Generation of high-range resolution radar signals using the Lorenz chaotic flow

Abstract

ABSTRACT We propose a novel approach to generate chaotic Frequency Modulated (FM) signals with potential applications in high-resolution radar imaging. The technique relies on the output of an n-dimensional (n>2) non-linear system that exhibits chaotic behavior. For simplicity, we have chosen the Lorenz system which has a set of thr ee state variables x, y and z, and three control parameters !, , and 1 . FM signals are generated using any one of the state variables as the instantaneous frequency by varying the values of ! and . The obtained FM signal is ergodic and stationary and the time samples exhibit an invariant probability density function. The corresponding pseudo-phase orbits reveal themselves as a strange attractor that may take on the shape of a Mobius strip depending on the time evolution of the signal. A time-frequency analysis of the signal shows that the spectrum is centered on a time-dependent carrier frequency. Thus, the FM signal has a high time-bandwidth product similar to that of a chirp. However, the carrier frequency continuously shifts in a linear or quadratic pattern over a finite frequency range. A desirable feature of th e signal is that the width of its autocorrelation’s mainlobe approaches the reciprocal of the bandwidth. Furthermore, simulations show that the average of the time autocorrelation falls quickly and is void of sidelobes. Keywords: Lorenz attractor, ergodic, Mobius strip, time-frequency analysis