## 1 Introduction  
The effect of sand storms, among other phenomena, on signal propagation has gathered notable attention from many studies as communication and distant sensing are being utilized by many civil applications. As sand storms are a common meteorological phenomenon that will interfere with the highly anticipated advantages of wireless connectivity, different authors have attempted to structure mathematical representations of path attenuation to estimate the loss of signal energy, particularly when under unique environments. [PERSON] [1] developed the first known attenuation coefficient (\(A\)) expression for propagating waves in dust or sand storms by employing related scattering theories and assuming a monodisperse particle size distribution. Following a series of assumptions, derivations, and substitutions, the author arrived at a general model containing the following parameters:  
\[A=2*\frac{2\pi}{\lambda}\alpha_{0}*r*\Im\left(\frac{\varepsilon-1}{\varepsilon+ 2}\right)\text{dB}/\text{km}, \tag{1}\]  
where \(\lambda\) is the wavelength in meters (2\(\pi\)/\(\lambda\) = free space wavenumber), \(\alpha_{0}\) is the optical attenuation coefficient (dB per km), \(r\) is the particle radius in meters, and \(\Im\) of the parenthesized expression corresponds to the imaginary part of the refractive index of the volume of space containing particulates; and \(\varepsilon\) is the complex relative permittivity of the particles given by \(\varepsilon^{\prime}-j\varepsilon^{\prime\prime}\). Furthermore, [PERSON] [1] demonstrated mathematically, before obtaining the attenuation coefficient expression, \(\alpha_{0}\)'s relationship to total particle density (\(N_{T}\)), and described it as follows:  
\[N_{T}=3.67*10^{-5}\frac{\alpha_{0}}{r^{2}}\ (\text{\# of particles}/\text{m}^{3}), \tag{2}\]  
The previous relationship helps solve for \(\alpha_{0}\), thus [PERSON]'s [1] attenuation coefficient expression may alternately be expressed as:  
\[A=3.43*10^{5}\frac{N_{T}}{\lambda}*r^{3}*\Im\left(\frac{\varepsilon-1}{ \varepsilon+2}\right)\text{dB}/\text{km}, \tag{3}\]  
However, \(\alpha_{0}\) and \(N_{T}\) in (2) and (3) impose a challenge in terms of fulfilment either due to difficulties involved with their measurements or because they are statistically very scarce [2]. Therefore, it has been suggested that visibility should be considered as an alternative parameter as mathematical expressions relate it to \(\alpha_{0}\) and \(N_{T}\). [PERSON] [1] gave the simple relation between the optical attenuation coefficient (\(\alpha_{0}\)) and visibility (\(V\)) in km as:  
\[\alpha_{0}=\frac{15}{V}\ \text{dB}/\text{km}, \tag{4}\]  
where the proportionality constant of 15 dB is simply the 10-log of 0.031, which is a measured median of the normalized difference in luminance between a mark and a reference background [1]. [PERSON] and [PERSON] [3], on the other hand, developed an empirical relationship between the dust mass concentration (\(M\)) in g/m\({}^{3}\) and the visibility (\(V\)) in km:  
\[MV^{\gamma}=C, \tag{5}\]  
where \(\gamma\) and \(C\) (g m\({}^{-3}\) km) are constants, and according to [PERSON] and [PERSON] [3], their value depends on the dust storm's geographical area of origin and associated climatic conditions. Essentially, Equation (5) is the ratio of the mass concentration, \(M\), to the extinction due to particles, \(\sigma_{P}\), which is designated by \(K\). At the same time, the ratio can be related to [PERSON]'s visibility law (\(V=|\ln 0.02|/\sigma\)) by equating \(\sigma_{P}\) to the total extinction \(\sigma\)-\(\sigma\) that includes gaseous as well as particulate optical effects, which is valid for low visibility conditions (\(\sigma_{p}\gg\) extinction by the air molecules; \(\sigma_{p}=\sigma\)) [4]. As a result, we obtain:  
\[V=\frac{3.912\ K}{M}=\frac{C}{M}\ km, \tag{6}\]  
where \(3.912K\) is denoted by \(C\), leading to the relation \(MV=C\).