  In this paper, we study the key properties of multi-antenna two-tier networks
under different system configurations. Based on stochastic geometry, we derive
the expressions and approximations for the users' average data rate. Through
the more tractable approximations, the theoretical analysis can be greatly
simplified. We find that the differences in density and transmit power between
two tiers, together with range expansion bias significantly affect the users'
data rate. Besides, for the purpose of area spectral efficiency (ASE)
maximization, we find that the optimal number of active users for each tier is
approximately fixed portion of the sum of the number of antennas plus one.
Interestingly, the optimal settings are insensitive to different configurations
between two tiers. Last but not the least, if the number of antennas of macro
base stations (MBSs) is sufficiently larger than that of small cell base
stations (SBSs), we find that range expansion will improve ASE.
