Cepstrum can reveal periodicities in a signal and has been widely used in audio and speech processing applications. In this project, the distributions of the cepstral coefficients of OFDM signals in additive white Gaussian noise (AWGN) channel are derived analytically. The problem of finding idle spectrum is modeled as a statistical hypothesis testing problem. For solving such problem, two local detection algorithms based on cepstral analysis for detecting OFDM signals are proposed. Further more, cepstrum-based algorithms for estimating the data length and the cyclic prefix (CP) length of an OFDM symbol are proposed.