Spatial and Temporal Correlation of the Interference in ALOHA Ad Hoc Networks

Interference is a main limiting factor of the performance of a wireless ad hoc network. The temporal and the spatial correlation of the interference makes the outages correlated temporally (important for retransmissions) and spatially correlated (important for routing). In this letter we quantify the temporal and spatial correlation of the interference in a wireless ad hoc network whose nodes are distributed as a Poisson point process on the plane when ALOHA is used as the multiple-access scheme.

💡 Research Summary

This paper investigates the spatio‑temporal correlation of interference in a wireless ad‑hoc network where nodes are distributed according to a homogeneous Poisson point process (PPP) on the plane and the ALOHA random access scheme is employed. The authors first define the interference at a given time slot as the sum of the received powers from all simultaneously active transmitters, each power being the product of an independent fading gain and a distance‑based path‑loss function ℓ(r)=r⁻ᵅ (α>2). By assuming that each node independently transmits with probability p in every slot, the set of active transmitters in slot t forms a thinned PPP with intensity pλ.

The temporal correlation analysis derives the covariance between interference measured at two slots separated by Δt. Because the thinning process is independent across slots, the only source of correlation is the overlap of the same nodes being active in both slots. The authors obtain a closed‑form expression for the covariance, which simplifies to Cov