This letter investigates the performance of amplify-and-forward relaying systems using maximum ratio transmission at the source. A closed-form expression for the outage probability and a closed-form lower bound for the average bit error probability of the system are derived. Also, the approximate expressions for the outage probability and average bit error probability in the high signal-to-noise ratio regime are given, based on which the optimal power allocation strategies to minimize the outage probability and average bit error probability are developed. Furthermore, numerical results illustrate that optimizing the allocation of power can improve the system performance, especially in the high signal-to-noise ratio regime.