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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 $e^{j \theta}$ on the diagonal such ...

Let $S\in\mathcal S_N$ be a $N\times N$ symmetric matrix over the reals, and introduce the (normalised) gaussian measure $$ \mathrm d\mu(S):=2^{-\frac 12N}\pi^{-\frac14N(N+1)}\exp\left[-\frac12\...