New Analytical Methods for the Analysis and Optimization of Energy-Efficient Cellular Networks by Using Stochastic Geometry. (Nouvelles méthodes d'analyse et d'optimisation des réseaux cellulaires à haute efficacité énergétique en utilisant la géométrie stochastique)

In communication networks, system-level analysis and optimization are useful when one is interested in optimizing the system performance across the entire network. System-level analysis and optimization, therefore, are relevant for optimally operating current networks, and for deploying and planning future networks. In the last few years, the system-level modeling and analysis of cellular networks have been facilitated by capitalizing on the mathematical tool of stochastic geometry and, more precisely, on the theory of spatial point processes. It has been empirically validated that, from the system-level standpoint, the locations of cellular base stations can be abstracted as points of a homogeneous Poisson point process whose intensity coincides with the average number of based stations per unit area.In this context, the contribution of the present Ph.D. thesis lies in developing new analytical methodologies for analyzing and optimizing emerging cellular network deployments. The present Ph.D. thesis, in particular, provides three main contributions to the analysis and optimization of energy-efficient cellular networks.The first contribution consists of introducing a tractable approach for assessing the feasibility of multiple-antenna cellular networks, where low-energy mobile devices decode data and harvest power from the same received signal. Tools from stochastic geometry are used to quantify the information rate vs. harvested power tradeoff. Our study unveils that large-scale antenna arrays and ultra-dense deployments of base stations are both necessary to harvest, with high reliability, a sufficiently high amount of power. Furthermore, the feasibility of receiver diversity for application to downlink cellular networks is investigated. Several options that are based on selection combining and maximum ratio combining are compared against each other. Our analysis shows that no scheme outperforms the others for every system setup. It suggests, on the other hand, that the low-energy devices need to operate in an adaptive fashion, by choosing the receiver diversity scheme as a function of the imposed requirements.The second contribution consists of introducing a new tractable approach for modeling and optimizing the energy efficiency of cellular networks. Unlike currently available analytical approaches that provide either simple but meaningless or meaningful but complex analytical expressions of the coverage probability and spectral efficiency of cellular networks, the proposed approach is conveniently formulated in a closed-form expression that is proved to be simple and meaningful at the same time. By relying on the new proposed formulation of the spectral efficiency, a new tractable closed-form expression of the energy efficiency of downlink cellular network is proposed, which is used for optimizing the transmit power and the density of cellular base stations. It is mathematically proved, in particular, that the energy efficiency is a unimodal and strictly pseudo-concave function in the transmit power, given the density of the base stations, and in the density of the base stations, given the transmit power. The optimal transmit power and density of base stations are proved to be the solution of simple non-linear equations.The third contribution consists of introducing a new tractable approach for analyzing the performance of multi-tier cellular networks equipped with renewable energy sources, such as solar panels. The proposed approach allows one to account for the spatial distribution of the base stations by using the theory of point processes, as well as for the random arrival and availability of energy by using Markov chain theory. By using the proposed approach, the energy efficiency of cellular networks can be quantified and the interplay between the density of base stations and energy arrival rate can be quantified and optimized.