  Hybrid precoding can significantly reduce the number of required radio
frequency (RF) chains and relieve the huge energy consumption in mmWave massive
MIMO systems, thus attracting much interests from academic and industry.
However, most existing hybrid precoding schemes are based on singular value
decomposition (SVD). Due to the very different sub-channel signal-to-noise
ratios (SNRs) after SVD, complicated bit allocations is usually required to
match the sub-channel SNRs. To solve this problem, we propose a geometric mean
decomposition (GMD)-based hybrid precoding scheme to avoid the complicated bit
allocation. Its basic idea is to seek a pair of analog and digital precoding
matrices that are sufficiently close to the optimal unconstrained GMD precoding
matrix. Specifically, we design the analog (digital) precoding matrix while
keeping the digital (analog) precoding matrix fixed. Further, the principle of
basis pursuit is utilized in the design of analog precoding matrix, while we
obtain the digital precoding matrix by projecting the GMD operation on the
digital precoding matrix. Simulation results verify that the proposed GMD-based
hybird precoding scheme outperforms conventional SVD-based hybrid precoding
schemes and achieves much better bit error rate (BER) performance with low
complexity.
