# Relation between channel and path loss exponent

I am referring a paper "Outage Analysis of Ambient Backscatter Communication Systems" wherein i came across the equation $$y_r(n) = \frac{\tilde{h_{sr}}}{\sqrt{d_{sr}^{\alpha}}}+\frac{\tilde{h_{tr}}}{\sqrt{d_{tr}^{\alpha}}} + w(n)$$------(1), where $$\tilde{h_{sr}}$$ and $$\tilde{h_{tr}}$$ are Gaussian channels between source to reader and tag to reader respectively, $$\alpha$$ is path loss exponent, $$d_{sr}$$, $$d_{tr}$$ is the distance between source to reader and tag to reader respectively.

My query is can we write the equation (1) if we consider other channels such as Nakagami-m, Rayleigh etc.

Any help in this regard is highly appreciated.