Given the following function of random variables

$$g = \frac{1}{n} \sum_{k=1}^{n}{|h_k|\exp\left( j \theta_k \right)},$$ where $h_1, \cdots, h_n$ are i.i.d. random variables following the complex Gaussian distribution $\mathcal{CN}(0,\beta)$ and $\theta_1, \cdots, \theta_n$ are i.i.d. random variables with probability density function (PDF) given by $\frac{1}{2\pi}$ ($i.e.$, the uniform distribution). Additionally, we assume that $h_k$ and $\theta_k$ are independent for all values of $k$.

What would be the PDF of $g$ for small $n$ ($e.g.$, n = 2) and for the case where $n \gg 1$?

This problem arises from the study on wireless communications channels and is of great importance to the research community.