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This paper deals with the case of a high speed mobile receiver operating in an orthogonal-frequency-division-multiplexing (OFDM) communication system. Assuming the knowledge of delay-related information, we propose an iterative algorithm for joint multi-path Rayleigh channel complex gains estimation and data recovery in fast fading environments. Each complex gain time-variation, within one OFDM symbol, is approximated by a polynomial representation. Based on the Jakes process, an auto-regressive (AR) model of the polynomial coefficients dynamics is built, making it possible to employ the Kalman filter estimator for the polynomial coefficients. Hence, the channel matrix is easily computed, and the data symbol is estimated with free inter-sub-carrier-interference (ICI) thanks to the use of a QR-decomposition of the channel matrix. Our claims are supported by theoretical analysis and simulation results, which are obtained considering Jakes' channels with high Doppler spreads.