Consumption Factor Optimization for Multihop Relaying over Nakagami-m   Fading channels
  In this paper, the energy efficiency of multihop relaying over Nakagami-$m$ fading channels is investigated. The "consumption factor" is used as a metric to evaluate the energy efficiency, and it is derived in closed-form for both amplify-and-forward and decode-and-forward relaying. Then, based on the obtained expressions, we propose a power allocation strategy maximizing the consumption factor. In addition, two sub-optimal, low complexity, power allocation algorithms are proposed and analyzed, and the obtained power allocation schemes are compared, in terms of energy efficiency as well as other common performance metrics, to other power allocation schemes from the literature. Analytical and simulation results confirm the accuracy of our derivations, and assess the performance gains of the proposed approach. 
Itsikiantsoa Randrianantenaina, Mustapha Benjillali, Mohamed-Slim   Alouini
cs.IT math.IT