## 6 Conclusions  
We have developed a method for calculating the probability for symbol error rate that considers variations in rainfall rate. This is in contrast to accepted methods which employ average values over time. We also gave a closed-form mathematical expression for the probability of error. Numerical calculation clearly shows that when the density distribution function of rain rate is considered, the probability of symbol error rate changes significantly. This model will enable the design of a system that will ensure the desired bit error rate, for example, by adapting the power transmitter, modulation constellation, and/or coding strength.  
Our aim in this work has been to include the rain rate probability, which is a major attenuating factor in signal transmission, in the symbol error rate calculation. There are other attenuating factors, including clouds, atmospheric gases, dust, and sandstorms. For the higher frequencies under discussion, the relation of wavelength to particle size makes these too increasingly significant in contributing to signal error. Attenuation by these has been calculated in various ways (see for instance [46]). The wave scattering by small raindrops could cause higher attenuation. If a modified specific attenuation model is available, it could be used in Equation (9) instead of the present one. Future work on higher frequencies should include models of specific attenuation that take DSD into account. In addition, future work could also extend our calculation to consider the probability of other atmospheric impairments.  
Future work should consider troposphere scintillation. When the wind blows, the mainly horizontal layers of the equal refractive index in the troposphere tend to become mixed due to turbulence. The troposphere being mixed leads to rapid refractive index variations over small distances or scale sizes and over short time intervals. Waves traveling through these rapid variations in the index vary in amplitude and phase. This situation creates dry tropospheric scintillation. Another source of tropospheric scintillation is rain, which tends to occur at slower rates than the dry effects. Scintillation is not an absorbent effect in that the signal's mean level is unchanged. The effect is strongly frequency-dependent in that shorter wavelengths will encounter more severe variations resulting from a given scale size [47].  
With 6G on the horizon and communication that will be used not only among people but with devices that may have life-or-death importance, the need for an exact calculation of symbol error rate is imperative. In addition, 6G will use very high frequencies, which make it particularly susceptible to attenuation and distortion by rain. Therefore, accurate calculation of symbol error will be necessary with the developing communication technology.  
Conceptualization, J.K. and S.A.; Formal analysis, J.K. and S.A.; Investigation, J.K. and S.A.; Methodology, J.K. and S.A.; Writing--original draft, J.K. and S.A.; Writing--review & editing, J.K. and S.A. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Error Probability**} & \multicolumn{2}{c}{**SNR Required for**} & \multirow{2}{*}{**SNR Required (dB)**} & \multirow{2}{*}{**Difference (dB)**} \\  & **Classical Case (dB)** & & \\ \hline \(10^{-4}\) & 26 & 23 & 3 \\ \(10^{-5}\) & 26.5 & 24.8 & 1.7 \\ \(10^{-6}\) & 27.8 & 26 & 1.8 \\ \(10^{-7}\) & 28.4 & 27.4 & 1 \\ \hline \hline \end{tabular}
\end{table}
Table 3: SNR for various probabilities for a rain rate of 10 mm/h for 80 GHz.