<b>Performance Analysis of Bayesian Methods to for the Spectrum Utilization in Cognitive Radio</b> Cognitive radio is an exciting wireless technology that has been introduced for the efficient used of spectrum. Using cognitive radios CRs , the secondary users unlicensed users are allowed to use the spectrum which is originally allocated to primary users PUs as far as the active primary users are not using it temporarily. In order to prevent harmful interference to primary users, the SUs need to perform spectrum sensing before transmitting signal over the spectrum. In this paper we use an optimal Bayesian detector for digitally modulated primary user to improve the spectrum utilization, without prior knowledge of transmitted sequence of the primary signals. And further suboptimal detectors in low and high SNR regime. We provide the performance analysis in terms of Detection probability and False alarm probability. Cognitive radio, Spectrum sensing, spectrum utilization, Energy Detector, Bayesian Detector 912-916 Issue-5 Volume-1 Abdul Hameed Ansari | Narode Sweety S.