论文标题
关于在添加剂白色高斯噪声下的高斯矢量规范的MMSE估计，随机缺少输入条目
On the MMSE Estimation of Norm of a Gaussian Vector under Additive White Gaussian Noise with Randomly Missing Input Entries
论文作者
论文摘要
本文考虑的任务是估计$ n $二维的$ n $二维随机高斯矢量的噪声测量值，该矢量的许多条目都是\ emph {tover emph {tover {tover {tover {nove n tover}，而仅$ k \（0 \ le le k \ le l n）$输入，其他则设置为$ 0 $ 0。具体而言，我们评估了未知的高斯矢量执行$ L_2 $ NORM的最小均方根误差（MMSE）估计器在添加剂白色高斯噪声（AWGN）下进行测量，此前数据缺失并得出相应的均方根误差（MSE）的数据丢失并得出表达式。我们发现，当$ K/n $保持恒定时，$ n $归一化的相应MSE趋向于$ 0 $ as $ n \ to \ infty $。此外，当AWGN噪声的差异趋于$ 0 $或$ \ infty $时，MSE的表达是得出的。这些结果概括了Dytso等人的结果。
This paper considers the task of estimating the $l_2$ norm of a $n$-dimensional random Gaussian vector from noisy measurements taken after many of the entries of the vector are \emph{missed} and only $K\ (0\le K\le n)$ entries are retained and others are set to $0$. Specifically, we evaluate the minimum mean square error (MMSE) estimator of the $l_2$ norm of the unknown Gaussian vector performing measurements under additive white Gaussian noise (AWGN) on the vector after the data missing and derive expressions for the corresponding mean square error (MSE). We find that the corresponding MSE normalized by $n$ tends to $0$ as $n\to \infty$ when $K/n$ is kept constant. Furthermore, expressions for the MSE is derived when the variance of the AWGN noise tends to either $0$ or $\infty$. These results generalize the results of Dytso et al.\cite{dytso2019estimating} where the case $K=n$ is considered, i.e. the MMSE estimator of norm of random Gaussian vector is derived from measurements under AWGN noise without considering the data missing phenomenon.
