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In this paper, we address the application of adaptive modulation and coding (AMC) for 3rd-generation (3G) wireless systems. We propose a new method for selecting the appropriate modulation and coding schemes (MCS) according to the estimated channel condition. In this method, we take a statistical decision making approach to maximize the average throughput while maintaining an acceptable frame error rate (FER). We use a first order finite state Markov model to approximate the time variations of the average channel signal to noise ratio (SNR) in subsequent frames. The MCS is selected in each state of this Markov model (among the choices proposed in the 3G standards proposals) to maximize the statistical average of the throughput in that state. Using this decision making approach, we also propose a simplified Markov model with fewer parameters, which is suitable in systems where changes in the fading characteristics need to be accounted for in an adaptive fashion. Numerical results are presented showing that both of our models substantially outperform the conventional techniques that use a memoryless threshold based decision making.