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This paper studies the outage capacity of a network consisting of a multitudeof heterogenous mobile users, and operating according to the classicalopportunistic beamforming framework. The base station is located at the centerof the cell, which is modeled as a disk of finite radius. The random userlocations are modeled using a homogenous spatial Poisson point process. Thereceived 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 mildconditions. Then, we focus on two specific path loss models (i.e., an unboundedmodel and a more realistic bounded one) to illustrate the applications of ourresults. In the large system limit where the cell radius tends to infinity, thebeam outage capacity and its scaling behavior are derived for the selectedspecific path loss models. It is shown that the beam outage capacity scaleslogarithmically for the unbounded model. On the other hand, this scalingbehavior becomes double logarithmic for the bounded model. Intuitiveexplanations are provided as to why we observe different scaling behavior fordifferent path loss models. Numerical evaluations are performed to give furtherinsights, and to illustrate the applicability of the outage capacity resultseven to a cell having a small finite radius.

Outage Capacity of Opportunistic Beamforming with Random User Locations