  We study the scaling laws of the signal-to-interference-plus-noise ratio
(SINR) and the area spectral efficiency (ASE) in multi-antenna cellular
networks, where the number of antennas scales with the base station (BS)
spatial density $\lambda$, under the assumption of independent and identically
distributed (i.i.d.) channels. We start with the MISO case with $N_t(\lambda)$
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 agnostic to $N_r(\lambda)$ and scale exactly the same as the MISO case.
Hence, deploying multi-antenna BSs can help maintain non-zero per-user
throughput and a corresponding linear increase in the ASE in dense cellular
networks.
