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In this paper, the energy efficiency of multihop relaying over Nakagami-$m$fading channels is investigated. The "consumption factor" is used as a metricto evaluate the energy efficiency, and it is derived in closed-form for bothamplify-and-forward and decode-and-forward relaying. Then, based on theobtained expressions, we propose a power allocation strategy maximizing theconsumption factor. In addition, two sub-optimal, low complexity, powerallocation algorithms are proposed and analyzed, and the obtained powerallocation schemes are compared, in terms of energy efficiency as well as othercommon performance metrics, to other power allocation schemes from theliterature. Analytical and simulation results confirm the accuracy of ourderivations, and assess the performance gains of the proposed approach.

Consumption Factor Optimization for Multihop Relaying over Nakagami-m Fading channels