Application of random matrix theory to acoustic modeling and signal processing

Abstract

Random matrix theory (RMT) characterizes the eigenvalues and eigenvectors of matrices composed of random entries [Bai/Silverstein, Springer, 2010]. Random matrices play an important role in a variety of acoustics and signal processing applications. For example, mode propagation through internal waves can modeled using random scattering matrices Hegewisch and Tomsovic showed that mode scattering can be analyzed using RMT [JASA, 2013]. In signal processing, the sample covariance matrix is an example of a random matrix that can be analyzed using RMT techniques. RMT differs from classical statistics because it derives results in the limit as both array size and number of measurements approach infinity. This type of asymptotic analysis is crucial because it facilitates the investigation of large dimensional matrices in scenarios with limited numbers of measurements. While results are derived in the infinite limit, many authors have shown that RMT provides useful predictions for finite size matrices derived from finite numbers of measurements. Research in RMT has grown substantially since the 1950s, and new theoretical results are rapidly emerging. This talk reviews several key results from the RMT literature and provides examples to illustrate the analysis of signal processing algorithms and acoustic propagation using these powerful methods.