  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.
