Fractal characterisation of sea-scattered signals and detection of sea-surface targets

Abstract

Fractal theory is applied to the analysis of real radar signals which are scattered from rough sea surfaces. The databases formed by sampling the radar signals include the two general cases, i.e. both forward-scattered and backscattered signals. The signals for the two cases were recorded using two entirely different radar systems and at two entirely differently geographic locations. The box counting method is used to estimate the fractal dimension of the scattered signals. To corroborate this result, a computation of the fractal dimension is based on the index α in the power spectrum relation, P(f) ∞f−α. The estimates derived from both methods are consistent. It is observed that the forward-scattered and back-scattered radar signals have very similar fractal dimensions, i.e. 1.746 ± 0.033 for the 9.6 GHz forward-scattered signals, 1.753 ± 0.024 for the 8.6 GHz forward-scattered signals, and 1.758 ± 0.015 for the 9.39 GHz back-scattered signals. Finally, it is shown that there is a detectable variation in the fractal dimension when a target is present. Based on this variation, it is therefore possible to detect the presence of a target by observing the fractal dimension of the radar returns.