Ergodic capacity analysis of amplify-and-forward MIMO dual-hop systems

This paper analyzes the ergodic capacity of dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay channels, assuming that the channel state information is available only at the destination terminal. We first present a new expression for the unordered eigenvalue density of a certain product of independent complex matrices, which is used to derive an exact expression for ergodic capacity. We then employ results from multivariate statistics to derive new closed-form upper and lower bounds of the ergodic capacity. In contrast to prior work, our results apply for arbitrary numbers of antennas and arbitrary relay configurations. Numerical results are provided to validate the theoretical analysis.