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Modern communication systems are based on orthogonal frequency division multiplexing (OFDM). They are designed for dealing with frequency selective channels considering invariance within the time-span of an OFDM symbol. However, this assumption is no longer valid when the transceivers operate in higher mobility scenarios or higher carrier frequencies. This condition provokes inter-carrier interference (ICI) that greatly degrades system performance. State-of-the-art approaches that satisfactorily mitigate this problem have a complexity of O(N3), which makes them infeasible with current technology. In this paper, a novel channel estimation algorithm to cope with this problem is presented. It is based on a subspace approach using two-dimensional Prolate functions, achieving a complexity of only O(N2). It depends only on the maximum delay spread and maximum Doppler spread while being robust in the sense that it is independent of the particular channel scattering function. Performance analysis of the proposed algorithm is presented. Simulation results under the WiMAX standard show that this algorithm improves previous results, achieving a bit error rate (BER) close to the one obtained with perfect channel state information (CSI) in very-fast transceiver mobility, as high as 874 Km/h over a 2.4 Ghz carrier frequency.