  The minimum mean square error of the estimation of a non Gaussian signal
where observed from an additive white Gaussian noise channel's output, is
analyzed. First, a quite general time-continuous channel model is assumed for
which the behavior of the non-Gaussianess of the channel's output for small
signal to noise ratio q, is proved. Then, It is assumed that the channel
input's signal is composed of a (normalized) sum of N narrowband, mutually
independent waves. It is shown that if N goes to infinity, then for any fixed q
(no mater how big) both CMMSE and MMSE converge to the signal energy at a rate
which is proportional to the inverse of N. Finally, a known result for the MMSE
in the one-dimensional case, for small q, is used to show that all the first
four terms in the Taylor expansion of the non-Gaussianess of the channel's
output equal to zero.
