Geometric Mean Decomposition Based Hybrid Precoding for Millimeter-Wave Massive MIMO

Hybrid precoding can significantly reduce the number of required radio frequency (RF) chains in millimeter-Wave (mmWave) massive MIMO systems. However, existing hybrid precoding based on singular value decomposition (SVD) requests the complicated bit allocation to match the different signal-tonoise-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. The key idea is to seek a pair of analog and digital precoders sufficiently close to the unconstrained fully digital GMD precoder. To achieve this, we propose to decompose the GMD-based hybrid precoder design problem into two sub-problems, i.e., fixing the analog (digital) precoder to design the digital (analog) precoder. The principle of basis pursuit is utilized to design the analog precoder with non-convex constraint, while GMD is used to obtain the digital precoder. Simulation results show that the proposed GMD-based hybrid precoding achieves much better bit error rate (BER) performance than the conventional SVD-based hybrid precoding with only a slight increase in complexity.