On Estimating the Norm of a Gaussian Vector Under Additive White Gaussian Noise
On Estimating the Norm of a Gaussian Vector Under Additive White Gaussian Noise
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DOI：
10.1109/lsp.2019.2929863
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发表时间：
2019-09-01
影响因子：
3.9
通讯作者：
Poor, H. Vincent
中科院分区：
文献类型：
--
作者：
Dytso, Alex;Cardone, Martina;Poor, H. Vincent
本文研究了n维高斯随机向量的范数估计问题，特别是考虑了加性高斯噪声扰动的情况，假设加性高斯噪声扰动与原始向量无关。首先推导了最优估计量的表达式，然后计算了相应的最小均方误差（MMSE）。还分析了大向量大小的情况，并且表明当n ->无穷大时，由n归一化的MMSE等于零。
This letter considers the task of estimating the norm of ann-dimensional Gaussian random vector given a noisy/perturbed observation of it. In particular, the focus is on the case of additive Gaussian noise perturbation, which is assumed to be independent of the original vector. First, an expression for the optimal estimator is derived, and then the corresponding minimum mean square error (MMSE) is computed. The regime of large vector size is also analyzed, and it is shown that the MMSE normalized by n equals zero when n -> infinity.