  In this paper, for the first time, we analytically prove that the uplink (UL)
inter-cell interference in frequency division multiple access (FDMA) small cell
networks (SCNs) can be well approximated by a lognormal distribution under a
certain condition. The lognormal approximation is vital because it allows
tractable network performance analysis with closed-form expressions. The
derived condition, under which the lognormal approximation applies, does not
pose particular requirements on the shapes/sizes of user equipment (UE)
distribution areas as in previous works. Instead, our results show that if a
path loss related random variable (RV) associated with the UE distribution
area, has a low ratio of the 3rd absolute moment to the variance, the lognormal
approximation will hold. Analytical and simulation results show that the
derived condition can be readily satisfied in future dense/ultra-dense SCNs,
indicating that our conclusions are very useful for network performance
analysis of the 5th generation (5G) systems with more general cell deployment
beyond the widely used Poisson deployment.
