  Co-existing wireless systems, which share a common spectrum, need to mitigate
out-of-band (OOB) radiation to avoid excessive interference. For legacy
systems, OOB radiation is well understood and is commonly handled by digital
precompensation techniques. When using large arrays, however, new phenomena and
hardware limitations have to be considered. First, signals can be radiated
directionally, which might focus the OOB radiation. Second, low-complexity
hardware is used for cost reasons, which increases the relative amount of OOB
radiation. Given that massive MIMO and millimeter wave communication rely on
base stations with a large number of antennas, the spatial behavior of OOB
radiation from large arrays will have significant implications for the hardware
requirements of future base stations. We show that, if the OOB radiation is
beamformed, its array gain is never larger than that of the in-band signal. In
many cases, the OOB radiation is close to isotropic even when the in-band
signal is highly directive. With the same total radiated power, the OOB
radiation from large arrays is therefore never more severe than from a legacy
system with the same adjacent-channel-leakage ratio. Further, the OOB radiation
is less detrimental than from a legacy system since the high array gain of the
in-band signal allows large arrays to radiate less total power than legacy
systems. We also show how OOB radiation from large arrays varies with location
in static propagation environments and how these effects vanish when averaged
over the small-scale fading. Since a higher relative amount of OOB radiation
can be tolerated for large arrays, the linearity requirement can be relaxed as
compared to legacy systems. Specifically, less stringent linearity requirements
on each transmitter makes it possible to build large arrays from low-complexity
hardware.
