The Optimal Transmission Power Per Round for Hybrid-ARQ Rayleigh Fading Links

We address the fundamental problem of identifying the optimal power allocation sequence for hybrid automatic-repeat-request (H-ARQ) communications over quasistatic 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. 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 optimal assignment is 9dB lower than the equal-power protocol. The difference in average total power cost grows further when the number of allowable retransmissions increases (for example, lldB gain with a cap of 5 transmissions) or the targeted outage probability decreases (27dB gain with outage probability 10^-5 and transmissions capped at 5).