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

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2010-07-01
Leveque, Olivier
Vignat, Christophe
Yüksel Turgut, Ayşe Melda
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.
IEEE TRANSACTIONS ON INFORMATION THEORY

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Citation Formats
O. Leveque, C. Vignat, and A. M. Yüksel Turgut, “Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay,” IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 56, no. 7, pp. 3356–3368, 2010, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/96654.