In many telecommunication systems, message signals which include a predefined sample bit sequence (training sequence) are transmitted, to improve the signal processing in the receiver, particularly the equalization. For this purpose, on the basis of the sample bit sequence, the channel pulse response is estimated within an iterative method. Extending the sample bit sequence by those bits which result from the reconstruction of the transmitted signal is known. It is here proposed that the equalization stage is synchronized to the received signal, by using at least the second channel pulse response which is estimated using the extended sample bit sequence. For this purpose, the receiver includes suitable synchronization means. In this way, it is achieved that the equalization is precisely adapted to the temporal course of the channel pulse response, so that the equalization of the received signal can be significantly improved. In tests, improvements to the signal-to-noise ratio of about 0.5 dB were achieved. Preferably, for the iterative channel estimate, the extended sample bit sequence is divided into two or more parts in the case of rapid channel changes such as can occur in mobile communication systems.