MM depends on receiving back from the phone information on the channel. That uplink information has practical limitations on many cases, including from interference. In this paper, Bjornson, Hoydis, and Sanguinetti take on the assumption that there is a theoretical limit of spectral efficiency. Beginning with Marzetta, potential problems have been recognized.

"The pilot resources are limited by the channel coherence time, the same pilots must be reused in multiple cells. This leads to pilot contamination. ... it appears that pilot contamination is a fundamental issue that manifests a finite SE limit, except in some impractical special cases."

In 30 page dense with mathematics, the authors claim, "We will show in this paper that this is basically a misunderstanding,

spurred by the popularity of analyzing independent Rayleigh fading channels and suboptimal combining schemes, such as MR and S-MMSE. We prove that the SE increases without bound in the presence of pilot contamination when using M-MMSE combining/precoding, if a simple condition on asymptotically linearly independent covariance matrices is satisfied."

In other words, in most cases you can in theory keep adding antennas to get any performance levels you like. Nominally that means you could cram nearly infinite data into a limited amount of spectrum.

Practical considerations of course limit capacity. Antennas need space and power. They have substantial costs. Heat often becomes a design limit.

Spectrum policy is obsolete in 2017 that doesn't recognize high capacity from MIMO as well as frequency agile systems. For example, a reasonable proposal at the U.S. FCC would allow WI-Fi like radios from 3.7 GHz to 4.2 GHz. But exclusive use should be minimized to a control channel of perhaps 20 MHz. Capacity can be added, at modest cost, with more antennas. Beyond that, a provider can find open spectrum in the hundreds of megabits available. That works. Wi-Fi was the first to prove sharing is possible, and Verizon/Qualcomm testing for LAA is convincing that sharing can be used in almost all bands. The request for 160 MHz of spectrum is absurd; most of the band should remain a lightly regulated commons.

Sharing spectrum allows 200% to 500% more capacity so is almost always the right choice today.

## Massive MIMO has Unlimited Capacity

Emil Bjornson, ¨ Member, IEEE, Jakob Hoydis, Member, IEEE, Luca Sanguinetti, Senior Member, IEEE

Abstract The spectral efficiency (SE) of cellular networks can be improved by the unprecedented array gain and spatial multiplexing offered by Massive MIMO. Since its inception, the coherent interference caused by pilot contamination has been believed to create a finite SE limit, as the number of antennas goes to infinity. In this paper, we prove that this is incorrect and an artifact from using simplistic channel models and suboptimal precoding/combining schemes. We show that with multicell MMSE precoding/combining and a tiny amount of spatial channel correlation or large-scale fading variations over the array, the SE increases without bound as the number of antennas increases, even under pilot contamination. More precisely, the result holds when the channel covariance matrices of the contaminating users are asymptotically linearly independent, which is generally the case. If also the diagonals of the covariance matrices are linearly independent, it is sufficient to know these diagonals (and not the full covariance matrices) to achieve an unlimited asymptotic capacity.