Asymptotic analysis of ergodic capacity for amplify-and-forward MIMO relaying systems

In this paper, we analyze asymptotic ergodic capacity of multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying systems with channel state information (CSI) at the relay. By exploiting the asymptotic results for eigenvalue distributions, we derive the ergodic capacity in various asymptotic antenna regimes as a closed-form expression with arbitrary system parameters. The analyzed results demonstrate that increasing the number of source antennas causes the capacity shrink phenomenon which is analogous to the channel hardening effect in multi-user MIMO systems. Although we assume asymptotically large antennas to obtain the closed-form expressions, simulation results show that our derived expressions are surprisingly accurate even with the moderate number of antennas, and thus can serve for analyzing practical MIMO relay networks.