Statistical Methods for Cooperative and Distributed Inference in Wireless Networks

This thesis is concerned with application of statistical methods – namely, random matrix theory (RMT) and belief propagation (BP) – in distributed inference problems in wireless communication networks. The term “distributed inference” denotes, in general, detection/estimation involving multiple network nodes (“sensors”) that collect physical measurements and communicate with each other. Such problems can be classified as homogeneous, where all nodes observe the same hidden variable, or heterogeneous, where a different hidden variable exists for each node. The first part of the thesis focuses on a homogeneous inference problem, i.e., multi-sensor signal detection in cognitive radio networks. Techniques based on the eigenvalues of sample covariance matrices are employed. The performance of such methods is analyzed mathematically, by using RMT results. The second part addresses several heterogeneous inference problems: 1. distributed localization (in a hybrid scenario with GPS and terrestrial range measurements); 2. signal detection in non-uniform radio environments; 3. cooperative signal detection in the presence of malicious users. For each of these problems, BP-based Bayesian inference methods are adopted. In cases 1 and 2, in particular, the BP algorithm is implemented in a decentralized fashion, by exploiting the correspondence between statistical graph and physical network structure. Finally, a variation of the BP algorithm is proposed, providing improved performance in the case of graphs containing cycles.