Nonparametric detection of the number of signals and random matrix theory

Nonparametric detection of the number of sources is a fundamental and extensively studied problem in signal processing. The common approach to solving this problem is via information theoretic criteria, in particular minimum description length (MDL). In this paper we propose a different approach and present a new algorithm based on a sequence of hypothesis tests. Our algorithm combines recent results from random matrix theory with a matrix perturbation approach. The new method has superior performance over the standard MDL estimator, as shown by simulations.