Abstract
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 covariancematrix having a central whiteWishart 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.
Highlights
The performance of information-theoretic-based methods for model selection is difficult to analyze for small sample sizes
We introduce a new method to evaluate the small sample performance of two information-theoretic-based methods commonly used in signal processing for a specific type of model selection: estimating the number of directional sources from the output signal of an array
Analyses show that for large sample sizes, the Minimum Description Length (MDL) is a consistent estimator for the number of sources, while the Akaike Information Criterion (AIC) tends to overestimate the number of samples [9]
Summary
The performance of information-theoretic-based methods for model selection is difficult to analyze for small sample sizes. We introduce a new method to evaluate the small sample performance of two information-theoretic-based methods commonly used in signal processing for a specific type of model selection: estimating the number of directional sources from the output signal of an array. The exact distribution of the largest sample eigenvalue has been derived for arbitrary array sizes but is only valid in the limit of large sample sizes [17]. A later attempt to derive an approximation to the exact distribution valid for finite sample sizes required the use of expressions that are difficult and computationally expensive to evaluate numerically [18].
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
