Statistical MIMO beam codebook design for mmWave transmissions

We propose a novel method for constructing beam codebooks, i.e., a set of beamforming weights, to be used for beam sweeping and data transmission in mmWave massive MIMO channels. The proposed beam codebooks are designed according to the statistical distribution of the channel's angles of departure in order to efficiently sectorize the angular space covered by the beams. In particular, the cumulative distribution function of these angles is used to sectorize the angular beam space in order to design the beams. We first present a general closed-form construction of beam codebooks for an arbitrary distribution and then tailor the results to the Laplace distribution. We consider both narrow and broad beams. The resulting beams are a priori better adapted to the channel statistics and thus enhance the spectral efficiency of the transmission as compared to the state-of-the-art beam designs. Finally, we investigate the performance of the design and also present some analytical bounds quantifying the inherent loss of a directional beamforming compared to the optimal beamforming with perfect channel state information at the transmitter.