Research on the distance equation of the submillimeter radiometer via Lambert W function

This paper put forward the distance equation for the SMMW radiometer based on the one for the MMW radiometer. In general case, the transmission attenuation was ignored as the detection distance of the radiometer was studied, because of the faint attenuation in some frequency band. But in the SMMW band, the effects of atmospheric attenuation were very significant. So the attenuation coefficient had been introduced into the distance equation. Then the solution of the equation was proposed by using the Lambert W, which is a transcendental function. Finally the simulation and analysis of the solution were given respectively.