1Downlink Multi-Antenna Heterogeneous Cellular Network with Load Balancing

Abstract—We model and analyze heterogeneous cellular net-works with multiple antenna BSs (multi-antenna HetNets) withK classes or tiers of base stations (BSs), which may differ in terms of transmit power, deployment density, number of transmit anten-nas, number of users served, transmission scheme, and path loss exponent. We show that the cell selection rules in multi-antenna HetNets may differ significantly from the single-antenna HetNets due to the possible differences in multi-antenna transmission schemes across tiers. While it is challenging to derive exact cell selection rules even for maximizing signal-to-interference-plus-noise-ratio (SINR) at the receiver, we show that adding an appropriately chosen tier-dependent cell selection bias in the received power yields a close approximation. Assuming arbitrary selection bias for each tier, simple expressions for downlink coverage and rate are derived. For coverage maximization, the required selection bias for each tier is given in closed form. Due to this connection with biasing, multi-antenna HetNets may balance load more naturally across tiers in certain regimes compared to single-antenna HetNets, where a large cell selection bias is often needed to offload traffic to small cells. Index Terms—Multi-antenna heterogeneous cellular network, stochastic geometry, coverage probability, cell selection bias. I