Downlink and uplink decoupling in two-tier heterogeneous networks with multi-antenna base stations

In order to improve the uplink performance of future cellular networks, the idea to decouple the downlink (DL) and uplink (UL) association has recently been shown to provide significant gain in terms of both coverage and rate performance. However, all the work is limited to SISO network. Therefore, to study the gain provided by the DL and UL decoupling in multi-antenna base stations (BSs) setup, we study a two tier heterogeneous network consisting of multi-antenna BSs, and single antenna user equipments (UEs). We use maximal ratio combining (MRC) as a linear receiver at the BSs and using tools from stochastic geometry, we derive tractable expressions for both signal to interference ratio (SIR) coverage probability and rate coverage probability. We observe that as the disparity in the beamforming gain of both tiers increases, the gain in term of SIR coverage probability provided by the decoupled association over non-decoupled association decreases. We further observe that when there is asymmetry in the number of antennas of both tier, then we need further biasing towards femto-tier on the top of decoupled association to balance the load and get optimal rate coverage probability