## 2 Concepts and Theory
### Tropospheric Scattering  
#### 2.3.1 Scattering Models  
Troposcatter refers to the scattering of signals caused by atmospheric irregularities in the troposphere. It has been recognized as a promising method for wireless communication beyond the line of sight by the Radiocommunication Sector of the International Telecommunication Union (ITU-R) [13]. Troposcatter has emerged as a promising candidate for communication beyond line-of-sight because it has important features including security and low transmission delay [28]. Since the 1950s, the characteristics of troposcatter propagation and its propagation mechanism have been detailed in numerous studies. Generally, three main theories have been proposed: turbulent incoherent scattering theory [15], coherent reflection by stable layers theory [16], and incoherent reflection by irregular layers theory [17]. The theory of incoherent scattering due to turbulence posits that the movement and variation of turbulent vortices create inhomogeneity with a continually changing dielectric permittivity and become sources of receiving signals. Coherent reflection by stable layers theory is based on the assumption that the atmosphere can be divided into a series of thin layers that reflect incident radio waves. In the theory of incoherent reflection by irregular layers, there are irregular layers in the troposphere formed by atmospheric convection. These layers have a wildly fluctuating refractive index gradient and reflect the radio waves from these irregular layer boundaries. It is obvious that incoherent scattering due to turbulence is essentially consistent with Bragg scattering, while stable layer reflection is similar to Fresnel reflection, which can be observed using UHF and VHF radars. It is generally accepted that troposcatter is the result of a combination of these three models. Therefore, the scattering of troposcatter can generate stronger signals than the scattering caused by a single model alone. A previous study noted that the combination of these three models has the same form of scattering cross-section, \(\sigma\), and \(\sigma\) of the troposcatter can be written as follows [14]:  
\[\sigma=\overline{B\left(\frac{\mathrm{d}\varepsilon_{r}}{\mathrm{d}h}\right)^{ 2}}\lambda^{n}\varphi^{-m} \tag{5}\]  
where \(B\), \(n\), and \(m\) are constants and are measured experimentally; \(\varepsilon_{r}\) is the dielectric constant; \(h\) is the height; and \(\varphi\) is the glancing angle. In fact, since radar mainly detects the backscattered signal, the value of the grazing angle is fixed (the grazing angle is a right angle). Therefore, the remaining terms other than wavelength can be regarded as constant terms affected by the atmosphere, and Equation (5) can be rewritten as  
\[\sigma=C\lambda^{n} \tag{6}\]  
where  
\[C=B\overline{\left(\frac{\mathrm{d}\varepsilon_{r}}{\mathrm{d}h}\right)^{2} }\varphi^{-m} \tag{7}\]  
Notably, when \(C\) equals \(0.38C_{n}^{2}\) and \(n\) equals \(-1/3\), Equation (6) for tropospheric scattering and Equation (3) for Bragg scattering are consistent. Thus, tropospheric scattering can be regarded as a general theory of Bragg scattering. It is known that troposcatter is a phenomenon of signal scattering caused by atmospheric irregularities in the troposphere. The turbulent air mass is highly irregular and is constantly changing in terms of its shape, location, and orientation. As a result, electromagnetic waves are scattered (and reflected) in all directions. For this reason, researchers refer to this communication mode as tropospheric \"scattering\" rather than tropospheric \"refraction\" or tropospheric \"reflection\". A visual schematic is shown in Figure 1. The wide radar beam radiates the inhomogeneous turbulent mass. Because the air mass is small and heterogeneous, the radar waves are reflected and scattered in all directions at the same time by different reflective surfaces of the same air mass and by reflective surfaces of different air masses.