Can Sea Clutter and Indoor Radio Propagation be Modeled as Strange Attractors?

Abstract

Sea clutter is the backscattered returns from a patch of the sea surface illuminated by a radar pulse. The amplitude waveforms of sea clutter and indoor radio propagation are very complicated. Can the apparent randomness of these waveforms be attributed to be generated by low‐dimensional chaos? Based on the assumption that a chaotic attractor is characterized by a non‐integer fractal dimension and a positive Lyapunov exponent, Haykin et al (1992) concluded that sea clutter while Tannous et al (1991) concluded that indoor radio propagation data were chaotic. However, a numerically estimated non‐integral fractal dimension and a positive Lyapunov exponent may not be sufficient indication of chaos. Other researchers have also indirectly questioned the chaoticness of the sea clutter. We employ a more stringent criterion for low‐dimensional chaos developed by Gao and Zheng (Phys. Rev. E, 1994) to study a two minute duration sea clutter data provided by Haykin, and indoor radio propagation data measured at UCLA, and show that these data are not chaotic. We carry out a multifractal analysis and find that sea‐clutter data can be modeled as multiplicative multifractals with a lognormal envelope distribution, while the radio propagation data can be modeled as a weak multifractal in the sense of structure function technique.