Observing the Earth with a microwave radiometer on board a geostationary satellite has generated interest for several decades. Such a mission would add a high observation rate in the microwave spectrum, offered by a geostationary orbit, to the sounding capabilities of the current observing system. The instrumental concept under study considers a microwave radiometer with six channels with different observation errors within the 183.31 GHz water vapour absorption band. Observing System Simulation Experiments (OSSEs) are conducted to examine if these very frequent microwave observations would be beneficial to mesoscale numerical weather prediction (NWP) and complement the current or soon-available satellite observations. The OSSE framework is built up on (i) simulated observations from a known 'truth' which is a long and uninterrupted forecast from the Météo-France ARPEGE global model, and (ii) the Météo-France AROME mesoscale model in which the simulated observations are assimilated using a 1 h update cycle 3D-Var data assimilation system. Benefits that may be expected from such a microwave sounder mission are evaluated in the context of a dense observing system including observations from the future hyper-spectral InfraRed Sounder on board Meteosat Third Generation. In particular, impacts of microwave observations with observation errors ranging from 1.25 to 5 K are studied. One of the main findings of this study is that fine-scale NWP systems do not only need observations that are frequent in space and time, but that these observations must be accurate as well.