With Multiple Transmit Covariance Constraints. IEEE Transactions on Information Theory, 58 (4), 2064 - 2078. doi:10.1109/tit.2011.2177760
DOI: doi:10.1109/tit.2011.2177760
ISSN: 0018-9448
EISSN: 1557-9654
Pages: 2064 - 2078
Type of Material: Journal Article
Journal/Proceeding Title: IEEE Transactions on Information Theory
Version: Author's manuscript

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