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21
Analysis of access and connectivity probabilities in vehicular relay networks
 IEEE J. Sel. Areas Commun
, 2011
"... Abstract—IEEE 802.11p and 1609 standards are currently under development to support VehicletoVehicle and VehicletoInfrastructure communications in vehicular networks. For infrastructurebased vehicular relay networks, access probability is an important measure which indicates how well an arbitra ..."
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Abstract—IEEE 802.11p and 1609 standards are currently under development to support VehicletoVehicle and VehicletoInfrastructure communications in vehicular networks. For infrastructurebased vehicular relay networks, access probability is an important measure which indicates how well an arbitrary vehicle can access the infrastructure, i.e. a base station (BS). On the other hand, connectivity probability, i.e. the probability that all the vehicles are connected to the infrastructure, indicates the service coverage performance of a vehicular relay network. In this paper, we develop an analytical model with a generic radio channel model to fully characterize the access probability and connectivity probability performance in a vehicular relay network considering both onehop (direct access) and twohop (via a relay) communications between a vehicle and the infrastructure. Specifically, we derive closeform
Interference Modeling in CSMA MultiHop Wireless Networks
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1Connectivity of Confined Dense Networks: Boundary Effects and Scaling Laws
"... In this paper, we study the probability that a dense network confined within a given geometry is fully connected. We employ a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the geometry have on connectivity. To maximize practicality and app ..."
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In this paper, we study the probability that a dense network confined within a given geometry is fully connected. We employ a cluster expansion approach often used in statistical physics to analyze the effects that the boundaries of the geometry have on connectivity. To maximize practicality and applicability, we adopt four important pointtopoint link models based on outage probability in our analysis: singleinput singleoutput (SISO), singleinput multipleoutput (SIMO), multipleinput singleoutput (MISO), and multipleinput multipleoutput (MIMO). Furthermore, we derive diversity and power scaling laws that dictate how boundary effects can be mitigated (to leading order) in confined dense networks for each of these models. Finally, in order to demonstrate the versatility of our theory, we analyze boundary effects for dense networks comprising MIMO pointtopoint links confined within a right prism, a polyhedron that accurately models many geometries that can be found in practice. We provide numerical results for this example, which verify our analytical results.
On the asymptotic connectivity of random networks under the random connection model
 in IEEE INFOCOM
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A Tractable Framework for Exact Probability of Node Isolation and Minimum Node Degree Distribution in Finite Multihop Networks
, 2013
"... This paper presents a tractable analytical framework for the exact calculation of the probability of node isolation and the minimum node degree distribution when N sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account f ..."
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This paper presents a tractable analytical framework for the exact calculation of the probability of node isolation and the minimum node degree distribution when N sensor nodes are independently and uniformly distributed inside a finite square region. The proposed framework can accurately account for the boundary effects by partitioning the square into subregions, based on the transmission range and the node location. We show that for each subregion, the probability that a random node falls inside a disk centered at an arbitrary node located in that subregion can be expressed analytically in closedform. Using the results for the different subregions, we obtain the exact probability of node isolation and minimum node degree distribution that serves as an upper bound for the probability of kconnectivity. Our theoretical framework is validated by comparison with the simulation results and shows that the minimum node degree distribution serves as a tight upper bound for probability of kconnectivity. The proposed framework provides a very useful tool to accurately account for the boundary effects in the design of finite wireless networks.
Connectivity of Large Wireless Networks under A Generic Connection Model
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Connectivity in Dense Networks Confined within Right Prisms
"... Abstract—We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a co ..."
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Abstract—We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries that can be found in practice. To maximize practicality and applicability, we adopt a general pointtopoint link model based on outage probability, and present example analytical and numerical results for a network employing 2 × 2 multipleinput multipleoutput (MIMO) maximum ratio combining (MRC) link level transmission confined within particular bounding geometries. Furthermore, we provide suggestions for extending the approach detailed herein to more general convex geometries. Index Terms—Connectivity, percolation, outage, MIMO, diversity, power scaling.
Interferenceaware scheduling for connectivity in MIMO ad hoc multicast networks
 IEEE Trans. Veh. Technol
, 2012
"... Abstract—We consider a multicast scenario that involves an ad hoc network of cochannel multipleinput–multipleoutput (MIMO) nodes in which a source node attempts to share a streaming message with all nodes in the network through some predefined multihop routing tree. The message is assumed to be b ..."
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Abstract—We consider a multicast scenario that involves an ad hoc network of cochannel multipleinput–multipleoutput (MIMO) nodes in which a source node attempts to share a streaming message with all nodes in the network through some predefined multihop routing tree. The message is assumed to be broken down into packets, and the transmission is conducted over multiple frames. Each frame is divided into time slots, and each link in the routing tree is assigned one time slot in which to transmit its current packet. We present an algorithm for determining the number of time slots and the scheduling of the links in these time slots to optimize the connectivity of the network, which we define to be the probability that all links can achieve the required throughput. In addition to time multiplexing, the MIMO nodes also employ beamforming to manage interference when links are simultaneously active, and the beamformers are designed with the maximum connectivity metric in mind. The effects of outdated channelstate information are taken into account in both the scheduling and the beamforming designs. We also derive bounds on the network connectivity and sum transmit power to illustrate the impact of interference on network performance. Our simulation results demonstrate that the choice of the number of time slots is critical in optimizing network performance and illustrates the significant advantage provided by multiple antennas in improving network connectivity. Index Terms—Ad hoc networks, beamforming, connectivity, interference networks, multipleinput–multipleoutput (MIMO) networks, scheduling.
Connectivity Analysis of Wireless Ad Hoc Networks With Beamforming
"... AbstractIn this paper, we present an analytical model for evaluating the impact of shadowing and beamforming on the connectivity of wireless ad hoc networks accommodating nodes equipped with multiple antennas. We consider two simple beamforming schemes: random beamforming, where each node selects ..."
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AbstractIn this paper, we present an analytical model for evaluating the impact of shadowing and beamforming on the connectivity of wireless ad hoc networks accommodating nodes equipped with multiple antennas. We consider two simple beamforming schemes: random beamforming, where each node selects a main beam direction randomly with no coordination with other nodes, and centerdirected beamforming, where each node points its main beam toward the geographical center of the network. Taking path loss, shadowing, and beamforming into account, we derive an expression for the effective coverage area of a node, which is used to analyze both the local network connectivity (probability of node isolation) and the overall network connectivity (1connectivity and path probability). We verify the correctness of our analytical approach by comparing with simulations. Our results show that the presence of shadowing increases the probability of node isolation and reduces the 1connectivity of the network, although moderate shadowing can improve the path probability between two nodes. Furthermore, we show that the impact of beamforming strongly depends on the level of the channel path loss. In particular, compared with omnidirectional antennas, beamforming improves both the local and the overall connectivity for a path loss exponent of α < 3. The analysis in this paper provides an efficient way for system designers to characterize and optimize the connectivity of wireless ad hoc networks with beamforming.