Systems and methods are provided to implement features in the IEEE 802.11ad+/ay protocols by utilizing combinations of analog and digital precoding (such as hybrid mmWave precoding) to enable multi-stream/multi-user transmissions. These systems and methods are also suitable for 5G wireless networks, such as found in 3GPP. These systems and methods address performing general precoder design, reducing of beam-training overhead with leak wave antennas, performing single-stage approximate precoding with enhanced SLS for SU-MIMO transmissions (eSLS1), performing multi-stage approximate precoding with enhanced SLS for SU-MIMO transmissions (eSLS2), and performing exact precoding with enhanced SLS for SU-MIMO transmissions.