Conisder $\mathbf X \in \mathbb C^{M_A M_S \times M_S T}$, $\mathbf W \in \mathbb C^{M_d \times T}$, and $\mathbf F \in \mathbb C^{M_A \times M_d}$. I am stuck on the following:
\begin{equation} \nabla_{\mathbf F} \, \operatorname{tr} \{\mathbf X (\mathbf I_{M_S} \otimes (\mathbf W^H \mathbf F^H)) \}. \end{equation}
I know the fact that $\nabla_{\mathbf F} \,\operatorname{tr}(\mathbf X \mathbf F^H) = \mathbf X$; however, it seems that the derivation of the given expression is not straightforward. Any help is highly appreciated.
