In this paper, the problem of joint carrier frequency offset (CFO) and channel estimation for OFDM systems over the fast time-varying frequency-selective channel is explored within the framework of the expectation-maximization (EM) algorithm and parametric channel model. Assuming that the path delays are known, a novel iterative pilot-aided algorithm for joint estimation of the multipath Rayleigh channel complex gains (CG) and the carrier frequency offset (CFO) is introduced. Each CG time-variation, within one OFDM symbol, is approximated by a basis expansion model (BEM) representation. An autoregressive (AR) model is built to statistically characterize the variations of the BEM coefficients across the OFDM blocks. In addition to the algorithm, the derivation of the hybrid Cramér-Rao bound (HCRB) for CFO and CGs estimation in our context of very high mobility is provided. We show that the proposed EM has a lower computational complexity than the optimum maximum a posteriori estimator and yet incurs only an insignificant loss in performance.
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