Random matrix theory enabled performance analysis and algorithms for underwater signal processing

Abstract

Random matrices arise naturally in many undersea signal processing applications such as sonar and underwater acoustic communications. For example, the matrix formed by stacking a noisy time series of observations collected at a sensor array alongside each other is a random matrix. Random matrix theory provides a mathematical framework for reasoning about and understanding the structure in such noisy matrix-valued signals in an analogous manner to how Fourier analysis provides us a mathematical framework for reasoning about and understanding the structure in noisy vector valued signals. We highlight some recent breakthroughs in random matrix theory that have allowed us to predict the fundamental performance limits of weak signal detection, estimation and classification and discuss some recent successes where the theory has led to the development of powerful new algorithms for better estimating weaker signals than previously thought possible.