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For non-contiguous OFDM (NC-OFDM) based cognitive radio systems, one challenge is to establish the spectrum synchronization before the data transmission over an idle channel. In this paper, we propose two novel detection schemes, i.e., hard-decision-based detection (HDD) and soft-decision-based detection (SDD) schemes, to detect NC-OFDM symbols without the information of out-of-band spectrum synchronization. The key idea of the proposed schemes is to employ the received training symbol to calculate a posterior probability (APP) of each subchannel's being active. Specifically, for the proposed HDD scheme, the secondary receiver detects whether a subchannel is active or not based on its APP. When the APP of a subchannel is larger than a preset threshold, it will be employed for the data detection. Moreover, we derive the miss detection and false alarm probabilities of the hard decision based detection of active subchannels, respectively. For the proposed SDD scheme, all subchannels are employed for the data detection, in which as a priori information of the subchannels' being active, all APPs are taken into account in the bit metric calculation. Theoretical analysis and simulation results show that the proposed schemes can provide satisfactory performance.