For decades, simultaneous ascending auction (SAA) has been the most popular mechanism used for spectrum auctions. It has recently been employed by many countries for the allocation of 5G licences. Although SAA presents relatively simple rules, it induces a complex strategic game for which the optimal bidding strategy is unknown. Considering the fact that sometimes billions of euros are at stake in an SAA, establishing an efficient bidding strategy is crucial. In this work, we model the auction as a$n$-player simultaneous move game with complete information and propose the first efficient bidding algorithm that tackles simultaneously its four major strategic issues: theexposure problem, theown price effect,budget constraints, and theeligibility management problem. Our solution, called$\text{SMS}^\alpha$, is based on simultaneous move Monte Carlo Tree Search and relies on a new method for the prediction of closing prices. By introducing a new reward function in$SMS^\alpha$, we give the possibility to bidders to define their own level of risk-aversion. Through extensive numerical experiments on instances of realistic size, we show that$\text{SMS}^\alpha$largely outperforms state-of-the-art algorithms, notably by achieving higher expected utility while taking less risks.

In this article, we tackle the problem of designing an efficient bidding strategy for simultaneous ascending auctions (SAA). SAA is a well-known mechanism for allocating spectrum to mobile networks operators and has been used for example to allocate 5G licenses in many countries. Although the rules are relatively simple, there is no known optimal bidding strategy for SAA. In a previous work, we proposed a Simultaneous move Monte Carlo Tree Search-based algorithm named$SMS^{\alpha }$that we extend here to an incomplete information framework. We consider and compare three determinization approaches of$SMS^{\alpha }$, and show how they are able to tackle four key strategic issues of SAA, namely, the exposure problem, the own price effect, the budget constraints and the eligibility management. Extensive numerical experiments on instances of realistic size and including an uncertain framework show that our extensions of$SMS^{\alpha }$outperform state-of-the-art algorithms by achieving higher expected utility while taking less risks.

This work addresses the challenge of Dynamic Multi-Channel Access (DMCA) in the context of Ultra Reliable Low Latency Communications (URLLC), a framework subjected to notably stringent constraints, required by numerous Internet of Things (IoT) applications across various sectors. We introduce a theoretically grounded approach, leveraging Deep Multi-Agent Reinforcement Learning (MARL) to tackle this problem. While prior research has not fully addressed the DMCA problem in URLLC networks under time-varying heterogeneous channels and traffic profiles, nor provided robust theoretical guarantees in the multi-agent context, this paper adapts the recent theoretical framework of Trust Region Policy Optimization (TRPO) in MARL to meet the specific challenges and requirements of the URLLC-DMCA problem. Specifically, we introduce Multi Channel Access - Proximal Policy Optimization (MCA-PPO), a MARL algorithm that benefits from theoretical guarantees and effectively handles the partial observability and the combinatorial nature of the DMCA challenge. We validate the superiority of our proposed method across a variety of heterogeneous scenarios, in terms of traffic models and system parameters, and show that we outperform the traditional multiple access benchmark and learning algorithms.

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.

We tackle in this work the problem for a player to efficiently bid in Simultaneous Ascending Auctions (SAA). Although the success of SAA partially comes from its relative simplicity, bidding efficiently in such an auction is complicated as it presents a number of complex strategical problems. No generic algorithm or analytical solution has yet been able to compute the optimal bidding strategy in face of such complexities. By modelling the auction as a turn-based deterministic game with complete information, we propose the first algorithm which tackles simultaneously two of its main issues: exposure and own price effect. Our bidding strategy is computed by Monte Carlo Tree Search (MCTS) which relies on a new method for the prediction of closing prices. We show that our algorithm significantly outperforms state-of-the-art existing bidding methods. More precisely, our algorithm achieves a higher expected utility by taking lower risks than existing strategies.

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.

This paper considers the Multiple Access problem where$N$Internet of Things (IoT) devices share a common wireless medium towards a central Base Station (BS). We propose a Reinforcement Learning (RL) method where the BS is the agent and the devices are part of the environment. A device is allowed to transmit only when the BS decides to schedule it. Besides the information packets, devices send additional messages like the delay or the number of discarded packets since their last transmission. This information is used to design the RL reward function and constitutes the next observation that the agent can use to schedule the next device. Leveraging RL allows us to learn the sporadic and heterogeneous traffic patterns of the IoT devices and an optimal scheduling policy that maximizes the channel throughput. We adapt the Proximal Policy Optimization (PPO) algorithm with a Recurrent Neural Network (RNN) to handle the partial observability of our problem and exploit the temporal correlations of the users' traffic. We demonstrate the performance of our model through simulations on different number of heterogeneous devices with periodic traffic and individual latency constraints. We show that our RL algorithm outperforms traditional scheduling schemes and distributed medium access algorithms.

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.

We study a millimeter wave (mm-wave) wireless network deployed along the roads of an urban area, to support localization and communication services simultaneously for outdoor mobile users. In this network, we propose a mm-wave initial beam-selection scheme based on localization-bounds, which greatly reduces the initial access delay as compared to traditional initial access schemes for standalone mm-wave small cell base station (BS). Then, we introduce a downlink transmission protocol, in which the radio frames are partitioned into three phases, namely, initial access, data, and localization, respectively. We establish a trade-off between the localization and communication performance of mm-wave systems, and show how enhanced localization can actually improve the data-communication performance. Our results suggest that dense BS deployments enable to allocate more resources to the data phase while still maintaining appreciable localization performance. Furthermore, for the case of sparse deployments and large beam dictionary size (i.e., with thinner beams), more resources must be allotted to the localization phase for optimizing the rate coverage. Based on our results, we provide several system design insights and dimensioning rules for the network operators that will deploy the first generation of mm-wave BSs.

Due to the increasing number of car-centered connected services, making efficient use of limited radio resources is critical in vehicular communications. Hybrid vehicular networks dispose of multiple Radio Access Technologies (RATs) like cellular and vehicle-to-vehicle (V2V) networks, with complementary characteristics that allow for developing smarter network traffic distribution methods. This paper proposes a self-adaptive clustering system for ensuring a suitable trade-off between data aggregation (over the cellular network) and communication congestion due to cluster management (within the V2V network). The system's algorithms use a distributive justice approach for selecting cluster heads, to improve fairness among car drivers and hence help the social acceptability of self-adaptive clustering. Simulation results show that this approach significantly improves fairness over time without affecting network performance. This solution can thus optimize the usage of radio resources, reducing cellular access costs, without the need for uniformization among different mobile operators' access plans.

We propose a distributed learning algorithm for the resource allocation problem in Device-to-Device (D2D) wireless networks that takes into account the throughput estimation noise. We first formulate a stochastic optimization problem with the objective of maximizing the generalized alpha-fair function of the network. In order to solve it distributively, we then define and use the framework of noisy-potential games. In this context, we propose a Binary Log-linear Learning Algorithm (BLLA), which is distributed across cells and converges to a Nash equilibrium of the resource allocation game. This equilibrium is also an optimal for the resource allocation optimization problem. A key enabler for the analysis of the convergence are the proposed rules for computation of resistance of trees of perturbed Markov chains. The convergence of BLLA is proved for bounded and unbounded noise, with fixed and decreasing temperature parameter. A sufficient number of estimation samples is also provided that guarantees the convergence to an optimal state in a single cell scenario and close to an optimal state in a multi-cell scenario. We assess the performance of BLLA by extensive simulations by considering both bounded and unbounded noise cases and show that BLLA achieves higher sum data rate compared to the state-of-the-art.

Reliable group video call is one of the main services offered by future Mission-Critical Communications (MCC). To support its requirements, coordinated multi-point transmission in multi-cell environments is an attractive feature for MCC over Multimedia Broadcast Multicast Services owing to its potential for coverage improvement and multicast transmission. In such a scheme, full cooperation among all cells of an area achieves the highest cooperative gain, but has stringent impact on system capacity. A trade-off in the cluster's size of serving cells thus arises between high Signal to Interference plus Noise Ratio (SINR) and network capacity. In this paper, we formulate an optimization problem to maintain an acceptable system blocking probability, while maximizing the average SINR of the multicast group users. For every multicast group to be served, a dynamic cluster of cells is selected based on the minimization of a submodular function that takes into account the traffic in every cell through some weights and the average SINR achieved by the group users. Traffic weights are then optimized using a modified Nelder-Mead simplex method with the objective of tracking a blocking probability threshold. The proposed clustering scheme is compared to full cooperation and to Single-Cell Point-To-Multipoint (SC-PTM) schemes. Results show that dynamic clustering offers the best trade-off between coverage and capacity for MCC.

Business and Mission critical communication (MCC) is a major communication paradigm that is used by public agencies, e.g., during emergency situations, or critical infrastructure companies, e.g., airports, transportation, etc. MCC has very stringent requirements in terms of reliability, coverage and should offer group communications. Coordinated Multimedia Multicast/Broadcast single frequency network (MBSFN) is considered as a potential technology for MCC as it benefits from increased coverage and inter-cell interference mitigation. In this paper, we propose multi-input-multi-output (MIMO) multimedia MBSFN system design wherein each base station (BS) of a coordinated cluster multicasts a common message to all the users in a group. We use a greedy algorithm to dynamically form the cluster of synchronized BSs for optimal utilization of resources within an MBSFN. We assume the availability of perfect channel state information (CSI) knowledge and jointly obtain the optimal precoder and receive filters by minimizing the overall sum-mean- square-error (sum-MSE) constrained over the total transmit power. We further extend the proposed design to a robust case by considering the imperfections in available channel knowledge and obtain the transceiver matrices that are resilient to channel errors. We also present both the joint and robust system design for Single-Cell point-to-multipoint (SC-PTM) which is an alternative solution to MBSFN in MCC. Numerical results show the effectiveness of the proposed network architecture for future mission critical communication. Furthermore, the comparison results show that the proposed robust design demonstrate better performance and is resilient to the presence of CSI errors.

Non-orthogonal multiple access (NOMA) has received significant attention for future wireless networks. NOMA outperforms orthogonal schemes, such as OFDMA, in terms of spectral efficiency and massive connectivity. The joint subcarrier and power allocation problem in NOMA is NP-hard to solve in general, due to complex impacts of signal superposition on each users achievable data rates, as well as combinatorial constraints on the number of multiplexed users per sub-carrier to mitigate error propagation. In this family of problems, weighted sum-rate (WSR) is an important objective function as it can achieve different tradeoffs between sum-rate performance and user fairness. We propose a novel approach to solve the WSR maximization problem in multi-carrier NOMA with cellular power constraint. The problem is divided into two polynomial time solvable sub-problems. First, the multi-carrier power control (given a fixed subcarrier allocation) is non-convex. By taking advantage of its separability property, we design an optimal and low complexity algorithm (MCPC) based on projected gradient descent. Secondly, the single-carrier user selection is a non-convex mixed-integer problem that we solve using dynamic programming (SCUS). This work also aims to give an understanding on how each sub-problem's particular structure can facilitate the algorithm design. In that respect, the above MCPC and SCUS are basic building blocks that can be applied in a wide range of resource allocation problems. Furthermore, we propose an efficient heuristic to solve the general WSR maximization problem by combining MCPC and SCUS. Numerical results show that it achieves near-optimal sum-rate with user fairness, as well as significant performance improvement over OMA.

International audience

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.

Non-orthogonal multiple access (NOMA) is a promising radio access technology for 5G. It allows several users to transmit on the same frequency and time resource by performing power- domain multiplexing. At the receiver side, successive interference cancellation (SIC) is applied to mitigate interference among the multiplexed signals. In this way, NOMA can outperform orthogonal multiple access schemes used in conventional cellular networks in terms of spectral efficiency and allows more simultaneous users. This paper investigates the computational complexity of joint subcarrier and power allocation problems in multi-carrier NOMA systems. We prove that these problems are strongly NP-hard for a large class of objective functions, namely the weighted generalized means of the individual data rates. This class covers the popular weighted sum-rate, proportional fairness, harmonic mean and max-min fairness utilities. Our results show that the optimal power and subcarrier allocation cannot be computed in polynomial time in the general case, unless P = NP. Nevertheless, we present some tractable special cases and we show that they can be solved efficiently.

This paper considers the problem of designing the user trajectory in a device-to-device communications setting. We consider a pair of pedestrians connected through a D2D link. The pedestrians seek to reach their respective destinations, while using the D2D link for data exchange applications such as file transfer, video calling, and online gaming. In order to enable better D2D connectivity, the pedestrians are willing to deviate from their respective shortest paths, at the cost of reaching their destinations slightly late. A generic trajectory optimization problem is formulated and solved for the case when full information about the problem in known in advance. Motivated by the D2D user's need to keep their destinations private, we also formulate a regularized variant of the problem that can be used to develop a fully online algorithm. The proposed online algorithm is quite efficient, and is shown to achieve a sublinear offline regret while satisfying the required mobility constraints exactly. The theoretical results are backed by detailed numerical tests that establish the efficacy of the proposed algorithms under various settings.

Mission-critical communications conveyed over Professional Mobile Radio (PMR) are characterized by a high level of reliability, an improved coverage and group call communications. Hybrid Automatic Repeat on re-Quest (HARQ) schemes are commonly used to provide a reliable communication over multipath noisy wireless channels. They, however, generate an excessive control signaling overhead on the uplink when downlink multicast is considered and groups include many members. In this paper, we propose a simple repetition scheme without request as an alternative to HARQ for group communications. When transport blocks are retransmitted several times, a tradeoff arises between coverage and capacity on the one hand, coverage and delay on the other hand. To evaluate the performance of our scheme, we use a link layer abstraction based on the Mean Instantaneous Capacity (MIC) together with BLER vs. SNR curves in AWGN. We carefully design our repetition scheme by considering the channel characteristics and the delay constraint imposed by video codecs. We show that up to 11 dB gain in SNR is achieved when compared to a scheme without repetition. System level simulations show that cell radius can be multiplied by three in a Multicast/Broadcast Single Frequency Network (MBSFN).

The analyses of cellular network performance based on stochastic geometry generally ignore the traffic dynamics in the network. This restricts the proper evaluation and dimensioning of the network from the perspective of a mobile operator. To address the effect of dynamic traffic, recently, the mean cell approach has been introduced, which approximates the average network load by the zero cell load. However, this is not a realistic characterization of the network load, since a zero cell is statistically larger than a random cell drawn from the population of cells, i.e., a typical cell. In this paper, we analyze the load of a noise-limited network characterized by high signal to noise ratio (SNR). The noise-limited assumption can be applied to a variety of scenarios, e.g., millimeter wave networks with efficient interference management mechanisms. First, we provide an analytical framework to obtain the cumulative density function of the load of the typical cell. Then, we obtain two approximations of the average load of the typical cell. We show that our study provides a more realistic characterization of the average load of the network as compared to the mean cell approach. Moreover, the prescribed closed-form approximation is more tractable than the mean cell approach.

We characterize a two tier heterogeneous network, consisting of classical sub-6 GHz macro cells, and multi radio access technology (RAT) small cells able to operate in sub-6 GHz and millimeter-wave (mm-wave) bands. For optimizing coverage and to balance loads, we propose a two-step mechanism based on two biases for tuning the tier and RAT selection, where the sub-6 GHz band is used to speed-up the initial access procedure in the mm-wave RAT. First, we investigate the effect of the biases in terms of signal-to-interference-plus-noise ratio (SINR) distribution, cell load, and user throughput. More specifically, we obtain the optimal biases that maximize either the SINR coverage or the user downlink throughput. Then, we characterize the cell load using the mean cell approach and derive upper bounds on the overloading probabilities. Finally, for a given traffic density, we provide the small cell density required to satisfy system constraints in terms of overloading and outage probabilities. Our analysis highlights the importance of deploying dual-band small cells, in particular, when small cells are sparsely deployed or in case of heavy traffic.

We characterize a multi tier network with classical macro cells, and multi radio access technology (RAT) small cells, which are able to operate in microwave and millimeter-wave (mm-wave) bands. The small cells are assumed to be deployed along roads modeled as a Poisson line process. This characterization is more realistic as compared to the classical Poisson point processes typically used in literature. In this context, we derive the association and RAT selection probabilities of the typical user under various system parameters such as the small cell deployment density and mm-wave antenna gain, and with varying street densities. Finally, we calculate the signal to interference plus noise ratio (SINR) coverage probability for the typical user considering a tractable dominant interference based model for mm-wave interference. Our analysis reveals the need of deploying more small cells per street in cities with more streets to maintain coverage, and highlights that mm-wave RAT in small cells can help to improve the SINR performance of the users.

International audience

In large low-power networks of battery-driven sensors, power outages are a major concern and communication rates have to be carefully designed in order to optimize energy consumption, network connectivity and sensors lifetime. In some IoT use cases, power can be supplied to sensors by way of renewable energy automatic harvesting (solar panels, etc.). Given the high variability of energy arrival processes, energy consumption in sensors, in particular caused by transmissions to the sink, has to be aligned with energy harvesting patterns, so as to maximize throughput while avoiding power outages that may arise when the battery is empty. This paper proposes ODMAC++, an extension to a well-known protocol for sensor transmission scheduling in a WSN. ODMAC++ relies on learning techniques to adapt sensors communication rate to energy harvesting patterns, and uses a beaconing mechanism whose frequency is adjusted based on past measurements on the harvested energy process. Simulations based on analytical energy arrival models and on real solar radiation measurements indicate that ODMAC++ is able to avoid power outages and to cope with battery limitation and energy variations due to variability in time.

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.

Long Term Evolution (LTE), designed by 3rd Generation Partnership Project (3GPP) to increase the capacity of radio mobile communications, has been endorsed by multiple public protection and disaster relief organizations as a next generation technology for Professional Mobile Radio (PMR) networks, which convey business and mission critical communications. One of the main services of PMR is the group communication that can be seen as a Multimedia Broadcast Multicast Service (MBMS). LTE offers functionality to transmit this type of flows either by MBMS over Single Frequency Network (MBSFN), or Single-Cell Point-To- Multipoint (SC-PTM). In this paper, we compare MBSFN, SC-PTM and unicast transmissions in terms of radio quality, system spectral efficiency and cell coverage. Our main conclusion is that SC-PTM together with Transmission Time Interval (TTI) bundling transmissions offers a flexible solution to trade coverage off for capacity.

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.

We use information theoretic achievable rate formulas for the multi-relay channel to study the problem of as-you-go deployment of relay nodes. The achievable rate formulas are for full-duplex radios at the relays and for decode-and-forward relaying. Deployment is done along the straight line joining a source node and a sink node at an unknown distance from the source. The problem is for a deployment agent to walk from the source to the sink, deploying relays as he walks, given the knowledge of the wireless path-loss model, and given that the distance to the sink node is exponentially distributed with known mean. As a precursor to the formulation of the deploy-as-you-go problem, we apply the multi-relay channel achievable rate formula to obtain the optimal power allocation to relays placed along a line, at fixed locations. This permits us to obtain the optimal placement of a given number of nodes when the distance between the source and sink is given. Numerical work for the fixed source-sink distance case suggests that, at low attenuation, the relays are mostly clustered close to the source in order to be able to cooperate among themselves, whereas at high attenuation they are uniformly placed and work as repeaters. We also prove that the effect of path-loss can be entirely mitigated if a large enough number of relays are placed uniformly between the source and the sink. The structure of the optimal power allocation for a given placement of the nodes, then motivates us to formulate the problem of as-you-go placement of relays along a line of exponentially distributed length, and with the exponential path-loss model, so as to minimize a cost function that is additive over hops. The hop cost trades off a capacity limiting term, motivated from the optimal power allocation solution, against the cost of adding a relay node. We formulate the problem as a total cost Markov decision process, establish results for the value function, and provide insights into the placement policy and the performance of the deployed network via numerical exploration.

Solar energy is currently a popular renewable resource, yet limited daily. In green cellular networks, multiple constraints optimization (MCO) problems arise naturally. For example, a typical objective is to control the power transmission of the hybrid base stations (BSs) (connected to both solar panels and electrical grid) in order to maximize user's average throughput, under the constraints of consumed grid energy and user's blocking rate. However, such problems have been generally proved to be NP-hard. In this paper, we formulate this generic MCO problem as a quantized Markovian cost-reward model, with no assumption on input data. We then propose a novel algorithm, namely cost-constrained Viterbi algorithm, which recursively returns the optimal policy with linear computational complexity for this model. As an application, we provide engineering rules for the design of hybrid BSs through extensive simulations. In comparison with brute force method for a simple scenario, we find that our algorithm does achieve the constrained optimal policy.

Decentralized cognitive radio networks (CRN) require efficient channel access protocols to enable cognitive secondary users (SUs) to access the primary channels in an opportunistic way Without any coordination. In this paper, we develop a distributed spectrum access protocol for the case where the SUs aim to maximize the total system throughput while competing for spectrum resources. To model the competition amongst SUs, we formulate the spectrum access problem as a {\it distributed welfare game}, in which at each iteration each SU has to compute its marginal contribution to the system's welfare. Moreover, the SUs also need to decide which resource (channel) they should access at the next iteration. To address these challenges, we propose a stochastic learning algorithm based on payoff-based log-linear learning and prove its convergence towards a Pareto-efficient Nash Equilibrium state.

The future demands of high data spectral efficiency and ubiquitous coverage are pushing the next generation of cellular networks towards network densification with massive deployments of small cells to complement macro base stations. In this paper, we study a network comprising of closed access small cells along with macro base stations using stochastic geometry. First, the cell association probability is characterized. Additionally, approximate values of the average downlink signal to interference and noise ratio (SINR) and the downlink spectral efficiency are derived. These derivations are carried out without using the classical approach of solving a Laplace functional. For this, the statistical independence of the useful signals and interference powers is exploited. The obtained results can be used to optimize the small cell network deployment and the inter-cell interference coordination functions.

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.

We are motivated by the need, in some applications, for impromptu or as-you-go deployment of wireless sensor networks. A person walks along a line, starting from a sink node (e.g., a base-station), and proceeds towards a source node (e.g., a sensor) which is at an a priori unknown location. At equally spaced locations, he makes link quality measurements to the previous relay, and deploys relays at some of these locations, with the aim to connect the source to the sink by a multihop wireless path. In this paper, we consider two approaches for impromptu deployment: (i) the deployment agent can only move forward (which we call a pure as-you-go approach), and (ii) the deployment agent can make measurements over several consecutive steps before selecting a placement location among them (the explore-forward approach). We consider a very light traffic regime, and formulate the problem as a Markov decision process, where the trade-off is among the power used by the nodes, the outage probabilities in the links, and the number of relays placed per unit distance. We obtain the structures of the optimal policies for the pure as-you-go approach as well as for the explore-forward approach. We also consider natural heuristic algorithms, for comparison. Numerical examples show that the explore-forward approach significantly outperforms the pure as-you-go approach in terms of network cost. Next, we propose two learning algorithms for the explore-forward approach, based on Stochastic Approximation, which asymptotically converge to the set of optimal policies, without using any knowledge of the radio propagation model. We demonstrate numerically that the learning algorithms can converge (as deployment progresses) to the set of optimal policies reasonably fast and, hence, can be practical model-free algorithms for deployment over large regions. Finally, we demonstrate the end-to-end traffic carrying capability of such networks via field deployment.

We present a novel approach for distributed load balancing in heterogeneous networks that use cell range expansion (CRE) for user association and almost blank subframe (ABS) for interference management. First, we formulate the problem as a minimization of an α-fairness objective function with load and outage constraints. Depending on α, different objectives in terms of network performance or fairness can be achieved. Next, we model the interactions among the base stations for load balancing as a near-potential game, in which the potential function is the α-fairness function. The optimal pure Nash equilibrium (PNE) of the game is found by using distributed learning algorithms. We propose log-linear and binary log-linear learning algorithms for complete and partial information settings, respectively. We give a detailed proof of convergence of learning algorithms for a near-potential game. We provide sufficient conditions under which the learning algorithms converge to the optimal PNE. By running extensive simulations, we show that the proposed algorithms converge within few hundreds of iterations. The convergence speed in the case of partial information setting is comparable to that of the complete information setting. Finally, we show that outage can be controlled and a better load balancing can be achieved by introducing ABS.

We present a novel approach for distributive load balancing in heterogeneous networks that use cell range expansion (CRE) for user association. First, we formulate the problem as a minimisation of an α-fairness objective function. Depending on α, different objectives in terms of network performance or fairness can be achieved. Next, we model the interactions among the base stations for load balancing as a potential game, in which the potential function is the α-fairness function. The optimal Nash equilibrium of the game is found by using distributed learning algorithms. We use log-linear and binary log-linear learning algorithms for complete and partial information settings, respectively. By running extensive simulations, we show that the proposed algorithms converge within a few tens of iterations. The convergence speed in the case of partial information setting is comparable to that of the complete information setting. We also show that the best response algorithm does not necessarily converge to the optimal Nash equilibrium.

This paper considers the problem of receive antenna selection (AS) in a multiple-antenna communication system having a single radio-frequency (RF) chain. The AS decisions are based on noisy channel estimates obtained using known pilot symbols embedded in the data packets. The goal here is to minimize the average packet error rate (PER) by exploiting the known temporal correlation of the channel. As the underlying channels are only partially observed using the pilot symbols, the problem of AS for PER minimization is cast into a partially observable Markov decision process (POMDP) framework. Under mild assumptions, the optimality of a myopic policy is established for the two-state channel case. Moreover, two heuristic AS schemes are proposed based on a weighted combination of the estimated channel states on the different antennas. These schemes utilize the continuous-valued received pilot symbols to make the AS decisions, and are shown to offer performance comparable to the POMDP approach, which requires one to quantize the channel and observations to a finite set of states. The performance improvement offered by the POMDP solution and the proposed heuristic solutions relative to existing AS training-based approaches is illustrated using Monte Carlo simulations.

In this work, the problem of receive antenna selection (AS) is considered, in a multiple antenna communication system having a single radio frequency (RF) chain at the receiver. The AS is performed on a per-packet basis, and AS decisions are based on noisy estimates of the channel gains obtained using pilot symbols embedded in the data packet for coherent demodulation, along with the receiver's knowledge of the time correlation of the channel. The problem is posed as a partially observable Markov decision process (POMDP) with the goal of minimizing the average packet error rate (PER). The performance of a myopic policy is compared with that of the POMDP solution, and it is shown that the former is optimal under certain conditions. As the POMDP approach requires the channel gains to be quantized to a finite set of states, we also propose two heuristic AS schemes that use the continuous-valued received pilot symbols to make AS decisions, and thereby offer comparable or better performance than the POMDP approach. Unlike previous work, the schemes proposed here for AS do not require a lengthy AS training phase to precede each data packet. The performance improvement offered by the POMDP solution and the proposed heuristic solutions relative to existing AS training-based approaches is illustrated using Monte Carlo simulations.

Decentralized cognitive radio networks (CRN) require efficient channel access protocols to enable cognitive secondary users (SUs) to access the primary channels in an opportunistic way without any coordination. In this paper, we develop a distributed retrospective spectrum access protocol that can orient the network towards a socially efficient and fair equilibrium state. With the developed protocol, each SU j chooses a channel to select based on the experienced payoff in past Hj periods. Each SU is thus supposed to be equipped with bounded memory and should make its decision based on only local observations. In that sense, the SUs behavioral rules are said to be payoff-based. The protocol also models a natural human decision making behavior of striking a balance between exploring a new choice and retrospectively exploiting past successful choices. With both analytical demonstration and numerical evaluation, we illustrate the two noteworthy features of our solution: (1) the entirely distributed implementation requiring only local observations and (2) the guaranteed statistical convergence to the equilibrium state within a bounded delay.

We are motivated by the problem of impromptu or as-you-go deployment of wireless sensor networks. As an application example, a person, starting from a sink node, walks along a forest trail, makes link quality measurements (with the previously placed nodes) at equally spaced locations, and deploys relays at some of these locations, so as to connect a sensor placed at some a priori unknown point on the trail with the sink node. In this paper, we report our experimental experiences with some as-you-go deployment algorithms. Two algorithms are based on Markov decision process (MDP) formulations, these require a radio propagation model. We also study purely measurement based strategies: one heuristic that is motivated by our MDP formulations, one asymptotically optimal learning algorithm, and one inspired by a popular heuristic. We extract a statistical model of the propagation along a forest trail from raw measurement data, implement the algorithms experimentally in the forest, and compare them. The results provide useful insights regarding the choice of the deployment algorithm and its parameters, and also demonstrate the necessity of a proper theoretical formulation.

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.

This paper considers antenna selection (AS) for packet reception at a receiver equipped with multiple antenna elements but only a single radio frequency chain. The receiver makes its AS decisions based on noisy channel estimates obtained from the training symbols (pilots). The time-correlation of the wireless channel and the results of the link-layer error checks upon data packet reception provide additional information that can be exploited for AS. This information can also be used to optimally distribute pilots among the antenna elements, so that packet loss due to selection errors is minimized. The task of the receiver, then, is to sequentially select (a) the pilot symbol allocation for channel estimation on each of the receive antennas and (b) the antenna to be used for data packet reception. The goal is to maximize the expected throughput, based on the history of allocation and selection decisions, and the corresponding noisy channel estimates and error check observations. This joint problem of pilot allocation and AS is solved as a partially observed Markov decision problem (POMDP) and the solutions yield the optimal policies that maximize the long-term expected throughput. The performance of the POMDP solution is compared with several other schemes for a 2-state Markov channel model, and it is illustrated that it outperforms the others.

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.

This paper considers antenna selection (AS) at a receiver equipped with multiple antenna elements but only a single radio frequency chain for packet reception. As information about the channel state is acquired using training symbols (pilots), the receiver makes its AS decisions based on noisy channel estimates. Additional information that can be exploited for AS includes the time-correlation of the wireless channel and the results of the link-layer error checks upon receiving the data packets. In this scenario, the task of the receiver is to sequentially select (a) the pilot symbol allocation, i.e., how to distribute the available pilot symbols among the antenna elements, for channel estimation on each of the receive antennas; and (b) the antenna to be used for data packet reception. The goal is to maximize the expected throughput, based on the past history of allocation and selection decisions, and the corresponding noisy channel estimates and error check results. Since the channel state is only partially observed through the noisy pilots and the error checks, the joint problem of pilot allocation and AS is modeled as a partially observed Markov decision process (POMDP). The solution to the POMDP yields the policy that maximizes the long-term expected throughput. Using the Finite State Markov Chain (FSMC) model for the wireless channel, the performance of the POMDP solution is compared with that of other existing schemes, and it is illustrated through numerical evaluation that the POMDP solution significantly outperforms them.

In this paper, we tackle the problem of opportunistic spectrum access in cognitive radio networks where a number of unlicensed Secondary Users (SU) operating on the standard CSMA/CA protocol access a number of frequency channels partially occupied by licensed Primary Users (PU). We apply evolutionary game theory to model the spectrum access problem and derive distributed mechanisms to converge to the Nash equilibrium. To this end, we combine a payoff computation methodology, relying on the estimation on the number of SUs on the same channel, with the channel access policy derived by the evolutionary game model. The conducted numerical analysis shows that a fast convergence is achieved and the proposed mechanisms are robust against errors in payoff computation.

We study the spectrum access problem in cognitive networks consisting of several frequency channels, each characterized by a channel availability probability due to the activity of the licensed primary users. The key challenge for the unlicensed secondary users to opportunistically access the unused spectrum of the primary users is to learn the channel availabilities and coordinate with others in order to choose the best channels for transmissions without collision in a distributed way. Moreover, due to the drastic cost of changing frequencies in current wireless devices (in terms of delay, packet loss and protocol overhead), an efficient channel access policy should avoid frequently channel switching, unless necessary. We address the spectrum access problem with channel switching cost by developing a block-based distributed channel access policy. Through mathematical analysis, we show that the proposed policy achieves logarithmic regret in spite of the channel switching cost. Extensive simulation studies show that the proposed policy outperforms the solutions in the literature.

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.

Extensive research in recent years has shown the benefits of cognitive radio technologies to improve the flexibility and efficiency of spectrum utilization. This new communication paradigm, however, requires a well-designed spectrum allocation mechanism. In this paper, we propose an auction framework for cognitive radio networks to allow unlicensed secondary users (SUs) to share the available spectrum of licensed primary users (PUs) fairly and efficiently, subject to the interference temperature constraint at each PU. To study the competition among SUs, we formulate a non-cooperative multiple-PU multiple-SU auction game and study the structure of the resulting equilibrium by solving a non-continuous two-dimensional optimization problem. A distributed algorithm is developed in which each SU updates its strategy based on local information to converge to the equilibrium. We then extend the proposed auction framework to the more challenging scenario with free spectrum bands. We develop an algorithm based on the no-regret learning to reach a correlated equilibrium of the auction game. The proposed algorithm, which can be implemented distributedly based on local observation, is especially suited in decentralized adaptive learning environments as cognitive radio networks. Finally, through numerical experiments, we demonstrate the effectiveness of the proposed auction framework in achieving high efficiency and fairness in spectrum allocation.

In this paper, we present and analyze a Tabu Search (TS) algorithm for DSA (Dynamic Spectrum Access) in cellular networks. We study a mono-operator case where the operator is providing packet services to the end-users. The objective of the cellular operator is to maximize its reward while taking into account the trade-off between the spectrum cost and the revenues obtained from end-users. These revenue are modeled here as an increasing function of the achieved throughput. Results show that the algorithm allows the operator to increase its reward by taking advantage of the spatial heterogeneity of the traffic in the network, rather than assuming homogeneous traffic for radio resource allocation. Our TS-based DSA algorithm is efficient in terms of the required memory space and convergence speed. Results show that the algorithm is fast enough to suit a dynamic context.

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.

In this paper, we present a game theoretical framework for DSA (Dynamic Spectrum Access) in cellular networks. We model and analyze the interaction between cellular operators with packet services, in a spectrum sharing context. We present inter-operator DSA algorithms based on game theory. A two-players non-zero sum game is formulated, where the operators are the players. We define a utility function, for the operator that takes: (1) the users throughput, (2) the spectrum price, and (3) the blocking probability into consideration. We present two system models: a) a centralized model where a DSA algorithm, for the global welfare in terms of the operators rewards, is inspired by the Pareto optimality concept. b) a distributed model, where a DSA algorithm is based on Nash equilibria concept. The convergence to NE in the distributed model is analyzed. The rewards of the operators in the centralized DSA algorithm are compared with those in the FSA (Fixed Spectrum Access) situation. The obtained rewards using the centralized DSA algorithm significantly exceed the FSA rewards. The obtained blocking probabilities are shown not to exceed the target value.

In this paper, a contention model for the IEEE 802.16e is first proposed to analyze the frame-based behavior of contention resolution in 802.16e network. Then a waiting-time dependent increasing rate adapted backoff (WDIA) algorithm is proposed to improve the contention efficiency. We introduce the concept of reduced overlapping between back-off windows of contending stations and we adopt an adapted increasing rate of the back-off window. The simulation results show that the WDIA algorithm achieves better performance in terms of number of retransmissions, access delay and resource utilization.

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 present a simple and accurate analytical model for performance evaluation of WiMAX networks with multiple traffic profiles. This very promising access technology has been designed to support numerous kinds of applications having different traffic characteristics. One of the QoS parameters considered by the standard for traffic classes is the maximum sustained traffic rate (MSTR), which is an upper bound for user throughput. Taking into account MSTR implies the implementation of a throttling scheduling policy that regulates the user peak rate. Our models take into account this policy and provides closed-form expressions giving all the required performance parameters for each traffic profile at a click speed. The model is compared with extensive simulations that show its accuracy and robustness.

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.

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.

In this paper, we investigate the performance of adaptive beamforming while using subcarrier permutation PUSC in WiMAX cellular network. In the literature, it has been shown that frequency reuse 1 is possible for beamforming capable WiMAX networks but with partial resource utilization or base station coordination. In this paper, we show however that using distributed subcarrier permutation (PUSC) offers sufficient diversity to allow full resource utilization without the need of coordination. We study an IEEE 802.16e cellular network employing adaptive beamforming per PUSC Major Group. Performance is evaluated in terms of radio quality parameters and system throughput. Results are based on Monte Carlo simulations performed in downlink. The simulation results show that even with reuse 1 and full load conditions, outage probability can be reduced to an acceptable value.

In this paper, we evaluate the performance of a WiMAX network in different frequency reuse scenarios with and without adaptive beamforming technique. We study the possibility of deploying reuse 1 networks. Radio quality in terms of SINR and outage probability on one hand, and throughput on the other hand, are the parameters considered for this analysis. Extensive Monte Carlo simulations, based on effective SINR computation using abstraction model mean instantaneous capacity (MIC), have been performed in downlink. The simulation results show that some frequency reuse schemes with a very good global throughput performance result however into significant user outage. The improvement in performance due to adaptive beamforming is evaluated. The frequency reuse patterns satisfying the two parameters (outage and throughput) in the best possible way are being suggested (based on simulation results) for WiMAX networks.

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 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.