Coverage and Rate Maximization via User Association in Multi-Antenna HetNets

We formulate two statistical optimization frameworks for multi-antenna heterogeneous networks (HetNets). The first one maximizes coverage, via user association, and the second one maximizes a rate utility function by jointly optimizing user association and the spectrum allocated to each tier. Since both performance metrics depend on the coverage probability, we first derive the exact analytical coverage expression for a frequency-partitioned multi-antenna HetNet. We then present a simple closed-form approximation using the Gil-Pelaez inversion theorem, making both optimization frameworks concave in the optimizing variables. We show that to maximize coverage, the user should connect to the tier with the highest ratio of the array gain to the multiplexing gain, highlighting that max-power association becomes far from optimal in terms of coverage. To maximize the rate utility, we show that the optimal resource allocation of a tier is equal to the portion of users connected to that tier. Furthermore, maximizing the rate utility breaks down into maximizing two objectives: coverage and the number of users to be served in a resource block. Several theoretical insights are presented and further validated via simulations, showing that both frameworks provide considerable coverage and rate gains compared to the standard max-power and small-cell range expansion schemes.