This paper deals with the performance comparison of blind adaptive equalization algorithm, the MMA and S-MMA, that is used for compensation of the amplitude and phase distortion simultaneously which occurs in the time dispersive channel. The present CMA algorithm is possible to compensates the amplitude only, but not in phase, so it needs to the another additional circuit for compensating the phase. In order to overcoming the abovemensioned shorthand, the improved cost function is applied to the MMA algorithm. In MMA algorithm, the error is consists of the dispersion constant only, but in S-MMA, the error is consists of the dispersion constant considering the output of decision device (sliced symbol) in order to updating the tap coefficients. By using the two kind error signal, the adaptive equalization algorithm has different performance. In this paper, we compare to the adaptive equalization algorithm performance by using the recovered constellation, residual isi, MD (Maximum Distortion) and SER as a index when the transmitting signal is 16 and 64-QAM and then passing through the same communication channel. As a result of simulation, the S-MMA can improving the Roburstness in SER performance compared to the MMA in the high order QAM signal.