Surface Air-pressure is one of the most important parameters used in Numerical Weather Prediction (NWP) models. Although it has been measured using weather stations on the ground for many decades, the numbers of measurements are sparse and concentrated on land. Global measurements can only be achieved by using remote sensing from Space, which is challenging; however, a novel design using Differential Absorption Radar (DAR) can provide a potential solution. The technique relies on two facts: firstly the electromagnetic fields are absorbed mainly by two atmospheric components the oxygen and water vapour, and secondly that oxygen is well mixed in the atmosphere. In this work we discuss a space-borne concept, which aims at providing near global, consistent, and regular observations for determining surface air pressure from space by a design of a multi-tone radar operating on the upper wing of the O2 absorption band with tones from 64 to 70 GHz. Simulations of radar vertical profiles based on the output of a state of-the-art microphysical retrievals applied to the A-Train suite of sensors are exploited to establish the performance of such a system for surface pressure determination. In particular the identification and quantification of errors introduced by the presence of water vapour, cloud liquid water and rain water and the potential of a correction via the three-tone method is discussed. Results show that accuracies of the order of few hPa are at reach.