Spectrum Management and Cognitive Radios

The ever increasing demand for new services from users who want high-quality broadband services while on the move, is straining the efficiency of current spectrum allocation paradigms, leading to an overall feeling of spectrum scarcity. In order to circumvent this problem, two possible solutions are being investigated: (i) implementing new technologies capable of accessing the temporarily/locally unused bands, without interfering with the licensed services, like Cognitive Radios; (ii) release some spectrum bands thanks to new services providing higher spectral efficiency, e.g., DVB-T, and allocate them to new wireless systems. These two approaches are promising, but also pose novel coexistence and interference management challenges to deal with. In particular, the deployment of devices such as Cognitive Radio, characterized by the inherent unplanned, irregular and random locations of the network nodes, require advanced mathematical techniques in order to explicitly model their spatial distribution. In such context, the system performance and optimization are strongly dependent on this spatial configuration. On the other hand, allocating some released spectrum bands to other wireless services poses severe coexistence issues with all the pre-existing services on the same or adjacent spectrum bands. In this thesis, these methodologies for better spectrum usage are investigated. In particular, using Stochastic Geometry theory, a novel mathematical framework is introduced for cognitive networks, providing a closed-form expression for coverage probability and a single-integral form for average downlink rate and Average Symbol Error Probability. Then, focusing on more regulatory aspects, interference challenges between DVB-T and LTE systems are analysed proposing a versatile methodology for their proper coexistence. Moreover, the studies performed inside the CEPT SE43 working group on the amount of spectrum potentially available to Cognitive Radios and an analysis of the Hidden Node problem are provided. Finally, a study on the extension of cognitive technologies to Hybrid Satellite Terrestrial Systems is proposed.

Ultra-low power WSNs: distributed signal processing and dynamic resource management

This thesis presents several data processing and compression techniques capable of addressing the strict requirements of wireless sensor networks. After introducing a general overview of sensor networks, the energy problem is introduced, dividing the different energy reduction approaches according to the different subsystem they try to optimize. To manage the complexity brought by these techniques, a quick overview of the most common middlewares for WSNs is given, describing in detail SPINE2, a framework for data processing in the node environment. The focus is then shifted on the in-network aggregation techniques, used to reduce data sent by the network nodes trying to prolong the network lifetime as long as possible. Among the several techniques, the most promising approach is the Compressive Sensing (CS). To investigate this technique, a practical implementation of the algorithm is compared against a simpler aggregation scheme, deriving a mixed algorithm able to successfully reduce the power consumption. The analysis moves from compression implemented on single nodes to CS for signal ensembles, trying to exploit the correlations among sensors and nodes to improve compression and reconstruction quality. The two main techniques for signal ensembles, Distributed CS (DCS) and Kronecker CS (KCS), are introduced and compared against a common set of data gathered by real deployments. The best trade-off between reconstruction quality and power consumption is then investigated. The usage of CS is also addressed when the signal of interest is sampled at a Sub-Nyquist rate, evaluating the reconstruction performance. Finally the group sparsity CS (GS-CS) is compared to another well-known technique for reconstruction of signals from an highly sub-sampled version. These two frameworks are compared again against a real data-set and an insightful analysis of the trade-off between reconstruction quality and lifetime is given.

Algorithms for network design and routing problems

In this thesis we study three combinatorial optimization problems belonging to the classes of Network Design and Vehicle Routing problems that are strongly linked in the context of the design and management of transportation networks: the Non-Bifurcated Capacitated Network Design Problem (NBP), the Period Vehicle Routing Problem (PVRP) and the Pickup and Delivery Problem with Time Windows (PDPTW). These problems are NP-hard and contain as special cases some well known difficult problems such as the Traveling Salesman Problem and the Steiner Tree Problem. Moreover, they model the core structure of many practical problems arising in logistics and telecommunications. The NBP is the problem of designing the optimum network to satisfy a given set of traffic demands. Given a set of nodes, a set of potential links and a set of point-to-point demands called commodities, the objective is to select the links to install and dimension their capacities so that all the demands can be routed between their respective endpoints, and the sum of link fixed costs and commodity routing costs is minimized. The problem is called non- bifurcated because the solution network must allow each demand to follow a single path, i.e., the flow of each demand cannot be splitted. Although this is the case in many real applications, the NBP has received significantly less attention in the literature than other capacitated network design problems that allow bifurcation. We describe an exact algorithm for the NBP that is based on solving by an integer programming solver a formulation of the problem strengthened by simple valid inequalities and four new heuristic algorithms. One of these heuristics is an adaptive memory metaheuristic, based on partial enumeration, that could be applied to a wider class of structured combinatorial optimization problems. In the PVRP a fleet of vehicles of identical capacity must be used to service a set of customers over a planning period of several days. Each customer specifies a service frequency, a set of allowable day-combinations and a quantity of product that the customer must receive every time he is visited. For example, a customer may require to be visited twice during a 5-day period imposing that these visits take place on Monday-Thursday or Monday-Friday or Tuesday-Friday. The problem consists in simultaneously assigning a day- combination to each customer and in designing the vehicle routes for each day so that each customer is visited the required number of times, the number of routes on each day does not exceed the number of vehicles available, and the total cost of the routes over the period is minimized. We also consider a tactical variant of this problem, called Tactical Planning Vehicle Routing Problem, where customers require to be visited on a specific day of the period but a penalty cost, called service cost, can be paid to postpone the visit to a later day than that required. At our knowledge all the algorithms proposed in the literature for the PVRP are heuristics. In this thesis we present for the first time an exact algorithm for the PVRP that is based on different relaxations of a set partitioning-like formulation. The effectiveness of the proposed algorithm is tested on a set of instances from the literature and on a new set of instances. Finally, the PDPTW is to service a set of transportation requests using a fleet of identical vehicles of limited capacity located at a central depot. Each request specifies a pickup location and a delivery location and requires that a given quantity of load is transported from the pickup location to the delivery location. Moreover, each location can be visited only within an associated time window. Each vehicle can perform at most one route and the problem is to satisfy all the requests using the available vehicles so that each request is serviced by a single vehicle, the load on each vehicle does not exceed the capacity, and all locations are visited according to their time window. We formulate the PDPTW as a set partitioning-like problem with additional cuts and we propose an exact algorithm based on different relaxations of the mathematical formulation and a branch-and-cut-and-price algorithm. The new algorithm is tested on two classes of problems from the literature and compared with a recent branch-and-cut-and-price algorithm from the literature.