Performance of Multi-Antenna MMSE Receivers in Non-homogeneous Poisson Networks

A technique to compute the Cumulative Distribution Function (CDF) of the Signal-to-Interference-plus-Noise-Ratio (SINR) for a wireless link with a multi-antenna, Linear, Minimum-Mean-Square-Error (MMSE) receiver in the presence of interferers distributed according to a non-homogenous Poisson point process on the plane, and independent Rayleigh fading between antennas is presented. This technique is used to compute the CDF of the SINR for several different models of intensity functions, in particular, power-law intensity functions, circular-symmetric Gaussian intensity functions and intensity functions described by a polynomial in a bounded domain. Additionally it is shown that if the number of receiver antennas is scaled linearly with the intensity function, the SINR converges in probability to a limit determined by the "shape" of the underlying intensity function. This work generalizes known results for homogenous Poisson networks to non-homogenous Poisson networks.