The Topology of Wireless Communication on a Line

This note considers a 1-dimensional wireless network consisting of a set of n stations located on a line, in the SINR model, which compares the received power of a signal at a receiver against the sum of strengths of other interfering signals plus background noise. The behavior of a multi-station network is described using the convenient representation of a reception diagram. In the SINR model, the resulting SINR diagram partitions the plane into reception zones, one per station, and the complementary region of the plane where no station can be heard. We use the minimum principle, recently shown to hold for the SINR function, to derive a tight bound on the number of connected components in 1-dimensional networks.