Optimal power assignment to minimize the average delay in hybrid-ARQ protocols

In this paper, the optimal power assignment strategy is determined for hybrid automatic-repeat-request (H-ARQ) protocols such that the average delay of the protocol is minimized for any given total transmission power budget and any targeted outage probability. A set of equations is derived that describe the optimal transmission power sequence and its optimality is shown based on the Karush-Kuhn-Tucker (KKT) Theorem. The set of equations enables an exact recursive calculation of the optimal transmission power per round, and the calculation complexity is fixed regardless of the maximum number of (re)transmission rounds allowed in the H-ARQ protocol. Compared to the conventional equal power assignment strategy, the optimal power assignment scheme achieves the same average delay with much less total transmission power. More importantly, for certain power budget levels, the optimal power assignment can make the H-ARQ protocol work while the equal power assignment cannot. Extensive numerical results are presented to illustrate the theoretical development.