We consider the problem of digital communication in a fading environment using the Multi-Carrier CDMA technology. By incorporating the effect of the pulse-shaping filter in the channel estimation and signal detection modules, we develop new estimator and detector structures which significantly outperform the commonly used time-domain equalizers and matched filter detector. Our simulation results demonstrate the elimination of some of the error floors which one would experience if usual time-domain techniques were used to cancel the effect of nonideal pulse-shaping filter.