Some Relations between Divergence Derivatives and Estimation in Gaussian channels

Details Some Relations between Divergence Derivatives and Estimation in Gaussian channels Some Relations between Divergence Derivatives and Estimation in Gaussian channels

2010-02-03

arxiv.org/abs/1002.0680v1

Computer Science

Information Theory

Submitted to the IEEE Transactions on Information Theory

Scientific paper

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.

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