Results 1  10
of
191
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 ..."
Abstract

Cited by 240 (42 self)
 Add to MetaCart
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.
A Tractable Approach to Coverage and Rate in Cellular Networks
 IEEE Trans. Commun
, 2011
"... ar ..."
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 ..."
Abstract

Cited by 91 (29 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 75 (27 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 53 (5 self)
 Add to MetaCart
(Show Context)
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 ..."
Abstract

Cited by 46 (10 self)
 Add to MetaCart
(Show Context)
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.
Communication over a Wireless Network with Random Connections
 IEEE Transactions on Information Theory
, 2006
"... We analyze a network of nodes in which pairs communicate over a shared wireless medium. We are interested in the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. Our model differs substantially from the many existing approaches in that the ..."
Abstract

Cited by 41 (2 self)
 Add to MetaCart
(Show Context)
We analyze a network of nodes in which pairs communicate over a shared wireless medium. We are interested in the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. Our model differs substantially from the many existing approaches in that the channel connections in our network are entirely random: we assume that, rather than being governed by geometry and a decayversusdistance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. We show that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least n (log n) d for some d> 0, which is significantly larger than the O ( √ n) results obtained for many geometric models. Our results provide guidelines for the connectivity that is needed for large aggregate traffic. We show how our model and distancebased models can be related in some cases. 1
Bandwidth Partitioning in Decentralized Wireless Networks
"... This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into in ..."
Abstract

Cited by 38 (12 self)
 Add to MetaCart
(Show Context)
This paper addresses the following question, which is of interest in the design of a multiuser decentralized network. Given a total system bandwidth of W Hz and a fixed data rate constraint of R bps for each transmission, how many frequency slots N of size W/N should the band be partitioned into in order to maximize the number of simultaneous links in the network? Dividing the available spectrum results in two competing effects. On the positive side, a larger N allows for more parallel, noninterfering communications to take place in the same area. On the negative side, a larger N increases the SINR requirement for each link because the same information rate must be achieved over less bandwidth, which in turn increases the area consumed by each transmission. Exploring this tradeoff and determining the optimum value of N in terms of the system parameters is the focus of the paper. Using stochastic geometry, the optimal SINR threshold – which directly corresponds to the optimal spectral efficiency – is derived for both the low SNR (powerlimited) and high SNR (interferencelimited) regimes. This leads to the optimum choice of the number of frequency bands N in terms of the path loss exponent, power and noise spectral density, desired rate, and total bandwidth. I.