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 is accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques, this is a comprehensive guide to the spatial stochastic models essential for modeling and analysis of wireless network performance.

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Since interference is the main performance-limiting factor in most wireless networks, it is crucial to characterize the interference statistics. The two main determinants of the interference are the network geometry (spatial distribution of concurrently transmitting nodes) and the path loss law (signal attenuation with distance). For certain classes of node distributions, most notably Poisson point processes, and attenuation laws, closed-form results are available, for both the interference itself as well as the signal-to-interference ratios, which determine the network performance. This monograph presents an overview of these results and gives an introduction to the analytical techniques used in their derivation. The node distribution models range from lattices to homogeneous and clustered Poisson models to general motion-invariant ones. The analysis of the more general models requires the use of Palm theory, in particular conditional probability generating functionals, which are briefly introduced in the appendix.

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The calculation of the SIR distribution at the typical receiver (or, equivalently, the success probability of transmissions over the typical link) in Poisson bipolar and cellular networks with Rayleigh fading is relatively straightforward, but it only provides limited information on the success probabilities of the individual links.This paper introduces the notion of the meta distribution of the SIR, which is the distribution of the conditional success probability P s given the point process, and provides bounds, an exact analytical expression, and a simple approximation for it. The meta distribution provides fine-grained information on the SIR and answers questions such as "What fraction of users in a Poisson cellular network achieve 90% link reliability if the required SIR is 5 dB?".Interestingly, in the bipolar model, if the transmit probability p is reduced while increasing the network density λ such that the density of concurrent transmitters λp stays constant as p → 0, P s degenerates to a constant, i.e., all links have exactly the same success probability in the limit, which is the one of the typical link. In contrast, in the cellular case, if the interfering base stations are active independently with probability p, the variance of P s approaches a non-zero constant when p is reduced to 0 while keeping the mean success probability constant.