Random matrix theory based distributed acoustic sensing

Random matrices exhibit interesting statistical properties which are studied under random matrix theory (RMT). In this research study, we present a novel approach for fiber optic distributed acoustic vibration sensing (DAS) systems which is based on the recent results of RMT. Our focus is the phase-sensitive optical time domain reflectometry (phi-OTDR) systems and the evaluation of the RMT at the photo-detection output. Inspired by the successful application of RMT in diverse signal processing applications, the RMT based signal detection methodology is transferred to DAS domain. The classical spectral theorem is revisited with special emphasis on the covariance of the measured Rayleigh backscattered optical energy which is a Wishart type random matrix. A real phi-OTDR system is evaluated for experimental verification of the statistical distributions of the extreme eigenvalues of the optical covariance matrix. It is shown that even with limited measured data, after proper conditioning and scaling of the optical detector output, the empirical bulk eigenvalue distributions are in good agreement with the analytical proof for the infinite data assumption. It is experimentally verified that the extreme eigenvalues of the optical covariance are bounded by the Marchenko-Pastur theorem and any outlier can be considered as a vibration presence. Additionally, it is shown that the eigenvalue bounds can be used to detect and track the vibrations along a fiber optic cable route.