  We consider the uplink of a single-cell multi-user multiple-input
multiple-output (MIMO) system with several single antenna transmitters/users
and one base station with $N$ antennas in the $N\rightarrow\infty$ regime. The
base station antennas are evenly distributed to $n$ admissable locations
throughout the cell.
  First, we show that a reliable (per-user) rate of $O(\log n)$ is achievable
through optimal locational optimization of base station antennas. We also prove
that an $O(\log n)$ rate is the best possible. Therefore, in contrast to a
centralized or circular deployment, where the achievable rate is at most a
constant, the rate with a general deployment can grow logarithmically with $n$,
resulting in a certain form of "macromultiplexing gain."
  Second, using tools from high-resolution quantization theory, we derive an
accurate formula for the best achievable rate given any $n$ and any user
density function. According to our formula, the dependence of the optimal rate
on the user density function $f$ is curiously only through the differential
entropy of $f$. In fact, the optimal rate decreases linearly with the
differential entropy, and the worst-case scenario is a uniform user density.
Numerical simulations confirm our analytical findings.
