海面散射信号的分形分析及分形维数估计

Fractal analysis and fractal dimension estimate of signal scattered from sea surface

针对经典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,提出了一种同时具有海浪稳态和瞬态特性的海面模型.该模型将Longuet-Higgins模型和归一化带限WM分形海面模型相结合,解决了分形海面模型不考虑从其他方向传来的涌浪问题.研究了增加涌浪后的分形海面所获得的散射信号的分形特性,从数学上证明了增加涌浪后的二维分形海面所获得的随时间变化的散射信号是分形的,确定了其分形维数的上下界,并进行了仿真验证.仿真结果表明：该散射信号的分形特性几乎不受海面和雷达状态的影响,分形维数是海面内在的固有参量.

Aiming at the problem that the power spectrum of sea surface fractal model could not satisfy the positive power law when spatial wave numbers was smaller than the fundamental wave number,a sea surface model with steady and transient characteristics was proposed by combining Longuet-Higgins sea surface model and normalization band-limited WM sea surface fractal model. This reconstructed sea surface model solved the problem that sea surface fractal model without considering surge coming from the other directions. The fractal characteristics of scattering signal from the fractal sea surface added surge was studied. Mathematical theory proved that the received scattering signal from the 2 D fractal sea surface added surge against time was fractal curves,and the upper and lower bounds of the fractal dimension was determined. Finally,the correctness of the demonstration conclusion was proved by simulation. Simulation results show that the fractal characteristics of this scattering signal are hardly affected by the situation of sea surface and radar,and the fractal dimension is the inherent parameter of the sea surface.