Optimum power and rate adaptation for MQAM in Rayleigh flat fading with imperfect channel estimation

We derive an optimum power and rate adaptation for maximizing the spectral efficiency based on an imperfect channel estimate and subject to average power and instantaneous bit error rate (BER) constraints for multilevel quadrature amplitude modulation (MQAM) over Rayleigh flat-fading channels. The optimal solution is derived for continuous- and discrete-rate adaptation and is expressed in terms of a specific bounded function that is the solution of a nonlinear equation and cannot be expressed in a closed mathematical form. The optimum power adaptation for the continuous rate is shown to be a generalization of water pouring for that function. It is also shown that the conventional water-pouring (with bias) strategy for power adaptation in the continuous-rate condition is a suboptimum solution of the general optimization problem, and it tends to the optimal solution as the correlation coefficient between the true channel gain and its estimate tends to one. We also show that less than 1 dB power is lost by using discrete-rate MQAM with only six different signal constellations compared to the continuous-rate adaptation with an unconstrained constellation size.