  Hybrid analog/digital precoding offers a compromise between hardware
complexity and system performance in millimeter wave (mmWave) systems. This
type of precoding allows mmWave systems to leverage large antenna array gains
that are necessary for sufficient link margin, while permitting low cost and
power consumption hardware. Most prior work has focused on hybrid precoding for
narrowband mmWave systems, with perfect or estimated channel knowledge at the
transmitter. MmWave systems, however, will likely operate on wideband channels
with frequency selectivity. Therefore, this paper considers wideband mmWave
systems with a limited feedback channel between the transmitter and receiver.
First, the optimal hybrid precoding design for a given RF codebook is derived.
This provides a benchmark for any other heuristic algorithm and gives useful
insights into codebook designs. Second, efficient hybrid analog/digital
codebooks are developed for spatial multiplexing in wideband mmWave systems.
Finally, a low-complexity yet near-optimal greedy frequency selective hybrid
precoding algorithm is proposed based on Gram-Schmidt orthogonalization.
Simulation results show that the developed hybrid codebooks and precoder
designs achieve very good performance compared with the unconstrained solutions
while requiring much less complexity.
