Gaussian Approximation for the Wireless Multi-access Interference Distribution and Its Applications

TL;DR

This paper develops a Gaussian approximation for the interference distribution in large wireless networks, providing convergence rates, explicit formulas, and applications to capacity bounds, validated through simulations.

Contribution

It introduces a general methodology for Gaussian approximation of interference distributions, including fading and shadowing effects, with explicit convergence rates and capacity bounds.

Findings

Interference distribution converges to Gaussian at rate 1/√λ.

Explicit scaling coefficient derived based on fading and path-loss.

Gaussian approximation accurately models interference for moderate to high λ.

Abstract

This paper investigates the problem of Gaussian approximation for the wireless multi-access interference distribution in large spatial wireless networks. First, a principled methodology is presented to establish rates of convergence of the multi-access interference distribution to a Gaussian distribution for general bounded and power-law decaying path-loss functions. The model is general enough to also include various random wireless channel dynamics such as fading and shadowing arising from multipath propagation and obstacles existing in the communication environment. It is shown that the wireless multi-access interference distribution converges to the Gaussian distribution with the same mean and variance at a rate $\frac{1}{\sqrt{\lambda}}$, where $\lambda>0$ is a parameter controlling the intensity of the planar (possibly non-stationary) Poisson point process generating node locations. An explicit expression for the scaling coefficient is obtained as a function of fading statistics and the path-loss function. Second, an extensive numerical and simulation study is performed to illustrate the accuracy of the derived Gaussian approximation bounds. A good statistical fit between the interference distribution and its Gaussian approximation is observed for moderate to high values of $\lambda$. Finally, applications of these approximation results to upper and lower bound the outage capacity and ergodic sum capacity for spatial wireless networks are illustrated. The derived performance bounds on these capacity metrics track the network performance within one nats per second per hertz.