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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 177 (7 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 128 (15 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 93 (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 37 (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 23 (3 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 22 (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.
On the Limiting Performance of Broadcast Algorithms over
 Unidimensional Adhoc Radio Networks,” WPMC’ 04, Abano Terme
, 2004
"... Abstract — Broadcast mechanisms are widely used in self–organizing wireless networks, for management, control and data exchange purposes. In general, broadcast algorithms are required to provide a rapid, reliable and energy–efficient way to diffuse information over a network of randomly distributed ..."
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Cited by 12 (0 self)
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Abstract — Broadcast mechanisms are widely used in self–organizing wireless networks, for management, control and data exchange purposes. In general, broadcast algorithms are required to provide a rapid, reliable and energy–efficient way to diffuse information over a network of randomly distributed nodes. In this paper, we address such issues in the context of uni– dimensional networks, with nodes distributed according to a 1dimension inhomogeneous Poisson process. We statistically derive the propagation dynamic of the optimum broadcast algorithm defined over the Minimum Connected Dominating Set (MCDS) of nodes. Hence, we derive the limiting broadcast performance over uni–dimensional networks, in terms of some useful measures, thus providing common reference values for comparing the effectiveness of different broadcast algorithms.
Connectivity in onedimensional ad hoc networks: A queueing theoretical approach
 WIRELESS NETW
, 2006
"... In this paper we analyze connectivity issues in onedimensional ad hoc networks. Starting with a deterministic channel model, we show how an equivalent GID∞ queueing model may be used to address network connectivity. In this way, we obtain exact results for the coverage probability, the node iso ..."
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Cited by 9 (0 self)
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In this paper we analyze connectivity issues in onedimensional ad hoc networks. Starting with a deterministic channel model, we show how an equivalent GID∞ queueing model may be used to address network connectivity. In this way, we obtain exact results for the coverage probability, the node isolation probability and the connectivity distance for various node placement statistics. We then show how a GIG ∞ model may be used to study broadcast percolation problems in ad hoc networks with general node placement in the presence of fading channels. In particular, we obtain explicit results for the case of nodes distributed according to a Poisson distribution operating in a fading / shadowing environment. In the latter case, heavy traffic theorems are applied to derive the critical transmission power for connectivity and broadcast percolation distance in highly dense networks. The impact of signal processing schemes able to exploit the diversity provided by smallscale fading by means of multiple antennas is considered. The analysis is then extended to the case of unreliable ad hoc networks, with an indepth discussion of asymptotic results.
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 9 (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.