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

• Published in: IEEE transactions on information theory Vol. 58; no. 4; pp. 2064 - 2078
• Main Authors: Lan Zhang, Rui Zhang, Ying-Chang Liang, Yan Xin, Poor, H. Vincent
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2012; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Antennas; Applied sciences; Array signal processing; Beamforming; broadcast channels; Communication channels; Covariance matrix; Detection, estimation, filtering, equalization, prediction; Encoding; Exact sciences and technology; Information theory; Information, signal and communications theory; Interference; MIMO; multiple antennas; Normal distribution; Optimization; Signal and communications theory; Signal to noise ratio; Signal, noise; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Transmission and modulation (techniques and equipments); Vectors; wireless systems; Access control; MIMO system; Multiple access; wireless systems; Two channel system; Wireless telecommunication; Beam forming; Optimization; Beamforming; Covariance; Minimax method; Signal processing; Broadcast channels; Convexity; multiple antennas; MISO system; Multiple channel; Antenna array; Antenna; Electroceramics
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2177760

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.