Statistical modeling and analysis of interference in wireless networks

In current wireless networks, interference is the main performance-limiting factor. The quality of a wireless link depends on the signal and interference power, which is strongly related to the spatial distribution of the concurrently transmitting network nodes, shortly denominated as the network geometry. Motivated by the ongoing revision of wireless network design, this dissertation aims to describe the relation between geometry and network performance. Given the exponential growth of wireless devices, it is meaningful to evaluate how network interference affects signal detection. We propose a unified statistical approach based on the characteristic function of the decision variable to describe the detection performance, accounting for single and multiple interference, as well as different detection schemes and architectures. The proposed framework is able to capture the deployment density of the interferers, transmission power, and fading distribution of the interferers and the signal of interest. In addition, we establish a fundamental limit of the interferer node density beyond which robust energy detection is impossible. This work highlights the crucial role of spatial statistics in the evaluation of signal detection. The capacity gain obtained through the densification of the network architecture comes at the expense of an increase in energy consumption. Although small cell access points consume little energy in comparison with the macrocell base stations, the massive deployment of these additional small cell base stations entails a significant increase in energy consumption. We extend the capacity analysis of small cell networks to include the energy consumption of the small cell tier. Considering a distributed sleep mode strategy for the small cell access points, we cast the trade-off between energy consumption and capacity as a set of optimization problems. We develop an analytical framework, which can be used in practice to correctly set sensing time and sensing probability whilst guaranteeing user quality of service. Furthermore, the analytical tool accounts for the network load and predicts the achievable energy reduction of the small cell tier by means of distributed sleep mode strategies as a function of the user density. Finally, given that current networks are interference-limited, we study i how signal processing can improve the signal quality. We present a probabilistic framework to describe the performance gain of successive interference cancellation and show that the benefit is modest when users connect to the base station that provides the highest average signal-to-interference ratio. We extend the analysis to include novel ways to associate users to their access points and demonstrate that the benefits of successive interference cancellation are substantial for these operational scenarios. By systematically incorporating the spatial statistics in the performance analysis, this dissertation presents a methodology and analytical toolset useful to enhance the understanding of the design, operation, and evaluation of future wireless networks. ii