  This paper analyzes how the distortion created by hardware impairments in a
multiple-antenna base station affects the uplink spectral efficiency (SE), with
focus on Massive MIMO. This distortion is correlated across the antennas, but
has been often approximated as uncorrelated to facilitate (tractable) SE
analysis. To determine when this approximation is accurate, basic properties of
distortion correlation are first uncovered. Then, we separately analyze the
distortion correlation caused by third-order non-linearities and by
quantization. Finally, we study the SE numerically and show that the distortion
correlation can be safely neglected in Massive MIMO when there are sufficiently
many users. Under i.i.d. Rayleigh fading and equal signal-to-noise ratios
(SNRs), this occurs for more than five transmitting users. Other channel models
and SNR variations have only minor impact on the accuracy. We also demonstrate
the importance of taking the distortion characteristics into account in the
receive combining.
