In this paper, we analytically derive an upper bound on the error in approximating the uplink (UL) single-cell interference by a lognormal distribution in frequency division multiple access (FDMA) small cell networks (SCNs). Such an upper bound is measured by the Kolmogorov Smirnov (KS) distance between the actual cumulative density function (CDF) and the approximate CDF. The lognormal approximation is important because it allows tractable network performance analysis. Our results are more general than the existing works in the sense that we do not pose any requirement on (i) the shape and/or size of cell coverage areas, (ii) the uniformity of user equipment (UE) distribution, and (iii) the type of multi-path fading. Based on our results, we propose a new framework to directly and analytically investigate a complex network with practical deployment of multiple BSs placed at irregular locations, using a power lognormal approximation of the aggregate UL interference. The proposed network performance analysis is particularly useful for the 5th generation (5G) systems with general cell deployment and UE distribution.
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