This master thesis was done in cooperation with RUAG Space AB. Currently RUAG is working on designing the next generation instrument using Radio Occultation (RO) for climate monitoring and atmospheric sounding. RO is a method used to measure the temperature, pressure and humidity of the Earth's atmosphere. It is based on the fact that radio signal is refracted when it passes through the atmosphere. The level of refraction depends on the properties of the atmosphere. To derive refraction profile, the bending angle needs to be calculated by using the Doppler shift of the signal and actual positions of the emitter GPS (Global Positioning System) satellite and receiver LEO (Low Earth Orbit) satellite. Several methods of the bending angle retrieval have been developed, but these algorithms have different performance on multipath, partial loss of the input data or calculations based on the noisy data. In this project Full Spectrum Inversion (FSI) method is implemented. It is shown in this work that FSI can accurately reproduce the bending angle profile on simulated occultation data. In this report different filters are also tested and the best filters reported. FSI is able to disentangle multipath area, shortens the calculation time and provides accurate bending angle profile.