Suppose $\mathbf{r} = \mathbf{D}\mathbf{W}\mathbf{h} + \mathbf{u}$ is a Gaussian random vector with mean $\mathbf{D}\mathbf{W}\mathbf{h}$ and variance $\sigma^2\mathbf{I}$.
I try to solve the following equation, but I think there is something wrong...
$$\hat{\mathbf{h}}(\mathbf{r}) = \arg \min_{\mathbf{h}} \left\{ \|\mathbf{r}-\mathbf{D}\mathbf{W}\mathbf{h}\|^2 \right\} \\ = \arg\min_{\mathbf{h}} \left\{\mathbf{r}^h\mathbf{r}+ \left(\mathbf{D}\mathbf{W}\mathbf{h}\right)^h\mathbf{D}\mathbf{W}\mathbf{h}-2\left(\mathbf{D}\mathbf{W}\mathbf{h}\right)^h\mathbf{r} \right\} $$
let $\mathbf{a} =\mathbf{r}^h\mathbf{r}+ \left(\mathbf{D}\mathbf{W}\mathbf{h}\right)^h\mathbf{D}\mathbf{W}\mathbf{h}-2\left(\mathbf{D}\mathbf{W}\mathbf{h}\right)^h\mathbf{r}$, and sloving
$$\frac{d\mathbf{a}}{d\mathbf{h}} = 0$$
so I got $$\hat{\mathbf{h}} = ((\mathbf{D}\mathbf{W})^h\mathbf{D}\mathbf{W})^{-1}(\mathbf{D}\mathbf{W})^h\mathbf{r}$$