  In millimeter wave (mmWave) communication systems, beamforming with large
antenna arrays is critical to overcome high path losses. Separating all-digital
beamforming into analog and digital stages can provide the large reduction in
power consumption and small loss in spectral efficiency needed for practical
implementations. Developing algorithms with this favorable tradeoff is
challenging due to the additional degrees of freedom in the analog stage and
its accompanying hardware constraints. In hybrid beamforming systems, for
example, channel estimation algorithms do not directly observe the channels,
face a high channel count, and operate at low SNR before transmit-receive beam
alignment. Since mmWave channels are sparse in time and beam domains, many
compressed sensing (CS) channel estimation algorithms have been developed that
randomly configure the analog beamformers, digital beamformers, and/or pilot
symbols. In this paper, we propose to design deterministic beamformers and
pilot symbols for open-loop channel estimation. We use CS approaches that rely
on low coherence for their recovery guarantees, and hence seek to minimize the
mutual coherence of the compressed sensing matrix. We also propose a precoder
column ordering to design the pilot symbols. Simulation results show that our
beamformer designs reduce channel estimation error over competing methods.
