Abstract
This paper lays a mathematical framework for estimating the energy saving of a relay assisting a pair of wireless devices. We derive closed-form expressions for describing the geometrical zone where relaying is energy efficient. In addition, we obtain the probabilistic distribution of the energy saving introduced by relays that are randomly distributed according to a spatial Poisson point process. Furthermore, we present a comparison methodology for fairly evaluating the energy consumption of conventional cellular network from one side and relay-assisted device-to-device communication from another side. Results suggest that a significant energy saving can be achieved when relay-assisted device-to-device communication is adopted for distances below a certain threshold. In order to test the analytical framework, we perform Monte-Carlo simulations and compare the results with those obtained from the mathematical framework.
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