Optimality of Frequency Flat Precoding in Frequency Selective Millimeter Wave Channels

Millimeter wave (mmWave) MIMO communication is a key feature of next generation wireless systems. The selection of precoders and combiners for wideband mmWave channels has involved frequency selective designs based on channel state information. In this letter, we show that under some assumptions, the dominant subspaces of the frequency domain channel matrices are equivalent. This means that semi-unitary frequency flat precoding and combining are sufficient to achieve the maximum spectral efficiency when there is not too much scattering in the channel. It also motivates the use of techniques such as compressive subspace estimation as an alternative to estimating the full channel.