Detection of stochastic signals in the frequency domain

The optimum detector for a random signal, the estimator-correlator, is diff icult to implement. If the power spectral density (PSD) of a continuous tim e signal is known, a locally optimum detector is available. It maximizes th e deflection ratio (DR), a measure of the detector output signal-to-noise r atio (SNR). A discrete version of this detector is developed here, called t he discrete-MDRD, which takes a weighted sum of the spectral components of the signal data as the detection statistic. Its derivation is applicable to nonwhite noise samples as well. A comparison of this new detector against three other common types, through their DR values and simulation results, r eveals that the discrete-MDRD is near optimal at low SNRs. When the PSD of a signal is not known, a common test statistic is the peak of the PSD of the data. To reduce spectral variations, the PSD estimator fi rst divides the data sequence into several segments and then forms the aver aged PSD estimate. The segment length affects the DR values; the length tha t maximizes the DR a approximately the reciprocal of the signal bandwidth. Thus for unknown signal PSD, a detector that approaches the maximum DR is r ealizable from just the knowledge of the signal bandwidth, which is normall y available. Examples and simulation results are provided to illustrate the properties and performance of the new detector.