I read this paper: https://arxiv.org/pdf/1305.2460.pdf
And there is a formula about MMSE:$\mathbf W^*_{MMSE}= E[\mathbf s \mathbf y^*]E[\mathbf y \mathbf y^*]^{-1}$
$\mathbf W _{BB}$:Baseband combiner
$\mathbf W _{RF}$:RF combiner
$\mathbf W $:The combination of $\mathbf W_{RF}$ and $\mathbf W _{BB}$
$\mathbf W^*$ : the hermitian of $\mathbf W$
$\mathbf s$:the signal on the left
$\mathbf y$:the signal when $\mathbf s$ goes through the channel
Why can the :$\mathbf W^*_{MMSE} $ be written as $E[\mathbf s \mathbf y^*]E[\mathbf y \mathbf y^*]^{-1}$.why should we multiply the these two signal ,$\mathbf s$ and $ \mathbf y$,and average them ?Does anyone have information about this formula ?