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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 20 (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.
Optimal base station density for energyefficient heterogeneous cellular networks
 in IEEE International Conf. on Commun
, 2012
"... Abstract—In this paper, we adopt stochastic geometry theory to analyze the optimal macro/micro BS (base station) density for energyefficient heterogeneous cellular networks with QoS constraints. We first derive the upper and lower bounds of the optimal BS density for homogeneous scenarios and, base ..."
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Cited by 16 (3 self)
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Abstract—In this paper, we adopt stochastic geometry theory to analyze the optimal macro/micro BS (base station) density for energyefficient heterogeneous cellular networks with QoS constraints. We first derive the upper and lower bounds of the optimal BS density for homogeneous scenarios and, based on these, we analyze the optimal BS density for heterogeneous networks. The optimal macro/micro BS density can be calculated numerically through our analysis, and the closedform approximation is also derived. Our results reveal the best type of BSs to be deployed for capacity extension, or to be switched off for energy saving. Specifically, if the ratio between the micro BS cost and the macro BS cost is lower than a threshold, which is a function of path loss and their transmit power, the micro BSs are preferred, i.e., deploy more micro BSs for capacity extension or switch off certain macro BSs for energy saving. Otherwise, the optimal choice is the opposite. Our work provides guidance for energy efficient cellular network planning and dynamic operation control.1 I.
Energy Efficient Heterogeneous Cellular Networks
"... Abstract—With the exponential increase in mobile internet traffic driven by a new generation of wireless devices, future cellular networks face a great challenge to meet this overwhelming demand of network capacity. At the same time, the demand for higher data rates and the everincreasing number of ..."
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Cited by 15 (0 self)
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Abstract—With the exponential increase in mobile internet traffic driven by a new generation of wireless devices, future cellular networks face a great challenge to meet this overwhelming demand of network capacity. At the same time, the demand for higher data rates and the everincreasing number of wireless users led to rapid increases in power consumption and operating cost of cellular networks. One potential solution to address these issues is to overlay small cell networks with macrocell networks as a means to provide higher network capacity and better coverage. However, the dense and random deployment of small cells and their uncoordinated operation raise important questions about the energy efficiency implications of such multitier networks. Another technique to improve energy efficiency in cellular networks is to introduce active/sleep (on/off) modes in macrocell base stations. In this paper, we investigate the design and the associated tradeoffs of energy efficient cellular networks through the deployment of sleeping strategies and small cells. Using a stochastic geometry based model, we derive the success probability and energy efficiency in homogeneous macrocell (singletier) and heterogeneous Ktier wireless networks under different sleeping policies. In addition, we formulate the power consumption minimization and energy efficiency maximization problems, and determine the optimal operating regimes for macrocell base stations. Numerical results confirm the effectiveness of switching off base stations in homogeneous macrocell networks. Nevertheless, the gains in terms of energy efficiency depend on the type of sleeping strategy used. In addition, the deployment of small cells generally leads to higher energy efficiency but this gain saturates as the density of small cells increases. In a nutshell, our proposed framework provides an essential understanding on the deployment of future green heterogeneous networks. Index Terms—Energy efficiency, green communications, heterogeneous wireless networks, power consumption, sleeping strategy, small cells, open access, stochastic geometry.
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.
Modeling nonuniform UE distributions in downlink cellular networks
 IEEE Wireless Commun. Letters
, 2013
"... Abstract—A recent way to model and analyze downlink cellular networks is by using random spatial models. Assuming user equipment (UE) distribution to be uniform, the analysis is performed at a typical UE located at the origin. At least one shortcoming of this approach is its inability to model non ..."
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Cited by 13 (4 self)
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Abstract—A recent way to model and analyze downlink cellular networks is by using random spatial models. Assuming user equipment (UE) distribution to be uniform, the analysis is performed at a typical UE located at the origin. At least one shortcoming of this approach is its inability to model nonuniform UE distributions, especially when there is dependence in the UE and the base station (BS) locations. To facilitate analysis in such cases, we propose a new tractable method of sampling UEs by conditionally thinning the BS point process and show that the resulting framework can be used as a tractable generative model to study current capacitycentric deployments, where the UEs are more likely to lie closer to the BSs. Index Terms—Cellular networks, nonuniform UE distribution, stochastic geometry, coverage probability. I.
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.
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 12 (7 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.
Analysis of blockage effects on urban cellular networks,” Submitted to
 IEEE Trans. on Wireless Communications, arXiv preprint
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