Determining the Ordering of a Line Topology under Correlated Shadowing and Fast Fading

We study the success rate of detecting the ordering of a line topology under correlated shadowing and fast fading for two methods from the literature which rely on signal strength measurements only. First we propose a model extension of the so far only existing spatially correlated model of log-normal shadowing for comparing two arbitrary links, which enables us to explore highly correlated links as well. For one method, we then formulate the detection probability in this correlation model when repeated nearby measurements are included, and study how far averaging can be used to mitigate small scale fading in the problem setting. Finally, for uncorrelated shadowing we observe an interesting connection between the detection probabilities with and without fading.