How channel state information is calculated from Sounding Packet
According to pages 5-7 in this, the Channel State Information (CSI) contains 2 measurements per matrix element.

The CSI essentially tells the Access Point (AP) two things: where is the client (bearing) and how far away on that bearing it is. However, because of multipath propagation, the "bearing" might not correspond to the true bearing of the client but the direction at which the signal is "louder". This means that the signal could be bouncing on a wall and then finding the client, rather than traveling to it in a straight line.

So, the task we have now is to calculate these two numbers. We assume that the channel identification pseudorandom sequences in the pre-amble are transmitted at the same time from the AP:


To estimate the $A$, simply sum the "strength" of the received signal at each antenna.
To estimate the $T$, you need to estimate the time differences between the times the signal was received. At this point, you need to decide on the ordering of the elements.


You can estimate both using a matched filter whose $h$ is the pseudorandom sequence.

The matched filter will return a relatively high output when it detects the pseudorandom sequence at its input.

So, imagine a bank of matched filters behind each receiver. Each one of the antennas receives the AP signal at slightly different times and amplitudes. Each one of the matched filters produces a slightly different amplitude (the $A$ component) when it "sees" the pseudorandom sequence at its input. Consequently, because of the difference in arrival times, each one of these high outputs will occur at slightly different times. To estimate $T$, take one of your antennas as a reference element and measure the time that passes between two high outputs at each matched filter.

You might also find reading up on the fundamental of the following techniques:


The Matched Filter and its applications in Radar and Sonar
Beamforming


Which sooner or later will lead you to Adaptive Beamforming which is what you are dealing with here.

Phased Arrays


Which, again, is what you are dealing with here.

Pseudorandom binary sequences (PRBS)


Which is what your header sequence is right here

PRB Sequences with applications to channel characterisation


In brief, by examining the distortions that a PRBS undergoes when transmitted through a "channel" (whatever this might be), you get an estimate of the channel's condition or state which you can then use to adapt some aspect of transmission (Forward error control sequence, beamforming, etc).
Characterisation of an acoustic communication channel using PRBS
Transmitter identification using PRBS
And more...



Hope this helps.