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 considers the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV) Base Station (BS). A map is considered, characterized by a traffic intensity of users to be served. The UAV BS must travel from a given initial location at an initial time 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. The problem is formulated using the framework of Lagrangian mechanics. When the traffic intensity is quadratic (single-phase), we derive closed-form formulas for the optimal trajectory. When the traffic intensity is bi-phase, necessary conditions of optimality are provided and an Alternating Optimization Algorithm is proposed, that returns a trajectory satisfying these conditions. The Algorithm is initialized with a Model Predictive Control (MPC) online algorithm. Numerical results show how the trajectory is improved with respect to the MPC solution.

Building detection has been a prominent area in the area of image classification. Most of the research effort is adapted to the specific application requirements and available datasets. Our dataset includes aerial orthophotos (with spatial resolution 20cm), a DSM generated from LiDAR (with spatial resolution 1m and elevation resolution 20 cm) and DTM (spatial resolution 2m) from an area of Athens, Greece. Our aim is to classify these data by means of Markov Random Fields (MRFs) in a Bayesian framework for building block extraction and perform a comparative analysis with other supervised classification techniques namely Feed Forward Neural Net (FFNN), Cascade-Correlation Neural Network (CCNN), Learning Vector Quantization (LVQ) and Support Vector Machines (SVM). We evaluated the performance of each method using a subset of the test area. We present the classified images, and statistical measures (confusion matrix, kappa coefficient and overall accuracy). Our results demonstrate that the MRFs and FFNN perform better than the other methods.

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, 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.

In this paper, we demonstrate how a Markov Random Field (MRF) based framework can be used for multihop networks analysis and design. In fields such as image processing it has been shown that MRFs is a powerful tool to analyse distributed systems with strong spacial interactions, which is also a defining characteristic of multihop networks. In this work we focus on using MRFs to model traffic intensity of sensor networks using shortest path routing. Later we propose a probabilistic relaying mechanism to recreate a traffic pattern similar to that observed in a network using shortest path routing. The objective is to emulate the shortest path performance without complex routing protocols and associated overheads. Using a simulation study we then show that the proposed mechanism achieves 95% of the throughput of shortest path, without using a routing protocol.

In this paper, we address the problem of optimal relay placement in a cellular network assuming network densification, with the aim of maximizing cell capacity. In our model, a fraction of radio resources is dedicated to the base-station (BS)/relay nodes (RN) communication. In the remaining resources, BS and RN transmit simultaneously to users. During this phase, the network is densified in the sense that the transmitters density and so network capacity are increased. Intra- and inter-cell interference is taken into account in Signal to Interference plus Noise Ratio (SINR) simple formulas derived from a fluid model for heterogeneous network. Optimization can then be quickly performed using Simulated Annealing. Performance results show that cell capacity is boosted thanks to densification despite a degradation of the signal quality. Bounds are also provided on the fraction of resources dedicated to the BS-RN link.

In this paper, we address the problem of the impact of relays on the performance of a LTE-A based network. In this aim, we propose a new framework, the “fluid model for LTE-A networks with relays”. We derive from this model analytical simple formulas for the Signal to Interference plus Noise ratio (SINR), taking into account inter-cell interference, which allow to study performance of wireless networks constituted by macro base stations and relays. In our analysis, a fraction τ of radio resources is dedicated to the base-station (eNode-B)/relay nodes (RN) communication. By using the fluid model, we instantaneously quantify an optimized value of τ, according to the number of relays, which allows to increase the capacity. In the remaining resources, eNodes-B and RNs transmit simultaneously to users. During this phase, the network is densified in the sense that the transmitters density and so network capacity are increased. Performance results show that cell capacity is boosted thanks to densification despite a degradation of the signal quality.

We describe basic properties of Markov chains on finite state spaces and their application to Green functions, partial differential equations, and their (approximate) solution using random walks on a graph. Attention is paid to the influence of boundary conditions (Dirichlet/von Neumann). We apply these ideas to the study of traffic propagation and distribution in ad hoc networks.

Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle noise. Markov random field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges. Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving nonconvex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the alpha -expansion) is too heavy specially when considering joint regularization of several images. We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut-based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.

In this paper, we present a new general framework allowing sensor networks design using random Markov fields (MRF) theory. We explain how the principles underlying MRF theory naturally fit design requirements in sensor networks in particular the need to rely on decentralised and distributed methods to solve global optimisation problems. We illustrate the potential of this new general concept with the practical problems of power control and resource allocation. In addition, we present a new method to improve the convergence rate of the simulated annealing when the sensor network design problem is a constrained optimisation problem.