On the Capacity of an Elemental Two-Way Two-Tier Network

A basic setup of a two-tier network, where two mobile users exchange messages with a multi-antenna macrocell basestation, is studied from a rate perspective subject to beamforming and power constraints. The communication is facilitated by two femtocell basestations which act as relays as there is no direct link between the macrocell basestation and the mobile users. We propose a scheme based on physical-layer network coding and compute-and-forward combined with a novel approach that solves the problem of beamformer design and power allocation. We also show that the optimal beamformers are always a convex combination of the channels between the macro- and femtocell basestations. We then establish the cut-set bound of the setup to show that the presented scheme almost achieves the capacity of the setup numerically.