Detection of Signals in Chaos

Abstract

<p>A new method for the detection of signals in "noise", which is based on the premise that the "noise" is chaotic with at least one positive Lyapunov exponent, is presented. The method is naturally rooted in nonlinear dynamical systems, and relies on neural networks for its implementation.</p> <p>We first present a theoretical basis for methods of modeling the underlying dynamics of a chaotic system using a time series. The subject matter selected for this part of the thesis is written with emphasis on experimental studies of chaos. Specifically, we discuss the issues involved in the reconstruction of chaotic dynamics, attractor dimensions, and Lyapunov exponents. We describe procedures for the estimation of the correlation dimension and the Lyapunov exponents. The method of false nearest neighbors analysis fur finding the minimum embedding dimension is described. The need for an adequate data length is stressed.</p> <p>In the second part of the thesis we apply the chaos-based method to the radar detection of a small target in sea clutter. To justify the applicability of the new method to this problem, we clearly need to show in a convincing way that sea clutter is indeed the result of a chaotic dynamical system. We do this by presenting the results of a detailed experimental study using surface-truthed real-life data collected by means of an instrument quality radar at different geographic locations. Specifically, we show that (1) sea clutter has a finite correlation dimension, (2) the largest Lyapunov exponent of sea clutter is positive, and (3) sea clutter is locally predictable. Most importantly, we show that both the correlation dimension and the largest Lyapunov exponent are essentially invariant to the choice of radar signal component used to construct the time series, and that the correlation dimension and Lyapunov exponent do not appear to change appreciably with sea state or with geographic locations. These results suggest that there may exist universal chaotic structure responsible for the generation of sea clutter. Perhaps the most dramatic result presented in the thesis is the fact that this prior information (i.e., the knowledge that sea clutter exhibits chaotic behavior) can be exploited to build a chaos-based detettor operating on amplitude information only (as in a noncoherent marine radar), realizing a performance comparable to that of a "conventional" receiver using coherent radar data (i.e., both amplitude and phase). This result points to the potential of trading off sophisticated but inexpensive computer software for expensive microwave hardware. Lastly, we show experimentally that a chaos-based coherent detector can provide a further improvement in radar detection performance.</p>