We propose and prove a theorem that allows the calculation of a class of functionals on Poisson point processes that have the form of expectations of sum-products of functions. In proving the theorem, we extend the Campbell-Mecke theorem from stochastic geometry. We proceed to apply our result in the calculation of expectations involving interference in wireless Poisson networks. Based on this, we derive outage probabilities for transmissions in a Poisson network with Nakagami fading. Our results extend the stochastic geometry toolbox used for the mathematical analysis of interference-limited wireless networks.
Schilcher et al. REF also derived the outage probability in a system with Nakagami fading in ad hoc networks.
Interference Functionals in Poisson Networks
IEEE Transactions on Information Theory, vol. 62, no. 1, pp. 370-383, Jan. 2016
Mathematics Computer Science