Abstract—We present an analytical characterization of the ergodic capacity for an amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay network over asymmetric chan- nels. In the two-hop system that we consider, the source-relay and relay-destination channels undergo Rayleigh and Rician fading, respectively. Considering arbitrary-rank means for the relay- destination channel, we first investigate the marginal distribution of an unordered eigenvalue of the cascaded AF channel, and we provide an analytical expression for the ergodic capacity of the system. The closed-form expressions that we derive are computationally efficient and validated by numerical simulation. Our results also show the impact of the signal-to-noise ratio and of the Rician factor on this asymmetric relay network.