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Time selectivity of multipath channels introduces significant inter-carrier interference (ICI) in OFDM systems demanding high levels of mobility and capacity. In this paper, a piecewise channel approximation is presented for improving the structure of the frequency-domain channel gain matrix, leading to a low-complexity iterative equalization scheme for OFDM receivers. The equalization is a sequential data detection based on a parallel-filtering architecture, avoiding matrix inversion adopted by classical equalizers with ICI cancellation. Meanwhile, information redundancy in the traditional cyclically prefixed OFDM is investigated for time-invariant channels, then a method of symbol reconstruction (SR) is proposed to enhance OFDM system performance, including compensation for SNR loss and improvements on the accuracy of parameter estimation. On the basis of the appropriate channel modeling in this work, the SR processing is proved to be effective for OFDM receivers over doubly selective channels. The iterative equalization, combined with the SR processing, is applied to the DVB-H receiver design. Numerical simulation indicates that the proposed equalizer significantly improves the immunity of OFDM systems to time selectivity with very little complexity increased, in contrast to the conventional one-tap equalizer without ICI cancellation.