  The spatial characteristics of the out-of-band radiation that a multiuser
MIMO system emits in the environment, due to its power amplifiers (modeled by a
polynomial model) are nonlinear, is studied by deriving an analytical
expression for the continuous-time cross-correlation of the transmit signals.
At a random spatial point, the same power is received at any frequency on
average with a MIMO base station as with a SISO base station when the two
radiate the same amount of power. For a specific channel realization however,
the received power depends on the channel. We show that the power received
out-of-band only deviates little from the average in a MIMO system with
multiple users and that the deviation can be significant with only one user.
Using an ergodicity argument, we conclude that out-of-band radiation is less of
a problem in massive MIMO, where total radiated power is lower compared to SISO
systems and that requirements on spectral regrowth can be relaxed in MIMO
systems without causing more total out-of-band radiation.
