  We study the impact of channel aging on the uplink of a cell-free (CF)
massive multiple-input multiple-output (mMIMO) system by considering i)
spatially-correlated Rician-faded channels; ii) hardware impairments at the
access points and user equipments (UEs); and iii) two-layer large-scale fading
decoding (LSFD). We first derive a closed-form spectral efficiency (SE)
expression for this system, and later propose two novel optimization techniques
to optimize the non-convex SE metric by exploiting the
minorization-maximization (MM) method. The first one requires a numerical
optimization solver, and has a high computation complexity. The second one with
closed-form transmit power updates, has a trivial computation complexity. We
numerically show that i) the two-layer LSFD scheme effectively mitigates the
interference due to channel aging for both low- and high-velocity UEs; and ii)
increasing the number of AP antennas does not mitigate the SE deterioration due
to channel aging. We numerically characterize the optimal pilot length required
to maximize the SE for various UE speeds. We also numerically show that the
proposed closed-form MM optimization yields the same SE as that of the first
technique, which requires numerical solver, and that too with a much reduced
time-complexity.
