Interference statistics of a poisson field of interferers with random puncturing

Assume that the transmitters in a random wireless network are distributed according to a Poisson Point Process (PPP) and that the receiver is interested in the signal transmitted by its kth nearest transmitter where k ∈ T and T denotes the set of desired transmitters. Excluding the desired transmitter(s) is equivalent to puncturing the points corresponding to the desired transmitters from the PPP which results in the field of interferers. In this paper, by assuming that the field of interferers keeps its Poisson property, we approximate the cumulants of interference. We show that to find the cumulants, the joint statistics of internodal distances in the PPP are required which we find in closed form. Simulation results show that the obtained analytical derivations provide very good approximation to the interference statistics.