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.

Original languageEnglish
Pages (from-to)188-219
Number of pages32
JournalIMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Issue number1
Early online date30 Dec 2020
Publication statusPublished - 28 Feb 2021


  • Asymptotic approximation
  • Distance estimation
  • Femtocells
  • Rayleigh fading
  • Self-organizing network
  • Wireless networks

ASJC Scopus subject areas

  • Applied Mathematics


Dive into the research topics of 'How close is the nearest node in a wireless network?'. Together they form a unique fingerprint.

Cite this