On Ergodic Capacity of Wireless Transmission Subject to Poisson Distributed Interferers over Rayleigh Fading Channels

Poisson point process has been widely adopted in the analysis of co-channel interference in dense frequency reuse systems. With the decaying power law, the aggregate co-channel interference in Poisson field can be viewed as the output of a shot noise process. In this paper, we first consider the wireless transmission of a single transmitter- receiver pair with a guard zone centered at the receiver. Other interfering transmitters are randomly distributed outside the guard zone according to a spatial Poisson process. We derive the generic closed-form moment generating function (MGF) of the aggregate interference over Rayleigh fading channels. Then we show that the ergodic capacity of wireless transmission in Poisson field over Rayleigh fading channels can be expressed as function of the MGF of the aggregate interference. Through numerical examples, we examine the accuracy of the Gaussian approximation on the aggregate interference in terms of ergodic capacity calculation. Finally we introduce the Matern point process to model the spatial distribution of multiple transmitter-receiver pairs with guard zones centered at respective receivers.