改进分形海面模型散射信号的分形特性分析

针对分形海面模型的功率谱在空间波数小于基波波数时不能满足正幂率的问题，提出一种统计模型和归一化带限Weierstrass分形模型相结合的1维海面模型，确定了表面功率谱的闭式解，表面功率谱和有关文献的数据进行了对比。在满足Kirchhoff近似的条件下推导该模型电磁散射系数的闭式解，计算了散射系数随时间变化的Hurst指数，进而求得其分形维数。从数值仿真结果可知，表面功率谱和PM谱、南海的实测数据都拟合得很好，验证了模型的有效性，海面所接收信号随时间变化是分形的，并且其分形维数与分形海表面的分形维数几乎相等。

Fractal analysis of the scattering signal from the improved fractal model of the sea surface

The power spectrum of the fractal sea-wave model is unable to satisfy the positive power law when spatial wave numbers are smaller than the fundamental wave number. To address this problem, a one-dimensional sea-wave model was proposed by combining the statistical sea model and the normalization band-limited Weierstrass-Mandelbrot fractal sea model. With the proposed method, the closed form expression of the power sea-wave spectrum was calculated, and the power sea-wave spectrum was compared with the results in literature. Electromagnetic scattering coefficient of the improved model based on the Kirchhoff approximation was derived. The Hurst parameters of the scattering coefficient against time were calculated and its fractal dimension was derived. Simulation results show that the power sea-wave spectrum corresponds to the common spectrum of Pierson-Moskowitz and the real data of the South China Sea. Thus, the accuracy of the improved model was validated. The received signal against time was plotted as the fractal curve, whose fractal dimension is equal to that of the sea surface.