  We substantiate and extend recent research on the behavior of the out-of-band
emissions in antenna array transmitters. Specifically, with multi-user
precoding, we show that the emissions are always beamformed in the directions
of the intended receivers, contrary to some claims in the recent literature.
Moreover, while also other spurious directions exist, we show that the
emissions are always strongest in the directions of the intended receivers. We
also show that power amplifiers with mutually different nonlinear phase
characteristics will reduce the beamforming gain of the unwanted emissions,
with the gain approaching the noncoherent combining limit as the phase
deviations are increased.
