Martin Haenggi

Stochastic geometry and random graphs for the analysis and design of wireless networks

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 networks 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.

Stochastic Geometry for Wireless Networks

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.

Stochastic Geometry for Modeling, Analysis, and Design of Multi-Tier and Cognitive Cellular Wireless Networks: A Survey

For more than three decades, stochastic geometry has been used to model large-scale ad hoc wireless networks, and it has succeeded to develop tractable models to characterize and better understand the performance of these networks. Recently, stochastic geometry models have been shown to provide tractable yet accurate performance bounds for multi-tier and cognitive cellular wireless networks. Given the need for interference characterization in multi-tier cellular networks, stochastic geometry models provide high potential to simplify their modeling and provide insights into their design. Hence, a new research area dealing with the modeling and analysis of multi-tier and cognitive cellular wireless networks is increasingly attracting the attention of the research community. In this article, we present a comprehensive survey on the literature related to stochastic geometry models for single-tier as well as multi-tier and cognitive cellular wireless networks. A taxonomy based on the target network model, the point process used, and the performance evaluation technique is also presented. To conclude, we discuss the open research challenges and future research directions.

Interference in Large Wireless Networks

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.

Wireless sensor networks: applications and challenges of ubiquitous sensing

Sensor networks offer a powerful combination of distributed sensing, computing and communication. They lend themselves to countless applications and, at the same time, offer numerous challenges due to their peculiarities, primarily the stringent energy constraints to which sensing nodes are typically subjected. The distinguishing traits of sensor networks have a direct impact on the hardware design of the nodes at at least four levels: power source, processor, communication hardware, and sensors. Various hardware platforms have already been designed to test the many ideas spawned by the research community and to implement applications to virtually all fields of science and technology. We are convinced that CAS will be able to provide a substantial contribution to the development of this exciting field.

On distances in uniformly random networks

The distribution of Euclidean distances in Poisson point processes is determined. The main result is the density function of the distance to the n-nearest neighbor of a homogeneous process in Ropfm, which is shown to be governed by a generalized Gamma distribution. The result has many implications for large wireless networks of randomly distributed nodes

A primer on spatial modeling and analysis in wireless networks

The performance of wireless networks depends critically on their spatial configuration, because received signal power and interference depend critically on the distances between numerous transmitters and receivers. This is particularly true in emerging network paradigms that may include femtocells, hotspots, relays, white space harvesters, and meshing approaches, which are often overlaid with traditional cellular networks. These heterogeneous approaches to providing high-capacity network access are characterized by randomly located nodes, irregularly deployed infrastructure, and uncertain spatial configurations due to factors like mobility and unplanned user-installed access points. This major shift is just beginning, and it requires new design approaches that are robust to spatial randomness, just as wireless links have long been designed to be robust to fading. The objective of this article is to illustrate the power of spatial models and analytical techniques in the design of wireless networks, and to provide an entry-level tutorial.

Design of a wireless assisted pedestrian dead reckoning system - the NavMote experience

In this paper, we combine inertial sensing and sensor network technology to create a pedestrian dead reckoning system. The core of the system is a lightweight sensor-and-wireless-embedded device called NavMote that is carried by a pedestrian. The NavMote gathers information about pedestrian motion from an integrated magnetic compass and accelerometers. When the NavMote comes within range of a sensor network (composed of NetMotes), it downloads the compressed data to the network. The network relays the data via a RelayMote to an information center where the data are processed into an estimate of the pedestrian trajectory based on a dead reckoning algorithm. System details including the NavMote hardware/software, sensor network middleware services, and the dead reckoning algorithm are provided. In particular, simple but effective step detection and step length estimation methods are implemented in order to reduce computation, memory, and communication requirements on the Motes. Static and dynamic calibrations of the compass data are crucial to compensate the heading errors. The dead reckoning performance is further enhanced by wireless telemetry and map matching. Extensive testing results show that satisfactory tracking performance with relatively long operational time is achieved. The paper also serves as a brief survey on pedestrian navigation systems, sensors, and techniques.

Interference and Outage in Clustered Wireless Ad Hoc Networks

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.

Bandwidth- and power-efficient routing in linear wireless networks

The goal of this paper is to establish which practical routing schemes for wireless networks are most suitable for power-limited and bandwidth-limited communication regimes. We regard channel state information (CSI) at the receiver and point-to-point capacity-achieving codes for the additive white Gaussian noise (AWGN) channel as practical features, interference cancellation (IC) as possible, but less practical, and synchronous cooperation (CSI at the transmitters) as impractical. We consider a communication network with a single source node, a single destination node, and N-1 intermediate nodes placed equidistantly on a line between them. We analyze the minimum total transmit power needed to achieve a desired end-to-end rate for several schemes and demonstrate that multihop communication with spatial reuse performs very well in the power-limited regime, even without IC. However, within a class of schemes not performing IC, single-hop transmission (directly from source to destination) is more suitable for the bandwidth-limited regime, especially when higher spectral efficiencies are required. At such higher spectral efficiencies, the gap between single-hop and multihop can be closed by employing IC, and we present a scheme based upon backward decoding that can remove all interference from the multihop system with an arbitrarily small rate loss. This new scheme is also used to demonstrate that rates of O(logN) are achievable over linear wireless networks even without synchronous cooperation.