Performance Gains of Optimal Antenna Deployment in Massive MIMO Systems

We consider the single-cell multi-user multiple-input multiple-output uplink with several single antenna transmitters/users and one base station (BS) with N antennas in the N -> infinity regime. The BS antennas are evenly distributed to n admissible locations throughout the cell. First, we show that a reliable (per-user) rate of O(log n) is achievable through the optimal locational optimization of BS 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 "macro-multiplexing gain." Second, using tools from high-resolution quantization theory, we present an accurate heuristic 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. We also describe a modified gradient ascent procedure for the numerical optimization of antenna locations. Simulations confirm our analytical findings.