Considering two matrices, $H_1$ and $H_2$, that are independent of each other and follows complex wishart distributions as $\mathcal{CW} _m(n_1,\Sigma_1)$ and $\mathcal{CW} _m(n_2,\Sigma_2)$ respectively. Now considering the sum
\begin{equation} Z=H_1+H_2. \end{equation}
Will $Z$ also follow a Wishart distribution?
I have only been able to find one example of something like this, in this paper, where the two matrices only differ in degrees of freedom. Is there a similar expression for when the degrees of freedom, $n $, but also the covariance matrix, $\Sigma$, differ?