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My understanding is that for transmit beamforming in 802.11ac the transmitter sends a channel sounding packet (the "null data packet"), the receiver uses this to calculate the channel state information (CSI), then responds with the "compressed beamforming feedback" which contains the transmit beamforming weights.

If beamforming is to be done both ways (e.g. the AP performs transmit beamforming towards the client and the client performs transmit beamforming towards the AP), does the channel sounding happen twice, once initiated by the client and once by the AP? Or does the channel sounding only happen once and the information is used for beamforming in both directions?

Furthermore, does bidirectional transmit beamforming happen often in practice? Or is it typically just the APs performing transmit beamforming?

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Yes, the procedure is symmetrical. If a station can be a beamformer, it sends a NDP and the router responds with NDPA. No, this is not quite common (yet).

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According to the Wi-Fi product finder, 1,079 devices have been certified with the "Tx SU Beamformer" feature, and all 1,079 are classified as routers. I don't haven't seen anything in the 802.11ac standard preventing a client from being a beamformer and an AP from being the beamformee, but it doesn't seem to be done in practice.

https://www.wi-fi.org/product-finder-results?sort_by=certified&sort_order=desc&certifications=19

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