Optimal power assignment for minimizing the average total transmission power in hybrid-ARQ rayleigh fading links

We address the fundamental problem of identifying the optimal power assignment sequence for hybrid automatic-repeat-request (H-ARQ) communications over quasi-static Rayleigh fading channels. For any targeted H-ARQ link outage probability, we find the sequence of power values that minimizes the average total expended transmission power. We first derive a set of equations that describe the optimal transmission power assignment and enable its exact recursive calculation. To reduce calculation complexity, we also develop an approximation to the optimal power sequence that is close to the numerically calculated exact result. The newly founded power allocation solution reveals that conventional equal-power H-ARQ assignment is far from optimal. For example, for targeted outage probability of 10^-3 with a maximum of two transmissions, the average total transmission power with the optimal assignment is 9 dB lower than the equal-power protocol. The difference in average total power cost grows further when the number of allowable retransmissions increases (for example, 11 dB gain with a cap of 5 transmissions) or the targeted outage probability decreases (27 dB gain with outage probability 10^-5 and transmissions capped at 5). Interestingly, the optimal transmission power assignment sequence is neither increasing nor decreasing; its form depends on given total power budget and targeted outage performance levels. Extensive numerical and simulation results are presented to illustrate the theoretical development.