Assessment of chaos-based FM signals for range–Doppler imaging

The authors analysed a set of random frequency modulated (FM) signals for wideband radar imaging and assessed their resolution capability and sidelobe distribution on the range–Doppler plane. To this effect deterministic, bounded, nonlinear iterated maps were first considered. The initial condition of each chaotic map was assigned to a random variable to obtain statistically independent samples with invariant probability density function. The resulting sequences, which have white time–frequency representations, are used to construct wideband stochastic FM signals. These FM signals are ergodic and stationary. The autocorrelation, spectrum and the ambiguity surface associated with each of the FM signals were characterised. It was also demonstrated that the ambiguity surface of an FM signal generated via a chaotic map with uniform sample distribution and tail-shifted chaotic attractor is comparable to the ambiguity function of a Gaussian FM signal.