Robust Estimation of Noise Standard Deviation in Presence of Signals With Unknown Distributions and Occurrences

In many applications, d-dimensional observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. An estimate of the noise standard deviation can then be very useful to detect or to estimate these signals, especially when standard likelihood theory cannot be applied because of too little prior knowledge about the signal probability distributions. The present paper introduces a new scale estimator of the noise standard deviation when the noisy signals have unknown probability distributions and unknown probabilities of presence less than or equal to one half. The latter assumption can be regarded as to a weak assumption of sparsity. Applied to the detection of noncooperative radio-communications, this new estimator outperforms the standard MAD and its alternatives as well as the trimmed and winsorized robust scale estimators. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor.