Performance of MMSE multi-antenna receiver under hierarchical Poisson random fields of interferences

The cumulative distribution function (CDF) of the signal-to-interference-plus-noise-ratio (SINR) for minimum-mean-square-error (MMSE) receivers is studied in this paper. It is discovered that, in the presence of multiple Poisson fields of interferers and independent Rayleigh fading between antennas, the CDF exhibits linear superposition property for multiple Poisson fields. This superposition property is used to generalize known results for a single homogenous Poisson field to multiple Poisson fields, non-homogenous Poisson fields and hierarchical clustered Poisson fields of interferers.