Gaussian, Rayleigh, and Exponential RVs
So you have a complex impulse response, and the real and imaginary parts of each tap are modeled as i.i.d. zero mean Gaussian variables with variance $\sigma^2/2$ (correct me if I'm wrong). The DFT of the impulse response is a weighted sum of the filter taps:

$$H[k]=\sum_{n=0}^{N-1}h[n]e^{-j2\pi nk/N}\tag{1}$$

where I assume $N\ge L$ (where $L$ is the number of taps), and in Eq. (1) $h[n]=0$ for $n\ge L$. From (1) it follows that $H[k]$ is also a complex Gaussian RV with zero mean and with variance $L\sigma^2$ (the variance of the real and imaginary part is $L\sigma^2/2$, respectively). From this it follows that the magnitude $|H[k]|$ has a Rayleigh distribution:

$$f_{|H|}(x)=\frac{2x}{L\sigma^2}e^{-x^2/(L\sigma^2)}\tag{2}$$

And, accordingly, the squared magnitude $|H[k]|^2$ has an exponential distribution:

$$f_{|H|^2}(x)=\lambda e^{-\lambda x},\quad x\ge 0\tag{3}$$

With $\lambda=1/(L\sigma^2)$, i.e. with mean $1/\lambda=L\sigma^2$, and variance $1/\lambda^2=L^2\sigma^4$.