  Densifying networks and deploying more antennas at each access point are two
principal ways to boost the capacity of wireless networks. However, the
complicated distributions of the signal power and the accumulated interference
power, largely induced by various space-time processing techniques, make it
highly challenging to quantitatively characterize the performance of
multi-antenna networks. In this paper, using tools from stochastic geometry, a
unified framework is developed for the analysis of such networks. The major
results are two innovative representations of the coverage probability, which
make the analysis of multi-antenna networks almost as tractable as the
single-antenna case. One is expressed as an $\ell_1$-induced norm of a Toeplitz
matrix, and the other is given in a finite sum form. With a compact
representation, the former incorporates many existing analytical results on
single- and multi-antenna networks as special cases, and leads to tractable
expressions for evaluating the coverage probability in both ad hoc and cellular
networks. While the latter is more complicated for numerical evaluation, it
helps analytically gain key design insights. In particular, it helps prove that
the coverage probability of ad hoc networks is a monotonically decreasing
convex function of the transmitter density and that there exists a peak value
of the coverage improvement when increasing the number of transmit antennas. On
the other hand, in multi-antenna cellular networks, it is shown that the
coverage probability is independent of the transmitter density and that the
outage probability decreases exponentially as the number of transmit antennas
increases.
