  The distortion from massive MIMO (multiple-input--multiple-output) base
stations with nonlinear amplifiers is studied and its radiation pattern is
derived. The distortion is analyzed both in-band and out-of-band. By using an
orthogonal Hermite representation of the amplified signal, the spatial
cross-correlation matrix of the nonlinear distortion is obtained. It shows
that, if the input signal to the amplifiers has a dominant beam, the distortion
is beamformed in the same way as that beam. When there are multiple beams
without any one being dominant, it is shown that the distortion is practically
isotropic. The derived theory is useful to predict how the nonlinear distortion
will behave, to analyze the out-of-band radiation, to do reciprocity
calibration, and to schedule users in the frequency plane to minimize the
effect of in-band distortion.
