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Cognitive radio (CR) is a dynamic spectrum access technology as a solution to spectrum under-utilization problem in some licensed bands. Operating over an exceedingly wide spectrum, CR systems usually adopt multi-carrier modulation (MCM) to implement flexible channelization. Consequently, efficient channel allocation scheme becomes extremely important to an MCM based CR (MCM-CR) system. In this paper, a maximum likelihood detection model is developed to detect the presence and locations of licensed users (LUs) signals in the frequency domain. Performance of the detection model, including the optimal detection region, detection probability and false alarm probability, is analyzed. A one-order two-state Markovian chain model is proposed to predict channel status information. In particular, a novel subcarrier allocation scheme for MCM-CR systems is proposed, taking into account the confidence of channel estimation, quality of services (QoS) of rental users (RUs) and throughput. To validate the analytical results, simulations have been conducted to show effectiveness of the proposed scheme.