Orthogonal frequency-division multiplexing (OFDM) is a popular transmission technology in cognitive radio (CR) networks, because the correlation of cyclic prex (CP) in OFDM signals can be utilized to improve the reliability of spectrum sensing of secondary users (SUs). However, the optimal spectrum sensing over multipath fading channels remains an important and challenging issue. Therefore, this work proposes an optimal Neyman- Pearson (NP) detector for spectrum sensing using CP. To detect the OFDM signal of primary users (PUs), the log- likelihood ratio (LR) test is formulated by using the correlation characteristics of the redundancy of CP. Analytical results indicate that the LR of received samples is equivalent to their log- likelihood function (LF) plus LR of an energy detector (ED), subsequently allowing us to gain insights on the optimal NP detector. Since many unknown parameters need to be resolved, a practical generalized log-likelihood ratio test (GLRT) is presented. Moreover, to achieve a good performance over multipath fading channels, a channel- independent GLRT (CI-GLRT) is employed to derive an estimation of correlation coefcient independent of multipath channel proles. Simulations conrm the advantages of the proposed detectors compared with state-of-the-art detectors.