This Battery Back Up paper concerns covariance matrix-based spectrum sensing over frequency-selective channels.The impact of frequency-selective channels on the covariance matrix of received signals is analyzed in frequency domain, and it is shown that the phases of channel spectra degrade the performance of covariance matrix-based detectors.To overcome this problem, we propose a new detector which tension wheel employs only the magnitude spectra of received signals and therefore achieves considerable performance gain.Theoretical performance, in terms of the false-alarm and detection probabilities of the proposed detector, is analyzed.Simulation results verify our theoretical analyses and demonstrate the superior performance of the proposed detector.