A more precise empirical formula for estimating normalized fog attenuation in the millimeter-wave frequency range 30 ∼ 100 GHz

At millimeter wavelengths, normalized fog attenuation (NFA) in units of (dB/km)/ (g/m³) is generally calculated by the Rayleigh approximation when working wavelengths are much larger than the average diameter of fog droplets. The calculations of the Rayleigh approximation are much less than those of Mie scattering theory, but still complex and heavy. To solve the above problem and facilitate the engineering applications of the Rayleigh approximation, a new empirical formula is discussed to estimate NFA in the frequency range 30 ∼ 100 GHz and the fog common temperature range -8 ∼ 20 C. The simulation results of the new formula are compared with those got by other three empirical formulae: the Altshuler empirical formula, the Liebe empirical formula and the Zhao empirical formula. Maximal absolute value of the relative errors (MAVRE) and Pearson correlation coefficient (PCC) indicate the largest deviation of estimated results and the fitting performance of an empirical formula, respectively. Comparisons show that the MAVRE of the new formula is only 4.482 %, which is much smaller than those of the other three formulae. The mean value of the Pearson correlation coefficients (PCCs) of the proposed formula is 0.999943, larger than those of other methods. Additionally, relative error (RE) curves of the four empirical formulae are given at four certain temperatures -8 C, 0 C, 10 C and 20 C.