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The general formulas of the wave propagation constant through sand and dust storms are developed in this paper, which is based on the forward scattering amplitude of particle under the Rayleigh approximation. Expressions for attenuation and phase shift coefficients for a medium with sand and dust particles are derived in terms of visibility and frequency. Computations show that the predicted values from the given mathematical expressions are an excellent agreement with the values by Goldhirsh's formula. Expressions for the differential attenuation and differential phase shift are also derived for both vertical and horizontal polarizations. Obtained results of the attenuation of horizontal and vertical polarization wave are compared with those obtained by Wenyan 's formula and Ghobriel 's formula, respectively. It is found that the attenuation obtained by our proposed formula and Ghobrial 's formula show close agreement. The cross-polar discrimination is calculated and discussed.