On the MMSE estimation of norm of a Gaussian vector under additive white Gaussian noise with randomly missing input entries

• Explicit expression of MMSE estimator is derived from noisy measurements with many missing entries. MSE for and asymptotic results are discussed. This paper considers the task estimating l 2 norm a n -dimensional random Gaussian vector taken after entries missed only K (0 ? ) retained while rest erased set to 0. Specifically, we evaluate minimum mean square error (MMSE) unknown performing under additive white noise (AWGN) on data derive expressions corresponding (MSE). We find that normalized by tends 0 as ? ? any 1 k . Furthermore, when variance AWGN either or ?. These generalize Dytso et al. [1] where case = considered, i.e. without considering phenomenon.