Energy Efficiency of Hybrid-ARQ under Statistical Queuing Constraints

In this paper, energy efficiency of hybrid automatic repeat request (HARQ) schemes with statistical queuing constraints is studied for both constant-rate and random Markov arrivals by characterizing the minimum energy per bit and wideband slope. In particular, two queuing models are considered. Specifically, when outage occurs, the transmitter keeps the packet, lowers its priority, and attempts to retransmit it later in the first queue model, while the packet is discarded and removed from the buffer in the second queue model. For both models, energy efficiency is investigated when outage constraints, statistical queuing constraints, and deadline constraints are imposed. The deadline constraint provides a limitation on the number of retransmissions or equivalently the number of HARQ rounds. Under these assumptions, closed-form expressions are obtained for the minimum energy per bit and wideband slope for HARQ with chase combining, and comparisons among different arrival models are made. For instance, it is shown that stricter queuing constraints and more bursty sources degrade the energy efficiency by lowering the wideband slope. In the numerical results, analytical characterizations are verified through simulations. Moreover, the impact of source variations/burstiness, deadline constraints, outage probability, and queuing constraints on the energy efficiency is analyzed.