Signal Detection in a Nonstationary Environment Reformulated as an Adaptive Pattern Classification Problem

The primary purpose of this paper is the improved detection of a nonstationary target signal embedded in a nonstationary background. Accordingly, the first part of the paper is devoted to a detailed exposition of how to deal with the issue of nonstationarity. The material presented here starts with Loève’s probabilistic theory of nonstationary processes. From this principled discussion, three important tools emerge: the dynamic spectrum, the Wigner–Ville distribution as an instantaneous estimate of the dynamic spectrum, and the Loève 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 Loève spectrum. In each case, the one-dimensional time series is transformed into a two-dimensional image where the presence of nonstationarity is displayed in a more visible manner than it is in the original time series. This transformation sets the stage for reformulating the signal detection problem as an adaptive pattern classification problem, whereby we are able to exploit the learning property of neural networks. Thus, in the second part of the paper 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. In the third part of the paper we present a case study based on real-life radar data. The case study demonstrates that the adaptive approach described in the paper is indeed superior to the classical approach for signal detection in a nonstationary background.