Uplink capacity of variable-density cellular system with distributed users and fading

In this paper, we extend the well-known model for Gaussian Cellular Multiple Access Channel originally presented by Wyner and later extended by Somekh et al. with fading. The extension to the model, incorporates the distance dependent path loss (maintaining a close relevance to path loss values in real world cellular systems) experienced by the users distributed in a planar cellular array. The density of base stations and hence the cell sizes are variable. In the context of Hyper-receiver joint decoder, a closed form expression for the information theoretic capacity is obtained assuming large number of users in each cell. The effect of the path loss factor, on the information theoretic capacity of the cellular system, is quantified and it is observed that higher path loss factor results in lower capacity. The results validate that larger cell sizes result in lower spectral efficiency. The closed form formula derived by the mathematical analysis is also validated by Monte Carlo simulations.