  This paper studies the outage capacity of a network consisting of a multitude
of heterogenous 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 homogenous 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. It is shown that the beam outage capacity scales
logarithmically for the unbounded model. On the other hand, this scaling
behavior becomes double logarithmic for the bounded model. Intuitive
explanations are provided as to why we observe different scaling behavior for
different path loss models. 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.
