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This paper proposes a pilot-aided joint channel estimation and synchronization scheme for burst-mode orthogonal frequency division multiplexing (OFDM) systems over time- and frequency-selective (doubly selective) channels. Based on the basis expansion model (BEM) for representing doubly-selective channels, a least-square (LS) cost function of carrier frequency offset (CFO) and BEM coefficients is formulated for the joint estimation problem. By applying the first-order Taylor series expansion, an approximately linearized estimation error is obtained to facilitate a recursive least-square (RLS)-based joint CFO and BEM estimation with the aid of pilot OFDM symbols. Simulation results demonstrate that, over a wide range of Doppler spreads, the proposed estimation scheme offers a high robustness against the time variation of fast fading channels and outperforms the linear minimum mean-square (LMMSE) algorithm using CFO estimates provided by the CFO estimation technique in.