Probability distribution of $g^h f f^h g$

Question

We define an $k \times k$ complex matrix $M=[V \, \mathbf{0}]$, where matrix $V$ is $k \times (k-l)$ dimensional and is unitary, and $\mathbf{0}$ is the $k \times l$ zero matrix. Let vector $f$ be a $k$ dimension ($k \times 1$) standard complex normal random vector. We assume that vector $f$ and matrix $M$ are independent.
We define $g$ as a unit norm vector obtained after the normalization of $M^hf$, where the superscript $h$ denotes the hermitian transpose.
Could you help me to find the distribution of $g^h f f^h g$ ?