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 retransmission request (ARQ) based multi-hop system is analyzed under power and throughput constraints. Two ARQ protocols including type-I (ARQ-I) and repetition redundancy (ARQ-RR) are considered and expressions 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 protocols and in arbitrary average channel gain values are obtained. It is shown that how different throughput 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 protocol. 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.