Assume that ${\bf{z}} \in {\mathbb{C}}^{n \times 1}$ is a CSCG random vector denoted with $\mathcal{C} ~ (\bf{\mu} _0,\bf \Sigma _0)$ where $\mu _0$ and $\bf \Sigma _0$ are mean and contrivance matrix, respectively, and defined as
$\mu _0=E({\bf z})$, $\Sigma _0=E({\bf zz}^H)$.
How can I obtain the following expectations versus $\bf{\mu}_0$ and $\bf{\Sigma}_0$.?
1) $E\left( {{\bf{x}} \otimes \left( {{\bf{x}}{{\bf{x}}^H}} \right)} \right)$
2)$E\left( {\left( {{\bf{x}}{{\bf{x}}^H}} \right) \otimes \left( {{\bf{x}}{{\bf{x}}^H}} \right)} \right)$
where $\mathbf{x}\triangleq\left[\mathbf{z},\mathbf{z}^*\right]$ and $(.)^*$ denote for complex conjugate.
