Over the past decade, many works on the modeling of wireless networks using stochastic geometry have been proposed. Results about probability of coverage, throughput or mean interference, have been provided for a wide variety of networks (cellular, ad-hoc, cognitive, sensors, etc). These results notably allow to tune network protocol parameters. Nevertheless, in their vast majority, these works assume that the wireless network deployment is flat: nodes are placed on the Euclidean plane. However, this assumption is disproved in dense urban environments where many nodes are deployed in high buildings. In this letter, we derive the exact form of the probability of coverage for the cases where the interferers form a 3D Poisson Point Process (PPP) and a 3D Modified Matern Process (MMP), and compare the results with the 2D case. The main goal of this letter is to show that the 2D model, although being the most common, can lead either to an optimistic or a pessimistic evaluation of the probability of coverage depending on the parameters of the model.
Consider n nodes located in a sphere of volume V m sup 3 , each capable of transmitting at a data rate of W bits sec. Under a protocol based model for successful receptions, the entire network can carry only spl Theta (WV1 3n2 3) bit-meters sec, where 1 bit carried a distance of 1 meter is counted as 1 bit-meter. This is the best possible performance even assuming the node locations, traffic patterns, and the range power timing of each transmission, are all optimally chosen. If the node locations and their destinations are randomly chosen, and all transmissions employ the same power range, then each node only obtains a throughput of spl Theta (w (nlog sup 2 n)1 3) bits sec, if the network is optimally operated. Similar results hold under an alternate physical model where a minimum signal-to-interference ratio is specified for successful receptions. The proofs of these results require determination of the VC-dimensions of certain geometric sets, which may be of independent interest. Network capacity investigation has been intensive in the past few years. A large body of work has appeared in the literature. However, so far most of the effort has been made on two-dimensional wireless networks only. With the great development of wireless technologies, wireless networks are envisioned to extend from two-dimensional space to three-dimensional space. In this paper, we investigate for the first time the throughput capacity of 3D regular ad hoc networks (RANETs) and of 3D heterogeneous ad hoc networks (HANETs), respectively, by employing a generalized physical model. In 3D RANETs, we assume that the nodes are regularly placed, while in 3D HANETs, we consider that the nodes are distributed according to a general Nonhomogeneous Poisson Process (NPP). We find both lower and upper bounds in both types of networks in a broad power propagation regime, i.e., when the path loss exponent is no less than 2. 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. Preface. Preface to Volume II. Contents of Volume II. Part IV Medium Access Control 1 Spatial Aloha: the Bipole Model 2 Receiver Selection in Spatial 3 Carrier Sense Multiple 4 Code Division Multiple Access in Cellular Networks Bibliographical Notes on Part IV. Part V Multihop Routing in Mobile ad Hoc Networks: 5 Optimal Routing 6 Greedy Routing 7 Time-Space Routing Bibliographical Notes on Part V. Part VI Appendix:Wireless Protocols and Architectures: 8 RadioWave Propagation 9 Signal Detection 10 Wireless Network Architectures and Protocols Bibliographical Notes on Part VI Bibliography Table of Notation Index.