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Doubly-selective wireless communication channels, i.e., those with significant selectivity in both time and frequency domains, arise in applications operating over wide bandwidths, at high carrier frequencies, and under high mobility conditions. Many systems designed to communicate over such channels are OFDM-based and employ large block lengths to combat capacity loss resulting from the use of a redundant prefix. The use of large block length renders channel estimation schemes whose complexities scale in proportion with the square or cube of the block length impractical. In this paper, we present two channel estimation schemes which leverage FFT and a careful choice of pilots to achieve low estimation error with low complexity.