A Flexible-Tailed Model for Radar Sea Clutter Amplitudes Based on the Smoothly Truncated Lévy Flight

Due to the intricate physical mechanisms of sea clutter, its amplitude distribution exhibits highly variable tails under different radar and environmental conditions. However, existing models have limited ability to capture such variability. This limitation impedes a comprehensive understanding of clutter characteristics and can result in mismatches between real-world data and the selected clutter models, potentially degrading radar performance in model-based applications such as clutter classification, target detection, and tracking. Given these challenges, we propose a flexible-tailed clutter amplitude model to enhance modeling generality, by exploiting the smoothly truncated Lévy flight (STLF). Specifically, we first introduce the STLF to model the real and imaginary parts of clutter. By adding a cut-off parameter, the STLF extends the symmetric <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\alpha$</tex-math></inline-formula>-stable (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S\alpha S$</tex-math></inline-formula>) distribution, enabling widely tunable tail behavior that ranges from Gaussian tails to heavy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$S\alpha S$</tex-math></inline-formula> tails. This flexible tail-tuning capability enhances its generality for varying conditions. Building on this, we then propose a bivariate isotropic STLF complex clutter model. The corresponding amplitude model is derived and named flexible-tailed Rayleigh (FT-Rayleigh). Moreover, an empirical characteristic function-based method is devised for estimating the FT-Rayleigh parameters. Finally, the FT-Rayleigh amplitude model is evaluated using the Council for Scientific and Industrial Research Fynmeet radar and McMaster IPIX radar data sets, encompassing various sea states, polarizations, and noise levels. The experimental results indicate its effectiveness and the superior generality over the existing models.