In this work, we assess the viability of heterogeneous networks composed of legacy macrocells which are underlaid with self-organizing picocells. Aiming to improve coverage, cell-edge throughput and overall system capacity, self-organizing solutions, such as range expansion bias, almost blank subframe and distributed antenna systems are considered. Herein, stochastic geometry is used to model network deployments, while higher-order statistics through the cumulants concept is utilized to characterize the probability distribution of the received power and aggregate interference at the user of interest. A compre- hensive analytical framework is introduced to evaluate the performance of such self-organizing networks in terms of outage probability and average channel capacity with respect to the tagged receiver. To conduct our studies, we consider a shadowed fading channel model incorporating log-normal shadowing and Nakagami-m fading. Results show that the analytical framework matches well with numerical results obtained from Monte Carlo simulations. We also observed that by simply using almost blank subframes the aggregate interference at the tagged receiver is reduced by about 12dB. Although more elaborated interference control techniques such as, downlink bitmap and distributed antennas systems become needed, when the density of picocells in the underlaid tier gets high.
The design and implementation of self-organizing functionalities in HN is a topic of significant interest as evidenced by the number of recent publications @cite_4 @cite_24 @cite_25 @cite_15 @cite_6 @cite_22 @cite_7 . For instance, the self-organization concept is used to devise cognitive radio resource management schemes to mitigate cross-tier interference and guarantee users QoS in distinct heterogeneous deployments scenarios @cite_43 . More recently, the REB concept is discussed within 3GPP as a baseline solution to boost the offloading potential of heterogeneous deployments. In that regard, Authors in @cite_42 investigate the cell range expansion and interference mitigation in heterogeneous networks. Following the same lines, G " u ven c instigates the capacity and fairness of heterogeneous networks with range expansion and interference coordination @cite_14 . In @cite_0 , Jo use the SG framework to assess how the biased cell association procedure performs in heterogeneous networks by means of the outage probability. black In multi-tier heterogeneous networks where the locations of BS are modeled as independent PPP , the joint distribution of the downlink SINR at the tagged receiver is derived when the serving BS is selected as either the nearest or the strongest with respect to the user of interest @cite_21 .
@cite_14 @cite_4 @cite_22 @cite_7 @cite_42 @cite_21 @cite_6 @cite_24 @cite_43 @cite_0 @cite_15 @cite_25
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We consider spatial stochastic models of downlink heterogeneous cellular networks (HCNs) with multiple tiers, where the base stations (BSs) of each tier have a particular spatial density, transmission power and path-loss exponent. Prior works on such spatial models of HCNs assume, due to its tractability, that the BSs are deployed according to homogeneous Poisson point processes. This means that the BSs are located independently of each other and their spatial correlation is ignored. In the current paper, we propose two spatial models for the analysis of downlink HCNs, in which the BSs are deployed according to @a-Ginibre point processes. The @a-Ginibre point processes constitute a class of determinantal point processes and account for the repulsion between the BSs. Besides, the degree of repulsion is adjustable according to the value of @[email protected]?(0,1]. In one proposed model, the BSs of different tiers are deployed according to mutually independent @a-Ginibre processes, where the @a can take different values for the different tiers. In the other model, all the BSs are deployed according to an @a-Ginibre point process and they are classified into multiple tiers by mutually independent marks. For these proposed models, we derive computable representations for the coverage probability of a typical user-the probability that the downlink signal-to-interference-plus-noise ratio for the typical user achieves a target threshold. We exhibit the results of some numerical experiments and compare the proposed models and the Poisson based model. This paper considers the joint optimization of frequency reuse and base-station (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 closed-form 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 system-level optimization solutions based on specific channel realization and network topology, our approach is off-line and is useful for deriving deployment insights. Numerical results show that optimizing user association and frequency reuse for multi-tier heterogeneous networks can effectively improve cell-edge user rate performance and utility. Cellular networks are in a major transition from a carefully planned set of large tower-mounted base-stations (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 Signal-to-Interference-plus-Noise-Ratio (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 closed-form 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 1-2 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 interference-limited open access networks is that at a given , adding more tiers and or BSs neither increases nor decreases the probability of coverage or outage when all the tiers have the same target-SINR. We develop a new tractable model for K-tier heterogeneous cellular networks (HetNets), where each base station (BS) is powered solely by a self-contained 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 k^ th tier BS can be kept ON, termed availability ρ_k, is a fundamental metric of interest. Using tools from random walk theory, fixed point analysis and stochastic geometry, we characterize the set of K-tuples (ρ_1,ρ_2,…ρ_K), 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 birth-death process, derive the energy utilization rate, and use hitting stopping time analysis to prove that there exists a fundamental limit on ρ_k that cannot be surpassed by any uncoordinated strategy.