On the capacity of MIMO relay channels

Bo Wang, Junshan Zhang, Anders Høst-Madsen

Research output: Contribution to journalArticlepeer-review

737 Scopus citations


We study the capacity of multiple-input multiple-output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks.

Original languageEnglish (US)
Pages (from-to)29-43
Number of pages15
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 2005


  • Cooperative communications
  • Ergodic capacity
  • Multiple-input multiple-output (MIMO)
  • Relay channel

ASJC Scopus subject areas

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


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