A Stochastic Geometry Approach for Outage Analysis of Ad Hoc SISO Networks in Rayleigh Fading

In this paper, a closed-form expression for the outage probability of an ad hoc single-input single-output (SISO) network is derived when the network is subject to Rayleigh fading and arbitrary path loss model. The underlying stochastic geometry of the network assumes a simple point process in which a single node is placed randomly in a square region. A closed-form expression of the distribution of the distance between a pair of nodes is derived. This expression is then generalized for positive powers to incorporate the path loss exponent. Moment matching is used to make the model analytically tractable. It is shown that the distribution of the distance is well approximated by the Weibull distribution with the scale parameter depending on the size of the network and a constant shape parameter. The coverage and outage behaviors of the network for various network sizes and path loss exponents are quantified. Numerical simulations are performed to validate the theoretical models.