  This work extends the concept of channel hardening to multi-antenna systems
that are aided by intelligent reflecting surfaces (IRSs). For fading links
between a multi-antenna transmitter and a single-antenna receiver, we derive an
accurate approximation for the distribution of the input-output mutual
information when the number of reflecting elements grows large. The asymptotic
results demonstrate that by increasing the number of elements on the IRS, the
end-to-end channel hardens as long as the physical dimensions of the IRS grow
as well. The growth rate however need not to be of a specific order and can be
significantly sub-linear. The validity of the analytical result is confirmed by
numerical experiments.
