On Gaussian MIMO BC-MAC duality with multiple transmit covariance constraints

Lan Zhang, Rui Zhang, Ying Chang Liang, Yan Xin, H. Vincent Poor

Research output: Contribution to journalArticlepeer-review

113 Scopus citations


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.

Original languageEnglish (US)
Article number6169204
Pages (from-to)2064-2078
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - Apr 2012

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Beamforming
  • broadcast channels
  • multiple antennas
  • wireless systems


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