Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

TLDR

Cellular base stations serve many single‑antenna terminals simultaneously, yet propagation is hindered by fast fading, shadowing, and path loss. The system employs TDD with reverse‑link pilots to estimate reciprocal channels, then uses the conjugate‑transpose of those estimates as linear precoders and combiners. With an infinite number of antennas, noise and fast fading vanish, throughput and terminal count become independent of cell size, spectral efficiency no longer depends on bandwidth, and energy per bit tends to zero, leaving only pilot‑contamination‑induced inter‑cell interference.

Abstract

A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.