Statistically-Aided Codebook-Based Hybrid Precoding for Millimeter Wave Channels

Abstract

In this paper, we propose practical yet effective statistically-aided codebook-based hybrid precoding schemes for massive multiple-input multiple-output systems in millimeter wave bands. Particularly, we develop novel low-overhead hybrid precoding algorithms for selecting the baseband digital and radio frequency analog precoders from statistically skewed DFT-based codebooks. The proposed algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder and the hybrid beamformer and maximizing the signal to the interference noise ratio for the single-user and multi-user cases, respectively. We investigate the performance of the proposed algorithms by considering the mutual information of the analog beamforming procedure (the common stage among the proposed algorithms) as a performance evaluation metric. We derive lower and upper bounds on the mutual information of the channel given the proposed algorithms. Moreover, we show that the performance gap between the lower and upper bounds depends heavily on how many DFT columns are aligned to the largest eigenvectors of the transmit antenna array response of the millimeter wave channel or equivalently the transmit channel covariance matrix when only statistical channel knowledge is available at the transmitter. Then, we show that the proposed algorithms are asymptotically optimal as the number of transmit antennas M goes to infinity and the millimeter wave channel has a limited number of paths P, i.e., P <; M. Further, we verify the performance of the proposed algorithms numerically where results illustrate that the spectral efficiency of the proposed algorithms can approach that of the optimal precoder in certain scenarios. Furthermore, these results show that the proposed hybrid precoding schemes have superior spectral efficiency performance while requiring lower (or at most comparable) channel feedback overhead in comparison with the prior art.

Keywords

• Codebook-based precoding
• hybrid beamforming
• massive MIMO
• mmWave channels
• statistical precoding