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Estimation of an unknown signal observed in the presence of an additive Gaussian noise process is reduced to the problem of estimating an unknown complex parameter. A new class of estimators for an unknown complex parameter is introduced, and their biases and mean-square errors are studied. The performance of a particular member of this class ( estimator) is compared with that of the maximum-likelihood (ML) estimator, and it is shown that the estimator reduces considerably the mean-square error for small values of SNR, at the expense of introducing a small bias. The and ML estimators of a complex parameter are applied to the problem of signal estimation, and some interesting numerical results are presented.