A stochastic geometry approach to wideband ad hoc networks with channel variations

We present a methodology for determining the outage probability of wideband ad hoc networks with random wireless channels. Assuming that the nodes are Poisson distributed and subject to a required SINR constraint, we develop a simple framework that gives upper and lower bounds on the outage probability. These bounds are important in that they can be manipulated to obtain bounds on the transmission capacity, i.e., the maximum permissible spatial density of transmissions ensuring an acceptably low outage probability. In this paper, we derive the outage probability of wireless ad hoc networks under path loss and shadowing, which are the dominant large-scale effects in wideband ad hoc networks. The analytical framework is rooted in stochastic geometry, employing marked point processes, void probabilities, Palm measure, and Campbell’s Theorem.