The performance of linear multiple-antenna receivers with interferers distributed on a plane

We find an asymptotic expression for the average signal to interference ratio (SIR) between a transmitter with a single isotropic antenna and a multi-antenna linear receiver in the presence of interferers with single isotropic transmit antennas distributed uniformly on an infinite plane. The channels are modeled as complex Gaussian random variables with average received power dependent on the distance separating nodes. We find that in large networks, the average SIR for a representative link depends primarily on the ratio of the number of receive antenna elements to the area density of interferers. Furthermore for our network model, the SIR grows super-linearly with the number of antenna elements. We also derive an approximate expression for the average capacity of the link when residual interference is treated as noise under certain conditions. We show via Monte-Carlo simulations that the asymptotic results are useful approximations to systems with finite parameters.