Capacity Bounds in Random Wireless Networks

We consider a receiving node, located at the origin, and a Poisson point process (PPP) that models the locations of the desired transmitter as well as the interferers. Interference is known to be non-Gaussian in this scenario. The capacity bounds for additive non-Gaussian channels depend not only on the power of interference (i.e., up to second order statistics) but also on its entropy power which is influenced by higher order statistics as well. Therefore, a complete statistical characterization of interference is required to obtain the capacity bounds. While the statistics of sum of signal and interference is known in closed form, the statistics of interference highly depends on the location of the desired transmitter. In this paper, we show that there is a tradeoff between entropy power of interference on the one hand and signal and interference power on the other hand which have conflicting effects on the channel capacity. We obtain closed form results for the cumulants of the interference, when the desired transmitter node is an arbitrary neighbor of the receiver. We show that to find the cumulants, joint statistics of distances in the PPP will be required which we obtain in closed form. Using the cumulants, we approximate the interference entropy power and obtain bounds on the capacity of the channel between an arbitrary transmitter and the receiver. Our results provide insight and shed light on the capacity of links in a Poisson network. In particular, we show that, in a Poisson network, the closest hop is not necessarily the highest capacity link.