Anaïs Vergne, Laurent Decreusefond, Philippe Martins
Simplicial homology is a tool that provides a mathematical way to compute the connectivity and the coverage of a cellular network without any node location information. In this article, we use simplicial homology in order to not only compute the topology of a cellular network, but also to discover the clusters of nodes still with no location information. We propose three algorithms for the management of future cellular networks. The first one is a frequency auto-planning algorithm for the self-configuration of future cellular networks. It aims at minimizing the number of planned frequencies while maximizing the usage of each one. Then, our energy conservation algorithm falls into the self-optimization feature of future cellular networks. It optimizes the energy consumption of the cellular network during off-peak hours while taking into account both coverage and user traffic. Finally, we present and discuss the performance of a disaster recovery algorithm using determinantal point processes to patch coverage holes.
Ashutosh Balakrishnan, Pierre Popineau, Philippe Martins
Low earth orbit (LEO) satellite based non-terrestrial networks are a key theme of the upcoming 6G networks. These space networks are proposed to be used for high-mobility use-cases like airplanes and vehicles. The initial access process between a base station (BS) and a user equipment (UE) involves timing advance (TA) value computation at the BS, requiring precise BS location information at the UE. It becomes more challenging in LEO satellite networks due to the fast moving LEO satellites and large pathloss, in addition to the mobile UE. This paper aims to compute the TA and Doppler shift experienced at the UE by modeling the joint system dynamics in a LEO satellite-mobile UE network through an extended Kalman filter (EKF) based recursive Bayesian framework. The framework accurately models the joint system dynamics by considering the LEO satellite acceleration. It constructs the Jacobian to linearize the inherent non-linearities present in the motion. Probabilistic insights regarding the state-update and propagation are also provided. The analytical framework factors in the limited satellite visibility at the UE and the satellite-UE geometry w.r.t. the earth center. The proposed framework is also useful when the satellite and UE clocks are not in sync, with the corresponding clock drift a function of the measured time difference of arrivals. Our results showcase the efficacy and robustness of the proposed EKF framework to estimate the TA and Doppler shift, even at very high UE speeds. The work is expected to be extremely useful in realizing LEO satellite based non-terrestrial networks.
Anaïs Vergne, Laurent Decreusefond, Philippe Martins
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.
Laurent Decreusefond, Eduardo Ferraz, Philippe Martins
For OFDMA systems, we find a rough but easily computed upper bound for the probability of loosing communications by insufficient number of sub-channels on downlink. We consider as random the positions of receiving users in the system as well as the number of sub-channels dedicated to each one. We use recent results of the theory of point processes which reduce our calculations to the first and second moments of the total required number of sub-carriers.
Ngoc-Khuyen Le, Anais Vergne, Philippe Martins, Laurent Decreusefond
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.
Anais Vergne, Laurent Decreusefond, Philippe Martins
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.
Laurent Decreusefond, Philippe Martins, Than-Tung Vu
We consider stochastic cellular networks where base stations locations form a homogenous Poisson point process and each mobile is attached to the base station that provides the best mean signal power. The mobile is in outage if the SINR falls below some threshold. The handover decision has to be made if the mobile is in outage for some time slots. The outage probability and the handover probability is evaluated in taking into account the effect of path loss, shadowing, Rayleigh fast fading, frequency factor reuse and conventional beamforming. The main assumption is that the Rayleigh fast fading changes each time slot while other network components remain static during the period of study.
Laurent Decreusefond, Eduardo Ferraz, Philippe Martins, Thanh-Tung Vu
This paper proposes an analytic model for dimensioning OFDMA based networks like WiMAX and LTE systems. In such a system, users require a number of subchannels which depends on their \SNR, hence of their position and the shadowing they experience. The system is overloaded when the number of required subchannels is greater than the number of available subchannels. We give an exact though not closed expression of the loss probability and then give an algorithmic method to derive the number of subchannels which guarantees a loss probability less than a given threshold. We show that Gaussian approximation lead to optimistic values and are thus unusable. We then introduce Edgeworth expansions with error bounds and show that by choosing the right order of the expansion, one can have an approximate dimensioning value easy to compute but with guaranteed performance. As the values obtained are highly dependent from the parameters of the system, which turned to be rather undetermined, we provide a procedure based on concentration inequality for Poisson functionals, which yields to conservative dimensioning. This paper relies on recent results on concentration inequalities and establish new results on Edgeworth expansions.
Laurent Decreusefond, Thanh-Tung Vu, Philippe Martins
In this paper we present a new analysis of energy consumption in cellular networks. We focus on the distribution of energy consumed by a base station for one isolated cell. We first define the energy consumption model in which the consumed energy is divided into two parts: The additive part and the broadcast part. The broadcast part is the part of energy which is oblivious of the number of mobile stations but depends on the farthest terminal, for instance, the energy effort necessary to maintain the beacon signal. The additive part is due to the communication power which depends on both the positions, mobility and activity of all the users. We evaluate by closed form expressions the mean and variance of the consumed energy. Our analytic evaluation is based on the hypothesis that mobiles are distributed according to a Poisson point process. We show that the two parts of energy are of the same order of magnitude and that substantial gain can be obtained by power control. We then consider the impact of mobility on the energy consumption. We apply our model to two case studies: The first one is to optimize the cell radius from the energetic point of view, the second one is to dimension the battery of a base station in sites that do not have access to permanent power supply.
Georges Nassif, Catherine Gloaguen, Philippe Martins
Indoor coverage is a major challenge for 5G millimeter waves (mmWaves). In this paper, we address this problem through a novel theoretical framework that combines stochastic indoor environment modeling with advanced physical propagation simulation. This approach is particularly adapted to investigate indoor-to-indoor 5G mmWave propagation. Its system implementation, so-called iGeoStat, generates parameterized typical environments that account for the indoor spatial variations, then simulates radio propagation based on the physical interaction between electromagnetic waves and material properties. This framework is not dedicated to a particular environment, material, frequency or use case and aims to statistically understand the influence of indoor environment parameters on mmWave propagation properties, especially coverage and path loss. Its implementation raises numerous computational challenges that we solve by formulating an adapted link budget and designing new memory optimization algorithms. The first simulation results for two major 5G applications are validated with measurement data and show the efficiency of iGeoStat to simulate multiple diffusion in realistic environments, within a reasonable amount of time and memory resources. Generated output maps confirm that diffusion has a critical impact on indoor mmWave propagation and that proper physical modeling is of the utmost importance to generate relevant propagation models.
Anaïs Vergne, Ian Flint, Laurent Decreusefond, Philippe Martins
In this paper, we present an algorithm for the recovery of wireless networks after a disaster. Considering a damaged wireless network, presenting coverage holes or/and many disconnected components, we propose a disaster recovery algorithm which repairs the network. It provides the list of locations where to put new nodes in order to patch the coverage holes and mend the disconnected components. In order to do this we first consider the simplicial complex representation of the network, then the algorithm adds supplementary vertices in excessive number, and afterwards runs a reduction algorithm in order to reach an optimal result. One of the novelty of this work resides in the proposed method for the addition of vertices. We use a determinantal point process: the Ginibre point process which has inherent repulsion between vertices, and has never been simulated before for wireless networks representation. We compare both the determinantal point process addition method with other vertices addition methods, and the whole disaster recovery algorithm to the greedy algorithm for the set cover problem.
Anne Josiane Kouam, Aline Carneiro Viana, Philippe Martins, Cedric Adjih, Alain Tchana
Despite their widespread adoption, cellular networks face growing vulnerabilities due to their inherent complexity and the integration of advanced technologies. One of the major threats in this landscape is Voice over IP (VoIP) to GSM gateways, known as SIMBox devices. These devices use multiple SIM cards to route VoIP traffic through cellular networks, enabling international bypass fraud with losses of up to $3.11 billion annually. Beyond financial impact, SIMBox activity degrades network performance, threatens national security, and facilitates eavesdropping on communications. Existing detection methods for SIMBox activity are hindered by evolving fraud techniques and implementation complexities, limiting their practical adoption in operator networks.This paper addresses the limitations of current detection methods by introducing SigN , a novel approach to identifying SIMBox activity at the cellular edge. The proposed method focuses on detecting remote SIM card association, a technique used by SIMBox appliances to mimic human mobility patterns. The method detects latency anomalies between SIMBox and standard devices by analyzing cellular signaling during network attachment. Extensive indoor and outdoor experiments demonstrate that SIMBox devices generate significantly higher attachment latencies, particularly during the authentication phase, where latency is up to 23 times greater than that of standard devices. We attribute part of this overhead to immutable factors such as LTE authentication standards and Internet-based communication protocols. Therefore, our approach offers a robust, scalable, and practical solution to mitigate SIMBox activity risks at the network edge.
Xiao Fei, Philippe Martins, Jialiang Lu
The classification of fifth-generation New-Radio (5G-NR) mobile network traffic is an emerging topic in the field of telecommunications. It can be utilized for quality of service (QoS) management and dynamic resource allocation. However, traditional approaches such as Deep Packet Inspection (DPI) can not be directly applied to encrypted data flows. Therefore, new real-time encrypted traffic classification algorithms need to be investigated to handle dynamic transmission. In this study, we examine the real-time encrypted 5G Non-Standalone (NSA) application-level traffic classification using physical channel records. Due to the vastness of their features, decision-tree-based gradient boosting algorithms are a viable approach for classification. We generate a noise-limited 5G NSA trace dataset with traffic from multiple applications. We develop a new pipeline to convert sequences of physical channel records into numerical vectors. A set of machine learning models are tested, and we propose our solution based on Light Gradient Boosting Machine (LGBM) due to its advantages in fast parallel training and low computational burden in practical scenarios. Our experiments demonstrate that our algorithm can achieve 95% accuracy on the classification task with a state-of-the-art response time as quick as 10ms.
Luis David Alvarez Corrales, Anastasios Giovanidis, Philippe Martins
Cooperation in cellular networks has been recently suggested as a promising scheme to improve system performance. In this work, clusters are formed based on the Mutually Nearest Neighbour relation, which defines which stations cooperate in pair and which do not. When node positions follow a Poisson Point Process (PPP) the performance of the original clustering model can be approximated by another one, formed by the superposition of two PPPs (one for the singles and one for the pairs) equipped with adequate marks. This allows to derive exact expressions for the network coverage probability under two user-cluster association rules. Numerical evaluation shows coverage gains from different signal cooperation schemes that can reach up to 15% compared to the standard non-cooperative network coverage. The analysis is general and can be applied to any type of cooperation or coordination between pairs of transmitting nodes.
Hamza Adrat, Laurent Decreusefond, Philippe Martins
Reconfigurable Intelligent Surfaces (RIS) are currently considered for adoption in future 6G stantards. ETSI and 3GPP have started feasibility and performance investigations of such a technology. This work proposes an analytical model to analyze RIS performance. It relies on a simple street model where obstacles and mobile units are all aligned. RIS is positioned onto a building parallel to the road. The coverage probability in presence of obstacles and concurrent communications is then computed as a performance criteria.
Anaïs Vergne, Laurent Decreusefond, Philippe Martins
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.
Feng Yan, Anais Vergne, Philippe Martins, Laurent Decreusefond
Homology theory provides new and powerful solutions to address the coverage problems in wireless sensor networks (WSNs). They are based on algebraic objects, such as Cech complex and Rips complex. Cech complex gives accurate information about coverage quality but requires a precise knowledge of the relative locations of nodes. This assumption is rather strong and hard to implement in practical deployments. Rips complex provides an approximation of Cech complex. It is easier to build and does not require any knowledge of nodes location. This simplicity is at the expense of accuracy. Rips complex can not always detect all coverage holes. It is then necessary to evaluate its accuracy. This work proposes to use the proportion of the area of undiscovered coverage holes as performance criteria. Investigations show that it depends on the ratio between communication and sensing radii of a sensor. Closed-form expressions for lower and upper bounds of the accuracy are also derived. For those coverage holes which can be discovered by Rips complex, a homology-based distributed algorithm is proposed to detect them. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.5%. Upper bound performance depends on the ratio of communication and sensing radii. Simulations also show that the algorithm can localize about 99% coverage holes in about 99% cases.
Feng Yan, Philippe Martins, Laurent Decreusefond
Homology theory has attracted great attention because it can provide novel and powerful solutions to address coverage problems in wireless sensor networks. They usually use an easily computable algebraic object, Rips complex, to detect coverage holes. But Rips complex may miss some coverage holes in some cases. In this paper, we investigate homology-based coverage hole detection for wireless sensor networks on sphere. The situations when Rips complex may miss coverage holes are first presented. Then we choose the proportion of the area of coverage holes missed by Rips complex as a metric to evaluate the accuracy of homology-based coverage hole detection approaches. Three different cases are considered for the computation of accuracy. For each case, closed-form expressions for lower and upper bounds of the accuracy are derived. Simulation results are well consistent with the analytical lower and upper bounds, with maximum differences of 0.5% and 3% respectively. Furthermore, it is shown that the radius of sphere has little impact on the accuracy if it is much larger than communication and sensing radii of each sensor.
Laurent Decreusefond, Philippe Martins, Thanh-Tung Vu
This paper introduces a general theoretical framework to analyze noise limited networks. More precisely, we consider two homogenous Poisson point processes of base stations and users. General model of radio signal propagation and effect of fading are also considered. The main difference of our model with respect to other existing models is that a user connects to his best servers but not necessarily the closest one. We provide general formula for the outage probability. We study functionals related to the SNR as well as the sum of these functionals over all users per cell. For the latter, the expectation and bounds on the variance are obtained.
Luis David Alvarez Corrales, Anastasios Giovanidis, Philippe Martins, Laurent Decreusefond
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.