We consider a large-scale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely ad-hoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected. We find that

We study the impact of interferences on the connectivity of large-scale ad-hoc networks, using percolation theory. We assume that a bi-directional connection can be set up between two nodes if the signal to noise ratio at the receiver is larger than some threshold. The noise is the sum of the contribution of interferences from all other nodes, weighted by a coefficient gamma, and of a background noise. We find that there is a critical value of gamma above which the network is made of disconnected clusters of nodes. We also prove that if gamma is non zero but small enough, there exist node spatial densities for which the network contains a large (theoretically infinite) cluster of nodes, enabling distant nodes to communicate in multiple hops. Since small values of gamma cannot be achieved without efficient CDMA codes, we investigate the use of a very simple TDMA scheme, where nodes can emit only every n-th time slot. We show qualitatively that it even achieves a better connectivity than the previous system with a parameter gamma/n.

Authors ’ preprint of an article accepted for ACM/Kluwer Wireless Networks, special issue on selected papers from ACM MSWiM 2003, to be published 2005. Abstract. This article analyzes the connectivity of multihop radio networks in a log-normal shadow fading environment. Assuming the nodes have equal transmission capabilities and are randomly distributed according to a homogeneous Poisson process, we give a tight lower bound for the minimum node density that is necessary to obtain an almost surely connected subnetwork on a bounded area of given size. We derive an explicit expression for this bound, compute it in a variety of scenarios, and verify its tightness by simulation. The numerical results can be used for the practical design and simulation of wireless sensor and ad hoc networks. In addition, they give insight into how fading affects the topology of multihop networks. It is explained why a high fading variance helps the network to become connected.

A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other’s transmission range. The critical transmission radius for kconnectivity is the smallest r such that if all nodes have the transmission radius r, the induced topology is k-connected. The critical neighbor number for k-connectivity is the smallest integer l such that if every node sets its transmission radius equal to the distance between itself and its l-th nearest neighbor, the induced topology is k-connected. In this paper, we study the asymptotic critical transmission radius for k-connectivity and asymptotic critical neighbor number for k-connectivity in a wireless ad hoc network whose nodes are uniformly and independently distributed in a unit-area square or disk. We provide a precise asymptotic distribution of the critical transmission radius for k-connectivity and an improved asymptotic almost sure upper bound on the critical neighbor number for k-connectivity.

In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in three-dimensional sensor networks. As in other large-scale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a critical threshold, corresponding to the minimum amount of the communication effort or power expenditure by individual nodes, above (resp. below) which the property exists with high (resp. a low) probability. For sensor networks, properties of interest include simple and multiple degrees of connectivity/coverage. First, we investigate the network topology according to the region of deployment, the number of deployed sensors and their transmitting/sensing ranges. More specifically, we consider the following problems: Assume that n nodes, each capable of sensing events within a radius of r, are randomly and uniformly distributed in a 3-dimensional region R of volume V, how large must the sensing range rSense be to ensure a given degree of coverage of the region to monitor? For a given transmission range rTrans, what is the minimum (resp. maximum) degree of the network? What is then the typical hop-diameter of the underlying network? Next, we show how these results affect algorithmic aspects of the network by designing specific distributed protocols for sensor networks. Keywords Sensor networks, ad hoc networks; coverage, connectivity; hop-diameter; minimum/maximum degrees; transmitting/sensing ranges; analytical methods; energy consumption; topology control. I.

We consider a large-scale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely ad-hoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected.

Abstract — Cooperative broadcast aims to deliver a source message to a locally connected network by means of collaborating nodes. In traditional architectures, node cooperation has been at the network layer. Recently, physical layer cooperative schemes have been shown to offer several advantages over the network layer approaches. This form of cooperation employs distributed transmission resources at the physical layer as a single radio with spatial diversity. In decentralized cooperation schemes, collaborating nodes make transmission decisions based on the quality of the received signal, which is the only parameter available locally. In this case, critical parameters that influence the broadcast performance include the source/relay transmission powers and the decoding threshold (the minimum SNR required to decode a transmission). We study the effect of these parameters on the number of nodes reached by cooperative broadcast. In particular, we show that there exists a phase transition in the network behavior: if the decoding threshold is below a critical value, the message is delivered to the whole network. Otherwise, only a fraction of the nodes is reached, which is proportional to the source transmit power. Our approach is based on the idea of continuum approximation, which yields closed-form expressions that are accurate when the network density is high. Index Terms — Broadcast, continuum, cooperative communication, limiting behavior of dense networks, multihop diversity,

In this paper we study the one dimensional random geometric (random interval) graph when the location of the nodes are independent and exponentially distributed. We derive exact results and limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph.

Abstract not found

Address autoconfiguration is an important mechanism required to set the IP address of a node automatically in a wireless network. The address autoconfiguration, also known as initialization or naming, consists to give a unique identifier ranging from 1 to n for a set of n indistinguishable nodes. We consider a wireless network where n nodes (processors) are randomly thrown in a square X, uniformly and independently. We assume that the network is synchronous and two nodes are able to communicate if they are within distance at most of r of each other (r is the transmitting/receiving range). The model of this paper concerns nodes without the collision detection ability: if two or more neighbors of a processor u transmit concurrently at the same time, then u would not receive either messages. We suppose also that nodes know neither the topology of the network nor the number of nodes in the network. Moreover, they start indistinguishable, anonymous and unnamed. Under this extremal scenario, we design and analyze a fully distributed protocol to achieve the initialization task for a wireless multihop network of n nodes uniformly scattered in a square X. We show how the transmitting range of the deployed stations can affect the typical characteristics such as the degrees and the diameter of the network. By allowing (1+ℓ) ln n |X| the nodes to transmit at a range r = (slightly greater than the one required to have a connected network), π n we show how to design a randomized protocol running in expected time O(n3/2 log2 n) in order to assign a unique number ranging from 1 to n to each of the n participating nodes. Keywords Multihop networks; address autoconfiguration; self-configuration in ad hoc networks; randomized distributed protocols; initialization; naming; fundamental limits of random networks.