How close is the nearest node in a wireless network?

The ability of small-cell wireless networks to self-organize is crucial for improving capacity and performance in modern communication networks. This paper considers one of the most basic questions: what is the expected distance to a cell's nearest neighbour in a spatially distributed network? We analyse a model problem in the asymptotic limit of large total received signal and compare the accuracy of different heuristics. We also analytically consider the effects of fading. Our analysis shows that the most naive heuristic systematically underestimates the distance to the nearest node; this is substantially corrected in cases of interest by inclusion of the next-order asymptotic term. We illustrate our theoretical results explicitly or several combinations of signal and path loss parameters and show that our theory is well supported by numerical simulations.