Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay

Creative Commons License

Leveque O., Vignat C., YÜKSEL TURGUT A. M.

IEEE TRANSACTIONS ON INFORMATION THEORY, vol.56, no.7, pp.3356-3368, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 7
  • Publication Date: 2010
  • Doi Number: 10.1109/tit.2010.2048471
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3356-3368
  • Keywords: Cooperation, diversity-multiplexing tradeoff (DMT), fading channels, multiple-input multiple-output (MIMO), relay channel, spherical integrals, wireless networks, COOPERATIVE DIVERSITY
  • Middle East Technical University Affiliated: No


In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e., the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas. Besides, the derivation of the upper bound involves a new asymptotic study of spherical integrals (that is, integrals with respect to the Haar measure on the unitary group u(n)), which is a topic of mathematical interest in itself.