I have the following quadratic maximization problem

$\max_{\mathbf X} \quad tr(\mathbf A\mathbf X\mathbf B\mathbf X^H)+tr(\mathbf C\mathbf X)+tr(\mathbf C^H\mathbf X^H)$

subject to the quadratic constraint $tr(\mathbf X \mathbf X^H)\leq r$ where $\mathbf A, \mathbf B \succeq \mathbf 0$ (positive semi-definite) and $\mathbf C$ is any matrix (not necessarily hermitian).

I am looking for a closed-form solution/structure for $\mathbf X$ or even a nice upper bound. A simple upper bound of it can be found using inequality results, so we know that the problem has a finite maximum.

I would really appreciate any help/comment/solution :)

Thanks in advance,

Saeed