On Antenna Array Out-of-Band Emissions

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.