On the Analytical Tractability of Hexagonal Network Model with Random Traffic Distribution

Explicit derivation of interferences in hexagonal wireless networks has been widely considered intractable and requires extensive computations with system level simulations. In this paper, we fundamentally tackle this problem and explicitly evaluate interference factor $f$ for any mobile location $m$ in a hexagonal network composed of omni-directional or tri-sectorized sites. The explicit formula of $f$ is a very convergent series on $m$ and involves the use of hypergeometric and Hurwitz Riemann zeta functions. Besides, we establish simple identities that well approximate this convergent series and turn out quite useful compared to other approximations in literature. The derived expression of $f$ is used to show further that the SINR distribution is explicit as well and it is provided for any arbitrary mobile location distribution, reflecting the spatial traffic density in the network. Knowing explicitly about interferences and SINR distribution is very useful information in capacity and coverage planning of wireless cellular networks and particularly for macro-cells' layer that forms almost a regular point pattern.