Estimation of the Number of Signals in White Noise via Large-Sample and High-Dimensional Asymptotic Theory

This paper focuses on estimating the number of source signals embedded in Gaussian white noise. We address this problem via a sequence of nested hypothesis tests, and construct variance statistics based on eigenvalues of the sample covariance for each candidate hypothesis. Then, a detailed statistical analysis of these statistics is carried out in both the large-sample and high-dimensional regimes. According to this analysis, we propose a new scheme for determining the number of source signals in both the sample-rich and sample-starved cases. Finally, numerical examples are presented to show its superiority compared to some existing estimation methods.