We consider the effect of an imperfect channel estimate on a variable rate and variable power (VRVP) multilevel quadrature amplitude modulation (MQAM) system, where the transmit power and data rate are varied relative to the estimate of the received signal. Based on the VRVPMQAM system operating over a Rayleigh flat-fading channel, we derive a bit error rate (BER) estimator using a maximum a posteriori (MAP) estimation approach. We apply the BER estimator to the VRVP-MQAM system, and thereby derive and obtain system expressions which are applicable to any channel estimation technique. In addition, the resulting formulations are also useful for analyzing the effect of channel state information (CSI). Consequently, we derive and obtain an optimal solution for our proposed system and generate numerical results to compare the variations of system performance with imperfect CSI.
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