Deterministic approximation conjecture for Nakagami fading channels

Consider a two-dimensional wireless network in which channel attenuation consists of a constant attenuation at a reference distance, distance-dependent attenuation with path-loss index $\alpha$, and random fading $h$. The fading is Nakagami-$m$ or Rayleigh fading, and ergodic performance metrics include throughput and delay.

Deterministic approximation conjecture. If $h$ has a Nakagami-$m$ distribution with $m \geq 3$, then the fading channel can be well approximated by a deterministic channel gain without introducing a significant gap in ergodic performance metrics such as spectral efficiency, energy efficiency, throughput, and delay. If $h$ has Rayleigh fading, replacing $h$ by its $2/\alpha$-th moment, $\mathbf{E}_h[h^{2/\alpha}]$, results in sufficiently accurate analysis of these metrics.

The conjecture concerns simplifying wireless-network interference and performance analysis by replacing random fading with a deterministic channel. The paper supports the claim through numerical observations, while the corresponding general statement is not established theoretically.