Effect of multiple antennas at the source on outage probability for amplify-and-forward relaying systems

The amplify-and-forward (AF) relaying system considered here consists of a source node with M transmit antennas, and relay and destination nodes with a single antenna each. The closed-form expressions for the outage probabilities for maximum-ratio-transmission (MRT) at the source are presented for some specific values of M. Numerical results show that increasing M from 1 to 2 can achieve roughly a 3 dB SNR gain, guaranteeing the same outage probability. However, we discover that for M ges 3, the additional gain compared to M = 2 decreases quickly as the SNR increases. Therefore, increasing M above 3 does not achieve significantly greater gain over M = 2 at high SNR.