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46
Connectivity in AdHoc and Hybrid Networks
 IN PROC. IEEE INFOCOM
, 2002
"... We consider a largescale 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 adhoc network and a hybrid network, where fixed base stations can be reached in multipl ..."
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Cited by 160 (6 self)
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We consider a largescale 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 adhoc 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
Impact of Interferences on Connectivity in Ad Hoc Networks
 in Proc. IEEE INFOCOM
, 2003
"... We study the impact of interferences on the connectivity of largescale adhoc networks, using percolation theory. We assume that a bidirectional 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 contri ..."
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Cited by 115 (13 self)
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We study the impact of interferences on the connectivity of largescale adhoc networks, using percolation theory. We assume that a bidirectional 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 nth time slot. We show qualitatively that it even achieves a better connectivity than the previous system with a parameter gamma/n.
Connectivity of wireless multihop networks in a shadow fading environment
, 2003
"... 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 lognormal shadow fading environment. Assuming the nodes have equal ..."
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Cited by 80 (5 self)
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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 lognormal 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.
Asymptotic critical transmission radius and critical neighbor number for kconnectivity in wireless ad hoc networks
 in Proceedings of the 5th ACM international
, 2004
"... 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 tra ..."
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Cited by 32 (3 self)
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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 kconnected. The critical neighbor number for kconnectivity is the smallest integer l such that if every node sets its transmission radius equal to the distance between itself and its lth nearest neighbor, the induced topology is kconnected. In this paper, we study the asymptotic critical transmission radius for kconnectivity and asymptotic critical neighbor number for kconnectivity in a wireless ad hoc network whose nodes are uniformly and independently distributed in a unitarea square or disk. We provide a precise asymptotic distribution of the critical transmission radius for kconnectivity and an improved asymptotic almost sure upper bound on the critical neighbor number for kconnectivity.
Extremal properties of threedimensional sensor networks with applications
 IEEE Transactions on Mobile Computing
"... In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in threedimensional sensor networks. As in other largescale complex systems, many global parameters of sensor networks undergo phase transitions: For a given property of the network, there is a cri ..."
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Cited by 21 (1 self)
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In this paper, we analyze various critical transmitting/sensing ranges for connectivity and coverage in threedimensional sensor networks. As in other largescale 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 3dimensional 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 hopdiameter 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; hopdiameter; minimum/maximum degrees; transmitting/sensing ranges; analytical methods; energy consumption; topology control. I.
Assignment of dynamic transmission range based on estimation of vehicle density
 in Proceedings of the 2nd ACM international workshop on Vehicular ad hoc networks. ACM
, 2005
"... Vehicular Ad Hoc Networks (VANET) have several characteristics that distinguish them from other ad hoc networks. Among those is the rapid change in topology due to traffic jams, which also disturbs the homogenous distribution of vehicles on the road. For this reason, a dynamic transmission range is ..."
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Cited by 16 (0 self)
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Vehicular Ad Hoc Networks (VANET) have several characteristics that distinguish them from other ad hoc networks. Among those is the rapid change in topology due to traffic jams, which also disturbs the homogenous distribution of vehicles on the road. For this reason, a dynamic transmission range is more effective in maintaining connectivity while minimizing the adverse effects of a high transmission power. We provide a relationship that allows vehicles to estimate the local density and distinguish between two phases of traffic, freeflow and congested traffic. The density estimate is used to develop an algorithm that sets a vehicle transmission range dynamically according to local traffic conditions. Simulations of various road configurations show that the algorithm is successful in maintaining connectivity in highly dynamic networks.
Asymptotic analysis of multistage cooperative broadcast in wireless networks
 IEEE Transactions on Information Theory
, 2006
"... 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 ove ..."
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Cited by 9 (1 self)
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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 closedform expressions that are accurate when the network density is high. Index Terms — Broadcast, continuum, cooperative communication, limiting behavior of dense networks, multihop diversity,
Performance of Ad Hoc Wireless Networks with Aloha and
 PRCSMA MAC Protocols,” Proc. IEEE Global Telecomm. Conf. (GLOBECOM
, 2003
"... Abstract — In this paper, bit error rate (BER) performance and connectivity characteristics of multihop ad hoc wireless networks are analyzed under a circuitswitched network communication scheme characterized by the creation of a multihop communication route, through intermediate relay nodes, for ..."
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Cited by 7 (3 self)
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Abstract — In this paper, bit error rate (BER) performance and connectivity characteristics of multihop ad hoc wireless networks are analyzed under a circuitswitched network communication scheme characterized by the creation of a multihop communication route, through intermediate relay nodes, for each sourcedestination pair. The proposed transmission scheme is packetized yet it does not employ retransmissions: in this sense, it can be considered as a hybrid scheme between circuit switching and packet switching. The ideal limiting performance under the assumption of no internode interference (INI) is evaluated. In particular, the concept of minimum spatial energy density is introduced, and quantified with a precise expression in the case of uncoded binary phase shift keying (BPSK) transmission. A realistic scenario with INI is then considered, and two different medium access control (MAC) protocols are proposed: Aloha and “perroute ” carrier sense multiple access (PRCSMA). In both cases, the BER performance is analyzed. Results show that MAC and physical layers are strictly interrelated, and designing one without considering the other may lead to wrong choices in ad hoc wireless network design. I.
Impact of Radio Link Unreliability on the Connectivity of Wireless Sensor Networks
, 2007
"... Many works have been devoted to connectivity of ad hoc networks. This is an important feature for wireless sensor networks (WSNs) to provide the nodes with the capability of communicating with one or several sinks. In most of these works, radio links are assumed ideal, that is, with no transmission ..."
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Cited by 5 (1 self)
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Many works have been devoted to connectivity of ad hoc networks. This is an important feature for wireless sensor networks (WSNs) to provide the nodes with the capability of communicating with one or several sinks. In most of these works, radio links are assumed ideal, that is, with no transmission errors. To fulfil this assumption, the reception threshold should be high enough to guarantee that radio links have a low transmission error probability. As a consequence, all unreliable links are dismissed. This approach is suboptimal concerning energy consumption because unreliable links should permit to reduce either the transmission power or the number of active nodes. The aim of this paper is to quantify the contribution of unreliable long hops to an increase of the connectivity of WSNs. In our model, each node is assumed to be connected to each other node in a probabilistic manner. Such a network is modeled as a complete random graph, that is, all edges exist. The instantaneous node degree is then defined as the number of simultaneous valid singlehop receptions of the same message, and finally the mean node degree is computed analytically in both AWGN and blockfading channels. We show the impact on connectivity of two MACs and routing parameters. The first one is the energy detection level such as the one used in carrier sense mechanisms. The second one is the reliability threshold used by the routing layer to select stable links only. Both analytic and simulation results show that using opportunistic protocols is challenging.
On the topological properties of one dimensional exponential random geometric graph
, 2005
"... 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 a ..."
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Cited by 4 (2 self)
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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.