Optimal Detection Using Bilinear Time Frequency and Time Scale Representations
Sayeed, Akbar M.
Jones, Douglas L.
Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. All existing time-frequency formulations of quadratic detection either implement classical optimal detectors equivalently in the time-frequency domain, without fully exploiting the structure of the TFR, or attempt to exploit the nonstationary structure of the signal in an <i>ad hoc</i> manner. We identify several important nonstationary composite hypothesis testing scenarios for which TFR/TSR-based detectors provide a "natural" framework; that is, in which TFR/TSR-based detectors are both optimal and exploit the many degrees of freedom available in the TFR/TSR. We also derive explicit expressions for the corresponding optimal TFR/TSR kernels. As practical examples, we show that the proposed TFR/TSR detectors are directly applicable to many important radar/sonar detection problems. Finally, we also derive optimal TFR/TSR-based detectors which exploit only partial information available about the nonstationary structure of the signal.