  In this paper, we consider the amplify-and-forward relay networks in mmWave
systems and propose a hybrid precoder/combiner design approach. The phase-only
RF precoding/combining matrices are first designed to support multi-stream
transmission, where we compensate the phase for the eigenmodes of the channel.
Then, the baseband precoders/combiners are performed to achieve the maximum
mutual information. Based on the data processing inequality for the mutual
information, we first jointly design the baseband source and relay nodes to
maximize the mutual information before the destination baseband receiver. The
proposed low-complexity iterative algorithm for the source and relay nodes is
based on the equivalence between mutual information maximization and the
weighted MMSE. After we obtain the optimal precoder and combiner for the source
and relay nodes, we implement the MMSE-SIC filter at the baseband receiver to
keep the mutual information unchanged, thus obtaining the optimal mutual
information for the whole relay system. Simulation results show that our
algorithm achieves better performance with lower complexity compared with other
algorithms in the literature. In addition, we also propose a robust joint
transceiver design for imperfect channel state information.
