On Association Cells in Random Heterogeneous Networks

Characterizing user to access point (AP) association strategies in heterogeneous cellular networks (HetNets) is critical for their performance analysis, as it directly influences the load across the network. In this letter, we introduce and analyze a class of association strategies, which we term stationary association, and the resulting association cells. For random HetNets, where APs are distributed according to a stationary point process, the area of the resulting association cells are shown to be the marks of the corresponding point process. Addressing the need of quantifying the load experienced by a typical user, a "Feller-paradox" like relationship is established between the area of the association cell containing origin and that of a typical association cell. For the specific case of Poisson point process and max power/\SINR association, the mean association area of each tier is derived and shown to increase with channel gain variance and decrease in the path loss exponents of the corresponding tier.