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Estimation of noise power and signal-to-noise ratio (SNR) are fundamental tasks in wireless communications. Existing methods to recover these parameters in orthogonal frequency-division multiplexing (OFDM) are derived by following heuristic arguments and assuming perfect carrier frequency offset (CFO) synchronization. Hence, it is currently unknown how they compare with an optimum scheme performing joint maximum likelihood (ML) estimation of CFO, noise power and SNR. In the present work, the joint ML estimator of all these parameters is found by exploiting the repetitive structure of a training preamble composed of several identical parts. It turns out that CFO recovery is the first task that needs to be performed. After CFO compensation, the ML estimation of noise power and SNR reduces to a scheme that is available in the literature, but with a computational saving greater than 60% with respect to the original formulation. To assess the ultimate accuracy achievable by the ML scheme, novel expressions of the Cramer-Rao bound for the joint estimation of all unknown parameters are provided.