  Hybrid beamforming (HB) architectures are attractive for wireless
communication systems with large antenna arrays because the analog beamforming
stage can significantly reduce the number of RF transceivers and hence power
consumption. In HB systems, channel estimation (CE) becomes challenging due to
indirect access by the baseband processing to the communication channels and
due to low SNR before beam alignment. Compressed sensing (CS) based algorithms
have been adopted to address these challenges by leveraging the sparse nature
of millimeter wave multi-input multi-output (mmWave MIMO) channels. In many CS
algorithms for narrowband CE, the hybrid beamformers are randomly configured
which does not always yield the low-coherence sensing matrices desirable for
those CS algorithms whose recovery guarantees rely on coherence. In this paper,
we propose a versatile deterministic HB codebook design framework for CS
algorithms with coherence-based recovery guarantees to enhance CE accuracy.
Simulation results show that the proposed design can obtain lower channel
estimation error and higher spectral efficiency compared with random codebook
for phase-shifter-, switch-, and lens-based HB architectures.
