Power-Optimized Amplify-and-Forward Multi-Hop Relaying Systems

Optimal power allocation schemes that maximize the instantaneous received signal-to-noise ratio in an amplify-and-forward multi-hop transmission system under short-term (ST) and long-term (LT) power constraints are presented. The optimal power allocation strategy under a ST power constraint requires a centralized architecture for implementation. However, the power allocation solutions to the LT power constraints can be implemented in a decentralized manner. Theoretical expressions for evaluation of the outage probability of the proposed power-optimized multi-hop relaying systems over Rayleigh fading channels are obtained. Numerical results show the superior performance of amplify-and-forward multi-hop relaying systems with the power allocation scheme over those with uniform power allocation. It is shown that at sufficiently large values of signal-to-noise ratio (SNR), an amplify-and-forward K-hop relaying system employing the optimal power allocation scheme under ST power constraint achieves K times better outage performance than that of the corresponding system employing uniform power allocation. It is also shown that the optimal power allocation schemes under LT power constraints provide substantial performance gain at both small and large values of SNR and achieve diversity gain 2.