A new estimator for an unknown signal imbedded in additive Gaussian noise

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 (
c-a
estimator) is compared with that of the maximum-likelihood (ML) estimator, and it is shown that the
c-a
estimator reduces considerably the mean-square error for small values of SNR, at the expense of introducing a small bias. The
c-a
and ML estimators of a complex parameter are applied to the problem of signal estimation, and some interesting numerical results are presented.