Given a $K\times M$ matrix $X$, where $M\gg K$, comprising independent complex Gaussian random variables, each one with mean $$E[X_{k,m}]=B_{k,m}$$ and variance $$Var[X_{k,m}]=\Sigma_{k,m}$$ define the random matrix $R(X)$ as $$R(X)=I +XX^{H}.$$

My problem is now to compute the expected value of $R^{-1}(X)$, i.e., compute $$E_X[R^{-1}(X)].$$

My idea was to perhaps use a Neumann series expansion of the matrix inverse and then to evaluate moments.

I noted that someone posted a similar question:Expected mean square error of an estimation problem

The questions are clearly related