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.