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 → ∞ 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.
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