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This paper presents a framework of maximum-a-posteriori (MAP) algorithms for the automatic modulation classification (AMC) in orthogonal frequency division multiplexing (OFDM) based communication systems with adaptive modulation (AM). The proposed classifiers intensively utilize side information typically available in wireless time-division duplex (TDD) systems that is channel reciprocity, the known frame structure and the knowledge about the total transmission data rate. As the computational complexity of the optimal algorithms is rather high, a metric approximation is used whose accuracy increases with rising signal-to-noise power ratio (SNR). Numerical results show that the system performance degradation in terms of the packet-error ratio (PER) due to erroneously detected modulation schemes is small in typical wireless communication scenarios if the proposed AMC algorithm is applied.