Energy efficiency of non-collaborative and collaborative Hybrid-ARQ protocols

In this paper, we consider the energy efficiency of truncated Hybrid-ARQ (HARQ) protocols in a single-user link (i.e., non-collaborative HARQ), or with the inclusion of a relay station (i.e., collaborative HARQ). The total energy consumption accounts for both the transmission energy and the energy consumed by the transmitting and receiving electronic circuitry of all involved terminals (source, destination and, possibly, the relay). Using the transmission time and transmission energy of each packet as optimization variables, the overall energy is minimized under an outage probability constraint for HARQ Type I, HARQ Chase Combining and HARQ Incremental Redundancy protocols (in the latter case, a tight lower bound is considered). Numerical optimization provides insight into the optimal design choices that enhance energy efficiency with HARQ protocols. It is shown, for instance, that, if the circuitry energy consumption is not negligible, selection of the transmission energy is not only dictated by the outage constraint, but is also significantly affected by the need to reduce the number of retransmissions. Our results also demonstrate the performance limitations of collaborative HARQ protocols in terms of energy efficiency, when circuitry consumption is properly accounted for.