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Based on the high probability that primary user is idle in cognitive radio networks, we propose an optimal Bayesian detector structure for spectrum sensing. Although the optimal detector by Neyman-Pearson theorem maximizes the detection probability for a given false alarm probability, Bayesian detector can achieve a higher overall spectrum utilization and SU throughput and at the same time the primary user is well protected from secondary user's interference. For BPSK modulated primary signals we show that the optimal Bayesian detector can be reduced to an energy detector in lower SNR regime, and it can be approximated to a detector employing the sum of received signal magnitudes in high SNR regime to detect primary signals. We give the analysis for optimal Bayesian detector and the corresponding suboptimal detector structure in both low and high SNR regimes, and verify the performance of the detector with simulation results.