Stochastic Geometry Approaches To Performance Analysis For Heterogeneous Cellular Networks

Due to the explosive growth in mobile data traffic, it is difficult for traditional ho-mogeneous cellular structures to cope with the crushing amount of data and the commu-nication quality of user requirements, and heterogeneous cellular network architecture has been widely considered to be one of the most effective ways to address this chal-lenge. The increasing heterogeneous trend of density, diversity and randomness in cel-lular networks has led to increasingly complex network architecture, thereby making the traditional network performance evaluation method not suitable for the heterogeneous cellular networks due to its complexity or idealized assumptions. However, the network performance assessment is a precondition to determine the network parameter setting and the introduction of novel network deployment and technique. Therefore, it is one of the most urgent problems to find a simple yet effective method to analyze and assess the network performance in the current research field of heterogeneous cellular network. Currently, stochastic geometry has been an important mathematical tool widely used for network modeling and analysis, and the corresponding theoretical results match the simulation ones well. Consequently, this dissertation considers the heterogeneous cellu-lar network scenarios modeled by different types of point processes, employ stochastic geometry theory to analyze different key network performance metrics and expect to provide more tractable theoretical results, thereby theoretically understanding the im-pact of the network techniques and parameters on the network performance metrics.Firstly, I consider the most tractable heterogeneous cellular networks modeled by Poisson point processes (PPP), and analyze the fundamental performance metrics, i.e., signal-to-interference ratio (SIR) distribution, achievable rate and the network-level permanence metrics such as area spectral efficiency (ASE) and network energy effi-ciency (NEE). Due to the tractability of the model, I consider a more practical relaying heterogeneous cellular networks in the multichannel environment, model the spatial dis-tribution of the base stations and relays using multi-tier Poisson heterogeneous cellular networks and give the corresponding theoretical analysis for the network performance, and then investigate the impact of the network parameters (e.g. stating density) on the network performance. Under this model, I derive the coverage probability and corre-sponding achievable rate of both macro users and relaying user, and based on these, I further give the analytical expressions of ASE and NEE. Using the independent thin-ning property of homogeneous PPP, I model the dynamic variation of station density by turning off/on one station independently with a certain probability and then investigate the correlation between network performance and the station density. Results reveal that relaying heterogeneous cellular networks outperform traditional single-tier cellular networks, where ASE increases while NEE first increases and then decreases with in-creasing station density, therefore there exists a certain tradeoff between the ASE and NEE caused by the station density.Secondly, The spatial point process for modeling heterogeneous cellular networks will be extended to the general non-Poisson point process, and in this case I propose simple yet effective analytical methods to further promote the application of more prac-tical non-Poisson models in the networking research and obtain the theoretical results with more practical insights. Using the fundamental performance metric SIR distribu-tion as the research objective, I propose two simple approximative approaches suitable for the non-Poisson multi-tier networks to give accurate and tractable results for the SIR distribution based on the ASAPPP method, which stands for "approximate SIR analysis based on the Poisson point process", thus both the accuracy and tractability of the network model can be taken into account. Specifically, I first establish a per-tier ASAPPP approximation to general HCNs and then present an effective gain ASAPPP method as a further simplification when the path loss exponents are the same for all the tiers, that is, I give an explicit expression for the effective gain of general HCNs such that the SIR distribution is obtained by scaling the SIR threshold with the effective gain. Besides, the asymptotic behavior for the tail of the SIR distribution is also given. Fur-thermore, to highlight effectiveness of the approximative approaches, I derive the exact distribution of the SIR in the two-tier HCNs modeled by β-Ginibre and Poisson point processes and compare it with the approximate results in terms of both accuracy and expression’s simplicity. The results demonstrate that the proposed approaches give a simple yet excellent approximation for the SIR distribution and thus it provides the basic analytical results and methods to further investigate other network-level performance metrics.Finally, under non-Poisson multi-tier network model, I further consider other network-level performance metrics and investigate the impact of the related technologies on the network performance with the help of the approximated SIR distribution. I also consider both ASE and NEE as the objective performance metrics, and based on the approxima-tive SIR distribution obtained by the ASAPPP methods, investigate how the spectrum allocation schemes affect these two metrics in general heterogeneous cellular networks to determine the optimum operating regime for different spectrum allocation schemes. To maximize these two metrics respectively as the goal, I optimize the required spectrum and SIR thresholds for each tier under a certain spectrum scheme. Firstly, I consider spectrum partitioning schemes where each tier uses a dedicated band, and formulate the corresponding optimization problem for the objective performance metrics, respec- tively. The spectrum partitioning problem can be equivalently decomposed into two sub-problems, where one is to obtain the optimal SIR thresholds for each tier that max-imize the corresponding spectral efficiency, and the other one is to give the optimal spectrum allocation schemes between tiers to maximize the ASE or NEE based on the optimal SIR thresholds. Secondly, it is shown that the spectrum sharing problem, where bands can be shared between tiers, can be translated into spectrum partitioning problem using effective gain ASAPPP methods in heterogeneous cellular networks and thus the proposed algorithm can also be used to solve the spectrum sharing optimization prob-lem. Moreover, I compare the network performance with different spectrum allocation schemes in both Poisson and non-Poisson models and find that these two metrics of these two models present similar trends with the varied network parameters.The results in this dissertation provide a feasible theoretical methods to investi-gate more complex and general multi-tier heterogeneous cellular networks and evaluate the impact of novel technologies and methods on network performance, which gives important theoretical insights and practical application value.