Performance Gains of Optimal Antenna Deployment for Massive MIMO Systems

TL;DR

This paper demonstrates that optimal antenna placement in massive MIMO systems can achieve a logarithmic growth in user rate with the number of antennas, surpassing traditional deployment methods, and provides a formula linking rate to user density entropy.

Contribution

It introduces an optimal antenna deployment strategy that achieves logarithmic rate growth and derives a formula relating rate to user density entropy.

Findings

Optimal deployment yields O(log n) rate growth.

Rate depends on the differential entropy of user density.

Numerical simulations confirm analytical results.

Abstract

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.