The optimal power assignment for cooperative hybrid-ARQ relaying protocol

In this work, we consider the problem of assigning optimal transmission power sequence for cooperative hybrid automatic-repeat-request (H-ARQ) relaying protocol over quasi-static Rayleigh fading channels. We try to determine the optimal power sequence by minimizing the average total transmission power that we analyzed in our previous work in [10]. However, the closed-form expression of the average total power consumption of the cooperative H-ARQ relaying protocol is complicated in general, so we develop first in this work a simple approximation of the average total transmission power that is tight at high SNR. Then, based on the asymptotically tight approximation, we are able to identify the sequence of power values that minimizes the average total power consumption of the cooperative H-ARQ relaying protocol for any given targeted outage probability. In particular, we derive a set of equations that describe the optimal power level in each (re)transmission and enable its recursive calculation with fixed searching complexity. When the maximum number of (re)transmissions allowed in the protocol is L = 2, we have a closed-form result for the optimal transmission power sequence. The optimal power assignment solution reveals that conventional equal power assignment scheme is not optimal in general. Extensive simulation and numerical results are provided to illustrate and validate the theoretical results.