Stochastic Geometry For Modeling,Analysis, And Design Of Heterogeneous Cellular Networks

Due to the rapid development of the wireless communication in recent years, the traditional homogeneous regular cellular architectures have been unable to meet the dramatic growth of the mobile users and service requirements with massive data, thus evolve to be multi-tier heterogeneous cellular architectures overlaid by irregular, diversified, and broad variety of cells. Interference is one of the main bottlenecks in restricting the performance improvement in multi-tier heterogeneous cellular networks, while the spatial distribution of base stations (BS) plays a vital role in evaluating the interference and corresponding performance metrics. Consequently, it is urgent to seek a rigorous, effective yet tractable point spatial distribution model for modern wireless networks.This dissertation employs the stochastic geometry, an emerging mathematical modeling method for the spatial point distribution, to model multi-tier heterogeneous cellular networks more realistically from different perspectives (e.g. presenting the heterogeneity, randomness, spatial dependence, etc.), and then analyzes the interference and key performance metrics of wireless networks, which can theoretically provides guiding insights for future development of wireless communication networks. Finally, based on the network model and analysis, we can give relevant designs concerning the network technology and network management and planning.Firstly, we start from the simplest model, i.e., multi-tier independent homogeneous Poisson point processes (PPP) model. In this model, different stations of heterogeneous networks are spatially distributed as multiple independent homogeneous PPPs, which means the locations of all the network nodes are independent. Specifically, for a two-tier relaying cellular network, the distributions of relays and macro-BSs are modeled by two independent homogeneous PPPs. We derive the distribution of signal-to-interference-plus-noise ratios (SINRs) and achievable rates for both cooperative and non-cooperative user with stochastic geometry theory, and thus the per-user capacity and area spectral efficiency are obtained. Though this model presents the heterogeneity and randomness vividly and yields the highly tractable results for the network performance, it cannot characterize the realistic distribution of network nodes. For instance, there exists no correlation between the BSs in Poisson modeled cellular networks, which is obviously unpractical. Therefore, we should gradually add some practical elements into the models in order to make them more practical and close to the actual networks.The foremost thing is to consider the macro-BS modeling in the multi-tier heterogeneous cellular networks. Since macro-BSs possess the property of high-power and large-coverage, there exists repulsive features between two macro-BSs to some extent, namely, any two macro-BSs cannot be too close to each other to avoid severe mutual interference. Based on this feature, we employ β-Ginibre point process (β-GPP) with soft-core property to model the spatial distribution of macro-BSs, and then derive the coverage probability under Rayleigh fading channel with the maximum average received power association. Further, the coverage probability performance with the realistic BS deployments can be fitted by adjusting the parameters of β-GPP which demonstrates that β-GPP accurately models the arbitrary spatial distribution of realistic BSs with the regularity between GPP and PPP.After modeling macro-BSs accurately, we focus on the spatial distribution of pico-BSs in multi-tier heterogeneous cellular networks. Specifically, two popular scenarios are considered. One is to deploy pico-BSs at the edge of macro-cells to improve the signal quality for edge users. The other one is to densely deploy pico-BSs in the hotspot areas to improve the capacity. The former is realized by artificially removing points from an independent homogeneous PPP to model the dependence between macro-BSs and pico-BSs, i.e., every macro-BS has an exclusion region (or central serving region) where the pico-BSs located are removed artificially and the resulting point process is called Poisson hole process. From an overall perspective, pico-BSs are mainly deployed at the edge of macro-cells to improve the serving quality of edged users. The latter divides the service region into hotspot and non-hotspot areas from the perspective of uneven service distribution, where the non-hotspot areas are served by macro-BSs and the hotspot areas are served by clustered pico-BSs. Thus, we employ Poisson cluster process to model the spatial distribution of pico-BSs. In addition, we derive the performance metrics such as user coverage probability, per-user capacity and area spectral efficiency based on both scenarios.Finally, take the relaying networks modeled by independent homogeneous PPP as an example. According to the developing requirements of current wireless communication networks, we consider more realistic factors, such as network energy efficiency and temporal-spatial variation property of service, to preliminarily design the future network planning and management. To begin with, from the perspective of energy efficiency with power consumption model, we investigate whether and how the energy efficiency of cellular networks can be improved with the introduction of relay station. Furthermore, considering the temporal-spatial variation property of realistic service distribution, a traffic-aware relay sleep control is proposed to satisfy user requirements in different time interval with minimal overhead. The simulation results demonstrate that the proposed strategy is robust and suitable for relaying cellular networks, since it can both satisfy the user requirements in peak service period and reduce the unnecessary energy overhead in low service period.The results in this dissertation provide important theoretical and practical values for the model and design of multi-tier heterogeneous cellular networks.