Robust signal selection for the matched filter

A matched filter's performance is strongly related to the signal being detected and can be shown to be optimal when the signal is an eigenvector of the noise correlation matrix corresponding to a minimum eigenvalue. When fewer correlations are known than would be necessary to specify such an eigenvector, it is natural to choose a signal which is robust to the implied uncertainty in the noise dependency structure. This is shown to be tantamount to finding a tight upper bound on the minimum eigenvalue over all correlation matrices within the uncertainty class. Such a bound is achieved by the reduced correlation matrix of order equal to the number of available correlations, and hence the robust signal is shown to have this length. No matter how reasonable, any assumption used to extend the correlation matrix can degrade performance; a system designer should not try to use information that is not available.<
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