  We consider the uplink of a hardware-impaired intelligent reflective surfaces
(IRS) aided multi-cell massive multiple-input multiple-output (mMIMO) system
with mobile user equipments, whose channel age with time. For this system, we
analyze the distortion due to hardware impairments, and the effect of channel
aging, and propose a novel distortion-and-aging-aware MMSE (DAA-MMSE) receiver
that not only provides a higher spectral efficiency (SE) than conventional
maximal ratio and distortion-unaware MMSE (DU-MMSE) receivers, but also reduces
the pilot overhead. By considering non-ideal hardware and spatially-correlated
Rician fading channels with phase shifts, we also derive the SE lower bound for
this system. We show that the SE gain of the DAA-MMSE receiver over DU-MMSE
receiver increases with hardware impairments, and channel aging. Along with
DAA-MMSE receiver, the IRS is also shown to reduce the pilot overhead in a
mMIMO system with channel aging.
