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We present a mathematically justifiable, computationally simple, sampleeigenvalue based procedure for estimating the number of high-dimensionalsignals in white noise using relatively few samples. The main motivation forconsidering a sample eigenvalue based scheme is the computational simplicityand the robustness to eigenvector modelling errors which are can adverselyimpact the performance of estimators that exploit information in the sampleeigenvectors.  There is, however, a price we pay by discarding the information in the sampleeigenvectors; we highlight a fundamental asymptotic limit of sample eigenvaluebased detection of weak/closely spaced high-dimensional signals from a limitedsample size. This motivates our heuristic definition of the effective number ofidentifiable signals which is equal to the number of "signal" eigenvalues ofthe population covariance matrix which exceed the noise variance by a factorstrictly greater than 1+sqrt(Dimensionality of the system/Sample size). Thefundamental asymptotic limit brings into sharp focus why, when there are toofew samples available so that the effective number of signals is less than theactual number of signals, underestimation of the model order is unavoidable (inan asymptotic sense) when using any sample eigenvalue based detection scheme,including the one proposed herein. The analysis reveals why adding more sensorscan only exacerbate the situation. Numerical simulations are used todemonstrate that the proposed estimator consistently estimates the true numberof signals in the dimension fixed, large sample size limit and the effectivenumber of identifiable signals in the large dimension, large sample size limit.

Sample eigenvalue based detection of high dimensional signals in white noise using relatively few samples