The main contribution of this paper can be summarized in two items as follws. Firstly, a modelling of mobile communication channel with Rayleigh fading characteristics is presented. Actual signal environments can be approximated as being real measurements by a proper mathematical representation of fluctuation of channel parameters due to Doppler effect, that is determined by the relative speed between transmitter and receiver, and noises, that vary at each sampling time. Secondly, an alternative procedure of synthesizing an adaptive equalizers is presented for recovering original signals that have been corrupted through the modelled channel. In order to compute the optimal tap coefficients for a high speed data(512 k symbol/sec) on a real-time basis, the CGM that guarantees fast and stable convergency is adopted during the training period of each frame. The coefficients obtained by the CGM are used as initial values for the LMS algorithm to trace the optimal coefficients during the data period that vary at each sampling time due to the mobility and noise at the receiver. Using the modelling presented in this paper, distributions of received signal power in various signal environments are demonstrated. The performance of the eqalizer proposed in this paper is shown as a function of BER under the various signal circumstances of mobile communications.