SNR-based vs. BER-based power allocation for an amplify-and-forward single-relay wireless system with MRC at destination

Optimum power allocation improves the efficiency of wireless systems. While optimizing the average received SNR would directly result in an optimized average BER in a non-relaying system, it is not clear whether we can achieve an optimized average BER in a relaying system by optimizing the average SNR at the destination terminal. In this paper, the problem of power allocation in a single-relay wireless system with maximal ratio combining (MRC) at the destination terminal is investigated via optimizing two different objective functions: average SNR and average BER. The average SNR and average BER expressions are derived for an amplify-and-forward relaying protocol with MRC at the destination as a function of source and relay transmit powers. Based on the derived SNR and BER expressions at the destination, closed-form expressions are derived for optimum transmit power of source and relay. It is observed that the BER-based power allocation scheme achieves considerable performance improvement over the SNR-based scheme when the relay is closer to the source than destination.