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The article discusses various reports published within the issue, including one on the use of a hierarchical model and Voronoi tessellations for cellular networks to identify distance distributions between low and high-level network components, one on a method which is developed for analyzing the probability that a given graph occurs as a subgraph of a random geometric graph, and one on a data transmission protocol called BeSpoken that aims at forwarding packets along straight path.

Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communication-theoretic results accounting for the network's geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs -- including point process theory, percolation theory, and probabilistic combinatorics -- have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue. [ABSTRACT FROM AUTHOR]

Diversity schemes permit efficient communication over fading channels but are often hard to analyze and design in networks with many nodes. For Rayleigh-fading channels, there exists an interesting relationship between resistive circuits and time and path diversity mechanisms in wireless ad hoc networks. A resistor-like network element, the erristor, representing the normalized noise-to-signal ratio, is introduced. Given an end-to-end packet delivery probability, the logarithmic mapping from link reception probabilities to erristor values greatly simplifies the problems of power allocation and the selection of time and path diversity schemes, which is illustrated in a number of examples. We focus on transmission strategies with selection combining and simple noncoherent "decode-and-forward" strategies, which is motivated by their practicality. Thanks to its conceptual simplicity, the formalism that is developed provides valuable insight into the benefits of diversity mechanisms. [ABSTRACT FROM AUTHOR]