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    A stochastic geometry approach for cellular wireless network analysis
    Arsal, Ali; Civanlar, Mehmet Reha; Civanlar, Mehmet Reha; Uysal, Murat; Beğen, Ali Cengiz; Erküçük, S.; Başar, E.; Department of Electrical and Electronics Engineering; Arsal, Ali
    Cellular wireless communications systems transformed the way people communicated by combining communication and mobility. Since the early 1970s, the mobile industry has been driving the development and evolution of cellular technology. The first generation only offered voice communication, whereas the second generation offered both voice and data services. Furthermore, as cellular wireless technology advanced, 3G enabled video conferencing and other services. With rising demand, 4G emerged, ensuring us with ultra-broadband internet access. 5G will be able to provide us with services that we have never had before. Cellular wireless networks are typically modeled by placing base stations on a regular hexagonal grid and mobile users either randomly or deterministically distributed. These models have been widely used, but they have the disadvantage of being both highly idealized and not very tractable, so complex system-level simulations are used to assess coverage probability and rate. Models that are more tractable have long been desired. In this dissertation, we develop novel methods based on stochastic geometry to analyze the coverage and average spectral efficiency of downlink cellular wireless networks. In the first part of the dissertation, we consider to analyze the performance of SISO (Single Input Single Output) transmission scheme. Regarding this analysis, both the positions of base stations (BS) and mobile users are modeled as points of an independent Poisson Point Process' (PPP). We consider to use the max C/I (Carrier to Interference Ratio) scheduling method, to select the user with the best SIR (Signal to Interference Ratio) value among the users that are connected to the same base station. Since the base stations are randomly placed and users are linked to their closest base stations, the C/I ratios of multiple users become conditionally dependent. For such a realistic deployment scenario, we utilize stochastic geometry tools and copula functions to take into account this correlation and analyze the coverage probability and spectral efficiency. Our simulation results demonstrate that the commonly used independence assumption of the user C/I values overestimates both actual coverage probability and spectral efficiency of the system. In the second part, we analyze the coverage performance of multi-user multiple-input multiple-output (MU-MIMO) downlink cellular networks. We model the locations of the base stations and mobile users using Poisson Point Processes and employ maximum ratio transmission precoding at the base station. Our analysis builds upon Prony's method to approximately calculate the coverage probability using the sum of exponentials which facilitates the computation of Laplace transform of both intra-cell and inter-cell interference. We demonstrate the accuracy of derived approximate coverage probability expressions through numerical simulations for different MU-MIMO configurations. In the third part, we analyze the downlink coverage performance of general user, arbitrarily located in the 2-D region, edge user and worst user sit on the boundary between two neighbor cells and vertex where three neighbor cells meet respectively, considering the Coordinated Multipoint (CoMP) transmission scheme by using stochastic geometry approach. In addition, we analyze the performance of two users, in terms of average spectral efficiency in the CoMP transmission scheme where the users are connected to the closest and second closest BS's, by using stochastic geometry approach. The correlation of SIR values of two users are again modeled by using copula functions. The max C/I scheduling method is employed to select the user in this scheme.