Statistically-Aided Codebook-Based Hybrid Precoding for mmWave Single-User MIMO Systems

Abstract

In this paper, we propose practical yet effective statistically-aided codebook-based hybrid precoding schemes for single-user massive MIMO systems operating in millimeter wave channels. We develop novel hybrid precoding algorithms for selecting analog and/or the digital precoders from DFT-based codebooks. The selection algorithms aim at maximizing the spectral efficiency based on minimizing the chordal distance between the optimal unconstrained precoder given by the dominant right singular vectors of the channel and the hybrid (digital/analog) beamformer selected from statistically skewed DFT codebooks. We investigate the performance of the proposed algorithms by considering the mutual information as a performance 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. 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, i.e., P <; M. Finally, we verify the performance of the proposed algorithms and the DFT codebook numerically. The results illustrate that the spectral efficiency performance of the proposed algorithms approaches the optimal precoder performance in certain scenarios.