We derive the optimum power and rate adaptation for maximizing the spectral efficiency of Multilevel Quadrature Amplitude Modulation (MQAM) over Multiple-Input Multiple-Output (MIMO) fading channels based on imperfect channel estimation. We use Pilot Symbol Assisted Modulation (PSAM)-based Minimum Mean Square Error (MMSE) channel estimator, and show that the optimum power adaptation on each sub-channel is a generalization of water-filling. We also show that the conventional water-filling (with bias) strategy for power adaptation is a suboptimum solution of the general optimization problem and it tends to the optimal solution as the correlation coefficients between eigenvalues of the true channel matrix and its estimate tend to one.