A recent approach in modeling and analysis of the supply and demand in heterogeneous wireless cellular networks has been the use of two independent Poisson point processes (PPPs) for the locations of base stations (BSs) and user equipments (UEs). This popular approach has two major shortcomings. First, although the PPP model may be a fitting one for the BS locations, it is less adequate for the UE locations mainly due to the fact that the model is not adjustable (tunable) to represent the severity of the heterogeneity (non-uniformity) in the UE locations. Besides, the independence assumption between the two PPPs does not capture the often-observed correlation between the UE and BS locations. This paper presents a novel heterogeneous spatial traffic modeling which allows statistical adjustment. Simple and non-parameterized, yet sufficiently accurate, measures for capturing the traffic characteristics in space are introduced. Only two statistical parameters related to the UE distribution, namely, the coefficient of variation (the normalized second-moment), of an appropriately defined inter-UE distance measure, and correlation coefficient (the normalized cross-moment) between UE and BS locations, are adjusted to control the degree of heterogeneity and the bias towards the BS locations, respectively. This model is used in heterogeneous wireless cellular networks (HetNets) to demonstrate the impact of heterogeneous and BS-correlated traffic on the network performance. This network is called HetHetNet since it has two types of heterogeneity: heterogeneity in the infrastructure (supply), and heterogeneity in the spatial traffic distribution (demand).
In @cite_51 , , presented an algorithm to create a random inhomogeneous node distribution based on a neighborhood-dependent thinning approach in a homogeneous PPP. The model, however, can not be used for generating BS-correlated UE patterns, as this is beyond the scope of that model.
@cite_51
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Most analysis and simulation of wireless systems assumes that the nodes are randomly located, sampled from a uniform distribution. Although in many real-world scenarios the nodes are non-uniformly distributed, the research community lacks a common approach to generate such inhomogeneities. This paper intends to go a step in this direction. We present an algorithm to create a random inhomogeneous node distribution based on a simple neighborhood-dependent thinning of a homogeneous Poisson process. We derive some useful stochastic properties of the resulting distribution (in particular the probability density of the nearest neighbor distance) and offer a reference implementation. Our goal is to enable fellow researchers to easily use inhomogeneous distributions with well-defined stochastic properties. 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-uniform 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 capacity-centric deployments, where the UEs are more likely to lie closer to the BSs. Future generation (5G and beyond) cellular networks have to deal not only with an extreme traffic demand increase, but also an extreme level of heterogeneity in the distribution of that demand in both space and time. Traffic modeling in the time domain has been investigated well in the literature. In the space domain, however, there is a lack of statistical models for the heterogeneous User Equipment (UE) distribution beyond the classical Poisson Point Process (PPP) model. In this paper, we introduce a methodology for the generation and analysis of spatial traffic which allows statistical adjustments. Only two parameters, namely, Coefficient of Variation (CoV) and Correlation Coefficient, are adjusted to control the UE distribution heterogeneity and correlation with Base Stations (BSs). The methodology is applied to cellular networks to show the impact of heterogeneous network geometry on network performance. 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.