| Summary: | In recent years, stochastic geometry has emerged as a powerful tool for the modeling, analysis, and design of wireless networks with random topologies. Stochastic geometry has been demonstrated to provide a tractable yet an accurate approach for the performance analysis of wireless networks, when the network nodes are modeled as a Poisson point process. This thesis develops analytical frameworks to study the performance of various large-scale wireless networks with random topologies. Firstly, it develops a mathematical model for the uplink analysis of heterogeneous cellular networks when the base stations have multiple antennas. Further, it studies how the gains of downlink and uplink decoupling can be optimized in such a network. Secondly, this thesis also models, analyzes, and designs an ad-hoc network architecture that utilizes both the wireless power transfer and backscatter communications. The performance of such a network is further compared with a regular powered network. Finally, this thesis for the first time develops a scheduling algorithm for cellular networks that has an information theoretic justification. Then using tools from stochastic geometry, this thesis quantifies the gains of such scheduling algorithm over the traditional scheduling algorithm for the downlink transmission. Furthermore, to find the optimal system parameters that provide the maximum gains, this thesis performs asymptotic analysis and provides a simple optimization algorithm. The accuracy of all the mathematical models have been verified with extensive Monte Carlo simulations.
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