Detection of Dependent Heavy-Tailed Signals

Abstract

This paper examines the problem of detection of dependent $\alpha$ -stable signals. Measurements of several phenomena exhibit non-Gaussian, heavy-tailed behavior in their probability density functions (p.d.f.); we use the class of $\alpha$ -stable distributions to characterize these signals. When two sensors make simultaneous measurements of such phenomena, these heavy-tailed realizations are dependent across sensors. The intersensor dependence is modeled using copulas. We consider a two-sided test in the Neyman–Pearson framework and present an asymptotic analysis of the generalized likelihood test (GLRT). Both, nested and non-nested models are considered in the analysis. The performance of the proposed scheme is evaluated numerically on simulated data, as well as indoor seismic data. With appropriately selected models, our results demonstrate that a high probability of detection can be achieved for false alarm probabilities of the order of $10^{-4}$ .