This paper proposes a cascade blockage model for analyzing the vision that a user has of a wireless network. This model, inspired by the classical multiplicative cascade models, has a radial structure meant to analyze blockages seen by the receiver at the origin in different angular sectors. The main novelty is that it is based on the geometry of obstacles and takes the joint blockage phenomenon into account. We show on a couple of simple instances that the Laplace transforms of total interference satisfies a functional equation that can be solved efficiently by an iterative scheme. This is used to analyze the coverage probability of the receiver and the effect of blockage correlation and penetration loss in both dense and sparse blockage environments. Furthermore, this model is used to investigate the effect of blockage correlation on user beamforming techniques. Another functional equation and its associated iterative algorithm are proposed to derive the coverage performance of the best beam selection in this context. In addition, the conditional coverage probability is also derived to evaluate the effect of beam switching. The results not only show that beam selection is quite efficient for multi-beam terminals, but also show how the correlation brought by blockages can be leveraged to accelerate beam sweeping and pairing.

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 macrocell 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 DTDD 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.

Multi-antenna technologies such as massive Multiple-Input Multiple-Output (massive MIMO) and beamforming are key features to enhance performance, in terms of capacity and coverage, by using a large number of antennas intelligently. With the upcoming 5G New Radio (NR), FD-MIMO (Full Dimension MIMO) will play a major key role. FD-MIMO consists in arranging a large number of antennas in a 2D array, which enables to use 3D beamforming i.e., beamforming in both horizontal and vertical dimensions. The present paper provides a 3D beamforming model where beam steering depends on the random spatial distribution of users. We attempt to derive some analytical results regarding the probability distribution of antenna beamforming radiation pattern. Also, through system level simulations, we show how 3D beamforming can reduce interference impact, compared to the traditional 2D beamforming, and enhances system performance in terms of the coverage probability and users throughput.

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.

Self-Organizing Networks (SON) functions have already proven to be useful for network operations. However, a higher automation level is required to make a network enabled with SON capabilities respond as a whole to the operator's objectives. For this purpose, a Policy Based SON Management (PBSM) layer has been proposed to manage the deployed SON functions. In this paper, we propose to empower the PBSM with cognition capability in order to manage efficiently SON enabled networks. We focus particularly on the implementation of such a Cognitive PBSM (C-PBSM) on a large scale network and propose a scalable approach based on distributed Reinforcement Learning (RL): RL agents are deployed on different clusters of the network. These clusters should be defined in such a way that the RL agents can learn independently. As the interaction between these clusters may evolve in time due for instance to traffic dynamics, we propose a flexible implementation of this C-PBSM framework with dynamic clustering to adapt to network's evolutions. We show how this flexible implementation is rendered possible under Software Defined Networks (SDN) framework. We also assess the performance of the proposed distributed learning approach on an LTE-A simulator.

Policy Based SON Management (PBSM) is the process of orchestrating the deployed Self-Organized Network (SON) functions, so that the network responds as a whole to the operator objectives. This process is based on the configuration of the SON functions in order to steer their actions in the network towards certain operator objectives. The PBSM ensures an automated translation of these objectives into configurations of the SON functions. An approach has been recently proposed to empower the PBSM with cognitive capabilities (C-PBSM), using a Multi-Armed Bandit algorithm, namely the UCB1. The C-PBSM learns the optimal SON configurations based on network feedback. In this paper we propose an alternative approach, based on the LinUCB algorithm, that is able to learn the optimal SON configuration much faster than the previous approach. The speed of convergence is a critical factor that has to be thoroughly considered in the deployment of online learning processes. Results are shown using an LTE-A simulator that considers real-like network topology and parameters, and accurate ray tracing based propagation.

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.

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.

Self organized networks has been one of the first concrete implementations of autonomic network management concept. Currently, several Self-Organizing-Network (SON) functions are developed by Radio Access Network (RAN) vendors and already deployed in many networks all around the world. These functions have been designed independently to replace different operational tasks. The concern of making these functions work together in a coherent manner has been studied later in particular in SEMAFOUR project where a Policy Based SON Management (PBSM) framework has been proposed to holistically manage a SON enabled network, namely a network with several individual SON functions. Enriching this PBSM framework with cognition capability is the next step towards the realization of the initial promise of SON concept: a unique self-managed network that responds autonomously and efficiently to the operator high level requirements and objectives. This paper proposes a cognitive PBSM system that enhances the SON management decisions by learning from past experience using Q-learning approach. Our approach is evaluated by simulation on a SON enabled Long-Term Evolution Advanced (LTE-A) network with several SON functions. The paper shows that the decisions are enhanced during the learning process and discusses the implementation options of this solution.

Many tasks in current mobile networks are automated through Self-Organizing Networks (SON) functions. The actual implementation consists in a network with several SON functions deployed and operating independently. A Policy Based SON Manager (PBSM) has been introduced to configure these functions in a manner that makes the overall network fulfill the operator objectives. Given the large number of possible configurations (for each SON function instance in the network), we propose to empower the PBSM with learning capability. This Cognitive PBSM (C-PBSM) learns the most appropriate mapping between SON configurations and operator objectives based on past experience and network feedback. The proposed learning algorithm is a stochastic multi-armed bandit, namely the UCB1. We evaluate the performances of the proposed C-PBSM on an LTE-A simulator. We show that it is able to learn the optimal SON configuration and quickly adapts to objective changes.

In this paper, we introduce a distributed load balancing algorithm for cellular networks. Traffic load in cellular networks is sometimes unbalanced. Some cells are overloaded, while others remain free. Simplicial homology is a tool from algebraic topology that allows to compute the coverage of a network by using only simple matrix computations. Our algorithm, which is based on simplicial homology, controls the transmission power of each cell in the network, not only to satisfy the coverage constraint, but also to redirect users from the overloaded cells to the underloaded ones. As a result, the traffic load of the cellular network is more balanced. The simulation results show that this algorithm improves the capacity of the whole network by 2.3% when the user demand is fast varying.

In this paper, we introduce a distributed algorithm to compute the Čech complex. This algorithm is aimed at solving the coverage problems in self organized wireless networks. The complexity to compute the minimal Čech complex that gives information about coverage and connectivity of the network is O(n2), where n is the average number of neighbors of each cell. An application based on the distributed computation of the Čech complex, which is aimed at optimizing the wireless network for energy saving, is also proposed. This application also has polynomial complexity. The performance of the proposed algorithm and its application are evaluated. The simulation results show that the distributed computation of the Čech complex provides a consistent outcome with the one obtained by the centralized computation that is introduced in [6], while requires a much shorter calculation time. The optimized coverage saves 65% of the total transmission power, while also keeps the maximal coverage for the network.

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.

In this paper, we introduce a centralized algorithm which constructs the generalized Cech complex. The generalized Cech complex represents the topology of a wireless network whose cells are different in size. This complex is useful to address a wide variety of problems in wireless networks such as: boundary holes detection, disaster recovery or energy saving. We have shown that our algorithm constructs the minimal generalized Cech complex, which satisfies the requirements of these applications, in polynomial time.

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.

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 paper, 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.

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 Čech complex and Rips complex. Čech 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 Čech 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 cannot 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 that 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.

In this paper, we proposed a general analytical model for mobile relay scenario using stochastic geometry approach. By applying different parameters into this general model, the Cumulative Distribution Function of the SINR and the average achievable rate on different links in both traditional mode and relay mode can be obtained. According to numerical results, we observed that penetration loss between outdoor and in-vehicle is a key factor to decide whether mobile relay could bring data rate gain into the system. When penetration loss is large, mobile relay could bring considerable data rate gain to embedded UEs inside the bus.

In this paper, the mobile deployment and subchannel number distribution are estimated for different values of Anisotropy Ratio (AR) and Mean Building Block Area (MBBA) pairs. This work proposes to model city maps with a particular family of random tessellations: Crack STIT tessellation to generate realistic city maps with a reduced number of parameters: i.e., AR and MBBA. The model is used to compute the received power map and further identify the impact of terrain topology parameters on wireless propagation. Simulations results show that mean mobile number and mean sub-channel number (SCN) both decrease with increasing MBBA following a power law dependency. The variance of SCN distribution increases with increasing MBBA by a potential exponential law. However, AR does not show obvious and strong impact on mobile and SCN. For different value of MBBA, AR leads to different mobile number and sub-channel evolutions gradually. Furthermore, the evolution of SCN does not monotonically decrease with increasing MBBA at 95% cumulative density function (CDF) bound of SCN distribution. Unlike the mean value (50% CDF bound), the SCN at 95% bound increases back for very large MBBA. The results are particularly promising for providing a parametric relation between mobile deployment/SCN and terrain topology. This considerably simplifies the radio estimation and planning of wireless networks.

Considering a damaged wireless network, presenting coverage holes or disconnected components, we propose a disaster recovery algorithm repairing the network. It provides the list of locations where to put new nodes 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 nodes in excessive number, and afterwards runs a reduction algorithm in order to reach a unimprovable result. One of the novelty of this work resides in the proposed method for the addition of nodes. We use a determinantal point process: the Ginibre point process which has inherent repulsion between vertices, which simulation is new in wireless networks application. 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.

This work proposes to model city maps with a particular family of random tessellations: Crack STIT tessellations. This family of tessellations allow the generation of realistic city maps with a reduced number of parameters: the Anisotropy Ratio (ξ) and the Mean Building Block Area (MBBA). These city models are then used as input to a 3D ray tracing simulator to compute received power distributions. The objective of this investigation is to identify the impact of random tessellation parameters on wireless propagation. For this purpose, path loss exponent γ is estimated from received power distributions obtained by simulation for different values of ξ and MBBA pairs. Simulations results clearly show a linear dependency between path loss γ, ξ and MBBA. Path loss γ increases with ξ while it decreases with MBBA. Furthermore the evolution of the surface occupation ratio between outdoor and overall surface is also investigated. This ratio is named Free Area Ratio (FAR) in the sequel. It decreases with MBBA according to a power law. The results obtained are particularly promising as they provide a parametric relation between path loss exponent γ and terrain topology. This considerably simplifies the radio planning and dimensionning process of cellular networks.

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 case when Rips complex may miss coverage holes is first identified. 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. Closed-form expressions for lower and upper bounds of the accuracy are derived. Asymptotic lower and upper bounds are also investigated when the radius of sphere tends to infinity. 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.

This work gives an analytical model for the radio dimensioning of uplink Long Term Evolution (LTE) systems. It relies on the computation of an upper bound of the outage probability, the outage being defined by an insufficient number of Resource Blocks (RBs) for serving all the users in the network. The number of RBs, that has to be dedicated to each communication in order to ensure its Quality of Service (QoS), depends on the transmitting users random positions and their radio conditions. Throughout this paper, this number of RBs is assimilated as a marked Poisson point process. The upper bound of the outage probability is computed for different service classes according to the users throughput requirements, for the fair and the opportunistic RB allocation algorithms. Once validated by Monte-Carlo simulations, it estimates the necessary cells bandwidth. Finally, we apply these results to LTE standard bandwidths and give the associated resulting outage probabilities. Our work shows that the analytical upper bound of the outage probability helps the radio system planners to decrease the networks outage probability to a desired threshold at the price of a slight and controlled radio over dimensioning.

In this paper, we aim at reducing power consumption in wireless sensor networks by turning off supernumerary sensors. Random simplicial complexes are tools from algebraic topology which provide an accurate and tractable representation of the topology of wireless sensor networks. Given a simplicial complex, we present an algorithm which reduces the number of its vertices, keeping its homology (i.e. connectivity, coverage) unchanged. We show that the algorithm reaches a Nash equilibrium, moreover we find both a lower and an upper bounds for the number of vertices removed, the complexity of the algorithm, and the maximal order of the resulting complex for the coverage problem. We also give some simulation results for classical cases, especially coverage complexes simulating wireless sensor networks.

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 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 area of undiscovered coverage holes per unit of surface as performance criteria. Investigations show that it depends on the ratio of communication and sensing ranges of each sensor. Closed form expressions for lower and upper bounds of the accuracy are also derived. Simulation results are consistent with the proposed analytical lower bound, with a maximum difference of 0.4%. Upper bound performance depends on the ratio of communication and sensing ranges.

Coverage is considered as an important measure of quality of service provided by a wireless sensor network (WSN). Yet, coverage holes may appear in the target field due to random deployment, depletion of sensor power or sensor destruction. Discovering the boundaries of coverage holes is important for patching the sensor network. In this paper, we adopt two types of simplicial complexes called Cech complex and Rips complex to capture coverage holes and classify coverage holes to be triangular and non-triangular. A distributed algorithm with only connectivity information is proposed for non-triangular holes detection. Some hole boundary nodes are found first and some of them initiate the process to detect coverage holes. Simulation results show that the area percentage of triangular holes is always below 0.03% when the ratio between communication radius and sensing radius of a sensor is two. It is also shown that our algorithm can discover most non-triangular coverage holes.

More and more data mining algorithms are applied to a large number of long time series issued by many distributed sensors. The consequence of the huge volume of data is that data warehouses often contain asynchronous time series, i.e. the values have been sampled and are not anymore observed at the same instants. This is a problem when applying data mining algorithms to such asynchronous time series. The standard way to solve this problem is to interpolate intermediate points. We present here two new interpolation approaches which take into account the knowledge of the integral of the time series between two points. The first approach is naive and uses the history of slope values. The second approach is stochastic and provides a confidence interval of interpolated values. The two methods have been assessed experimentally on a real dataset of electric power consumption time series issued from smart meters.

Dual transfer mode (DTM) has been defined by 3GPP for EGPRS networks. It provides simultaneous usage of GSM and GPRS services without requiring a full fledged GPRS class A terminal. DTM relies on the usage of half rate coders that make it possible to share a timeslot between a voice call and a data session. The data session can be extended to more time slots if necessary. This work examines an optimal policy adapted for resource allocation in a cell providing DTM capability. At the end of one part of a DTM call, the policy decides whether the released half slot should be reallocated to an existing data session or not. In earlier work, this optimal policy was proven to be a threshold strategy. The optimal policy is compared with the two policies where the same decision is taken regardless of the state of the system. Its performance is evaluated with respect to system load and configuration parameters