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

In this paper, we analyze and optimize the energy efficiency of downlink cellular networks. With the aid of tools from stochastic geometry, we introduce a new closed-form analytical expression of the potential spectral efficiency. Unlike currently available analytical frameworks, the proposed analytical formulation explicitly depends on the transmit power and density of the base stations. This is obtained by generalizing the definition of coverage probability and by taking into account the sensitivity of the receiver not only during the detection of information data, but during the cell association phase as well. Based on the new analytical representation of the potential spectral efficiency, the energy efficiency is formulated in a tractable closed-form expression. The resulting optimization problem is studied and it is mathematically proved that the energy efficiency is a unimodal and strictly pseudo-concave function in the transmit power. Numerical results are illustrated and discussed.