Stochastic Geometry and Wireless Networks, Volume I - Theory

Stochastic Geometry and Wireless Networks, Volume II - Applications; see http://hal.inria.fr/inria-00403040This monograph surveys recent results on the use of stochastic geometry for the performance analysis of large wireless networks. It is structured in two volumes. Volume I focuses on stochastic geometry and on the evaluation of spatial averages within this context. It contains two main parts, one on classical stochastic geometry (point processes, Boolean models, percolation, random tessellations, shot noise fields, etc.) and one on a new branch of stochastic geometry which is based on information theoretic notions, such as signal to interference ratios, and which is motivated by the modeling of wireless networks. This second part revisits several basic questions of classical stochastic geometry such as coverage or connectivity within this new framework. Volume II - Applications (see http://hal.inria.fr/inria-00403040) bears on more practical wireless network modeling and performance analysis. It leverages the tools developed in Volume I to build the time-space framework needed for analyzing the phenomena which arise in these networks. The first part of Volume II focuses on medium access control protocols used in mobile ad hoc networks and in cellular networks. The second part bears on the analysis of routing algorithms used in mobile ad hoc networks. For readers with a main interest in wireless network design, the monograph is expected to offer a new and comprehensive methodology for the performance evaluation of large scale wireless networks. This methodology consists in the computation of both time and space averages within a unified setting which inherently addresses the scalability issue in that it poses the problems in an infinite domain/population case. For readers with a background in applied probability, this monograph is expected to provide a direct access to an emerging and fast growing branch of spatial stochastic modeling

System Performance Analysis of Cooperative Communication in Wireless Ad Hoc Networks

Wireless ad hoc networks have been attracting more and more attentions in recent years from both academia and industry, because of their low deployment costs and broad applications. Due to the scarcity of the radio spectrum, supporting concurrent transmissions by exploiting the spatial frequency reuse gain is necessary to enhance spectrum utilization. On the other hand, cooperative communication is a practical technique for realizing the spatial diversity gain to mitigate the detrimental effect of wireless channel and enhance the transmission reliability. Enabling concurrent cooperative transmissions across a network can achieve both types of gains. Due to the broadcast nature of wireless communications, the concurrent cooperative transmissions using the same radio channel generate interference to each other, which is the main performance-limiting factor. Accurate characterization of interference is a fundamental step towards evaluating the performance of cooperative communication in a wireless ad hoc network. However, the distributed network operation, random node locations, interference redistribution due to relay transmissions, and dynamic traffic arrival pose significant challenges in interference characterization. Under the protocol interference model, this thesis evaluates the effectiveness of cooperative communication in a wireless ad hoc network from a perspective of overall network performance through investigating the network throughput, which captures the tradeoff between single-link cooperation gain and network-wide reduced spatial frequency reuse due to relay transmissions. In particular, based on stochastic geometry, the outage probabilities of direct and cooperative transmissions are derived to characterize single-link cooperation gain. On the other hand, according to a randomized scheduling scheme, the expected numbers of concurrent direct and cooperative transmissions that can be accommodated within the network coverage area are calculated to characterize network-wide reduced spatial frequency reuse. The analytical results show that a locally beneficial cooperation decision is not guaranteed to be network-wide beneficial. The number of potential relays determines the achievable performance of a cooperative link, and varies for different source-destination pairs due to random relay locations. This thesis proposes an opportunistic cooperation strategy based on the number of potential relays available for each source-destination pair. Under the physical interference model, the correlation of node locations induces the correlation of interference power. Via modeling node locations as a Poisson point process (PPP) and based on the Campbell's theorem, the temporal correlation coefficient of interference power at a destination node is analyzed. In addition, we derive the outage probability of opportunistic cooperation while taking into account the spatial and temporal interference correlation. The overall network performance can be enhanced by adjusting the proportion of concurrent cooperative transmissions. In addition to random node locations and interference redistribution, dynamic traffic arrival further complicates the interference characterization. This thesis investigates the performance of cooperative communication in a wireless ad hoc network with unsaturated traffic, which introduces a correlation between the interferer density and packet retransmission probability. Based on queueing theory and stochastic geometry, the interference power is characterized from two aspects, namely stationary interferer density and interference correlation in two consecutive time-slots, to evaluate the network performance. The analytical results show that the performance analysis under the assumption of independent interference power overestimates the network performance. The proposed theoretical performance analysis framework provides a step towards better understanding of the benefits and limitations of cooperative communication in wireless ad hoc networks with spatially random nodes, and in turn provides useful insights on protocol design and parameter setting for large-scale networks.4 month

Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Rethinking Information Theory for Mobile Ad Hoc Networks

The subject of this paper is the long-standing open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks (MANETs). A MANET is a peer-to-peer network with no pre-existing infrastructure. MANETs are the most general wireless networks, with single-hop, relay, interference, mesh, and star networks comprising special cases. The lack of a MANET capacity theory has stunted the development and commercialization of many types of wireless networks, including emergency, military, sensor, and community mesh networks. Information theory, which has been vital for links and centralized networks, has not been successfully applied to decentralized wireless networks. Even if this was accomplished, for such a theory to truly characterize the limits of deployed MANETs it must overcome three key roadblocks. First, most current capacity results rely on the allowance of unbounded delay and reliability. Second, spatial and timescale decompositions have not yet been developed for optimally modeling the spatial and temporal dynamics of wireless networks. Third, a useful network capacity theory must integrate rather than ignore the important role of overhead messaging and feedback. This paper describes some of the shifts in thinking that may be needed to overcome these roadblocks and develop a more general theory that we refer to as non-equilibrium information theory.Comment: Submitted to IEEE Communications Magazin

Interference in Poisson Networks with Isotropically Distributed Nodes

Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in network modeling. In this work, interference in networks with nodes distributed according to an isotropic but not necessarily stationary Poisson point process (PPP) are studied. The resulting link performance is precisely characterized as a function of (i) an arbitrary receiver location and of (ii) an arbitrary isotropic shape of the spatial distribution. Closed-form expressions for the first moment and the Laplace transform of the interference are derived for the path loss exponents $\alpha=2$ and $\alpha=4$, and simple bounds are derived for other cases. The developed model is applied to practical problems in network analysis: for instance, the accuracy loss due to neglecting border effects is shown to be undesirably high within transition regions of certain deployment scenarios. Using a throughput metric not relying on the stationarity of the spatial node distribution, the spatial throughput locally around a given node is characterized.Comment: This work was presented in part at ISIT 201