Carrier frequency offset (CFO) causes spectrum misalignment of transmitter and receiver filters. This misalignment leads to energy loss and distortion of received signal, resulting in performance degradation of the whole system. However, these issues are often overlooked by existing works. This paper presents an exact signal model for OFDM that takes into account the CFO-induced spectral misalignment and related aliasing effects. Incorporating these practical issues, we also propose a new preamble structure and a new CFO compensation approach to mitigate their negative effects. Theoretical analysis and simulation results substantiate the importance of the exact signal model and the advantage of the proposed CFO compensation scheme.