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In orthogonal frequency division multiplexing (OFDM) systems over fast-varying fading channels, channel estimation and tracking is generally carried out by transmitting known pilot symbols in given positions of the frequency-time grid. The traditional approach consists of two steps. First, the least-squares (LS) estimate is obtained over the pilot subcarriers. Then, this preliminary estimate is interpolated/smoothed over the entire frequency-time grid. In this paper, we propose to add an intermediate step, whose purpose is to increase the accuracy of the estimate over the pilot subcarriers. The presented techniques are based on the observation that the wireless radio channel can be parametrized as a combination of paths, each characterized by a delay and a complex amplitude. The amplitudes show fast temporal variations due to the mobility of terminals while the delays (and their associated delay-subspace) are almost constant over a large number of OFDM symbols. We propose to track the delay-subspace by a subspace tracking algorithm and the amplitudes by the least mean square algorithm (or modifications of the latter). The approach can be extended to multiple input multiple output OFDM or multicarrier code-division multiple-access systems. Analytical results and simulations prove the relevant benefits of the novel structure.