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首页> 外文期刊>Waves in Random Media >New results in applied scattering theory: the physical-statistics approach, including strong multiple scatter versus classical statistical-physical methods and the Born and Rytov approximations versus exact strong scatter probability distributions
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New results in applied scattering theory: the physical-statistics approach, including strong multiple scatter versus classical statistical-physical methods and the Born and Rytov approximations versus exact strong scatter probability distributions

机译：应用散射理论的新结果：物理统计方法，包括强多重散射与经典统计物理方法以及Born和Rytov逼近与精确强散射概率分布

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In order to carry out effective signal processing for signal detection and estimation in scatter-dominated environments, it is necessary to obtain the needed probability distributions and probability densities (PDFs) of the received scatter. In general, the received scatter is non-Gaussian and often strongly so. It is also dominated by multiple-scatter contributions. This is particularly the case for (radar) scatter off random interfaces at small angles, e.g. ocean wave surfaces and terrain, as well as acoustically (sonar) off the ocean surface and bottom. For 'classical' theory, based on statistical-physical (S-P) models and methods, the analytical construction of the required PDFs is beyond the general reach of S-P theory. The present paper reviews, amplifies and extends with new material the author's recently developed physical-statistical (P-S) alternative equivalent to classical (S-P) formulations. Here the fundamental innovation., starting with the basic Langevin equation of propagation in operational form, is to replace the explicit physical model, including boundary and initial conditions, with a purely statistical model based on a counting functional representation of the scattering process. A decomposition principle (DP) establishes the independence of different (k greater than or equal to 1) orders of multiple scatter. This in turn leads to the application of Poisson statistics, from which the characteristic functions of each scatter order and their totality can then be constructed. The appropriate Fourier and Hilbert transforms next provide the desired (first-order) PDFs and exceedance probabilities (EPs). Characteristic two-scale environments are next considered, in which the scattering ensemble is accordingly modulated slowly vis-a-vis the more rapidly decorrelating local scatter. For this it is shown that the modulation effect is physically well modelled by a Gamma-PDF. The result is the well known Jakeman K-distribution. In addition, when there are a few 'large' scatterers (e.g. breaking waves, bubble patches, irregular terrain, etc), the author's canonical class A non-Gaussian noise model is indicated and results in the new KA-PDF. The latter is also a common phenomenon, as shown by sample data from radar and sonar experiments, and is well replicated by theory. Both 'single-look' and 'multiple-look' results are developed for the first-order PDFs and exceedance probabilities of the normalized envelope sums epsilon(L) (= Sigma(l)epsilon(l)) under I.i.d. conditions. A number of equivalent analytic methods for evaluating their integral forms are also developed for the more complex cases including coherent components (signals) and accompanying ambient noise. Finally, using the classical operational form of the Langevin equation for the scattered field, one can readily show that the (nonlinear) Rytov approximation (similar to exp psi(1)) contains all orders (k greater than or equal to 1) of scatter versus the weak-scatter Born approximation, which is linear and limited to single scatter (k = 1). Furthermore, it is seen that the Rytov approximation is a quasi-weak approximation, since its magnitude is limited to psi(1) much less than 2, but is still better than the Born approach, as expected. Under these conditions the Rytov approximation supports a log-normal (first-order) PDF. The paper concludes with a concise comparison of the various capabilities of the P-S and classical S-P approaches to scattering phenomena, along with the scope of the resulting PDFs in describing clutter and reverberation. [References: 47]
机译：为了在散射为主的环境中执行有效的信号处理，以进行信号检测和估计，必须获得接收到的散射所需的概率分布和概率密度（PDF）。通常，接收到的散射是非高斯的，并且通常是非高斯的。它也以多散点贡献为主。对于（雷达）以小角度散射随机界面的情况尤其如此，例如海浪表面和地形，以及海面和海底的声音（声纳）。对于“经典”理论，基于统计物理（S-P）模型和方法，所需PDF的分析构造超出了S-P理论的一般范围。本文回顾，扩大并用新材料扩展了作者最近开发的等效于经典（S-P）公式的物理统计（P-S）替代品。此处的基本创新是，从基本的兰格文运算形式的传播形式开始，以基于散射过程的计数函数表示的纯统计模型代替显式物理模型（包括边界条件和初始条件）。分解原理（DP）建立了不同（k大于或等于1）阶多重散布的独立性。反过来，这导致了泊松统计的应用，由此可以构造每个散布顺序的特征函数及其总和。接下来，适当的傅里叶和希尔伯特变换将提供所需的（一阶）PDF和超出概率（EP）。接下来考虑特征性的两级环境，其中相对于较快速地去相关的局部散射，散射集合被缓慢地调制。为此，表明调制效果在物理上可以通过Gamma-PDF很好地建模。结果就是众所周知的Jakeman K分布。此外，当存在一些“大”散射体（例如，碎波，气泡斑块，不规则地形等）时，将指示作者的规范A类非高斯噪声模型，并生成新的KA-PDF。后者也是一种常见现象，如雷达和声纳实验的样本数据所示，并在理论上得到了很好的复制。针对一阶PDF开发了“单眼”和“多眼”结果，并且I.i.d下归一化包络和epsilon（L）（= Sigma（l）epsilon（l））的超出概率。条件。对于更复杂的情况，还开发了许多等效的分析方法来评估其整体形式，包括相干分量（信号）和伴随的环境噪声。最后，对于散射场，使用Langevin方程的经典运算形式，可以很容易地表明，（非线性）Rytov近似值（类似于exp psi（1））包含所有阶数的散射（k大于或等于1）。相对于弱散射Born近似，后者是线性的并且限于单散射（k = 1）。此外，可以看出Rytov逼近是准弱逼近，因为它的大小被限制为 psi（1）远小于2，但仍然比Born方法好，如预期的那样。在这些条件下，Rytov近似值支持对数正态（一阶）PDF。本文以对P-S和经典S-P散射现象的各种功能的简要比较进行了总结，并得出了描述杂波和混响的PDF的范围。 [参考：47]

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