It is well known that diversity performance of communication systems using signals with high dimensions in time, frequency and/or spatial domains depends on correlation of the channel characteristics along signal dimensions. On the other hand, it has not been payed due attention how the coherent receiver which combines the signals is greatly affected by the erroneous channel estimation which can undermine the diversity gain. In this paper, assuming that the estimator is given the a priori probability of the channel characteristics, we propose an optimum estimation scheme based on MAP criterion, in an uplink-MC/CDMA system on channels with frequency selective fading, with an array of antennas at the receiver. The MAP estimator effectively takes into account the correlation of the channel characteristics that the conventional estimator neglects. We also propose a signal design in pilot symbol periods that enables the receiver to separately obtain the sufficient statistic for estimating the channel characteristics without MAI. Using computer simulation, we obtained MSE error performances of the proposed estimator compared with the conventional estimator and their effect on BER performances of the diversity combining receiver. It was observed that using the conventional estimator for combining greater number of signals than the effective channel dimension deteriorated the BER performance while using the proposed estimator kept the optimum performance just as the error-free estimator did. Also obtained for MC/CDMA systems are BER performances of the single user matched filter and MMSE receivers using the proposed and the conventional estimators. A considerable improvement of the MMSE performance was achieved owing to the optimum estimator. It remains for the a priori probability of the channel characteristics to be properly assumed and dealt with in sequential estimation.