ISSN : 1796-203X
Volume : 2    Issue : 7    Date : September 2007

Algorithms and Applications for Estimating the Standard Deviation of AWGN when Observations
are not Signal-Free
Dominique Pastor and Asmaa Amehraye
Page(s): 1-10
Full Text:
PDF (413 KB)

Consider observations where random signals are randomly present or absent in independent and
additive white Gaussian noise (AWGN). By using a recently established limit theorem, we introduce
a new estimator for the estimation of the noise standard deviation 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, the experimental results that are presented are very promising. First, when the Minimum-
Probability-of-Error decision scheme for the non-coherent detection of modulated sinusoidal
carriers in independent AWGN is tuned with the outcome of our estimator instead of the true value of
the noise standard deviation, the Binary Error Rate tends to the optimal error probability when the
number of observations is large enough. Second, given some speech signal corrupted by
independent AWGN, our estimator can be used to estimate the noise standard deviation so as to
adjust the standard Wiener filtering of the noisy speech. The objective performance measurements
obtained by so proceeding are very close to those achieved when the Wiener filtering is tuned with
the true value of the noise standard deviation.

Index Terms
Binary hypothesis testing, decision, estimation, likelihood theory, multivariate normal distribution,
speech denoising.