Abstract: A spectrum sensing technique using the covariance matrix of the discrete Fourier transform (DFT) output of the detector's input vector is proposed. It is found that the covariance matrix is diagonal in the absence of primary user's signal and non-diagonal otherwise. Therefore in the detection procedure, the result can be obtained through comparing the power of the non-diagonal elements of the covariance matrix and the predefined threshold. The probability of distribution functions(PDFs) of the decision metric as well as the threshold and probability of detection in both hypotheses of the signal presence or absence are derived. The numerical results confirm that the proposed algorithm is more robust to the carrier frequency offset compared with the existing methods, and it also enjoys better detection performance.