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Adaptive modulation is one of key technologies in wireless communication systems. The modulation order can be adaptively adjusted via different space-time coding under constrained transmission rate. Constellation-constrained capacity of different modulations under the constrained transmission rate and the adaptive modulation and space-time coding(AM-STC) scheme are analyzed in this paper. Analysis suggests that lower modulation satisfying the transmission rate can get higher spectrum efficiency at high SNRs and the simulations show that the AM-STC scheme is helpful to select the best modulation at low SNRs. Moreover, the simulation results are reasonable agreement with the results of theoretical analysis.