  The large beamforming gain used to operate at millimeter wave (mmWave)
frequencies requires obtaining channel information to configure hybrid antenna
arrays. Previously proposed wideband channel estimation strategies, however,
assume perfect time-frequency synchronization and neglect phase noise, making
these approaches impractical. Consequently, achieving time-frequency
synchronization between transmitter and receiver and correcting for phase noise
(PN) as the channel is estimated, is the greatest challenge yet to be solved in
order to configure hybrid precoders and combiners in practical settings. In
this paper, building upon our prior work, we find the Maximum A Posteriori
(MAP) solution to the joint problem of timing offset (TO), carrier frequency
offset (CFO), PN and compressive channel estimation for broadband mmWave MIMO
systems with hybrid architectures. Simulation results show that, using
significantly less training symbols than in the beam training protocol in the
5G New Radio communications standard, joint synchronization and channel
estimation at the low SNR regime can be achieved, and near-optimum data rates
can be attained.
