Optimal Frequency-Flat Precoding for Frequency-Selective Millimeter Wave Channels

The two key features of millimeter wave-(mmWave) based MIMO communication are the use of large antenna arrays at the transceivers and large bandwidth. The former complicates the design of optimal beamformers, while the latter makes the system frequency-selective and, thus, requires equalization. Conventionally, for wideband mmWave channels, choosing the precoders/combiners have involved frequency-selective designs that are based on channel state information. In this paper, we show that under some assumptions, semi-unitary frequency-flat precoding and combining are sufficient for low-scattering millimeter wave channels. To show this, we evaluate the conditions and practical settings under which the dominant subspaces of the frequency-domain channel matrices are similar. We model the frequency-dependence of uniform linear antenna arrays, which leads to what is known as beam-squint, for two different practical setting to analyze the optimality of frequency-flat beamforming designs under practical hardware impairments. For the cases when the optimality conditions hold, we propose novel techniques based on compressive subspace estimation to design the optimal frequency-flat, semi-unitary precoders and combiners. Simulation results show that the system achieves near-digital spectral efficiencies at very small implementation cost of beamformers and channel training overhead.