Remote measurements of atmospheric trace gases are critical to the understanding of both Earth and planetary meteorological systems. The conventional lidar technique currently applied is Differential Absorption lidar (DIAL). A potentially more sensitive method is Frequency Modulation (FM) spectroscopy. An original analysis will investigate the feasibility of using FM techniques for remote sensing of water vapor in the Martian atmosphere. Original mathematical models, both analytic and computer models, will be used in this effort. This analysis will establish the limitations of using scattered light for the return. Using FM sounding techniques will be shown to overcome these limitations. A SNR equation based on the FM sounding technique will be developed. A model of the Martian atmosphere will be described and used along with the SNR equation to evaluate the performance of an FM sounding system for detection of water vapor on Mars.