In previous work, we constructed wideband FM signals for high range resolution applications using the non-linear Lorenz system, which has a set of three state variables and three control parameters. The FM signals were generated using any one of the three state variables as the instantaneous frequency which was then controlled by adjusting the values of the parameters in the chaotic regime. We now determine the spectral characteristics of the Lorenz FM signal and compare the spectral characteristics to those of a similar FM signal based on the Lang-Kobayashi system. We show that for either chaotic system, the local linearity of the attractor yields an FM signal with a distinct chirp behavior. Irrespective of the statistical independence of the chaotic flow samples, we show that the chaotic FM signal follows Woodward's theorem in the sense that the spectrum of the FM signal follows the shape of the probability density function of the state variable. The chirp rate of the FM signal can be controlled through a time-scale parameter that compresses or expands the chaotic flow. As the chaotic flow evolves in time, so does the spectrum of the corresponding FM signal, which experiences changes in center frequency and bandwidth. We show that segments of the signal with a high chirp rate can be significantly compressed to achieve high range-Doppler resolution. The ability to change the center frequency and the shape of the spectrum is interpreted as added frequency agility.

Date Published: 21 June 2011
PDF: 10 pages
Proc. SPIE 8021, Radar Sensor Technology XV, 80210V (21 June 2011); doi: 10.1117/12.884391

Published in SPIE Proceedings Vol. 8021:
Radar Sensor Technology XV
Kenneth I. Ranney; Armin W. Doerry, Editor(s)