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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 (38 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 91 (18 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.
Heterogeneous cellular networks with flexible cell association: A comprehensive downlink SINR analysis
 IEEE Trans. on Wireless Communications
, 2012
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Offloading in heterogeneous networks: Modeling, analysis and design insights
 IEEE TRANS. WIRELESS COMMUN
, 2013
"... Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the overloaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To ..."
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Cited by 67 (17 self)
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Pushing data traffic from cellular to WiFi is an example of inter radio access technology (RAT) offloading. While this clearly alleviates congestion on the overloaded cellular network, the ultimate potential of such offloading and its effect on overall system performance is not well understood. To address this, we develop a general and tractable model that consists of M different RATs, each deploying up to K different tiers of access points (APs), where each tier differs in transmit power, path loss exponent, deployment density and bandwidth. Each class of APs is modeled as an independent Poisson point process (PPP), with mobile user locations modeled as another independent PPP, all channels further consisting of i.i.d. Rayleigh fading. The distribution of rate over the entire network is then derived for a weighted association strategy, where such weights can be tuned to optimize a particular objective. We show that the optimum fraction of traffic offloaded to maximize SINR coverage is not in general the same as the one that maximizes rate coverage, defined as the fraction of users achieving a given rate.
Seven Ways that HetNets are a Cellular Paradigm Shift
, 2012
"... Imagine a world with more base stations than cell phones: this is where cellular technology is headed in 1020 years. This megatrend requires many fundamental differences in visualizing, modeling, analyzing, simulating and designing cellular networks versus the current textbook approach. In this pa ..."
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Cited by 64 (10 self)
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Imagine a world with more base stations than cell phones: this is where cellular technology is headed in 1020 years. This megatrend requires many fundamental differences in visualizing, modeling, analyzing, simulating and designing cellular networks versus the current textbook approach. In this paper, the most important shifts are distilled down to seven key factors, with the implications described and new models and techniques proposed for some, while others are ripe areas for future exploration.
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.
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 34 (5 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.
Joint Resource Partitioning and Offloading in Heterogeneous Cellular Networks
, 2013
"... In heterogeneous cellular networks (HCNs), it is desirable to offload mobile users to small cells, which are typically significantly less congested than the macrocells. To achieve sufficient load balancing, the offloaded users often have much lower SINR than they would on the macrocell. This SINR d ..."
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Cited by 23 (2 self)
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In heterogeneous cellular networks (HCNs), it is desirable to offload mobile users to small cells, which are typically significantly less congested than the macrocells. To achieve sufficient load balancing, the offloaded users often have much lower SINR than they would on the macrocell. This SINR degradation can be partially alleviated through interference avoidance, for example time or frequency resource partitioning, whereby the macrocell turns off in some fraction of such resources. Naturally, the optimal offloading strategy is tightly coupled with resource partitioning; the optimal amount of which in turn depends on how many users have been offloaded. In this paper, we propose a general and tractable framework for modeling and analyzing joint resource partitioning and offloading in a twotier cellular network. With it, we are able to derive the downlink rate distribution over the entire network, and an optimal strategy for joint resource partitioning and offloading. We show that load balancing, by itself, is insufficient, and resource partitioning is required in conjunction with offloading to improve the rate of cell edge users in cochannel heterogeneous networks.
LoadAware Modeling and Analysis of Heterogeneous Cellular Networks
 IEEE TRANS. ON WIRELESS COMMUN
, 2013
"... 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 assu ..."
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Cited by 22 (10 self)
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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.
Downlink capacity and base station density in cellular networks.” Available: http://arxiv.org/abs/1109.2992
"... AbstractThere have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis c ..."
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Cited by 22 (3 self)
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AbstractThere have been a bulk of analytic results about the performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model cannot reflect the reality, and tends to overestimate the network performance. Moreover, tractable analysis can be performed only for a fixed location user (e.g., cell center or edge user). In this paper, we use the stochastic geometry approach, where base stations can be modeled as a homogeneous Poisson point process. We also consider the user density, and derive the user outage probability that an arbitrary user is under outage owing to low signaltointerferenceplusnoise ratio or high congestion by multiple users. Using the result, we calculate the density of success transmissions in the downlink cellular network. An interesting observation is that the success transmission density increases with the base station density, but the increasing rate diminishes. This means that the number of base stations installed should be more than ntimes to increase the network capacity by a factor of n. Our results will provide a framework for performance analysis of the wireless infrastructure with a high density of access points, which will significantly reduce the burden of networklevel simulations.