  Synchronization is a fundamental procedure in cellular systems whereby an UE
acquires the time and frequency information required to decode the data
transmitted by a BS. Due to the necessity of using large antenna arrays to
obtain the beamforming gain required to compensate for small antenna aperture,
synchronization must be performed either jointly with beam training as in 5G
NR, or at the low SNR regime if the high-dimensional mmWave MIMO channel is to
be estimated. To circumvent this problem, this work proposes the first
synchronization framework for mmWave MIMO that is robust to both TO, CFO, and
PN synchronization errors and, unlike prior work, implicitly considers the use
of multiple RF chains at both transmitter and receiver. I provide a theoretical
analysis of the estimation problem and derive the HCRLB for the estimation of
both the CFO, PN, and equivalent beamformed channels seen by the different
receive RF chains. I also propose two novel algorithms to estimate the
different unknown parameters, which rely on approximating the MMSE estimator
for the PN and the ML estimators for both the CFO and the equivalent beamformed
channels. Thereafter, I propose to use the estimates for the equivalent
beamformed channels to perform compressive estimation of the high-dimensional
frequency-selective mmWave MIMO channel and thus undergo data transmission. For
performance evaluation, I consider the QuaDRiGa channel simulator, which
implements the 5G NR channel model, and show that both compressive channel
estimation without prior synchronization is possible, and the proposed
approaches outperform current solutions for joint beam training and
synchronization currently considered in 5G NR.
