Massive MIMO in the UL/DL of Cellular Networks: How Many Antennas Do We Need?

TLDR

In multi‑cellular TDD systems with many base‑station antennas, performance is ultimately limited by pilot contamination, and as the number of antennas grows large the simplest precoders/detectors become optimal while transmit power can be reduced arbitrarily. The study investigates how many antennas per user are required to reach a target fraction of the asymptotic performance and how many additional antennas are needed with matched‑filter and eigen‑beamforming to match MMSE and RZF performance. The authors model channel estimation, pilot contamination, path loss, and antenna correlation, and derive asymptotically tight approximations of achievable rates for linear precoders/detectors, validated by simulations. The derived rate approximations are asymptotically tight and match simulation results for realistic system sizes.

Abstract

We consider the uplink (UL) and downlink (DL) of non-cooperative multi-cellular time-division duplexing (TDD) systems, assuming that the number N of antennas per base station (BS) and the number K of user terminals (UTs) per cell are large. Our system model accounts for channel estimation, pilot contamination, and an arbitrary path loss and antenna correlation for each link. We derive approximations of achievable rates with several linear precoders and detectors which are proven to be asymptotically tight, but accurate for realistic system dimensions, as shown by simulations. It is known from previous work assuming uncorrelated channels, that as N→∞ while K is fixed, the system performance is limited by pilot contamination, the simplest precoders/detectors, i.e., eigenbeamforming (BF) and matched filter (MF), are optimal, and the transmit power can be made arbitrarily small. We analyze to which extent these conclusions hold in the more realistic setting where N is not extremely large compared to K. In particular, we derive how many antennas per UT are needed to achieve η% of the ultimate performance limit with infinitely many antennas and how many more antennas are needed with MF and BF to achieve the performance of minimum mean-square error (MMSE) detection and regularized zero-forcing (RZF), respectively.