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In this paper, we derive analytical expressions for the exact Cramer-Rao lower bounds (CRLBs) for the joint estimation of the carrier frequency, the carrier phase, the noise power and the signal amplitude of square quadrature amplitude (QAM) modulated signals. The channel is assumed to be slowly timevarying so that it can be assumed constant over the observation interval. The signal is assumed to be corrupted by additive white Gaussian noise (AWGN). The closed-form expressions for the corresponding modified Cramer-Rao lower bounds (MCRLBs) are also derived in this paper.