  In millimeter-wave (mmWave) MIMO systems, while a hybrid digital/analog
precoding structure offers the potential to increase the achievable rate, it
also faces the challenge of the need of a low-complexity design. In specific,
the hybrid precoding may require matrix operations with a scale of antenna
size, which is generally large in mmWave communication. Moreover, the channel
estimation is also rather time consuming due to the large number of antennas at
both Tx/Rx sides. In this paper, a low-complexity hybrid precoding and channel
estimation approach is proposed. In the channel estimation phase, a
hierarchical multi-beam search scheme is proposed to fast acquire $N_{\rm{S}}$
(the number of streams) multipath components (MPCs)/clusters with the highest
powers. In the hybrid precoding phase, the analog and digital precodings are
decoupled. The analog precoding is designed to steer along the $N_{\rm{S}}$
acquired MPCs/clusters at both Tx/Rx sides, shaping an equivalent
$N_{\rm{S}}\times N_{\rm{S}}$ baseband channel, while the digital precoding
performs operations in the baseband with the reduced-scale channel. Performance
evaluations show that, compared with a state-of-the-art scheme, while achieving
a close or even better performance when the number of radio-frequency (RF)
chains or streams is small, both the computational complexity of the hybrid
precoding and the time complexity of the channel estimation are greatly
reduced.
