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The authors consider joint estimation of carrier frequency offset and Channel Impulse Response (CIR) for Orthogonal Frequency Division Multiplexing (OFDM) systems with pilot symbols and Virtual subCarriers (VCs). The authors derive the receive-signal correlation structure due to the pilots and VCs, give the evidence of joint multivariate Gaussian distribution of the received samples, and derive an approximate Maximum Likelihood (ML) frequency offset estimator. The authors also derive the asymptotic Mean-Square Error (MSE) and an approximate Cramer-Rao Bound (CRB) and establish the asymptotic unbiasedness.
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