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This paper considers the task of estimating the $l_2$ norm of a$n$-dimensional random Gaussian vector from noisy measurements taken after manyof 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 theminimum mean square error (MMSE) estimator of the $l_2$ norm of the unknownGaussian vector performing measurements under additive white Gaussian noise(AWGN) on the vector after the data missing and derive expressions for thecorresponding mean square error (MSE). We find that the corresponding MSEnormalized 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 AWGNnoise tends to either $0$ or $\infty$. These results generalize the results ofDytso et al.\cite{dytso2019estimating} where the case $K=n$ is considered, i.e.the MMSE estimator of norm of random Gaussian vector is derived frommeasurements under AWGN noise without considering the data missing phenomenon.

On the MMSE Estimation of Norm of a Gaussian Vector under Additive White Gaussian Noise with Randomly Missing Input Entries