  High-speed train (HST) communications with orthogonal frequency division
multiplexing (OFDM) techniques have received significant attention in recent
years. Besides, cell-free (CF) massive multiple-input multiple-output (MIMO) is
considered a promising technology to achieve the ultimate performance limit. In
this paper, we focus on the performance of CF massive MIMO-OFDM systems with
both matched filter and large-scale fading decoding (LSFD) receivers in HST
communications. HST communications with small cell and cellular massive
MIMO-OFDM systems are also analyzed for comparison. Considering the bad effect
of Doppler frequency offset (DFO) on system performance, exact closed-form
expressions for uplink spectral efficiency (SE) of all systems are derived.
According to the simulation results, we find that the CF massive MIMO-OFDM
system with LSFD achieves both larger SE and lower SE drop percentages than
other systems. In addition, increasing the number of access points (APs) and
antennas per AP can effectively compensate for the performance loss from the
DFO. Moreover, there is an optimal vertical distance between APs and HST to
achieve the maximum SE.
