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Channel variation during an OFDM block leads to the loss of orthogonality among subcarriers, resulting in inter-carrier interference (ICI) in orthogonal frequency division multiplexing (OFDM) systems. Many schemes have been proposed to suppress ICI, but they are computationally complex or at the price of sacrificing bandwidth. In some cases, such as high-density television (HDTV) broadcasting and satellite OFDM systems, the very long delay spreads pose the possibility that the channel length exceeds that of the moderate cyclic prefix (CP), resulting in intersymbol interference (ISI) and intercarrier interference (ICI). A time-domain equalizer (TEQ) is usually used in the receiver to reduce the duration of the overall response of the transmission system, and therefore minimize the ISI and ICI. However, the optimum design of TEQ turns out to be a difficult task. The ICI's introduced by insufficient CP and channels variations are different and usually exploit different methods to mitigate them. In this paper, we provide an ICI and ISI analysis in time- and frequency- domain for OFDM systems with insufficient CP over time-variant channels. Basing on this analysis, we propose an iterative method for joint ICI and ISI cancellation whose complexity is linear in the OFDM symbol length. Theoretical analysis and simulation results indicate that the proposed method can effectively mitigate ICI and ISI introduced by channel variation and insufficient CP with high bandwidth efficiency.