Coverage-Rate Tradeoff in mmWave Heterogeneous Networks with Generalized User Association

In this paper, we first introduce a generalized modeling and analysis framework to explore the fundamental interactions between user association, coverage probability and link rate in a millimeter wave (mmWave) heterogeneous network (HetNet) in which there are multiple tiers of the ultra-highfrequency (UHF) macrocell and small cell base stations (BSs) and a single tier of mmWave small cell BSs. A generalized user association scheme that can cover many pathloss-based user association schemes is proposed and its related probabilistic properties that facilitate the derivations of the coverage probability and link rate are derived. The derived general expressions of the coverage and link rate not only shed light on how to design user association functions in order to maximize the coverage and rate but also show that it is impossible to devise a user association scheme that maximizes the coverage and link rate at the same time. Namely, there exists a fundamental tradeoff between coverage and link rate in an mmWave HetNet with distinct bandwidths in the UHF and mmWave bands. We characterize the coverage-optimal and rate-optimal user association schemes and numerically validate their performances and show the tradeoff problem.