Sample Eigenvalue Based Detection of High-Dimensional Signals in White Noise Using Relatively Few Samples

The detection and estimation of signals in noisy, limited data is a problem of interest to many scientific and engineering communities. We present a mathematically justifiable, computationally simple, sample-eigenvalue-based procedure for estimating the number of high-dimensional signals in white noise using relatively few samples. The main motivation for considering a sample-eigenvalue-based scheme is the computational simplicity and the robustness to eigenvector modelling errors which can adversely impact the performance of estimators that exploit information in the sample eigenvectors. There is, however, a price we pay by discarding the information in the sample eigenvectors; we highlight a fundamental asymptotic limit of sample-eigenvalue-based detection of weak or closely spaced high-dimensional signals from a limited sample size. This motivates our heuristic definition of the effective number of identifiable signals which is equal to the number of "signal" eigenvalues o...

• Type: Journal
• Year: 2008
• Where: TSP
• Authors: R. R. Nadakuditi, A. Edelman
• Keywords: Effective Number, Fundamental Asymptotic Limit, Sample Size, TSP 2008