In this short page, several verified facts about CSI phase information are listed. More is pending, and discussions are welcome.
1. 0-th subcarrier of the 1st antenna, the most dominating.
CSI phase measurement contains several noises/errors: CFO (Carrier Frequency Offset), SFO (Sampling Frequency Offset), PDD (Packet Detection Delay), and random initial phase, etc.
Their impacts to OFDM CSI is different. SFO and PDD cause phase rotation (or slope component across subcarriers); CFO and random initial phase together cause random-like overall phase shift (or intercept component).
The phase the 0-th subcarrier, not suffering from SFO and PDD due to 0 frequency offset from DC, defines the phase basis for the rest subcarriers.
If the propagation environment is steady, we observe steady(yet with ambiguity) phase difference between antenna 1-2 and 1-3, but not between antenna 2-3.
In another word, the phase measurement of antenna 2 and 3 are computationally based on that of antenna 1.
As a conclusion, the 0-th subcarrier of the 1st antenna is the most representative value for the whole measurement.
2. 4-Way Phase Ambiguity
4-way ambiguity is massively observed and verified.
Put it simply: the measured phase of the 0-th subcarrier of any antenna, has 4 candidate true phases measurements(0, +pi/2, +pi, +pi/2*3).