Stochastic Geometry Modeling of Cellular Networks: A New Definition of Coverage and its Application to Energy Efficiency Optimization

Abstract : In this paper, we analyze and optimize the energyefficiency of downlink cellular networks. With the aid oftools from stochastic geometry, we introduce a new closed-form analytical expression of the potential spectral efficiency.Unlike currently available analytical frameworks, the proposedanalytical formulation explicitly depends on the transmit powerand density of the base stations. This is obtained by generalizingthe definition of coverage probability and by taking intoaccount the sensitivity of the receiver not only during thedetection of information data, but during the cell associationphase as well. Based on the new analytical representationof the potential spectral efficiency, the energy efficiency isformulated in a tractable closed-form expression. The resultingoptimization problem is studied and it is mathematically provedthat the energy efficiency is a unimodal and strictly pseudo-concave function in the transmit power. Numerical results areillustrated and discussed.