The rate adaptation of MQAM systems is achieved by selecting suitable MQAM constellation sizes through comparing instantaneous received signal-to-noise-ratio (SNR) against the SNR threshold intervals. In this paper, we present an approach to study the capacity with imperfect channel estimation. Under channel estimation errors, there will be a shift in the SNR threshold intervals compared to perfect channel estimation, if a pre-defined BER performance needs to be satisfied. We first address the problem of how to obtain the SNR threshold intervals under imperfect channel estimation, given the statistics of fading channel and estimation errors, for both single receiver and diversity reception systems. Our derivation shows that the SNR threshold intervals in both cases remain unchanged. The capacity achieved by rate adaptive MQAM systems under imperfect channel estimation is computed after obtaining the SNR threshold intervals.