Clock Synchronization in Wireless Sensor Networks: Statistical and Algorithmic Analysis

In the past few years, the impressive growth of applications performing tasks in a distributed fashion has been enabled by the availability of tiny, inexpensive devices which, in turn, has been made possible by the recent micro-electromechanical technology advancements. Sparsely disposing small intelligent appliances throughout a specific area is something that the community has become used to. Low cost and low power sensing devices equipped with telecommunication hardware are attractive for use in an infrastructure-less network in which the absence of a central node stands out, making robustness be one of the strengths of this kind of networks. Environmental monitoring and military surveillance are just a few examples of the number of applications suitable for sensor networks; in fact, home automation and several health services also can be implemented given that a distributed network of sensors exists. Sensors need to keep track of a common time scale. This is fundamental for prolonging the network lifetime, making channel access schemes work properly, for example, or for allowing precise duty cycling among the nodes. Clock synchronization is also basic if the goal of a running application is to track moving objects in the battlefield or, more generally, to perform distributed processing of the sensed data. Since the local notion of time in a sensor is based on a low quality local oscillator, it turns out that even small changes in the environmental conditions, like temperature and pressure, lead to modification in the oscillation frequency of the quartz crystals, thus producing time discrepancies among different sensor nodes as time goes by. This thesis tackles the problem of clock synchronization in sensor networks, both from a perspective of clock parameters estimation and from an algorithmic point of view, to pursue the final goal of making nodes agree on a common time scale, all across the network. In the first part of the thesis, the so-called two-way message exchange between two nodes is thoroughly analyzed. After recalling existing results on clock parameters estimation exploiting data collected via this message exchange process on the wireless channel, an innovative mathematical framework is introduced, which encompasses several common assumptions for the random delays present in the collected data, in a more general treatment. Based on this new framework, a factor graph-based clock offset estimator for wireless sensor networks is proposed and evaluated. Comparison of the variance of the estimation error with classical bounds available in the literature shows that the new estimator has extremely good performance, therefore it can be considered outstanding among Bayesian clock offset estimators. The focus of the second part of the thesis is on the design of distributed consensus algorithms in wireless sensor networks, especially for observations averaging purposes. In fact, an innovative fast consensus algorithm is proposed and evaluated, based on the alternating direction multipliers method, which is a distributed method used to solve minimization problems in an iterative fashion. The new consensus algorithm is compared with the state-of-the-art of fast consensus, showing an excellent convergence rate and an outstanding noise resilience. The proposed algorithm is then applied to solve a network-wide clock synchronization issue, assuming both clock skew and offset for the nodes in the network, showing a relevant performance improvement with respect to previously proposed consensus-based synchronization schemes. Finally, the Appendix contains a work whose topic falls out of the main stream of this thesis: in uplink cellular networks, based on the knowledge of channel statistics, surrounding base stations are carefully and iteratively chosen in order to provide the mobile terminal a certain quality of service in terms of the maximum allowed outage probability, with the aim of minimizing the overall backhaul network usage.