Recent regulatory changes proposed by the Federal Communications Commission (FCC) permitting unlicensed use of television white space (TVWS) channels present new opportunities for designing wireless networks that make efficient use of this spectrum. The favorable propagation characteristics of these channels and their widespread availability, especially in rural areas, make them well-suited for providing broadband services in sparsely populated regions where economic factors hinder deployment of such services on licensed spectrum. In this context, this paper explores the deployment of an outdoor Wi-Fi-like network operating in TVWS channels, referred to commonly as a Super Wi-Fi network. Since regulations governing unlicensed use of these channels allow (a) mounting fixed devices up to a height of 30 m and operation at transmit powers of up to 4 W EIRP, and (b) operation at transmit powers of up to 100 mW EIRP for portable devices, such networks can provide extended coverage and higher rates than traditional Wi-Fi networks. However, these gains are subject to the viability of the uplink from the portable devices (clients) to the fixed devices (access points (AP)) because of tighter restrictions on transmit power of clients compared to APs. This paper leverages concepts from stochastic geometry to study the performance of such networks with specific focus on the effect of (a) transmit power asymmetry between APs and clients and its impact on uplink viability and coverage, and (b) the interplay between height and transmit power of APs in determining the network throughput. Such an analysis reveals that (a) maximum coverage of no more than 700 m is obtained even when APs are deployed at 30 m height, and (b) operating APs at transmit power of more than 1 W is beneficial only at sparse deployment densities when rate is prioritized over coverage.
A comprehensive overview of using stochastic geometry to model a wide variety of wireless networks is given in @cite_17 @cite_11 . The mathematical tools and theory of point processes used in the current analysis are presented in @cite_2 and @cite_15 .
@cite_15 @cite_11 @cite_2 @cite_17
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Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed according to homogeneous Poisson point processes. This means that the wireless nodes are located independently of each other and their spatial correlation is ignored. In this work we propose a stochastic geometry model of cellular networks such that the wireless base stations are deployed according to the Ginibre point process. The Ginibre point process is one of the determinantal point processes and accounts for the repulsion between the base stations. For the proposed model, we derive a computable representation for the coverage probability—the probability that the signal-to-interference-plus-noise ratio (SINR) for a mobile user achieves a target threshold. To capture its qualitative property, we further investigate the asymptotics of the coverage probability as the SINR threshold becomes large in a special case. We also present the results of some numerical experiments. This volume bears on wireless network modeling and performance analysis. The aim is to show how stochastic geometry can be used in a more or less systematic way to analyze the phenomena that arise in this context. It first focuses on medium access control mechanisms used in ad hoc networks and in cellular networks. It then discusses the use of stochastic geometry for the quantitative analysis of routing algorithms in mobile ad hoc networks. The appendix also contains a concise summary of wireless communication principles and of the network architectures considered in the two volumes. Stochastic geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the stochastic geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the stochastic geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed. Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.