A new method for computing the transmission capacity of non-Poisson wireless networks

The relative locations of concurrent transmitting nodes play an important role in the performance of wireless networks because it largely determines their mutual interference. In most prior work the set of interfering transmitters has been modeled by a homogeneous Poisson distribution, which assumes independence in the transmitting node positions, and hence precludes intelligent scheduling protocols. One of the main difficulties in extending the numerous Poisson results is the absence of an analytical form for the probability generating functional and the Palm characterization of the underlying spatial node distribution. In this paper we take an alternative approach based on the second-order product density of the node distribution, which is asymptotically tight as the outage probability tends to zero. Unlike the probability generating functional, the second order product density can be easily obtained for a wide range of point processes and hence this approach is useful in analyzing complex wireless networks and MAC protocols. We use this approach to then provide accurate approximations of the transmission capacity of wireless ad hoc networks for three plausible point processes, corresponding to ALOHA, clustering, and carrier sensing schedulers. The mathematical framework introduced can be used to analyze other relevant metrics.