高斯信道中发散导数与估计的关系
Some Relations between Divergence Derivatives and Estimation in Gaussian channels
摘要：
分析了在加性高斯白噪声信道下，对非高斯信号的估计的最小均方误差。首先，假设一个相当一般的时间连续信道模型，证明了在小信噪比q时信道输出的非高斯性。然后，假设通道输入的信号由N个窄带、相互独立的波的（归一化）和组成。它表明，如果N趋于无穷大，那么对于任何固定的q（无论多大），CMMSE和MMSE都以与N的倒数成比例的速率收敛到信号能量。最后，一个已知的结果MMSE在一维的情况下，对于小q，被用来表明，所有的前四项在泰勒展开的非高斯信道的输出等于零。
英文摘要：
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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