Performance Bounds and Associated Design Principles for Multi-Cellular Wireless OFDMA Systems (with Detailed Proofs)

In this paper, we consider the downlink of large-scale multi-cellular OFDMA-based networks and study performance bounds of the system as a function of the number of users $K$, the number of base-stations $B$, and the number of resource-blocks $N$. Here, a resource block is a collection of subcarriers such that all such collections, that are disjoint have associated independently fading channels. We derive novel upper and lower bounds on the sum-utility for a general spatial geometry of base stations, a truncated path loss model, and a variety of fading models (Rayleigh, Nakagami-$m$, Weibull, and LogNormal). We also establish the associated scaling laws and show that, in the special case of fixed number of resource blocks, a grid-based network of base stations, and Rayleigh-fading channels, the sum information capacity of the system scales as $\Theta(B \log\log K/B)$ for extended networks, and as $O(B \log\log K)$ and $\Omega(\log \log K)$ for dense networks. Interpreting these results, we develop some design principles for the service providers along with some guidelines for the regulators in order to achieve provisioning of various QoS guarantees for the end users and, at the same time, maximize revenue for the service providers.