Hexagonal vs Circular Cell Shape: A Comparative Analysis and Evaluation of the Two Popular Modeling Approximations

Recent years have witnessed an explosion in wireless communications. In the last decades, the development of wireless communication systems and networks is taking us from a world where communications were mostly carried over PSTN, packet-switched and high speed LAN networks to one where the wireless transmission dominates. Nowadays, high data rates carry multimedia communications, real-time services for delay-sensitive applications are added and networks are asked to deal with a traffic mix of voice, data and video. Next generation mobile systems will further include a variety of heterogeneous access technologies, support multimedia applications and provide end-to-end IP connectivity (Bolton et al., 2007; Xylomenos et al., 2008; Demestichas et al., 2010). Undoubtedly, new possibilities are created for both telcos and users and important design and traffic issues emerge. This revolution has spurred scientists toward the development of reliable and computationally efficient models for evaluating the performance of wireless networks. A crucial parameter in the modeling of a cellular communication system is the shape of the cells. In real life, cells are irregular and complex shapes influenced by terrain features and artificial structures. However, for the sake of conceptual and computational simplicity, we often adopt approximate approaches for their design and modeling. In the published literature, cells are usually assumed hexagons or circles. The hexagonal approximation is frequently employed in planning and analysis of wireless networks due to its flexibility and convenience (Jan et al., 2004; Goldsmith, 2005; Pirinen, 2006; Chan & Liew, 2007; Hoymann et al., 2007; Baltzis, 2008, 2010a; Choi & You, 2008; Dou et al., 2008; Xiao et al., 2008; Baltzis & Sahalos, 2010). However, since this geometry is only an idealization of the irregular cell shape, simpler models are often used. In particular, the circular–cell approximation is very popular due to its low computational complexity (Petrus et al., 1998; Baltzis & Sahalos, 2005, 2009b; Goldsmith, 2005; Pirinen, 2006; Bharucha & Haas, 2008; Xiao et al., 2008; Baltzis, 2010b). Among various performance degradation factors, co-channel interference (CCI) is quite significant since the cells in cellular networks tend to become denser in order to increase system capacity (Stavroulakis, 2003). The development of models that describe CCI generates great interest at the moment. Several reliable models can be found in the