Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks

In this paper, we provide closed form expressions for the probability density functions (PDF) of the interference power in a network whose transmitters are arranged according to the Poisson Point Process (PPP). These expressions apply for any integer path loss exponent \eta greater than 2. Using the stretched exponential or Kohlrausch function, we show that the PDF formulas can be obtained as long as the Laplace transform (LT) for the PDF follows a specific common (exponential) formulation. Moreover, we show that such closed form expressions can be useful in deriving performance metrics for the network for any fading type experienced by the signals. Finally, using Monte-Carlo simulations and numerical analysis, we validate the accuracy of the proposed analytical derivations.