Wireless Signal Point Processes with a Reflecting Wall

Abstract

A long reflecting wall gives every wireless transmitter a mirror image, pairing its direct and reflected paths. Motivated by intelligent surfaces, we study the resulting signal point processes under two treatments: keeping the powers apart and superposing their point processes, or adding the powers transmitter by transmitter to form a recombined process. A threshold on inverse received power selects a region of transmitter locations, so Campbell's theorem reduces the mean measures to area calculations without assuming Poisson transmitters. For power-law path loss and paired fading marks, we derive the ratio of the recombined and superposed mean measures at large thresholds. The limit is independent of transmitter density and wall distance, but generally depends on the joint fading distribution. Under common fading, that dependence disappears and the limit depends only on the reflection coefficient and path-loss exponent. For Poisson transmitters, we derive paired count fluctuations and convergence of the count ratio. We also calculate the probability that the strongest individual path is direct. When the wall passes through the receiver, this probability has a closed form and the strongest received power has an exact Fréchet distribution. These results provide a reference model for wireless networks with reflecting surfaces.