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225
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 240 (42 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
"... 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 informat ..."
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Cited by 91 (29 self)
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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.
Transmission Capacity of Ad Hoc Networks with Spatial Diversity
, 2008
"... This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or nonfading environments. Th ..."
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Cited by 75 (27 self)
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This paper derives the outage probability and transmission capacity of ad hoc wireless networks with nodes employing multiple antenna diversity techniques, for a general class of signal distributions. This analysis allows system performance to be quantified for fading or nonfading environments. The transmission capacity is given for interferencelimited uniformly random networks on the entire plane with path loss exponent α> 2 in which nodes use: (1) static beamforming through M sectorized antennas, for which the increase in transmission capacity is shown to be Θ(M 2) if the antennas are without sidelobes, but less in the event of a nonzero sidelobe level; (2) dynamic eigenbeamforming (maximal ratio transmission/combining), in which the increase is shown to be Θ(M 2 α); (3) various transmit antenna selection and receive antenna selection combining schemes, which give appreciable but rapidly diminishing gains; and (4) orthogonal spacetime block coding, for which there is only a small gain due to channel hardening, equivalent to Nakagamim fading for increasing m. It is concluded that in ad hoc networks, static and dynamic beamforming perform best, selection combining performs well but with rapidly diminishing returns with added antennas, and that spacetime block coding offers only marginal gains.
Stochastic analysis of spatial and opportunistic aloha
 IEEE Journal on Selected Areas in Communications
"... Spatial Aloha is probably the simplest medium access protocol to be used in a large mobile ad hoc network: Each station tosses a coin independently of everything else and accesses the channel if it gets heads. In a network ..."
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Cited by 63 (15 self)
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Spatial Aloha is probably the simplest medium access protocol to be used in a large mobile ad hoc network: Each station tosses a coin independently of everything else and accesses the channel if it gets heads. In a network
Optimal Backpressure Routing for Wireless Networks with MultiReceiver Diversity
, 2006
"... We consider the problem of optimal scheduling and routing in an adhoc wireless network with multiple traffic streams and time varying channel reliability. Each packet transmission can be overheard by a subset of receiver nodes, with a transmission success probability that may vary from receiver t ..."
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Cited by 60 (8 self)
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We consider the problem of optimal scheduling and routing in an adhoc wireless network with multiple traffic streams and time varying channel reliability. Each packet transmission can be overheard by a subset of receiver nodes, with a transmission success probability that may vary from receiver to receiver and may also vary with time. We develop a simple backpressure routing algorithm that maximizes network throughput and expends an average power that can be pushed arbitrarily close to the minimum average power required for network stability, with a corresponding tradeoff in network delay. The algorithm can be implemented in a distributed manner using only local link error probability information, and supports a “blind transmission” mode (where error probabilities are not required) in special cases when the power metric is neglected and when there is only a single destination for all traffic streams.
Enabling Wireless Power Transfer in Cellular Networks: Architecture, Modeling and Deployment
, 2012
"... Microwave power transfer (MPT) delivers energy wirelessly from stations called power beacons (PBs) to mobile devices by microwave radiation. This provides mobiles practically infinite battery lives and eliminates the need of power cords and chargers. To enable MPT for mobile charging, this paper pro ..."
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Cited by 53 (5 self)
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Microwave power transfer (MPT) delivers energy wirelessly from stations called power beacons (PBs) to mobile devices by microwave radiation. This provides mobiles practically infinite battery lives and eliminates the need of power cords and chargers. To enable MPT for mobile charging, this paper proposes a new network architecture that overlays an uplink cellular network with randomly deployed PBs for powering mobiles, called a hybrid network. The deployment of the hybrid network under an outage constraint on data links is investigated based on a stochasticgeometry model where singleantenna base stations (BSs) and PBs form independent homogeneous Poisson point processes (PPPs) with densities λb and λp, respectively, and singleantenna mobiles are uniformly distributed in Voronoi cells generated by BSs. In this model, mobiles and PBs fix their transmission power at p and q, respectively; a PB either radiates isotropically, called isotropic MPT, or directs energy towards target mobiles by beamforming, called directed MPT. The model is applied to derive the tradeoffs between the network parameters (p, λb, q, λp) under the outage constraint. First, consider the deployment of the cellular network. It is proved that the outage constraint is satisfied so long as the product pλ α 2 b is above a given threshold where α is the pathloss exponent. Next, consider the deployment of the hybrid network assuming infinite energy storage at mobiles. It is shown that for isotropic MPT, the product qλpλ α 2 b has to be above a given threshold so that PBs are sufficiently dense; for directed MPT, zmqλpλ α 2 b with zm denoting the array gain should exceed a different threshold to ensure short distances between PBs and their target mobiles. Furthermore, for directed MPT, (zmq) 2 αλb has to be sufficiently large as otherwise PBs fail to deliver sufficient power to target mobiles regardless of powertransfer distances. Last, similar results are derived for the case of mobiles having small energy storage.
local throughput, and capacity of random wireless networks
 IEEE Trans. Wireless Commun
, 2009
"... Outage probabilities and singlehop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the conven ..."
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Cited by 46 (10 self)
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Outage probabilities and singlehop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks, and there is no systematic approach that permits the convenient comparison of the performance of networks with different geometries and levels of randomness. The uncertainty cube is introduced to categorize the uncertainty present in a network. The three axes of the cube represent the three main potential sources of uncertainty in interferencelimited networks: the node distribution, the channel gains (fading), and the channel access (set of transmitting nodes). For the performance analysis, a new parameter, the socalled spatial contention, is defined. It measures the slope of the outage probability in an ALOHA network as a function of the transmit probability p at p = 0. Outage is defined as the event that the signaltointerference ratio (SIR) is below a certain threshold in a given time slot. It is shown that the spatial contention is sufficient to characterize outage and throughput in large classes of wireless networks, corresponding to different positions on the uncertainty cube. Existing results are placed in this framework, and new ones are derived. Further, interpreting the outage probability as the SIR distribution, the ergodic capacity of unitdistance links is determined and compared to the throughput achievable for fixed (yet optimized) transmission rates. I.
Rethinking information theory for mobile ad hoc networks
 IEEE Communications Magazine, Submitted
, 2007
"... The subject of this paper is the longstanding open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks (MANETs). A MANET is a peertopeer network with no preexisting infrast ..."
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Cited by 38 (6 self)
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The subject of this paper is the longstanding open problem of developing a general capacity theory for wireless networks, particularly a theory capable of describing the fundamental performance limits of mobile ad hoc networks (MANETs). A MANET is a peertopeer network with no preexisting infrastructure. MANETs are the most general wireless networks, with singlehop, relay, interference, mesh, and star networks comprising special cases. The lack of a MANET capacity theory has stunted the development and commercialization of many types of wireless networks, including emergency, military, sensor, and community mesh networks. Information theory, which has been vital for links and centralized networks, has not been successfully applied to decentralized wireless networks. Even if this was accomplished, for such a theory to truly characterize the limits of deployed MANETs it must overcome three key roadblocks. First, most current capacity results rely on the allowance of unbounded delay and reliability. Second, spatial and timescale decompositions have not yet been developed for optimally modeling the spatial and temporal dynamics of wireless networks. Third, a useful network capacity theory must integrate rather than ignore the important role of overhead messaging and feedback. This paper describes some of the shifts in thinking that may be needed to overcome these roadblocks and