Large‐scale fading behavior for a cellular network with uniform spatial distribution

Large‐scale fading (LSF) between interacting nodes is a fundamental element in radio communications, responsible for weakening the propagation, and thus worsening the service quality. Given the importance of channel‐losses in general, and the inevitability of random spatial geometry in real‐life wireless networks, it was then natural to merge these two paradigms together in order to obtain an improved stochastical model for the LSF indicator. Therefore, in exact closed‐form notation, we generically derived the LSF distribution between a prepositioned reference base‐station and an arbitrary node for a multi‐cellular random network model. In fact, we provided an explicit and definitive formulation that considered at once: the lattice profile, the users' random geometry, the effect of the far‐field phenomenon, the path‐loss behavior, and the stochastic impact of channel scatters. The veracity and accuracy of the theoretical analysis were also confirmed through Monte Carlo simulations. We derived an exact closed‐form large‐scale fading probability density function between a reference base‐station and a randomly positioned node over a flexible multi‐cellular network model. Precisely, this comprehensive formulation took into account: the lattice profile, users' geometry, the effect of the far‐field phenomenon, the PL behavior, and the stochastic impact of channel scatterers. Because of this comprehensive approach, the determined distribution notation precisely characterizes the channel‐loss while remaining fully generic and compatible for different network parameters and channel environments.