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252
A Tractable Approach to Coverage and Rate in Cellular Networks
 IEEE Trans. Commun
, 2011
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Modeling and analysis of Ktier downlink heterogeneous cellular networks
 IEEE J. Sel. Areas Commun
, 2012
"... Abstract—Cellular networks are in a major transition from a carefully planned set of large towermounted basestations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this pap ..."
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Cited by 154 (41 self)
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Abstract—Cellular networks are in a major transition from a carefully planned set of large towermounted basestations (BSs) to an irregular deployment of heterogeneous infrastructure elements that often additionally includes micro, pico, and femtocells, as well as distributed antennas. In this paper, we develop a tractable, flexible, and accurate model for a downlink heterogeneous cellular network (HCN) consisting of K tiers of randomly located BSs, where each tier may differ in terms of average transmit power, supported data rate and BS density. Assuming a mobile user connects to the strongest candidate BS, the resulting SignaltoInterferenceplusNoiseRatio (SINR) is greater than 1 when in coverage, Rayleigh fading, we derive an expression for the probability of coverage (equivalently outage) over the entire network under both open and closed access, which assumes a strikingly simple closedform in the high SINR regime and is accurate down to −4 dB even under weaker assumptions. For external validation, we compare against an actual LTE network (for tier 1) with the other K − 1 tiers being modeled as independent Poisson Point Processes. In this case as well, our model is accurate to within 12 dB. We also derive the average rate achieved by a randomly located mobile and the average load on each tier of BSs. One interesting observation for interferencelimited open access networks is that at a given SINR, adding more tiers and/or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same targetSINR. Index Terms—Femtocells, heterogeneous cellular networks, stochastic geometry, point process theory, coverage probability. I.
Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis
 IEEE Trans. on Wireless Communications
, 2012
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Using Poisson processes to model lattice cellular networks
 in INFOCOM, 2013 Proceedings IEEE, 2013
"... Abstract—An almost ubiquitous assumption made in the stochasticanalytic approach to study of the quality of userservice in cellular networks is Poisson distribution of base stations, often completed by some specific assumption regarding the distribution of the fading (e.g. Rayleigh). The former (P ..."
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Cited by 29 (12 self)
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Abstract—An almost ubiquitous assumption made in the stochasticanalytic approach to study of the quality of userservice in cellular networks is Poisson distribution of base stations, often completed by some specific assumption regarding the distribution of the fading (e.g. Rayleigh). The former (Poisson) assumption is usually (vaguely) justified in the context of cellular networks, by various irregularities in the real placement of base stations, which ideally should form a lattice (e.g. hexagonal) pattern. In the first part of this paper we provide a different and rigorous argument justifying the Poisson assumption under sufficiently strong lognormal shadowing observed in the network, in the evaluation of a natural class of the typicaluser servicecharacteristics (including pathloss, interference, signaltointerference ratio, spectral efficiency). Namely, we present a Poissonconvergence result for a broad range of stationary (including lattice) networks subject to lognormal shadowing of increasing variance. We show also for the Poisson model that the distribution of all these typicaluser service characteristics does not depend on the particular form of the additional fading distribution. Our approach involves a mapping of 2D network model to 1D image of it “perceived ” by the typical user. For this image we prove our Poisson convergence result and the invariance of the Poisson limit with respect to the distribution of the additional shadowing or fading. Moreover, in the second part of the paper we present some new results for Poisson model allowing one to calculate the distribution function of the SINR in its whole domain. We use them to study and optimize the mean energy efficiency in cellular networks. Index Terms—Wireless cellular networks, Poisson, Hexagonal, convergence, shadowing, fading, spectral/energy efficiency, optimization
Towards a communicationtheoretic understanding of systemlevel power consumption
"... Traditional communication theory focuses on minimizing transmit power. Increasingly, however, communication links are operating at shorter ranges where transmit power can drop below the power consumed in decoding. In this paper, we model the required decoding power and investigate the minimization o ..."
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Cited by 27 (6 self)
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Traditional communication theory focuses on minimizing transmit power. Increasingly, however, communication links are operating at shorter ranges where transmit power can drop below the power consumed in decoding. In this paper, we model the required decoding power and investigate the minimization of total system power from two complementary perspectives. First, an isolated pointtopoint link is considered. Using new lower bounds on the complexity of messagepassing decoding, lower bounds are derived on decoding power. These bounds show that 1) there is a fundamental tradeoff between transmit and decoding power; 2) unlike the implications of the traditional “waterfall ” curve which focuses on transmit power, the total power must diverge to infinity as error probability goes to zero; 3) Regular LDPCs, and not their capacityachieving counterparts, can be shown to be power order optimal in some cases; and 4) the optimizing transmit power is bounded away from the Shannon limit. Second, we consider a collection of pointtopoint links. When systems both generate and face interference, coding allows a system to support a higher density of transmitterreceiver pairs (assuming interference is treated as noise). However, at low densities, uncoded transmission may be more power efficient in some cases. I.
Statistics of CoChannel Interference in a Field of Poisson and PoissonPoisson Clustered Interferers
, 2010
"... With increasing spatial reuse of radio spectrum, cochannel interference is becoming a dominant noise source and may severely degrade the communication performance of wireless transceivers. In this paper, we consider the problem of statisticalphysical modeling of cochannel interference from an ann ..."
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Cited by 26 (2 self)
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With increasing spatial reuse of radio spectrum, cochannel interference is becoming a dominant noise source and may severely degrade the communication performance of wireless transceivers. In this paper, we consider the problem of statisticalphysical modeling of cochannel interference from an annular field of Poisson or PoissonPoisson cluster distributed interferers. Poisson and PoissonPoisson cluster processes are commonly used to model interferer distributions in large wireless networks without and with interferer clustering, respectively. Further, by considering the interferers distributed over a parametric annular region, we derive interference statistics for finite and infinitearea interference region with and without a guard zone around the receiver. Statistical modeling of interference is a useful tool to analyze outage probabilities in wireless networks and design interferenceaware transceivers. Our contributions include (1) developing a unified framework for deriving interference models for various wireless network environments, (2) demonstrating the applicability of the symmetric alpha stable and Gaussian mixture (with Middleton Class A as a particular form) distributions in modeling cochannel interference, and (3) deriving analytical conditions on the system model parameters for which these distributions accurately model the statistical properties of the interference. Applications include cochannel interference modeling for various wireless networks, including wireless ad hoc, cellular, local area, and femtocell networks.
SINRbased kcoverage probability in cellular networks
 MATLAB Central File Exchange, 2013. [Online]. Available: http://www.mathworks.fr/matlabcentral/fileexchange/ 40087sinrbasedkcoverageprobabilityincellularnetworks
"... Abstract—We give numerically tractable, explicit integral expressions for the distribution of the signaltointerferenceandnoiseratio (SINR) experienced by a typical user in the downlink channel from the kth strongest base stations of a cellular network modelled by Poisson point process on the pl ..."
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Cited by 26 (6 self)
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Abstract—We give numerically tractable, explicit integral expressions for the distribution of the signaltointerferenceandnoiseratio (SINR) experienced by a typical user in the downlink channel from the kth strongest base stations of a cellular network modelled by Poisson point process on the plane. Our signal propagationloss model comprises of a powerlaw pathloss function with arbitrarily distributed shadowing, independent across all base stations, with and without Rayleigh fading. Our results are valid in the whole domain of SINR, in particular for SINR < 1, where one observes multiple coverage. In this latter aspect our paper complements previous studies reported in [1]. Index Terms—Wireless cellular networks, Poisson process, shadowing, fading, SINR, multiple coverage, symmetric sums. I.
A tractable framework for coverage and outage in heterogeneous cellular networks
 in Proc., Information Theory and its Applications (ITA
, 2011
"... Abstract—We develop a tractable, flexible, and accurate model for downlink heterogeneous cellular networks. It consists of K tiers of randomlylocated base stations (BSs), where each tier may differ in terms of the average transmit power, the supported data rate and the BS density. This allows eleme ..."
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Cited by 23 (15 self)
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Abstract—We develop a tractable, flexible, and accurate model for downlink heterogeneous cellular networks. It consists of K tiers of randomlylocated base stations (BSs), where each tier may differ in terms of the average transmit power, the supported data rate and the BS density. This allows elements spanning traditional, micro, pico, and femtocell BSs to be simultaneously considered. Assuming a mobile user connects to its strongest BS, we derive its SignaltoInterferenceRatio (SIR) distribution and use that to find the coverage (equivalently outage) probability over the entire network. We verify the accuracy of these analytical results through empirical comparisons with an actual 4G macrocell network. I.
Loadaware modeling and analysis of heterogeneous cellular networks
 IEEE Trans. on Wireless Commun
, 2013
"... Abstract—Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically b ..."
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Cited by 22 (12 self)
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Abstract—Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For aKtier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the ith tier are assumed to transmit independently with probability pi, which models the load. Assuming – reasonably – that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage. Index Terms—Heterogeneous cellular networks, loadaware model, Poisson point process, stochastic geometry, HetNet performance analysis.