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

Abstract: A technique is presented to evaluate the performance of a wireless link with a multi-antenna linear Minimum-Mean-Square Error (MMSE) receiver in the presence of interferers distributed according to non-homogeneous Poisson processes or Poisson cluster processes on the plane. The Cumulative Distribution Function (CDF) of the Signal-to-Interference-plus-Noise Ratio (SINR) of a representative link is derived for both types of networks assuming independent Rayleigh fading between antennas. Several representative spatial node distributions are considered, for which the derived CDFs are verified by numerical simulations. In addition, for non-homogeneous Poisson networks, it is shown that the Signal-to-Interference Ratio (SIR) converges to a deterministic non-zero value if the number of antennas at the representative receiver increases linearly with the nominal interferer density. This indicates that to the extent that the system assumptions hold, it is possible to scale such networks by increasing the number of receiver antennas linearly with user density. The results presented here are useful in characterizing the performance of multiantenna wireless networks with non-homogenous spatial node distributions and networks with clusters of users which often arise in practice, but for which few results are available.