The interested reader can look at an understanding of Transmit beamforming here <Transmit Beamforming in 802.11n and 802.11ac>.
A brief explanation of implicit and explit feedback in Transmit Beamforming can be obtained here <Implicit Feedback and Explicit Feedback for Transmit Beamforming>.
As discussed in the above article, Explict feedback methods were defined by the standard and they are
- channel state information feedback (CSI feedback)
- Non-compressed beamforming feedback
- Compressed Beamforming feedback
Channel State Information feedback :
The beamforming Transmitter station (Beamformer) can request channel state information (CSI) from the receiver station. Any WLAN station (beamformee) should be capable of obtaining the channel state information and providing the same to the Access Point. The Access Point should create a Channel state Information map of the channel and then create the transmit weights for beamforming to the station.
Non-Compressed Beamforming feedback :
In the Non-compressed Beamforming feedback, the beamforming transmit weights are calculated and generated by the receiver station (beamformee) on receiving an Null data packet. The transmitter (beamformer) station on receiving the beamforming feedback will apply the beamforming weight for subsequent transmissions without any modifications. The complete weights with its complex values are provided and to avoid loss of dynamic range would require a huge number of bits.
Compressed Beamforming feedback :
Non-Compressed Beamforming feedback method requires a large number of bits in order to maintain the complex values and to preserve the dynamic range. The simplest way to explain Compressed Beamforming feedback would be the following. A mathematical operation (Givens Rotation) is applied on the beamforming matrix to decompose the beamforming matrix to polar values. The angles that are computed from the mathematical rotation are sent from the receiver (Beamformee) to the Transmitter (Beamformer). By doing this, the number of bits required to be transmitted are greatly reduced. The Transmitter (beamformer) on receipt of the the feedback angles recomputes the beamforming Feedback matrix at its end. Since only the angles are sent out, the procedure is termed Compressed Beamforming feedback.
The mathematics for the compressed beamforming feedback can be referred in the book “Next Generation Wireless LANs, 802.11n and 802.11ac by Eldad Perhaia and Robert Stacey”