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81
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.
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.
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.
Fundamentals of Heterogeneous Cellular Networks with Energy Harvesting
 IEEE TRAN. WIRELESS COMMUNICATIONS
, 2014
"... We develop a new tractable model for Ktier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a selfcontained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deploym ..."
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Cited by 15 (2 self)
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We develop a new tractable model for Ktier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a selfcontained energy harvesting module. The BSs across tiers differ in terms of the energy harvesting rate, energy storage capacity, transmit power and deployment density. Since a BS may not always have enough energy, it may need to be kept OFF and allowed to recharge while nearby users are served by neighboring BSs that are ON. We show that the fraction of time a kth tier BS can be kept ON, termed availability ρk, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of Ktuples (ρ1, ρ2,... ρK), termed the availability region, that is achievable by general uncoordinated operational strategies, where the decision to toggle the current ON/OFF state of a BS is taken independently of the other BSs. If the availability vector corresponding to the optimal system performance, e.g., in terms of rate, lies in this availability region, there is no performance loss due to the presence of unreliable energy sources. As a part of our analysis, we model the temporal dynamics of the energy level at each BS as a birthdeath process, derive the energy utilization rate, and use hitting/stopping time analysis to prove that there exists a fundamental limit on ρk that cannot be surpassed by any uncoordinated strategy.
Modeling, analysis, and design for carrier aggregation in heterogeneous cellular networks
 IEEE Tran. Commun
, 2013
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Downlink MIMO HetNets: Modeling, Ordering Results and Performance Analysis
 IEEE TRANS. ON WIRELESS COMMUN
, 2013
"... We develop a general downlink model for multiantenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signaltointerferenceratio (SIR), deployment density, number of transmit antennas and the type of multiantenna tr ..."
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Cited by 14 (6 self)
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We develop a general downlink model for multiantenna heterogeneous cellular networks (HetNets), where base stations (BSs) across tiers may differ in terms of transmit power, target signaltointerferenceratio (SIR), deployment density, number of transmit antennas and the type of multiantenna transmission. In particular, we consider and compare space division multiple access (SDMA), single user beamforming (SUBF), and baseline singleinput singleoutput (SISO) transmission. For this general model, the main contributions are: (i) ordering results for both coverage probability and per user rate in closed form for any BS distribution for the three considered techniques, using novel tools from stochastic orders, (ii) upper bounds on the coverage probability assuming a Poisson BS distribution, and (iii) a comparison of the area spectral efficiency (ASE). The analysis concretely demonstrates, for example, that for a given total number of transmit antennas in the network, it is preferable to spread them across many singleantenna BSs vs. fewer multiantenna BSs. Another observation is that SUBF provides higher coverage and per user data rate than SDMA, but SDMA is in some cases better in terms of ASE.
Equivalence and comparison of heterogeneous cellular networks
 in Proc. of PIMRC’13 – WDNCN2013
, 2013
"... Abstract—We consider a general heterogeneous network in which, besides general propagation effects (shadowing and/or fading), individual base stations can have different emitting powers and be subject to different parameters of Hatalike pathloss models (pathloss exponent and constant) due to, for ..."
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Cited by 12 (5 self)
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Abstract—We consider a general heterogeneous network in which, besides general propagation effects (shadowing and/or fading), individual base stations can have different emitting powers and be subject to different parameters of Hatalike pathloss models (pathloss exponent and constant) due to, for example, varying antenna heights. We assume also that the stations may have varying parameters of, for example, the link layer performance (SINR threshold, etc). By studying the propagation processes of signals received by the typical user from all antennas marked by the corresponding antenna parameters, we show that seemingly different heterogeneous networks based on Poisson point processes can be equivalent from the point of view a typical user. These neworks can be replaced with a model where all the previously varying propagation parameters (including pathloss exponents) are set to constants while the only tradeoff being the introduction of an isotropic base station density. This allows one to perform analytic comparisons of different network models via their isotropic representations. In the case of a constant pathloss exponent, the isotropic representation simplifies to a homogeneous modification of the constant intensity of the original network, thus generalizing a previous result showing that the propagation processes only depend on one moment of the emitted power and propagation effects. We give examples and applications to motivate these results and highlight an interesting observation regarding random pathloss exponents. Index Terms—Heterogeneous networks, multitier networks, Poisson process, shadowing, fading, propagation invariance, stochastic equivalence. I.
1 Modeling Heterogeneous Network Interference
"... Abstract—Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complex, making evaluation of different communication strategies for ..."
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Cited by 11 (1 self)
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Abstract—Cellular systems are becoming more heterogeneous with the introduction of low power nodes including femtocells, relays, and distributed antennas. Unfortunately, the resulting interference environment is also becoming more complex, making evaluation of different communication strategies for cellular systems more challenging in both analysis and simulation. This paper suggests a simplified interference model for heterogeneous network. Leveraging recent applications of stochastic geometry to analyze cellular systems, this paper propose to analyze performance in a fixedsize typical cell surrounded by an interference field consisted of superposition of marked Poisson point processes outside a guard region. The proposed model simplifies the simulation of cellular systems and may provide analytical insights for certain signaling strategies. I.
Structured Spectrum Allocation and User Association in Heterogeneous Cellular Networks
, 2014
"... We study joint spectrum allocation and user association in heterogeneous cellular networks with multiple tiers of base stations. A stochastic geometric approach is applied as the basis to derive the average downlink user data rate in a closedform expression. Then, the expression is employed as the ..."
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Cited by 11 (8 self)
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We study joint spectrum allocation and user association in heterogeneous cellular networks with multiple tiers of base stations. A stochastic geometric approach is applied as the basis to derive the average downlink user data rate in a closedform expression. Then, the expression is employed as the objective function in jointly optimizing spectrum allocation and user association, which is of nonconvex programming in nature. A computationally efficient Structured Spectrum Allocation and User Association (SSAUA) approach is proposed, solving the optimization problem optimally when the density of users is low, and nearoptimally with a guaranteed performance bound when the density of users is high. A Surcharge Pricing Scheme (SPS) is also presented, such that the designed association bias values can be achieved in Nash equilibrium. Simulations and numerical studies are conducted to validate the accuracy and efficiency of the proposed SSAUA approach and SPS.