On The Minimum Mean-Square Estimation Error of the Normalized Sum of Independent Narrowband Waves in the Gaussian Channel

Details On The Minimum Mean-Square Estimation Error of the Normalized Sum of Independent Narrowband Waves in the Gaussian Channel On The Minimum Mean-Square Estimation Error of the Normalized Sum of Independent Narrowband Waves in the Gaussian Channel

2006-01-28

arxiv.org/abs/cs/0601120v1

Computer Science

Information Theory

3 pages, Submitted to IEEE Symposium on Information Theory ISIT 2006

Scientific paper

The minimum mean-square error of the estimation of a signal where observed from the additive white Gaussian noise (WGN) channel's output, is analyzed. 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 signal energy to noise energy ratio (no mater how big) both the causal minimum mean-square error CMMSE and the non-causal minimum mean-square error MMSE converge to the signal energy at a rate which is proportional to 1/N.

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