Ergodic Capacity of M-1-1 AF Relaying Systems over Rayleigh Fading Channels

The amplify-and-forward relaying system considered here consists of a base station (BS) with M transmit antennas, K relay stations (RSs) with a single antenna each, and a mobile station (MS) with a single antenna. Upper bounds of ergodic capacities are derived for some specific values of M and general values of K where the best relay selection (BRS) is used, and the maximum-ratio-transmission (MRT) is applied for the BS-RS transmission. Numerical results show that increasing M enhances the ergodic capacity due to the reduction of noise propagation, and increasing K also enhances the ergodic capacity due to the K-th order diversity gain from the BRS. In addition, the effect of increasing K on capacity enhancement is much significant compared to that of increasing M. On the other hand, the capacity enhancement from increasing M is limited, whereas the capacity enhancement from increasing K is unlimited. In addition, the capacity enhancement from M and that from K are independent.