arXiv subjects

Laurent Decreusefond

Publications and source records attributed to Laurent Decreusefond.

At least 37 records · Page 2Linked to original sources

arXiv2020

How To Dimension Radio Resources When Users Are Distributed on Roads Modeled by Poisson Line Process

Resources dimensioning aims at finding the number of radio resources required to carry a forecast data traffic at a target users Quality of Services (QoS). The present paper attempts to provide a new approach of radio resources dimensioning considering the congestion probability, qualified as a relevant metric for QoS evaluation. Users are assumed to be distributed according to a linear Poisson Point Process (PPP) in a random system of roads modeled by Poisson Line Process (PLP) instead of the widely-used spatial PPP. We derive the analytical expression of the congestion probability for analyzing its behavior as a function of network parameters. Finally we show how to dimension radio resources by setting a value of the congestion probability, often targeted by the operator, in order to find the relation between the necessary resources and the forecast data traffic expressed in terms of cell throughput. Different numerical results are presented to justify this dimensioning approach.

cs.NI↗

arXiv2020

3D Beamforming based Dynamic TDD Interference Mitigation Scheme

Dynamic Time Division Duplexing (D-TDD) allows cells to accommodate asymmetric traffic variations with high resource assignment flexibility. However, this feature is limited by two additional types of interference between cells in opposite transmission direction: downlink (DL) to uplink (UL) and UL to DL interference. Therefore, using this mode with macro-cell deployments requires interference mitigation techniques to reduce the strong DL to UL interference. 3D beamforming is an efficient technique that minimizes interference and enhances performance by exploiting a large 2D array of antennas intelligently. Combining D-TDD and 3D beamforming can make D-TDD feasible for macro-cells. The aim of this work is to provide a 3D beamforming analytical model in a D-TDD based macro-cells' deployment where beamforming horizontal and vertical radiation patterns depend on the spatial distribution of random users' locations. We evaluate interference in terms of Interference to Signal Ratio (ISR). We show that the cumulative ISR can be written in terms of convergent series and its expectation is an almost sure convergent series. Different numerical results are presented to justify the applicability of this scheme.

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arXiv2019

Radio Resource Dimensioning with Cox Process Based User Location Distribution

The upcoming fifth generation (5G) New Radio (NR) interface inherits many concepts and techniques from 4G systems such as the Orthogonal Frequency Division Multiplex (OFDM) based waveform and multiple access. Dimensioning 5G NR interface will likely follow the same principles as in 4G networks. It aims at finding the number of radio resources required to carry a forecast data traffic at a target users Quality of Services (QoS). The present paper attempts to provide a new approach of radio resources dimensioning considering the congestion probability, qualified as a relevant metric for QoS evaluation. We distinguish between the spatial random distribution of indoor users, modeled by a spatial Poisson Point Process (spatial PPP) in a typical area covered by a 5G cell, and the distribution of outdoor users modeled by a linear PPP generated in a random system of roads modeled according to a Poisson Line Process (PLP). Moreover, we show that the total requested Physical Resource Blocks (PRBs) follows a compound Poisson distribution and we attempt to derive the explicit expression of the congestion probability by introducing a mathematical tool from combinatorial analysis called the exponential Bell polynomials. Finally we show how to dimension radio resources, for a given target congestion probability, by solving an implicit relation between the necessary resources and the forecast data traffic expressed in terms of cell throughput. Different numerical results are presented to justify this dimensioning approach.

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arXiv2019

Donsker's theorem in {Wasserstein}-1 distance

We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in $R^d$ and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulus of the solution of the Stein's equation. As an application, we can evaluate the rate of convergence towards the local time at 0 of the Brownian motion.

math.PR↗

arXiv2018

Computing the $k$-coverage of a wireless network

Coverage is one of the main quality of service of a wirelessnetwork. $k$-coverage, that is to be covered simultaneously by $k$network nodes, is synonym of reliability and numerous applicationssuch as multiple site MIMO features, or handovers. We introduce here anew algorithm for computing the $k$-coverage of a wirelessnetwork. Our method is based on the observation that $k$-coverage canbe interpreted as $k$ layers of $1$-coverage, or simply coverage. Weuse simplicial homology to compute the network's topology and areduction algorithm to indentify the layers of $1$-coverage. Weprovide figures and simulation results to illustrate our algorithm.

cs.NI↗

arXiv2018

Malliavin and dirichlet structures for independent random variables

On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian processes. We obtain versions of almost all the classical functional inequalities in discrete settings which show that the Efron-Stein inequality can be interpreted as a Poincar{é} inequality or that Hoeffding decomposition of U-statistics can be interpreted as a chaos decomposition. We obtain a version of the Lyapounov central limit theorem for independent random variables without resorting to ad-hoc couplings, thus increasing the scope of the Stein method.

math.PR↗

arXiv2018

Stein's method and Papangelou intensity for Poisson or Cox process approximation

In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a measure and another finite point process is bounded by the $L^1$-distance between their respective Papangelou intensities. Then, we deduce some convergence rates for sequences of point processes approaching a Poisson or a Cox point process.

math.PR↗

arXiv2018

Stein's method for rough paths

The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to enriched random walks and enriched Brownian motion. We use the Stein-Dirichlet method to precise the rate of this convergence in the topology of fractional Sobolev spaces.

math.PR↗

arXiv2018

Interference Analysis in Dynamic TDD System Combined or not With Cell Clustering Scheme

Dynamic Time Division Duplex (TDD) has been introduced as a solution to deal with the uplink and downlink traffic asymmetry, mainly observed for dense heterogeneous network deployments. However, the use of this feature requires new interference mitigation schemes capable to handle two additional types of interferences between cells in opposite transmission cycle: downlink to uplink and uplink to downlink interferences. Among them, Cell clustering has been proposed as an efficient solution to minimize inter-cell interferences in opposite transmission directions and somehow responds to the requirements of enhanced Interference Mitigation and Traffic Adaptation (eIMTA) problem. This work is devoted to provide a new analytical approach to model inter-cell interferences and quantify performances of Dynamic TDD system in terms of SINR (Signal to Interferences plus Noise Ratio) distribution. Analytical system performance investigation concerns two scenarios: i) basic Dynamic TDD without any other feature and ii) Dynamic TDD with interference mitigation schemes.

cs.NI↗

arXiv2018

Building a coverage hole-free communication tree

Wireless networks are present everywhere but their management can be tricky since their coverage may contain holes even if the network is fully connected. In this paper we propose an algorithm that can build a communication tree between nodes of a wireless network with guarantee that there is no coverage hole in the tree. We use simplicial homology to compute mathematically the coverage, and Prim's algorithm principle to build the communication tree. Some simulation results are given to study the performance of the algorithm and compare different metrics. In the end, we show that our algorithm can be used to create coverage hole-free communication groups with a limited number of hops.

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arXiv2017

Random Abstract Simplicial Complexes Reduction

Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this type of network, we intend to reduce the number of network nodes without modifying neither the connectivity nor the coverage of the network. In this paper, we present a reduction algorithm that lower the number of points of an abstract simplicial complex in an optimal order while maintaining its topology. Then, we study the complexity of such an algorithm for a network simulated by a binomial point process and represented by a Vietoris-Rips complex.

math.PR↗

arXiv2017

Volterra differential equations with singular kernels

Motivated by the potential applications to the fractional Brownianmotion, we study Volterra stochasticdifferential of the form~:\begin{equation}X\_t = x+ \int\_0^tK(t,s)b(s,X\_s)ds + \int\_0^tK(t,s) σ(s,X\_s)\,dB\_s ,\tag{E} \label{eq:sdefbm}\end{equation}where $(B\_s, \, s\in [0,1])$ is a one-dimensional standard Brownianmotion and $(K(t,s), \, t,s \in [0,1])$ is a deterministic kernelwhose properties will be precised below but for which we don't assumeany boundedness property.

math.PR↗

arXiv2017

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.

cs.NI↗

arXiv2016

Distributed Computation of the Cech Complex and Applications in Wireless Networks

In this paper, we introduce a distributed algorithm to compute thě Cech complex. This algorithm is aimed at solving coverage problems in self organized wireless networks. Two applications based on the distributed computation of thě Cech complex are proposed. The first application detects coverage holes while the later one optimizes coverage of wireless networks.

cs.NI↗

arXiv2016

Analysis of Static Cellular Cooperation between Mutually Nearest Neighboring Nodes

Cooperation in cellular networks is a promising scheme to improve system performance. Existing works consider that a user dynamically chooses the stations that cooperate for his/her service, but such assumption often has practical limitations. Instead, cooperation groups can be predefined and static, with nodes linked by fixed infrastructure. To analyze such a potential network, we propose a grouping method based on node proximity. With the Mutually Nearest Neighbour Relation, we allow the formation of singles and pairs of nodes. Given an initial topology for the stations, two new point processes are defined, one for the singles and one for the pairs. We derive structural characteristics for these processes and analyse the resulting interference fields. When the node positions follow a Poisson Point Process (PPP) the processes of singles and pairs are not Poisson. However, the performance of the original model can be approximated by the superposition of two PPPs. This allows the derivation of exact expressions for the coverage probability. Numerical evaluation shows coverage gains from different signal cooperation that can reach up to 15% compared to the standard noncooperative coverage. The analysis is general and can be applied to any type of cooperation in pairs of transmitting nodes.

cs.NI↗

arXiv2016

Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry

A Poisson or a binomial process on an abstract state space and a symmetric function $f$ acting on $k$-tuples of its points are considered. They induce a point process on the target space of $f$. The main result is a functional limit theorem which provides an upper bound for an optimal transportation distance between the image process and a Poisson process on the target space. The technical background are a version of Stein's method for Poisson process approximation, a Glauber dynamics representation for the Poisson process and the Malliavin formalism. As applications of the main result, error bounds for approximations of U-statistics by Poisson, compound Poisson and stable random variables are derived, and examples from stochastic geometry are investigated.

math.PR↗

arXiv2016

Cournot-Nash Equilibria for Bandwidth Allocation under Base-Station Cooperation

-In this paper, a novel resource allocation scheme based on discrete Cournot-Nash equilibria and optimal transport theory is proposed. The originality of this framework lies in the joint optimization of downlink bandwidth allocation and cooperation between base stations. A tractable formalization is given in the form of a quadratic optimization problem. A low complexity approximate solution is derived and theoretically characterized. Simulations highlight the existence of an optimal working point, that maximizes user satisfaction ratio and network load. The impact of the network deployment on the optimum is numerically investigated, thanks to the $β$-Ginibre model. Indeed, base stations are assumed to be drawn according to $β$-Ginibre point processes. Numerical analysis shows that the network performance increases with $β$ going to one.

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arXiv2016

Stochastic simulation of urban environments. Application to Path-loss in wireless systems

We are interested in the assessment of electromagnetic Path-Loss in complex environments. The Path-loss is the attenuation function $P$ of the electromagnetic power at a distance $d$ of an antenna. In free-space, $P(d) \propto 1/d^2$, in complex environments like cities, wave trajectory is altered by successive reflections and absorptions, the path-loss is not theoretically known and engineering rules postulate that $P(d) \simeq 1/d^γ, \, γ>2$. We place in a stochastic geometry context to answer the problem statistically. We present random models of 3D-city. These models reproduce main real cities' features, can be calibrated with simple mean formulae and can be fast simulated. For collections of random cities with the same mean morphology, we estimate by Monte-Carlo ray tracing techniques their attenuation maps. By averaging these maps, we show that the power expectancy actually follows a function $\sim 1/d^γ$ with $γ$ depending on the environment morphology.

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