On the outage capacity of opportunistic beamforming with random user locations

This paper studies the outage capacity of a network consisting of a multitude of heterogeneous mobile users and operating according to the classical opportunistic beamforming framework. The base station is located at the center of the cell, which is modeled as a disk of finite radius. The random user locations are modeled using a homogeneous spatial Poisson point process. The received signals are impaired by both fading and location dependent path loss. For this system, we first derive an expression for the beam outage probability. This expression holds for all path loss models that satisfy some mild conditions. Then, we focus on two specific path loss models (i.e., an unbounded model and a more realistic bounded one) to illustrate the applications of our results. In the large system limit, where the cell radius tends to infinity, the beam outage capacity and its scaling behavior are derived for the selected specific path loss models. This paper also studies opportunistic schemes that achieve fairness among the heterogeneous users. Numerical evaluations are performed to give further insights and to illustrate the applicability of the outage capacity results even to a cell having a small finite radius.