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This paper is concerned with the challenging and timely problem of joint channel estimation and data detection for orthogonal frequency division multiplexing (OFDM) systems in the presence of frequency selective and very rapidly time varying channels. The detection and estimation algorithm is based on the space alternating generalized expectation maximization (SAGE) technique which is particularly well-suited to multicarrier signal formats. In order to reduce the computational complexity of the algorithm, we apply the cosine orthogonal basis functions to describe the time-varying channel. It is shown that, depending on the normalized Doppler frequency, only a small number of expansion coefficients is sufficient to approximate the channel perfectly and there is no need to know the correlation function of the input signal. The proposed SAGE joint detection algorithm updates the data sequences in serial and the channel parameters are updated in parallel, leading to a receiver structure that also incorporates a partial interference cancellation of the interchannel interference. Computer simulations show that the cosine transformation represents the time-varying channel very effectively and the proposed algorithm has excellent symbol error rate and channel estimation performance even with a very small number of channel expansion coefficients employed in the algorithm, resulting in reduction of the computational complexity substantially.