Techniques for power saving by remote wireless mobile devices are provided, in particular by stations (STAs) during downlink (DL) multiple-user multiple-input and multiple-output (MU-MIMO) transmissions in an Institute of Electrical and Electronics Engineers (IEEE) 802.11ay network when reverse direction (RD) transmissions are either enabled and not enabled. Various embodiments enable each STA in a group of STAs to determine an order in which the STAs are requested to send a block acknowledgement (BACK) and which STAs will be granted an RD transmission. Further, a duration of each RD transmission is provided to each STA. Based on the provided information, each STA can determine times to enter a power saving mode. Other embodiments are described and claimed.