Geometric mean decomposition based hybrid precoding for millimeter-wave massive MIMO

Hybrid precoding can reduce the number of required radio frequency (RF) chains in millimeter-Wave (mmWave) massive MIMO systems. However, existing hybrid pre-coding based on singular value decomposition (SVD) requires the complicated bit allocation to match the different signal-to-noise-ratios (SNRs) of different sub-channels. In this paper, we propose a geometric mean decomposition (GMD)-based hybrid precoding to avoid the complicated bit allocation. Specifically, we seek a pair of analog and digital precoders sufficiently close to the unconstrained fully digital GMD precoder. To achieve this, we fix the analog precoder to design the digital precoder, and vice versa. The analog precoder is designed based on the orthogonal matching pursuit (OMP) algorithm, while GMD is used to obtain the digital precoder. Simulations show that the proposed GMD-based hybrid precoding achieves better performance than the conventional SVD-based hybrid precoding with only a slight increase in complexity.