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268
Breaking Spectrum Gridlock with Cognitive Radios: An Information Theoretic Perspective
, 2008
"... Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified b ..."
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Cited by 244 (3 self)
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Cognitive radios hold tremendous promise for increasing spectral efficiency in wireless systems. This paper surveys the fundamental capacity limits and associated transmission techniques for different wireless network design paradigms based on this promising technology. These paradigms are unified by the definition of a cognitive radio as an intelligent wireless communication device that exploits side information about its environment to improve spectrum utilization. This side information typically comprises knowledge about the activity, channels, codebooks and/or messages of other nodes with which the cognitive node shares the spectrum. Based on the nature of the available side information as well as a priori rules about spectrum usage, cognitive radio systems seek to underlay, overlay or interweave the cognitive radios ’ signals with the transmissions of noncognitive nodes. We provide a comprehensive summary of the known capacity characterizations in terms of upper and lower bounds for each of these three approaches. The increase in system degrees of freedom obtained through cognitive radios is also illuminated. This information theoretic survey provides guidelines for the spectral efficiency gains possible through cognitive radios, as well as practical design ideas to mitigate the coexistence challenges in today’s crowded spectrum.
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.
The effect of fading, channel inversion, and threshold scheduling on ad hoc networks
 IEEE Trans. Inf. Theory
, 2007
"... Abstract—This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state ..."
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Cited by 95 (35 self)
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Abstract—This paper addresses three issues in the field of ad hoc network capacity: the impact of i) channel fading, ii) channel inversion power control, and iii) threshold–based scheduling on capacity. Channel inversion and threshold scheduling may be viewed as simple ways to exploit channel state information (CSI) without requiring cooperation across transmitters. We use the transmission capacity (TC) as our metric, defined as the maximum spatial intensity of successful simultaneous transmissions subject to a constraint on the outage probability (OP). By assuming the nodes are located on the infinite plane according to a Poisson process, we are able to employ tools from stochastic geometry to obtain asymptotically tight bounds on the distribution of the signaltointerference (SIR) level, yielding in turn tight bounds on the OP (relative to a given SIR threshold) and the TC. We demonstrate that in the absence of CSI, fading can significantly reduce the TC and somewhat surprisingly, channel inversion only makes matters worse. We develop a thresholdbased transmission rule where transmitters are active only if the channel to their receiver is acceptably strong, obtain expressions for the optimal threshold, and show that this simple, fully distributed scheme can significantly reduce the effect of fading. Index Terms—Ad hoc networks, channel inversion, fading, threshold scheduling, transmission capacity (TC). I.
Multicast capacity of wireless ad hoc networks
 IEEE/ACM Trans. Netw
, 2009
"... Abstract—We study the multicast capacity of largescale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = p n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the powe ..."
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Cited by 71 (23 self)
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Abstract—We study the multicast capacity of largescale random extended multihop wireless networks, where a number of wireless nodes are randomly located in a square region with side length a = p n, by use of Poisson distribution with density 1. All nodes transmit at a constant power P, and the power decays with attenuation exponent> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR), where B is the bandwidth. There are ns randomly and independently chosen multicast sessions. Each multicast session has k randomly chosen terminals. n We show that when k 1 and ns (log n) 2n 1=2+, the capacity that each multicast p session can achieve, with high proban bility, is at least c8 p, where 1, 2, and c8 are some special conn k stants and> 0 is any positive real number. We also show that for k = O( n), the perflow multicast capacity under Gaussian log n p n channel is at most O ( p) when we have at least ns = (log n) n k random multicast flows. Our result generalizes the unicast capacity for random networks using percolation theory.
The capacity of wireless networks: Informationtheoretic and physical limits
 IEEE Transactions on Information Theory
, 2009
"... Abstract—It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of users wishing to ..."
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Cited by 58 (1 self)
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Abstract—It is shown that the capacity scaling of wireless networks is subject to a fundamental limitation which is independent of power attenuation and fading models. It is a degrees of freedom limitation which is due to the laws of physics. By distributing uniformly an order of users wishing to establish pairwise independent communications at fixed wavelength inside a twodimensional domain of size of the order of , there are an order of communication requests originating from the central half of the domain to its outer half. Physics dictates that the number of independent information channels across these two regions is only of the order of , so the peruser information capacity must follow an inverse squareroot of law. This result shows that informationtheoretic limits of wireless communication problems can be rigorously obtained without relying on stochastic fading channel models, but studying their physical geometric structure. Index Terms—Ad hoc networks, capacity, network information theory, scaling laws, wireless networks. I.
Capacity of large scale wireless networks under gaussian channel model
 in Mobicom08
, 2008
"... In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes vi(1 ≤ i ≤ n) are randomly located in a square region with sidelength a = √ n, by use of Poisson distribution with density 1. ..."
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Cited by 48 (20 self)
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In this paper, we study the multicast capacity of a large scale random wireless network. We simply consider the extended multihop network, where a number of wireless nodes vi(1 ≤ i ≤ n) are randomly located in a square region with sidelength a = √ n, by use of Poisson distribution with density 1. All nodes transmit at constant power P, and the power decays along path, with attenuation exponent α> 2. The data rate of a transmission is determined by the SINR as B log(1 + SINR). There are ns randomly and independently chosen multicast sessions. Each multicast has k rann domly chosen terminals. We show that, when k ≤ θ1 (log n) 2α+6, and ns ≥ θ2n 1/2+β, the capacity that each multicast session can n achieve, with high probability, is at least c8 √ , where θ1, θ2, ns k and c8 are some special constants and β> 0 is any positive real number. Our result generalizes the unicast capacity [3] for random networks using percolation theory.
A Unifying Perspective on the Capacity of Wireless Ad Hoc
"... Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casti ..."
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Cited by 46 (14 self)
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Abstract—We present the first unified modeling framework for the computation of the throughput capacity of random wireless ad hoc networks in which information is disseminated by means of unicast routing, multicast routing, broadcasting, or different forms of anycasting. We introduce (n, m, k)casting as a generalization of all forms of onetoone, onetomany and manytomany information dissemination in wireless networks. In this context, n, m, and k denote the total number of nodes in the network, the number of destinations for each communication group, and the actual number of communicationgroup members that receive information (i.e., k ≤ m), respectively. We compute upper and lower bounds for the (n, m, k)cast throughput capacity in random wireless networks. When m = k = Θ(1), the resulting capacity equals the wellknown capacity result for multipair unicasting by Gupta and Kumar. We demonstrate that Θ(1 / √ mn log n) bits per second constitutes a tight bound for the capacity of multicasting (i.e., m = k < n) when m ≤ Θ (n/(log n)). We show that the multicast capacity of a wireless network equals its capacity for multipair unicasting when the number of destinations per multicast source is not a function of n. We also show that the multicast capacity of a random wireless ad hoc network is Θ (1/n), which is the broadcast capacity of the network, when m ≥ Θ(n / log n). Furthermore, we show that Θ ( √ m/(k √ n log n)), Θ(1/(k log n)) and Θ(1/n) bits per second constitutes a tight bound for the throughput capacity of multicasting (i.e., k < m < n) when Θ(1) ≤ m ≤ Θ (n / log n), k ≤ Θ (n / log n) ≤ m ≤ n and Θ (n / log n) ≤ k ≤ m ≤ n respectively.
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.
On secrecy capacity scaling in wireless networks
"... We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λe = O ( (lo ..."
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Cited by 44 (3 self)
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We study a random extended network, where the legitimate and eavesdropper nodes are assumed to be placed according to Poisson point processes in a square region of area n. It is shown that, when the legitimate nodes have unit intensity, λ = 1, and the eavesdroppers have an intensity of λe = O ( (log n) −2) , almost all of the nodes achieve a perfectly