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Owing to the loss of subcarrier orthogonalities in high-speed applications, the use of conventional frequency-domain-based channel estimation in high mobility orthogonal frequency division multiple access (OFDMA) systems such as mobile WiMax may give rise to an unacceptable high channel estimation error floor. To alleviate this problem, the authors develop some basis expansion model (BEM)-based estimation schemes for the OFDMA uplink. Specifically, the authors express the time-varying channel as a superposition of a small number of complex exponential basis functions spanning the entire Doppler range, and then formulate least square (LS) and linear minimum mean square error (LMMSE) algorithms to estimate the basis coefficients for two different types of pilot patterns. The authors also derive the respective Cramer-Rao lower bounds for these estimators. It has been shown that the time domain BEM using a pilot scheme where pilots are placed over time axis will give better performance under a high Doppler scenario. Lastly, using simulation results, the proposed algorithms have been found to have better estimation accuracy over current frequency domain estimation techniques. This is in addition to the advantage that the proposed algorithms have in general a lower computational complexity.