A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications

Alex Dytso, H. Vincent Poor, Shlomo Shamai

Consider a channel $\mathbf{Y}=\mathbf{X}+\mathbf{N}$ where $\mathbf{X}$ is an $n$-dimensional random vector, and $\mathbf{N}$ is a Gaussian vector with a covariance matrix ${\bf \mathsf{K}}_{\b…