Capacity of cellular uplink with multiple tiers of users and path loss

With the emergence and continuous growth of wireless data services, the value of a wireless network is not only defined by how many users it can support, but also by its ability to deliver higher data rates. Information theoretic capacity of cellular systems with fading is usually estimated using models originally inspired by Wyner's Gaussian Cellular Multiple Access Channel (GCMAC). In this paper we extend this model to study the cellular system with users distributed over the cellular coverage area. Based on the distance from the cell-site receiver, users are grouped as tiers, and received signals from each tier are scaled using a distance dependent attenuation factor. The optimum capacity in fading environment is then found by calculating the path-loss for users in each tier using a specific path-loss law and some interesting insights are derived. The results correspond to a more realistic model which boils down to Wyner's model with fading, with appropriate substitutions of parameter values. The results are verified using Wyner's model with fading and Monte-Carlo simulations. Insights are provided for the real world scenarios.