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22
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.
Femtocells: Past, Present, and Future
 IEEE Journal on Selected Areas in Communications
, 2012
"... Abstract—Femtocells, despite their name, pose a potentially large disruption to the carefully planned cellular networks that now connect a majority of the planet’s citizens to the Internet and with each other. Femtocells – which by the end of 2010 already outnumbered traditional base stations and at ..."
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Cited by 88 (20 self)
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Abstract—Femtocells, despite their name, pose a potentially large disruption to the carefully planned cellular networks that now connect a majority of the planet’s citizens to the Internet and with each other. Femtocells – which by the end of 2010 already outnumbered traditional base stations and at the time of publication are being deployed at a rate of about five million a year – both enhance and interfere with this network in ways that are not yet well understood. Will femtocells be crucial for offloading data and video from the creaking traditional network? Or will femtocells prove more trouble than they are worth, undermining decades of careful base station deployment with unpredictable interference while delivering only limited gains? Or possibly neither: are femtocells just a “flash in the pan”; an exciting but shortlived stage of network evolution that will be rendered obsolete by improved WiFi offloading, new backhaul regulations and/or pricing, or other unforeseen technological developments? This tutorial article overviews the history of femtocells, demystifies their key aspects, and provides a preview of the next few years, which the authors believe will see a rapid acceleration towards small cell technology. In the course of the article, we also position and introduce the articles that headline this special issue.
Analytical modeling of uplink cellular networks
 IEEE Trans. Wireless Commun
, 2013
"... Abstract—Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wynertype model, or via complex system level simulations that often do not provide insight into why various trends are observ ..."
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Cited by 39 (9 self)
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Abstract—Cellular uplink analysis has typically been undertaken by either a simple approach that lumps all interference into a single deterministic or random parameter in a Wynertype model, or via complex system level simulations that often do not provide insight into why various trends are observed. This paper proposes a novel middle way using point processes that is both accurate and also results in easytoevaluate integral expressions based on the Laplace transform of the interference. We assume mobiles and base stations are randomly placed in the network with each mobile pairing up to its closest base station. Compared to related recent work on downlink analysis, the proposed uplink model differs in two key features. First, dependence is considered between user and base station point processes to make sure each base station serves a single mobile in the given resource block. Second, permobile power control is included, which further couples the transmission of mobiles due to locationdependent channel inversion. Nevertheless, we succeed in deriving the coverage (equivalently outage) probability of a typical link in the network. This model can be used to address a wide variety of system design questions in the future. In this paper we focus on the implications for power control and show that partial channel inversion should be used at low signaltointerferenceplusnoise ratio (SINR), while full power transmission is optimal at higher SINR. Index Terms—Uplink, cellular networks, SINR, outage probability, stochastic geometry, fractional power control.
Topological interference management through index coding
, 2013
"... While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topolo ..."
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Cited by 30 (14 self)
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While much recent progress on interference networks has come about under the assumption of abundant channel state information at the transmitters (CSIT), a complementary perspective is sought in this work through the study of interference networks with no CSIT except a coarse knowledge of the topology of the network that only allows a distinction between weak and significant channels and no further knowledge of the channel coefficients ’ realizations. Modeled as a degreesoffreedom (DoF) study of a partially connected interference network with no CSIT, the problem is found to have a counterpart in the capacity analysis of wired networks with arbitrary linear network coding at intermediate nodes, under the assumption that the sources are aware only of the end to end topology of the network. The wireless (wired) network DoF (capacity) region, expressed in dimensionless units as a multiple of the DoF (capacity) of a single point to point channel (link), is found to be bounded above by the capacity of an index coding problem where the antidotes graph is the complement of the interference graph of the original network and the bottleneck link capacity is normalized to unity. The problems are shown to be equivalent under linear solutions over the same field. An interference alignment
Coverage and ergodic rate in Ktier downlink heterogeneous cellular networks
 in Proc., Allerton Conf. on Comm., Control, and Computing
, 2011
"... Abstract—Cellular networks are becoming increasingly heterogeneous due to the codeployment of many disparate infrastructure elements, including micro, pico and femtocells, and distributed antennas. This introduces new challenges in the modeling, analysis, and design of these networks. While grid ..."
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Cited by 13 (8 self)
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Abstract—Cellular networks are becoming increasingly heterogeneous due to the codeployment of many disparate infrastructure elements, including micro, pico and femtocells, and distributed antennas. This introduces new challenges in the modeling, analysis, and design of these networks. While gridbased models have been quite popular in modeling classical macrocell networks, they are both analytically intractable and have limited applicability to heterogeneous cellular networks (HCNs). We propose a flexible, accurate and tractable model for a general downlink 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 1) a mobile connects to the strongest BS, and 2) received power is subject to Rayleigh fading and path loss, we derive expressions for the coverage probability, ergodic rate and the average rate conditioned on the mobile being in coverage as the functions of target SignaltoInterferenceRatio (SIR). I.
Coverage Probability of Uplink Cellular Networks
"... Abstract—The cellular uplink has typically been studied using simple Wynertype analytical models where interference is modeled as a constant or a single random variable, or via complex systemlevel simulations for a given set of parameters, which are often insufficient to evaluate performance in a ..."
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Cited by 6 (2 self)
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Abstract—The cellular uplink has typically been studied using simple Wynertype analytical models where interference is modeled as a constant or a single random variable, or via complex systemlevel simulations for a given set of parameters, which are often insufficient to evaluate performance in all operational regimes. In this paper, we take a fresh look at this classic problem using tools from point process theory and stochastic geometry, and develop a new tractable model for the cellular uplink which provides easytoevaluate expressions for important performance metrics such as coverage probability. The main idea is to model the locations of mobiles as a realization of a Poisson Point Process where each base station (BS) is located uniformly in the Voronoi cell of the mobile it serves, thereby capturing the dependence in two spatial processes. In addition to modeling interference accurately, it provides a natural way to model permobile power control, which is an important aspect of the uplink and one of the reasons why uplink analysis is more involved than its downlink counterpart. We also show that the same framework can be used to study regular as well as irregular BS deployments by choosing an appropriate distribution for the distance of a mobile to its serving BS. We verify the accuracy of this framework with an actual urban/suburban cellular network. I.
Energy Efficiency Analysis of Small Cell Networks
"... Abstract—Small cell networks have recently been proposed as an important evolution path for the nextgeneration cellular networks. While such approach has the potential of meeting the growing network throughput requirement, the energy efficiency of small cell networks is of great concern as the base ..."
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Cited by 6 (4 self)
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Abstract—Small cell networks have recently been proposed as an important evolution path for the nextgeneration cellular networks. While such approach has the potential of meeting the growing network throughput requirement, the energy efficiency of small cell networks is of great concern as the base station (BS) density will be significantly increased. The objective of this paper is to analyze the energy efficiency in small cell networks. To do so, we adopt a random spatial network model, where BSs and users are modeled as two independent spatial Poisson point processes (PPPs). We shall derive analytical results for the network energy efficiency, which show that the BS power consumption model plays a critical role. In particular, it will be shown that increasing the BS density can actually improve the energy efficiency if the BS power consumption that is not related to signal transmission is less than a certain threshold. By comparing the cases between singleantenna and multiantenna BSs, we find that singleantenna BSs provide a higher energy efficiency if the circuit power is larger than a threshold. Simulation results will demonstrate that our conclusions which are based on the random network model also hold in a regular gridbased model.
Average rate of downlink heterogeneous cellular networks over generalized fading channels – A stochastic geometry approach
 IEEE Trans. Commun
, 2013
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Optimality of orthogonal access for onedimensional convex cellular networks
, 2013
"... It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all onedimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the netw ..."
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Cited by 4 (1 self)
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It is shown that a greedy orthogonal access scheme achieves the sum degrees of freedom of all onedimensional (all nodes placed along a straight line) convex cellular networks (where cells are convex regions) when no channel knowledge is available at the transmitters except the knowledge of the network topology. In general, optimality of orthogonal access holds neither for twodimensional convex cellular networks nor for onedimensional nonconvex cellular networks, thus revealing a fundamental limitation that exists only when both onedimensional and convex properties are simultaneously enforced, as is common in canonical information theoretic models for studying cellular networks. The result also establishes the capacity of the corresponding class of index coding problems.