The present invention relates to a receiving apparatus for a mobile communications system which can be modulated using different modulation types at the transmitter end. According to one embodiment of the invention, in the middle of a data burst of a Bluetooth communications system, a GFSK modulation method is switched to an M-DPSK modulation method, which is used for the payload data. A frequency offset estimation unit is provided for GFSK-modulated signals in a first receiving section and estimates the frequency offset by averaging over a bit sequence of a trailer of a data burst. The frequency offset is corrected in a second receiving section, by means of a frequency correction unit which operates on the basis of the CORDIC algorithm.