Structure and dynamics of wireless communication systems

Wireless networks are going through a fundamental change. User-deployed and selforganizing networks are becoming key technologies to meet the exponentially increasing requirements for capacity. This implies a shift from carefully planned networks, for which basic feedback control techniques suffice for maintaining stability and good performance, towards deployment and analysis of more complex spatio-temporal networked dynamical systems. Further, techniques such as dynamic spectrum access will potentially couple the dynamics of multiple heterogeneous wireless systems together in a manner not present in current networks. There is accordingly an urgent need to develop the necessary theoretical foundations for reasoning about and developing optimization and control solutions for such systems. The work reported in this thesis comprises a first attempt at developing such foundations applying techniques developed in spatial statistics, theoretical physics and dynamical systems communities. The approach taken consists of both laying out the theoretical fundamentals of the methods that appear as most promising in dealing with the above mentioned challenges, and specifically applying them for a number of problems in the wireless communications domain. In several cases the presented applications yield first quantitative results on structure and dynamics of networked systems beyond simple mean value analyses. The obtained results can be divided into three categories, focusing on node locations, spectrum usage, and applications of dynamical systems techniques, respectively. First, we give detailed characterization of the correlation structures in network node locations for a number of different communication systems. We show how these can be modeled accurately using so-called Gibbs point process models originating from statistical physics and spatial statistics, and explore the performance implications of the derived models. Second, we develop an extensive quantitative understanding of usage of radio spectrum in both spatial and temporal domains, and use these models to arrive at alternative methods for estimating and reasoning about radio coverage for both off-line network planning applications as well as for online use. Third, we apply state space techniques from modern dynamical systems theory for characterization of complexity of network dynamics as well as for developing systematic techniques for evaluation of the performance impact and sensitivity of probabilistic models. For each of these three focus areas there is a strong emphasis on working with actual network data, obtained from different sources including some measurement campaigns to which the author has participated in. Synthetic models used in the literature are analyzed as well, but mainly by way of contrast. We have also attempted to cover as wide range of data sets as possible, usually obtained from completely different types of systems, in order to assess the true range of applicability for the methods utilized and developed.