Differential Form of Bivariate MMSE Estimator Based on Gaussian Noise

Abstract

In fact, the noise signal is an important problem in signal, circuits and systems. The minimum mean square error (MMSE) estimation technique is useful in several additive white Gaussian noise (AWGN) reduction methods. Original form of MMSE estimator is the integral form. Unfortunately, integral form of MMSE estimator cannot be obtained in simple form for any interesting peaked, heavy-tailed densities (also known as super-Gaussian densities). In this work, we proposed a differential form of bivariate MMSE estimator. The development depends on bivariate Taylor series. The proposed estimator requires no integration. In fact, the derivation is an extension of the existing results for differential form of univariate MMSE estimator.