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Closed-Form Expressions for the Exact Cramer-Rao Bound for Parameter Estimation of Arbitrary Square QAM-Modulated Signals

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 time-varying 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.