Average Rate of Downlink Heterogeneous Cellular Networks over Generalized Fading Channels - A Stochastic Geometry Approach

In this paper, we introduce an analytical framework to compute the average rate of downlink heterogeneous cellular networks. The framework leverages recent application of stochastic geometry to other-cell interference modeling and analysis. The heterogeneous cellular network is modeled as the superposition of many tiers of Base Stations (BSs) having different transmit power, density, path-loss exponent, fading parameters and distribution, and unequal biasing for flexible tier association. A long-term averaged maximum biased-received-power tier association is considered. The positions of the BSs in each tier are modeled as points of an independent Poisson Point Process (PPP). Under these assumptions, we introduce a new analytical methodology to evaluate the average rate, which avoids the computation of the Coverage Probability (Pcov) and needs only the Moment Generating Function (MGF) of the aggregate interference at the probe mobile terminal. The distinguishable characteristic of our analytical methodology consists in providing a tractable and numerically efficient framework that is applicable to general fading distributions, including composite fading channels with small- and mid-scale fluctuations. In addition, our method can efficiently handle correlated Log-Normal shadowing with little increase of the computational complexity. The proposed MGF-based approach needs the computation of either a single or a two-fold numerical integral, thus reducing the complexity of Pcov-based frameworks, which require, for general fading distributions, the computation of a four-fold integral.Comment: Accepted for publication in IEEE Transactions on Communications, to appea

Optimal Non-uniform Deployments in Ultra-Dense Finite-Area Cellular Networks

Network densification and heterogenisation through the deployment of small cellular access points (picocells and femtocells) are seen as key mechanisms in handling the exponential increase in cellular data traffic. Modelling such networks by leveraging tools from Stochastic Geometry has proven particularly useful in understanding the fundamental limits imposed on network coverage and capacity by co-channel interference. Most of these works however assume infinite sized and uniformly distributed networks on the Euclidean plane. In contrast, we study finite sized non-uniformly distributed networks, and find the optimal non-uniform distribution of access points which maximises network coverage for a given non-uniform distribution of mobile users, and vice versa.Comment: 4 Pages, 6 Figures, Letter for IEEE Wireless Communication

Distance Distributions for Real Cellular Networks

This paper presents the general distribution for the distance between a mobile user and any base station (BS). We show that a random variable proportional to the distance squared is Gamma distributed. In the case of the nearest BS, it can be reduced to the well established result of the distance being Rayleigh distributed. We validate our results using a random node simulation and real Vodafone 3G network data, and go on to show how the distribution is tractable by deriving the average aggregate interference power.Comment: 2 pages, 1 figure, IEEE Conference on Computer Communications (INFOCOM

Analyzing Interference from Static Cellular Cooperation using the Nearest Neighbour Model

The problem of base station cooperation has recently been set within the framework of Stochastic Geometry. Existing works consider that a user dynamically chooses the set of stations that cooperate for his/her service. However, this assumption often does not hold. Cooperation groups could be predefined and static, with nodes connected by fixed infrastructure. To analyse such a potential network, in this work we propose a grouping method based on proximity. It is a variation of the so called Nearest Neighbour Model. We restrict ourselves to the simplest case where only singles and pairs of base stations are allowed to be formed. For this, two new point processes are defined from the dependent thinning of a Poisson Point Process, one for the singles and one for the pairs. Structural characteristics for the two are provided, including their density, Voronoi surface, nearest neighbour, empty space and J-function. We further make use of these results to analyse their interference fields and give explicit formulas to their expected value and their Laplace transform. The results constitute a novel toolbox towards the performance evaluation of networks with static cooperation.Comment: 10 pages, 6 figures, 12 total subfigures, WIOPT-SPASWIN 201

Wireless Node Cooperation with Resource Availability Constraints

Base station cooperation is a promising scheme to improve network performance for next generation cellular networks. Up to this point research has focused on station grouping criteria based solely on geographic proximity. However, for the cooperation to be meaningful, each station participating in a group should have sufficient available resources to share with others. In this work we consider an alternative grouping criterion based on a distance that considers both geographic proximity and available resources of the stations. When the network is modelled by a Poisson Point Process, we derive analytical formulas on the proportion of cooperative pairs or single stations, and the expected sum interference from each of the groups. The results illustrate that cooperation gains strongly depend on the distribution of available resources over the network.Comment: submitted, 12 pages, double-column, 7 figures, 8 sub-figures in tota

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers