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67
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.
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.
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.
Optimizing user association and frequency reuse for heterogeneous network under stochastic model
 in Proc. IEEE Global Commun. Conf. (GLOBECOM
, 2013
"... Abstract—This paper considers the joint optimization of frequency reuse and basestation (BS) bias for user association in downlink heterogeneous networks for load balancing and intercell interference management. To make the analysis tractable, we assume that BSs are randomly deployed as point pro ..."
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Cited by 9 (2 self)
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Abstract—This paper considers the joint optimization of frequency reuse and basestation (BS) bias for user association in downlink heterogeneous networks for load balancing and intercell interference management. To make the analysis tractable, we assume that BSs are randomly deployed as point processes in multiple tiers, where BSs in each tier have different transmission powers and spatial densities. A utility maximization framework is formulated based on the user coverage rate, which is a function of the different BS biases for user association and different frequency reuse factors across BS tiers. Compared to previous works where the bias levels are heuristically determined and full reuse is adopted, we quantitatively compute the optimal user association bias and obtain the closedform solution of the optimal frequency reuse. Interestingly, we find that the optimal bias and the optimal reuse factor of each BS tier have an inversely proportional relationship. Further, we also propose an iterative method for optimizing these two factors. In contrast to systemlevel optimization solutions based on specific channel realization and network topology, our approach is offline and is useful for deriving deployment insights. Numerical results show that optimizing user association and frequency reuse for multitier heterogeneous networks can effectively improve celledge user rate performance and utility. I.
Average rate of downlink heterogeneous cellular networks over generalized fading channels – A stochastic geometry approach
 IEEE Trans. Commun
, 2013
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Understanding the Benefits of Open Access in Femtocell Networks: Stochastic Geometric Analysis in the Uplink
"... We introduce a comprehensive analytical framework to compare between open access and closed access in twotier femtocell networks, with regard to uplink interference and outage. Interference at both the macrocell and femtocell levels is considered. A stochastic geometric approach is employed as the ..."
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Cited by 4 (3 self)
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We introduce a comprehensive analytical framework to compare between open access and closed access in twotier femtocell networks, with regard to uplink interference and outage. Interference at both the macrocell and femtocell levels is considered. A stochastic geometric approach is employed as the basis for our analysis. We further derive sufficient conditions for open access and closed access to outperform each other in terms of the outage probability, leading to closedform expressions to upper and lower bound the difference in the targeted received power between the two access modes. Simulations are conducted to validate the accuracy of the analytical model and the correctness of the bounds.
Optimal Combination of Base Station Densities for EnergyEfficient TwoTier Heterogeneous Cellular Networks
"... Abstract—In this paper, the optimal BS (Base Station) density for both homogeneous and heterogeneous cellular networks to minimize network energy cost is analyzed with stochastic geometry theory. For homogeneous cellular networks, both upper and lower bounds of the optimal BS density are derived. Fo ..."
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Cited by 4 (1 self)
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Abstract—In this paper, the optimal BS (Base Station) density for both homogeneous and heterogeneous cellular networks to minimize network energy cost is analyzed with stochastic geometry theory. For homogeneous cellular networks, both upper and lower bounds of the optimal BS density are derived. For heterogeneous cellular networks, our analysis reveals 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, then the optimal strategy is to deploy micro BSs for capacity extension or to switch off macro BSs (if possible) for energy saving with higher priority. Otherwise, the optimal strategy is the opposite. The optimal combination of macro and micro BS densities can be calculated numerically through our analysis, or alternatively be conservatively approximated with a closedform solution. Based on the parameters from EARTH, numerical results show that in the dense urban scenario, compared to the traditional macroonly homogeneous cellular network with no BS sleeping, deploying micro BSs can reduce about 40 % of the total energy cost, and further reduce up to 35 % with BS sleeping capability. Index Terms—Base station density, Poisson point process, energy efficiency, heterogeneous cellular networks. I.
Joint Spectrum Partition and User Association in MultiTier Heterogeneous Networks
"... Abstract—The joint spectrum partition and user association problem for multitier heterogeneous networks is studied in this paper, where disjoint spectrums are allocated among tiers and users are associated with each tier with a biased received power. The random placement of basestations (BSs) of d ..."
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Cited by 4 (1 self)
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Abstract—The joint spectrum partition and user association problem for multitier heterogeneous networks is studied in this paper, where disjoint spectrums are allocated among tiers and users are associated with each tier with a biased received power. The random placement of basestations (BSs) of different tiers are modeled using stochastic geometry, which accounts for their practical deployment and also makes analysis tractable. We derive an upper bound of the average user proportional fair utility based on the user coverage rate, from which we formulate a network utility maximization problem. The optimization of the proposed utility bound shows that the optimal spectrum allocation for each BS tier matches the average proportion of users associated with that tier. The solution to the optimization problem also provides closedform expressions for the optimal user associated bias factors. Compared to systemlevel optimization solutions based on specific network topology and channel realization, our offline analytical approach offers deployment insights. Simulation results demonstrates the effectiveness of the proposed approach. I.