Estimating the Standard Deviation of Some Additive White Gaussian Noise on the Basis of Non Signal-Free Observations

Consider n-dimensional observations where random signals are present or absent in independent and additive white Gaussian noise (AWGN) with standard deviation sigma_O. On the basis of recent results in statistical decision theory, this paper presents a new algorithm for estimating sigma_O when the signals are less present than absent and have unknown probability distributions. The bias, the consistency and the minimum attainable mean square estimation error of the estimator we propose are still unknown. However, experimental results are very promising. When the minimum-probability-of-error decision scheme for the non-coherent detection of modulated sinusoidal carriers in independent AWGN is tuned with the estimate instead of the true value sigma_O, the binary error rate obtained tends rapidly to the optimal error probability after a few hundred observations