  The detection and estimation of signals in noisy, limited data is a problem
of interest to many scientific and engineering communities. We present a
computationally simple, sample eigenvalue based procedure for estimating the
number of high-dimensional signals in white noise when there are relatively few
samples. We highlight a fundamental asymptotic limit of sample eigenvalue based
detection of weak high-dimensional signals from a limited sample size and
discuss its implication for the detection of two closely spaced signals.
  This motivates our heuristic definition of the 'effective number of
identifiable signals.' Numerical simulations are used to demonstrate the
consistency of the algorithm with respect to the effective number of signals
and the superior performance of the algorithm with respect to Wax and Kailath's
"asymptotically consistent" MDL based estimator.
