Performance of an Asymptotically Optimum Estimator of the Amplitude of a Coherent Signal

An easily implemented estimator of the amplitude (including sign) of a sine wave of known phase is described. The performance of this estimator when zero-mean Gaussian noise is added to the signal is then determined by computing its probability density, mean, and second moment. These statistics are shown to converge to those of the maximum likelihood estimate for large values of signal-to-noise ratio.