Signal detection in a nonstationary environment reformulated as an adaptive pattern classification problem

Concerns the improved detection of a nonstationary target signal in a nonstationary background. Ways to deal with the issue of nonstationarity are discussed, starting with Loeve's probabilistic theory of stationarity processes (1946, 1963). Three important tools emerge: the dynamic spectrum, the Wigner-Ville distribution as an instantaneous estimate of the dynamic spectrum and the Loeve spectrum. Procedures for the estimation of these spectra are described, and their applications are demonstrated using real-life radar data. Time, an essential dimension of learning, appears explicitly in the dynamic spectrum and Wigner-Ville distribution and implicitly in the Loeve spectrum. In each case, the 1D time series is transformed into a 2D image where the presence of nonstationarity is displayed in a more visible manner than in the original time series. This sets the stage for reformulating the signal detection problem as an adaptive pattern classification whereby we can exploit the learning property of neural nets. Hence, we describe a novel learning strategy for distinguishing between the different classes of received signals, such as 1) there is no target signal present in the received signal; 2) the target signal is weak; and 3) the target signal is strong. We present a case study based on real-life radar data. The case study demonstrates that the adaptive approach described is superior to the classical approach.