  In this paper, we investigate the impact of channel aging on the performance
of cell-free (CF) massive multiple-input multiple-output (MIMO) systems with
both spatial correlation and pilot contamination. We derive novel closed-form
uplink and downlink spectral efficiency (SE) expressions that take imperfect
channel estimation into account. More specifically, we consider large-scale
fading decoding and matched-filter receiver cooperation in the uplink. The
uplink performance of a small-cell (SC) system is derived for comparison. The
CF massive MIMO system achieves higher 95\%-likely uplink SE than the SC
system. In the downlink, the coherent transmission has four times higher
95\%-likely per-user SE than the non-coherent transmission. Statistical channel
cooperation power control (SCCPC) is used to mitigate the inter-user
interference. SCCPC performs better than full power transmission, but the
benefits are gradually weakened as the channel aging becomes stronger.
Furthermore, strong spatial correlation reduces the SE but degrades the effect
of channel aging. Increasing the number of antennas can improve the SE while
decreasing the energy efficiency. Finally, we use the maximum normalized
Doppler shift to design the SE-improved length of the resource block.
Simulation results are presented to validate the accuracy of our expressions
and prove that the CF massive MIMO system is more robust to channel aging than
the SC system.
