Results 1  10
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66
Hierarchical Cooperation Achieves Optimal Capacity Scaling in Ad Hoc Networks
, 2007
"... n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r −α as well as a random phase. We identify the scaling laws of the information theoretic capacity of the ne ..."
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Cited by 273 (18 self)
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n source and destination pairs randomly located in an area want to communicate with each other. Signals transmitted from one user to another at distance r apart are subject to a power loss of r −α as well as a random phase. We identify the scaling laws of the information theoretic capacity of the network. In the case of dense networks, where the area is fixed and the density of nodes increasing, we show that the total capacity of the network scales linearly with n. This improves on the best known achievability result of n 2/3 of [1]. In the case of extended networks, where the density of nodes is fixed and the area increasing linearly with n, we show that this capacity scales as n 2−α/2 for 2 ≤ α < 3 and n for α ≥ 3. The best known earlier result [2] identified the scaling law for α> 4. Thus, much better scaling than multihop can be achieved in dense networks, as well as in extended networks with low attenuation. The performance gain is achieved by intelligent node cooperation and distributed MIMO communication. The key ingredient is a hierarchical and digital architecture for nodal exchange of information for realizing the cooperation.
Stochastic Geometry and Random Graphs for the Analysis and Design of Wireless Networks
"... Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accoun ..."
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Cited by 231 (43 self)
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Wireless networks are fundamentally limited by the intensity of the received signals and by their interference. Since both of these quantities depend on the spatial location of the nodes, mathematical techniques have been developed in the last decade to provide communicationtheoretic results accounting for the network’s geometrical configuration. Often, the location of the nodes in the network can be modeled as random, following for example a Poisson point process. In this case, different techniques based on stochastic geometry and the theory of random geometric graphs – including point process theory, percolation theory, and probabilistic combinatorics – have led to results on the connectivity, the capacity, the outage probability, and other fundamental limits of wireless networks. This tutorial article surveys some of these techniques, discusses their application to model wireless networks, and presents some of the main results that have appeared in the literature. It also serves as an introduction to the field for the other papers in this special issue.
Optimal ThroughputDelay Scaling in Wireless Networks  Part I: The Fluid Model
"... Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per sourcedestination pair is Θ ( 1 / √ n log n). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant thr ..."
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Cited by 79 (2 self)
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Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per sourcedestination pair is Θ ( 1 / √ n log n). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per sourcedestination pair. In most applications delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughputdelay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughputdelay tradeoff is given by D(n) = Θ(nT (n)), where T (n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of Θ(1) for the GrossglauserTse scheme is given and the associated delay scaling is shown to be Θ(n log n). The optimal throughputdelay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random walk model for node mobility is assumed. It is shown that for throughput of O ( 1 / √ n log n) , which can also be achieved in static networks, the throughputdelay tradeoff is the same as in static networks, i.e., D(n) = Θ(nT (n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be Θ(n log n), which is the delay for throughput of Θ(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in realworld networks would necessitate an abrupt and very large increase in delay.
On the pathloss attenuation regime for positive cost and linear scaling of transport capacity in wireless networks
 IEEE Trans. Inf. Theory
, 2006
"... Abstract—Wireless networks with a minimum internode separation distance are studied where the signal attenuation grows in magnitude as 1 with distance. Two performance measures of wireless networks are analyzed. The transport capacity is the supremum of the total distance–rate products that can be ..."
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Cited by 58 (6 self)
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Abstract—Wireless networks with a minimum internode separation distance are studied where the signal attenuation grows in magnitude as 1 with distance. Two performance measures of wireless networks are analyzed. The transport capacity is the supremum of the total distance–rate products that can be supported by the network. The energy cost of information transport is the infimum of the ratio of the transmission energies used by all the nodes to the number of bitmeters of information thereby transported. If the phases of the attenuations between node pairs are uniformly and independently distributed, it is shown that the expected transport capacity is upperbounded by a multiple of the total of the transmission powers of all the nodes, whenever 2 for twodimensional networks or 5 4
Cognitive networks achieve throughput scaling of a homogeneous network,” in arXiv:cs.IT/0801.0938
, 2008
"... Abstract — We study two distinct, but overlapping, networks which operate at the same time, space and frequency. The first network consists of randomly distributed primary users, which form either an ad hoc network, or an infrastructuresupported ad hoc network in which additional base stations suppo ..."
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Cited by 45 (2 self)
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Abstract — We study two distinct, but overlapping, networks which operate at the same time, space and frequency. The first network consists of randomly distributed primary users, which form either an ad hoc network, or an infrastructuresupported ad hoc network in which additional base stations support the primary users. The second network consists of randomly distributed secondary or cognitive users. The primary users have priority access to the spectrum and do not change their communication protocol in the presence of secondary users. The secondary users, however, need to adjust their protocol based on knowledge about the locations of the primary users so as not to harm the primary network’s scaling law. Base on percolation theory, we show that surprisingly, when the secondary network is denser than the primary network, both networks can simultaneously achieve the same throughput scaling law as a standalone ad hoc network. I.
Crystallization in Large Wireless Networks
, 2005
"... We analyze fading interference relay networks where M singleantenna sourcedestination terminal pairs communicate concurrently and in the same frequency band through a set of K singleantenna relays using halfduplex twohop relaying. Assuming that the relays have channel state information (CSI), ..."
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Cited by 25 (1 self)
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We analyze fading interference relay networks where M singleantenna sourcedestination terminal pairs communicate concurrently and in the same frequency band through a set of K singleantenna relays using halfduplex twohop relaying. Assuming that the relays have channel state information (CSI), it is shown that in the largeM limit, provided K grows fast enough as a function of M, the network “decouples ” in the sense that the individual sourcedestination terminal pair capacities are strictly positive. The corresponding required rate of growth of K as a function of M is found to be sufficient to also make the individual sourcedestination fading links converge to nonfading links. We say that the network “crystallizes ” as it breaks up into a set of effectively isolated “wires in the air”. A largedeviations analysis is performed to characterize the “crystallization” rate, i.e., the rate (as a function of M, K) at which the decoupled links converge to nonfading links. In the course of this analysis, we develop a new technique for characterizing the largedeviations behavior of certain sums of dependent random variables. For the case of no CSI at the relay level, assuming amplifyandforward relaying, we compute the per sourcedestination terminal pair capacity for M, K → ∞, with K/M → β fixed, using tools from large random matrix theory.
1 Random Access Transport Capacity
, 909
"... We develop a new metric for quantifying endtoend throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful endtoend transmissions, multi ..."
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Cited by 20 (5 self)
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We develop a new metric for quantifying endtoend throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful endtoend transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closedform in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the wellknown square root scaling law while providing exact expressions for the preconstants as well. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability. I.