In recent times, the popularity of Cognitive Radio has been increased because of its spectrum sensing characteristics. Using CR, the spectrum is utilized efficiently and maintain efficient communication when the primary user is not using the spectrum. In this paper, Bayesian detector is used for detecting the presence of primary user's signal. This approach is optimal when PU is not using the spectrum. The optimal Bayesian Detector with QAM modulation is deduced and analyzed in terms of probability of false alarm and detection over over AWGN channel. Simulation results show that the Bayesian Detector with 8-QAM modulation has optimum performance over Bayesian Detector with 8-PSK modulation. © 2016 IEEE.