This paper introduces a model to study both single tier and multitier wireless communication systems consisting of a multitude of wireless access points (AP), and operating according to the classical opportunistic beamforming framework. The AP locations in the proposed network model are determined by using planar Poisson point processes. The extreme value distribution of signal-to-interference-plus-noise-ratio (  ${\rm{ SINR}}$  ) on a beam is of fundamental importance for obtaining performance bounds for such an opportunistic communication system. Two tight distribution approximation results are provided for the distribution of maximum   ${\rm{ SINR}}$   on a beam, which is hard to obtain due to correlation structure of the underlying inter-AP interference field, using key tools from stochastic geometry. These approximations hold for general path loss models that satisfy some mild conditions. Simulations and numerical evaluations are presented to validate the results, to provide further insights into the derived approximate maximum beam   ${\rm{ SINR}}$   distributions, and to illustrate the utility of these approximations in obtaining performance bounds for opportunistic communication systems having multiple interfering APs. In particular, key performance measures such as beam outage probability and ergodic aggregate data rate of an AP are derived by utilizing the approximated distributions.
['Tharaka Samarasinghe', 'Hazer Inaltekin', 'Jamie S. Evans']
Modeling and Analysis of Opportunistic Beamforming for Poisson Wireless Networks