On the Asymptotic Properties of Amplify-and-Forward MIMO Relay Channels

This paper studies the asymptotic properties of amplify-and-forward (AF) multiple-input multiple-output (MIMO) two-hop relay channels, where the source, relay and destination terminals are equipped with a number of correlated antennas and there is a direct link between the source and destination terminals. Our first main contribution is the derivation of the asymptotic mutual information expressions for the MIMO-AF relay channel for any given signaling input distributions (not necessarily Gaussian) in the large-system regime, which is particularly relevant if practical modulation schemes are used. In addition to the formula that uses joint optimal decoding (JOD) at the destination terminal, we also obtain the asymptotic result for a more practical system which performs separate detection and decoding (SDD) (i.e., spatial detection followed by a temporal error-correction decoder). Another major contribution of this paper is an efficient algorithm that can compute the optimal source covariance matrix and the relay precoding matrix to maximize the asymptotic mutual information of the MIMO-AF relay system if channel covariance information (CCI) is known at the source and relay terminals. Index Terms Asymptotic analysis, Large system, MIMO, Relay channels, Replica method.