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In millimeter wave (mmWave) communication systems, beamforming with largeantenna arrays is critical to overcome high path losses. Separating all-digitalbeamforming into analog and digital stages can provide the large reduction inpower consumption and small loss in spectral efficiency needed for practicalimplementations. Developing algorithms with this favorable tradeoff ischallenging due to the additional degrees of freedom in the analog stage andits accompanying hardware constraints. In hybrid beamforming systems, forexample, channel estimation algorithms do not directly observe the channels,face a high channel count, and operate at low SNR before transmit-receive beamalignment. Since mmWave channels are sparse in time and beam domains, manycompressed sensing (CS) channel estimation algorithms have been developed thatrandomly configure the analog beamformers, digital beamformers, and/or pilotsymbols. In this paper, we propose to design deterministic beamformers andpilot symbols for open-loop channel estimation. We use CS approaches that relyon low coherence for their recovery guarantees, and hence seek to minimize themutual coherence of the compressed sensing matrix. We also propose a precodercolumn ordering to design the pilot symbols. Simulation results show that ourbeamformer designs reduce channel estimation error over competing methods.

Hybrid Beamformer Codebook Design and Ordering for Compressive mmWave Channel Estimation