False Alarm Rate Estimation for Information-Theoretic-Based Source Enumeration Methods

The Tracy-Widom distribution is used to determine the false alarm rate of information theoretic methods that statistically estimate the number of sources in a multichannel receiver input. The Tracy-Widom distribution is the limiting distribution for the largest eigenvalue of a covariance matrix having a central white Wishart distribution. Such covariance matrices are produced by the output of multi-channel receivers whose signals can be characterized as zero-mean Gaussian processes. The Tracy-Widom distribution is used to estimate the false alarm rate of the Akaike Information Criterion and Minimum Description Length methods when no external sources are present. The Tracy-Widom distribution along with the eigenvalue inclusion principle is used to obtain an upper bound on the false alarm rate of the Akaike Information Criterion and Minimum Description Length when one external source is present. Monte-Carlo simulations were performed to demonstrate the effectiveness of both methods for cases where both the array and data sample sizes are small.