Sample size cognizant detection of signals in white noise

Details Sample size cognizant detection of signals in white noise Sample size cognizant detection of signals in white noise

2007-04-25

arxiv.org/abs/0704.3287v1

Computer Science

Information Theory

To appear in the Proceedings of the 8th IEEE International Workshop on Signal Processing Advances in Wireless Communications (

Scientific paper

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.

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