On the Analytical Tractability of Hexagonal Network Model with Random User Location

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 the downlink Interference-to-Signal Ratio (ISR) for any mobile location $m$ in a hexagonal wireless network, whether composed of omni-directional or tri-sectorized sites. The explicit formula of ISR is a very convergent series on $m$ and involves the use of Gauss 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 ISR is easily extended to any frequency reuse pattern. Moreover, it is also exploited in the derivation of an explicit form of SINR distribution for any arbitrary distribution of mobile user locations, 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.