  In this paper, we investigate the impact of channel aging on the uplink
performance of a cell-free~(CF) massive multiple-input multiple-output (mMIMO)
system with a minimum mean squared error (MMSE) receiver. To this end, we
present a new model for the temporal evolution of the channel, which allows the
channel to age at different rates at different access points (APs). Under this
setting, we derive the deterministic equivalent of the per-user achievable
signal-to-interference-plus-noise ratio (SINR). In addition to validating the
theoretical expressions, our simulation results reveal that, {at low user
mobilities,} the SINR of CF-mMIMO is nearly 5 dB higher than its cellular
counterpart with the same number of antennas, and about 8 dB higher than that
of an equivalent small-cell network with the same number of APs. {On the other
hand, at very high user velocities, and when the channel between the UEs the
different APs age at same rate, the relative impact of aging is higher for
CF-mMIMO compared to cellular mMIMO. However, when the channel ages at the
different APs with different rates, the effect of aging on CF-mMIMO is
marginally mitigated, especially for larger frame durations.
