I have a square matric $H = (ABC)(ABC)^H$ where $A$ and $C$ are complex Gaussian matrices with some correlation matrices and $B$ is a diagonal matrix with entries $e^{j \theta}$ is the diagonal elements such that each $\theta$ is uniformly chosen from $[0, 1]$, Do you have any idea about the distribution of determinant of this matrix? i.e., $\text{det}[H] \sim ?$