  Beamforming (BF) training is crucial to establishing reliable millimeter-wave
communication connections between stations (STAs) and an access point. In IEEE
802.11ad BF training protocol, all STAs contend for limited BF training
opportunities, i.e., associated BF training (A-BFT) slots, which results in
severe collisions and significant BF training latency, especially in dense user
scenarios. In this paper, we first develop an analytical model to evaluate the
BF training protocol performance. Our analytical model accounts for various
protocol components, including user density, the number of A-BFT slots, and
protocol parameters, i.e., retry limit and contention window size. We then
derive the average successful BF training probability, the BF training
efficiency and latency. Since the derived BF training efficiency is an implicit
function, to reveal the relationship between system parameters and BF training
performance, we also derive an approximate expression of BF training
efficiency. Theoretical analysis indicates that the BF training efficiency
degrades drastically in dense user scenarios. To address this issue, we propose
an enhancement scheme which adaptively adjusts the protocol parameters in tune
with user density, to improve the BF training performance in dense user
scenarios. Extensive simulations are carried out to validate the accuracy of
the developed analytical model. In addition, simulation results show that the
proposed enhancement scheme can improve the BF training efficiency by 35% in
dense user scenarios.
