  We study the scaling laws of the signal-to-interference-plus-noise ratio
(SINR) and area spectral efficiency (ASE) in multi-antenna cellular networks,
where the number of antennas scales with the base station (BS) spatial density
$\lambda$. We start with the MISO case having $N_t(\lambda)$ transmit antennas
and a single receive antenna and prove that the average SINR scales as
$\frac{N_t(\lambda)}{\lambda}$ and the average ASE scales as
$\lambda\log\left(1+\frac{N_t(\lambda)}{\lambda}\right)$. For the MIMO case
with single-stream eigenbeamforming and $N_r(\lambda) \leq N_t(\lambda)$
receive antennas, we prove that the scaling laws of the conditional SINR and
ASE are exactly the same as the MISO case, i.e. not dependent on
$N_r(\lambda)$. We also show that coordinated beamforming amongst $K\leq
N_t(\lambda)$ neighboring BSs does not improve the scaling laws regardless of
$K$. From a system design perspective, our results suggest that deploying
multi-antenna BSs can help maintain the per-user throughput and the linear
increase in the ASE with BS density, while the number of antennas at the user
equipment and the use of BS cooperation do not matter much.
