Performance Gains of Optimal Antenna Deployment for Massive MIMO Systems

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.