Energy Efficiency in ARQ-Based Multi-Hop Systems and the Tradeoff with Throughput

The minimum energy per bit (EPB) as the energy efficiency (EE) metric in an automatic retrans-mission request (ARQ) based multi-hop system is an-alyzed under power and throughput constraints. Two ARQ protocols including type-I (ARQ-I) and repeti-tion redundancy (ARQ-RR) are considered and ex-pressions for the optimal power allocation (PA) are obtained. Using the obtained optimal powers, the EE-throughput tradeoff (EETT) is analyzed and the EETT closed-form expressions for both ARQ proto-cols and in arbitrary average channel gain values are obtained. It is shown that how different through-put requirements, especially the high levels, affect the EE performance. Additionally, asymptotic analysis is made in the feasible high throughput values and lower and upper EETT bounds are derived for ARQ-I pro-tocol. To evaluate the EE a distributed PA scenario, as a benchmark, is presented and the energy saving-gain obtained from the optimal PA in comparison with the distributed PA for ARQ-I and ARQ-RR protocols is discussed in different throughput values and node locations.