Low Earth orbit (LEO) satellite systems experience significant Doppler effects due to high mobility. While Doppler shifts can be largely compensated, residual frequency uncertainty induces a structured form of channel uncertainty that can limit achievable rates. We model this effect using a block-fading channel of the form $ \mathbf{H} = \mathbf{F} + s \mathbf{G} $, where $s$ is an unknown scalar random parameter. We first study this model in a general $N\times N$ MIMO setting. For this channel, we derive achievable rate lower bounds based on explicit transmission schemes and capacity upper bounds using a duality approach. We study Gaussian signaling and propose a practical superposition scheme with subspace alignment (SN) and successive interference cancellation, where a coarse-layer stream serves as an implicit pilot for decoding refined-layer data. We characterize asymptotic capacity in the near-coherent and high-SNR regimes, and show via Doppler-OFDM simulations that the proposed SN scheme achieves near-optimal rates with low complexity.

In this paper, we consider multiple Unmanned Aerial Vehicles (UAV) serving as flying Base Stations (BS) of a wireless network and the problem of jointly optimizing their trajectory with respect to a running cost. This cost accounts for the consumed energy related to the vehicle velocity and for the amount of data traffic collected or served by the UAVs. The data traffic is supposed to be spatially distributed around a hotspot and is equivalent to a potential in Physics. Using the principles of Lagrangian Mechanics, we derive a scalable algorithm able to optimize the trajectory of thousands of drones in milliseconds on a off-the-shelf laptop. Our model allows to control the distance between the UAVs to avoid collisions by using a coupling between the drone trajectories.

We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given initial location to a final position within a given duration and serves the traffic on its way. The problem consists in finding the optimal trajectory that minimizes a certain cost depending on the velocity and on the amount of served traffic. We formulate the problem using the framework of Lagrangian mechanics. We derive closed-form formulas for the optimal trajectory when the traffic intensity is quadratic (single-phase) using Hamilton-Jacobi equations. When the traffic intensity is bi-phase, i.e. made of two quadratics, we provide necessary conditions of optimality that allow us to propose a gradient-based algorithm and a new algorithm based on the linear control properties of the quadratic model. These two solutions are of very low complexity because they rely on fast convergence numerical schemes and closed form formulas. These two approaches return a trajectory satisfying the necessary conditions of optimality. At last, we propose a data processing procedure based on a modified K-means algorithm to derive a bi-phase model and an optimal trajectory simulation from real traffic data.

This paper studies the coverage performance of device-to-device (D2D) communication under the millimeter wave (mmW) spectrum. The transmitter and receiver sides of users are equipped with directional antennas and adopt beamforming (BF). By considering a truncated Gaussian misalignment assumption, we derive computationally tractable expressions of the conditional rate coverage probability's moments as a function of the number of antenna elements. The Beta approximation of the rate meta-distribution is obtained based on the first and the second moment. The numerical simulations confirm our analytical results. They show that the coverage performance can deteriorate significantly due to misalignment. Furthermore, an optimal number of antenna elements must be chosen to get the best coverage. In addition, there exists an optimal number of antennas which maximizes the number of users who satisfy the reliability constraints. This optimal value is a function of the reliability threshold.

In this paper, we investigate the beam misalignment impacts of a dynamic device-to-device (D2D) communication model, where both transmitters and receivers adopt beamforming (BF) by using uniform linear array (ULA). A time continuous dynamic model is adopted for this network. We use tools of stochastic geometry and the Miyazawa rate conversation law to analyse the stability condition of such a network. An analytical expression of the critical arrival rate is given under a uniform or truncated Gaussian alignment error assumption. In contrast to our previous result, where the beam alignment is perfect, our analytical and numerical results show that, if the beam alignment is not perfect, the critical arrival rate can no longer increase without limit as a function of the number of antenna elements. Closed-form expressions of the upper bounds for critical arrival rates are given for both the uniform and the truncated Gaussian misalignment models.

Full Duplex (FD) in cellular networks is expected to increase the cell spectral efficiency. However, while the downlink (DL) spectral efficiency (SE) increases with FD, the uplink (UL) SE decreases because of the Base Station to Base Station (BS) interference. In this paper, assuming a three-node model, we propose a method based on Successive Interference Cancellation (SIC) to reduce the BS-to-BS interference present in FD cellular networks. The approach consists in coordinating BSs to enable the decoding and the suppression of undesired signals that impair uplink transmissions. We analyze both distributed and Centralized Radio Access Networks (CRAN) architectures. Stochastic geometry is used to derive the coverage probability and mean data rate of the proposed scheme. In the distributed scenario, the FD UL average data rate is increased by 25% with our solution compared to a classical FD network, while our FD scheme still outperforms Half-Duplex (HD) on the DL. In the centralized scenario, our solution outperforms HD by 10% and classical FD by 78% on the UL, while preserving classical FD gains on the DL.

In this paper, we consider a dynamic device-to-device (D2D) communication model where transmitters and receivers have multiple antennas and adopt beamforming (BF). A continuous spatio-temporal model for the wireless network is analyzed, which combines a spatial stochastic point process and a dynamic birth-death process. We model BF by using a uniform linear array (ULA) and extend the result of Sankararaman and Baccelli on the stability condition of such a network. We show that the critical arrival rate increases with the number of antennas at the transmitter and the receiver.

Ambient backscatter communications have been identified for ultra-low energy wireless communications. Indeed, a tag can send a message to a reader without emitting any wave and without battery, simply by backscattering the waves generated by a source. In the simplest implementation of such a system, the tag sends a binary message by oscillating between two states and the reader detects the bits by comparing the two distinct received powers. In this paper, for the first time, we propose to study an ambient backscatter communication system, in the presence of a diffusing surface, a simple flat panel that diffuses in all directions. We establish the analytical closed form expression of the power contrast in the presence of the surface. We show that the diffusing surface improves the power contrast. Moreover our approach allows us to express the contrast to noise ratio, and therefore to establish the BER performance. Furthermore, we derive the optimum source transmit power for a given target power contrast. This makes it possible to quantify the amount of energy that can be saved at the source side, thanks to the diffusing surface.

Despite the huge number of contributions dealing with the evaluation of cellular networks performance, tackling with more and more complex systems including multi-tier networks or MIMO systems, the fundamental limits in terms of capacity in an information theory sense is not known for these networks. Stochastic geometry helped doing a step forward, relying on Palm theory and providing coverage statistic at the network scale. However, this statistic is not sufficient to establish a fundamental limit, namely to characterise a Shannon capacity region of the network. In this paper, we propose a new approach exploiting the cell capacity of the Spatial Continuum Broadcast Channel (SCBC) recently introduced for an isolated cell. The network capacity is linked to the cells' geometry statistics in a Voronoi tessellation. The fundamental limit is characterised by the minimal average cell power required in a network modelled as a Point Process (PP) to achieve a desired rate distribution. A direct relation is established between this minimum average power and the partial area statistics of the cells geometry, which constitute a sufficient statistic. Our approach is validated through Monte-Carlo simulations.

Full-duplex (FD) is a principle in which a transceiver can receive and transmit on the same time-frequency radio resource. Assuming perfect self-interference cancellation (self-IC), FD can potentially double the spectral efficiency (SE) of a given point-to-point communication. However in cellular networks, we may be far from this upper bound due to base stations (BSs) and users interference. In particular, even if the overall SE is improved, the uplink (UL) performance is degraded compared to a traditional half-duplex (HD) system. In this paper, we propose and evaluate a new duplex-switching (DS) policy in which BSs can adopt FD- or HD-mode according to the position of their scheduled users. This system is analyzed using stochastic geometry in terms of average SE (ASE) and signal-to-interference-plus-noise ratio (SINR). The proposed scheme allows to trade-off the downlink (DL) for the UL performance when comparing to a FD scenario. In terms of cell performance (UL+DL), our DS policy even outperform both HD and FD systems when the parameters are optimized.

In this paper, we develop a powerful analytical model of wireless network with Superposition Coding (SC), also referred to as Non Orthogonal Multiple Access (NOMA). This model allows to establish a closed form expression of the minimum power a base station need to transmit, for a user to achieve a given SINR (signal to interference plus noise ratio) whatever its location over the area covered by the base station. It moreover allows to establish a closed form expression of the minimum total transmit power of a base station. These closed form expressions allow to establish performance of wireless networks, by minimizing the base stations transmit powers. As an application, we show that these closed form expressions allow to quantify the energetic performance, spectral efficiency, total throughput and the coverage of a BS, in a simple and quick way.

Device-to-device (D2D) communication and beamforming technology are identified as promising innovations in the next generation wireless ecosystem. D2D technology allows direct communication between devices, which will be a key technology to meet the 5G's requirements in terms of delay and throughput. In this regard, resource allocation and interference management are two major challenges. In this paper we present a centralized architecture to manage discovery phase for D2D communications in 5G. Furthermore, we propose the three dimensional (3D) beamforming technique as a way to manage interferences when D2D communication is used. Numerical evaluation shows improvement in terms of outage probability, reachable throughput and energy consumption.

Multicast/Broadcast Single Frequency Network (MBSFN) is envisioned to be a key technology for business and mission critical communications. The need arises to define simple and efficient dimensioning rules for such networks. The Signal to Interference plus Noise Ratio (SINR) is an important key performance parameter since other metrics such as outage probability and capacity can be deduced from it. In this work, we propose an analytical model to derive an approximate closed-form formula of the SINR in a MBSFN. Our model takes into account Inter-Symbol Interference (ISI) due to the different propagation delays between the User Equipment (UE) and its serving evolved Nodes-B (eNBs). The comparison with Monte Carlo simulations shows that our approach provides accurate results when shadowing standard deviation is low. When shadowing is highly variable, our model, while less accurate, outperforms the traditional approach based on Fenton-Wilkinson. This phenomenon is due to the fact that several eNBs serve the same UE so that shadowing on every individual link compensate.

The envisioned Internet of Things (IoT) will involve a massive deployment of objects connected through wireless cells. While commercial solutions are already available, the fundamental limits of such networks in terms of node density, achievable rates or reliability are not known. To address this question, this paper uses a large scale Multiple Access Channel (MAC) to model IoT nodes randomly distributed over the coverage area of a unique base station. The traffic is represented by an information rate spatial density ρ(x). This model, referred to as the Spatial Continuum Multiple Access Channel, is defined as the asymptotic limit of a sequence of discrete MACs. The access capacity region of this channel is defined as the set of achievable information rate spatial densities achievable with vanishing transmission errors and under a sum-power constraint. Simulation results validate the model and show that this fundamental limit theoretically achievable when all nodes transmit simultaneously over an infinite time, may be reached even with a relatively small number of simultaneous transmitters (typically around 20 nodes) which gives credibility to the model. The results also highlight the potential interest of non-orthogonal transmissions for IoT uplink transmissions when compared to an ideal time sharing strategy.

In multi-rate IEEE 802.11 WLANs, the traditional user association based on the strongest received signal and the well-known anomaly of the MAC protocol can lead to overloaded access points (APs), and poor or heterogeneous performance. Our goal is to propose an alternative game-theoretic approach for association. We model the joint resource allocation and user association as a matching game with complementarities and peer effects consisting of selfish players solely interested in their individual throughputs. Using recent game-theoretic results, we first show that various resource sharing protocols actually fall in the scope of the set of stability-inducing resource allocation schemes. The game makes an extensive use of the Nash bargaining and some of its related properties that allow controlling the incentives of the players. We show that the proposed mechanism can greatly improve the efficiency of 802.11 with heterogeneous nodes and reduce the negative impact of peer effects such as its MAC anomaly. The mechanism can be implemented as a virtual connectivity management layer to achieve efficient APs-user associations without modification of the MAC layer.

This paper proposes a new model called spatial continuum asymmetric channels to study the channel capacity region of asymmetric scenarios in which either one source transmits to a spatial density of receivers or a density of transmitters transmit to a unique receiver. This approach is built upon the classical broadcast channel (BC) and multiple access channel (MAC). For the sake of consistency, the study is limited to Gaussian channels with power constraints and is restricted to the asymptotic regime (zero-error capacity). The reference scenario comprises one base station in Tx or Rx mode, a spatial random distribution of nodes (resp. in Rx or Tx mode) characterized by a probability spatial density of users u(x) where each of them requests a quantity of information with no delay constraint, thus leading to a requested rate spatial density ρ(x). This system is modeled as an ∞-user asymmetric channel (BC or MAC). To derive the fundamental limits of this model, a spatial discretization is first proposed to obtain an equivalent BC or MAC. Then, a specific sequence of discretized spaces is defined to refine infinitely the approximation. Achievability and capacity results are obtained in the limit of this sequence while the access capacity region DΩ(Pm) is defined as the set of requested rates spatial densities ρ(x) that are achievable with a transmission power Pm. The uniform capacity defined as the maximal symmetric achievable rate is also computed.

In this paper we analyze the performance of wireless networks by using stratospheric balloons equipped by base stations (BS). We show that such a solution can be interesting in terms of performance and coverage. Considering a high altitude wireless network, we first establish an analytical expression of the Signal to Interference plus Noise Ratio (SINR) received by a user equipment (UE) located on the ground. We establish the cumulative distribution function (CDF) of the SINR, since it allows an accurate evaluation of the performance and the quality of service (QoS). We compare different deployment scenarios of high altitude balloons. This allows us to analyze and to quantify the impact of the use of balloons, in terms of coverage and performance for low dense population wide areas.

This paper proposes an analytical study of 3D beamforming for 5G wireless networks. In a first step, we develop a three dimensional analytical beamforming model for wireless networks. This 3D model enables in particular, to focus the analyzes on the specific zone covered by an antenna beam. This 3D beamforming model is validated by comparison with Monte Carlo simulations: the two approaches give very close SINR (Signal to Interference plus Noise Ratio) values. Thanks to this model, it becomes easy to quantify the impact of 3D beamforming in terms of performance, quality of service and coverage in a future 5G wireless network. Different scenarios are presented, which quantify the impact of the 3D beamforming wireless network and show the accuracy of the model. The proposed model is then used to compare 2D and 3D beamforming and to show the interest of exploiting the third dimension.

Relay nodes-enhanced architectures are deemed a viable solution to enhance coverage and capacity of nowadays cellular networks. Besides a number of desirable features, these architectures reduce the average distance between users and network nodes, thus allowing for battery savings for users transmitting on the uplink. In this paper, we investigate the extent of these savings, by optimizing relay nodes deployment in terms of uplink energy consumption per transmitted bit, while taking into account a minimum uplink average user delay that has to be guaranteed. A novel performance evaluation framework for uplink relay networks is first proposed to study this energy-delay trade-off. A simulated annealing is then run to find an optimized relay placement solution under a delay constraint; exterior penalty functions are used in order to deal with a difficult energy landscape, in particular when the constraint is tight. Finally, results show that relay nodes deployment consistently improve users uplink energy efficiency, under a wide range of traffic conditions and that relays are particularly efficient in non-uniform traffic scenarios.

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.

We are interested in high data rates internet access, by the mean of LTE based wireless networks. In the aim to improve performance of wireless networks, we propose an approach focused on the use of UE equipped by directional receiving antennas. Indeed, these antennas allow to mitigate the interference and to improve the link budget. Therefore, the Signal to Interference plus Noise Ratio (SINR) can be improved, and consequently the performance and quality of service (QoS), too. We establish the analytical expression of the SINR reached by a user with directional antenna, whatever its location. This expression shows that directional antennas allow an improvement of the SINR, and to quantify it. We develop different scenarios to compare the use of directional antennas instead of omnidirectional ones. They allow to quantify the impact of directional antennas in terms of performance and QoS.

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.

In this paper, we address the problem of optimally placing relay nodes in a cellular network with the aim of maximizing cell capacity. In order to accurately model interference, we use a dynamic framework, in which users arrive at random time instants and locations, download a file and leave the system. A fixed point equation is solved to account for the interactions between stations. We also propose an extension of a fluid model to relay based cellular networks. This allows us to obtain quick approximations of the Signal to Interference plus Noise Ratio (SINR) that are very close to 3GPP LTE-A guideline results in terms of SINR distribution. We then use these formulas to develop a dedicated Simulated Annealing (SA) algorithm, which adapts dynamically the temperature to energy variations and uses a combination of coarse and fine grids to accelerate the search for an optimized solution. Simulations results are provided for both in-band and out-of-band relays. They show how relays should be placed in a cell in order to increase the capacity in case of uniform and non-uniform traffic. The crucial impact of the backhaul link is analyzed for in-band relays. Insights are given on the influence of shadowing.

An important topic in performance evaluation of wireless networks is the modeling of inter-cell interference, to predict the distribution of the Signal to Interference plus Noise Ratio (SINR) in the network. The classical hexagonal model is generally intractable and requires extensive numerical calculations. Two approaches have been shown to produce tractable, closed-form formulas: Poisson networks (the interfering Base Stations (BSs) locations form a Poisson process) and fluid networks (the interfering BSs are replaced by a continuum of infinitesimal interferers). Compared to network measurements, the fluid model is known to be optimistic, while the Poisson model is pessimistic. We show that fluid networks are equivalent to dense Poisson networks. We show a Central Limit Theorem (CLT)-like result: the difference of interference predicted by the two models is Gaussian for dense networks with a known mean and variance. These results provide a justification of the fluid model. Furthermore, there is an interesting duality: for dense networks, all results proven for Poisson networks hold for fluid networks and vice-versa.

In this paper, we deal with a dynamic and stochastic admission control and mobile association problem in an heterogeneous wireless network. We extend the usual problem by adding mobility features described by a Markov Modulated Poisson Process. The aim is to optimize the average performance of the system. This dynamic control problem is modeled and solved using a Semi Markov Decision Process (SMDP) framework. We then assess the impact of the mobility and show that (i) our network centric approach outperforms a simple user centric algorithm and (ii) mobility improves the performance of the system when optimal policy of the problem is used.

We propose an analysis of the impact of the deployment of small base stations in a wireless network constituted of macro base stations. This analysis is particularly focused on the influence of the position and the transmitting power of small base stations on the performance of the network. In this aim, we consider an analytical model for heterogeneous cellular networks, composed of macro cells and small cells. The network model framework developed allows to derive closed form formulas for the Signal to Interference plus Noise Ratio (SINR) received by a mobile, whatever its location. Moreover, the proposed analytical model is validated by numerical simulations and it is shown that it is a good approximation of the SINR. Performance and quality of service (QoS) in terms of throughput and coverage can therefore be analyzed in a simple way. It makes it possible to analyze the deployment of small cells in an existing macro cells network.

We propose a new network model framework, denoted heterogeneous fluid model network, which allows to derive closed formula for the Signal to Interference plus Noise Ratio (SINR) received by a mobile in heterogeneous cellular networks, composed of macro cells and femto cells. Quality of service (QoS) and performance of wireless networks can therefore be analyzed in a simple way. We apply our model to Long Term Evolution (LTE) and indoor/outdoor environment. This model allows to analyze the deployment of a femto cells network when the femto base stations share the same bandwidth as deployed macro cells. We propose an analysis of the impact of transmitting power femto base stations on the performance in terms of coverage, throughput and QoS.

In this paper we propose an analytical evaluation of the performance of the zero forcing precoding technique in terms of outage probability in a multicellular multiuser context. The channel model includes path loss shadowing and Rayleigh flat fading. Two cases are examined. The first one considers a constant lognormal shadowing. In this case, a closed form expression of the outage probability is derived. In the second case we consider a randomly variable lognormal shadowing and we propose an easily computable expression of the outage probability. Simulation results show the degradation of performance induced by the shadowing.

Reducing power transmission is of primary importance in future green cellular networks. First of all, the induced reduction of the interference encourages the deployment of opportunistic radios in the same spectrum. Then, it directly implies a reduction of the energy consumption. At last, electric field radiations reduction mitigates the potential risks on health. From a technical point of view, power control is however likely to degrade network performance. In this paper, we evaluate the impact of power reduction on the coverage and the capacity of cellular networks. We establish closed form formulas of outage probability by taking into account shadowing, thermal noise and base stations (BS) transmitting power impacts. We quantify the transmitting power needed for different kinds of environments (urban, rural) and frequencies and we show that the transmitting power can be optimized according to networks characteristics without decreasing the quality of service. We show at last that increasing the BS density results in a reduction of the global power density in the network.

In this paper, we study the performance of time reversal (TR) pre-equalization technique in terms of outage probability for downlink multi-cellular wideband indoor communication environments. We derive a closed form expression of the cumulative distribution function (CDF) of the output signal to interference ratio (SIR) or equivalently the outage probability. This expression allows for faster and simpler performance analysis of newly designed wireless communication systems.

This paper proposes an analytical study of the shadowing impact on the outage probability in cellular radio networks. We establish that the downlink other-cell interference factor, f, which is defined here as the ratio of outer cell received power to the inner cell received power, plays a fundamental role in the outage probability. From f, we are able to derive the outage probability of a mobile station (MS) initiating a new call. Taking into account the shadowing, f is expressed as a lognormal random variable. Analytical expressions of the interference factor's mean mfand standard deviation sfare provided in this paper. These expressions depend on the topology of the network characterized by a G factor. We show that shadowing increases the outage probability, and using our analytical method, we are able to quantify this impact. However, we establish that the network topology, or correlated received powers, may limit this increase.

This article studies the impact of mobility when mobiles are under a simultaneous power and rate assignment scheme based on a fair assignment policy. Using a fluid model for expressing the long-range impact of neighboring cells, we are able to derive an analytical expression of the impact of one moving mobile to a fixed one, both being under a fair policy of rate assignment. These policies include max-min, Nash equilibria, harmonic equilibria and many others. We validate our model on a stochastic geometric model where we measure the elasticity of the rate of the moving terminal and show more complex situations when more than two mobiles influence each other. As a result, we show how mobility impacts a network of mobile terminals and derive conclusions on how to correctly manage such a network.

In this paper, we develop an analytical study of the mobility in cellular networks and its impact on quality of service and outage probability. We first express analytically the downlink other-cell interference factor f by using a fluid model network. It is defined here as the ratio of outer cell received power to the inner cell received power. It allows us to analyze users mobility and to derive expressions of the outage probability. We show that mobility can modify the capacity of a cell and we quantify the outage probability variations. We moreover establish how mobility plays a role in quality of service management. All results are compared to Monte Carlo simulations performed in a traditional hexagonal network.

In this paper, we establish a closed form formula of the other-cell interference factor f for omni-directional and sectored cellular networks. That formula is based on a fluid model that approximates the discrete base stations (BS) entities by a continuum of transmitters which are spatially distributed in the network. Simulations show that the obtained closed-form formula is a very good approximation, even for the traditional hexagonal network. From f, we are able to derive the outage probability on the downlink as a function of the mobile density and the coverage range. From a maximum acceptable outage probability, we can deduce the link between cell coverage and mobile density and thus highlight with a new, easy and fast method the notion of cell breathing. At last, we show how an operator can use this approach in order to evaluate the impact of sectorization or BS densification on the cell coverage.

The design of CDMA networks (such as HSDPA, UMTS) and in particular the implementation of base stations is a crucial point for operators. For economical reasons, the number of base stations has to be well balanced to answer to traffic and services needs. In UMTS networks, each base station can serve a limited number of mobile nodes. This number is related to the maximum power that a base station can handle (see [1]). We will describe this problem for a homogeneous UMTS network. Since the base stations of a real network are not regularly distributed, we will consider a 'disturbance' of the base stations positions. In this new configuration, the mobiles stay in set positions and the base stations are distributed according to a random location. In this context, we show that the network total transmitting power is an increasing function of the perturbation amplitude. We establish that the difference with the total transmitting power of a homogeneous network is very low.

In this paper, we propose a way of achieving optimally in radio resource management (RRM) for heterogeneous networks. We consider a micro or femto cell with two co-localized radio access technologies (RAT), e.g. WLAN and HSDPA. RAT are mainly characterized by the data rates they offer at a given distance of the access point. Dual-technology mobile stations (MS) are initiating downlink sessions in the considered cell. A network controlled joint RRM algorithm is responsible to assign MS to a RAT, while taking into account the joint spatial distribution of already accepted MS, the current load of each RAT, the location of the newly accepted session and its influence on the global performance. In a study based on the Semi Markov Decision Process (SMDP) theory, we show how to obtain an optimal policy. Optimality is here defined through a utility function accounting for user satisfaction.

We establish a closed form formula of the other-cell interference factor f for omni-directional and sectored cellular networks, as a function of the location of the mobile. That formula is based on a fluid model of cellular networks: The key idea is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. Simulations show that the obtained closed-form formula is a very good approximation, even for the traditional hexagonal network. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call. Although initially focused on CDMA (UMTS, HSDPA) and OFDMA (WiMax) networks, we show this approach is applicable to any kind of wireless system such as TDMA (GSM) or even ad-hoc ones.

In this paper, we propose a new framework for the study of cellular networks called the fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. This allows us to obtain simple analytical expressions of the main characteristics of the network. In this paper, we focus on the downlink other-cell interference factor, f, which is defined here as the ratio of outer cell received power to the inner cell received power. Although this factor has been firstly defined for CDMA networks (in particular UMTS and HSDPA), the analysis presented hereafter is still valid for other systems using frequency reuse 1, like OFDMA (WiMAX), TDMA (GSM with frequency hopping), or even ad hoc networks. A closed- form formula of f is provided in this paper. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call. All results are compared to Monte Carlo simulations performed in a traditional hexagonal network.

In this paper, we propose an analytical fluid model for adhoc wireless networks. Our fluid model consists in replacing a finite number of nodes by an equivalent continuum - characterized by a density of nodes - and disseminated in the network according to some distribution function. The key feature of our model is that it takes into account the effect of interference, the CSMA/CA mechanism and radio propagation aspects in an easy and straightforward way. We will give closed form formulae of the Mean Capacity per node and the Coverage Probability, along with an evaluation of the impact of nodes density, network size and carrier sense range on overall performance.

In this paper, we propose a new framework for the study of cellular networks called the fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. This allows us to obtain simple analytical expressions of the main characteristics of the network. In this paper, we focus on CDMA systems. This approach is however also applicable to other technologies like OFDMA. A closed-form formula of the downlink other-cell interference factor, f, is provided and compared to simulations performed in a traditional hexagonal network. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call.

We develop an analytical approach of omni-directional and sectored CDMA systems, adapted to each given zone of the network: we establish explicit expressions of the interference factors, which represent a characteristic of these networks. This model considers the base stations transmitting powers as a continuum field. We show this assumption is accurate even for low base stations densities. Thanks to this model we analyze, without simulation, the multiservice mobile admission in CDMA systems. We particularly show the advantage of a sectorisation and the influence of the admission control strategy chosen by a provider.

The signals to interferences ratio (SIR) received by the mobiles and the base stations of a CDMA network have to satisfy some constraints for a mobile to be connected to a base station. We show that the uplink and downlink interference factors, which represent the "weight" of the network on a given cell, characterize the CDMA networks. We develop, and validate, an analytical fluid model of the network, and establish explicit formulas of the interference factors for each link. This analytical model, simpler than the existing ones, can easily be used for different kinds of CDMA networks analysis, without any computation. As an application, we propose an analytical call admission control (CAC) study for the two links, which takes into account the whole network around a given cell, and show that it is sufficient to do the analysis only for one link. We end our analysis with the development and the validation of the fluid model for a more realistic non homogeneous network.