AoA math

[g.cutri]

Hi,

According to the Direction Finding White Paper, the CTE is a pure sin function at 2.4GHz. This is mixed with a local oscillator at 250KHz (for 1Mbps PHY) to obtain a in-phase and quadrature signals.

So, given the signal

a(t) = A sin(ω t + φ)

we should have:

I(t) = A sin(ω t + φ) cos(ω_LO t)

Q(t) = A sin(ω t + φ) sin(ω_LO t)

I've seen aroud that to obtain the phase φ it is sufficent to compute atan(Q / I) but, according to the previous equations, if you divide Q over I, the term A sin(ω t + φ) is simplified and you will just get sin(ω_LO t) / cos(ω_LO t) that does not depend on φ.

What am I missing?

[PaKa]

There seems to be some misunderstanding in you original request:

On the transmitter side the carrier (2404-2478GHz nominal frequency depending on channel number) is mixed with a sine with 250KHz nominal frequency.

    Note: none of these frequencies will be exact!

On the receiver side the incoming signal is down converted through mixing with a frequency that depends on than channel, the I&Q data is then gathered from this down mixed signal and feed into the algorithm.

The formulas from SwRa can then be used to calculate the resulting signal.

Do note that since the nominal modulation signal is 250KHz and the I&Q data are only sampling at 1Msps you will not get a "nice sinewave" as a result, you will get a signal that is only 2x the Nyquist frequency and this very often looks like a AM modulated signal if you try to print it as a sine. This will also be impacted by differences in LO for the 2 sides of the link so may change over channels and over devices.

[g.cutri]

Hi,

thank you very much for you answer. Now everything is more clear. Anyhow, the main problem remeains. If we compute the phase difference on the same antenna (compensating with the reference period) we are not getting 0, as expected. What is worse is that we get very different results depending on the actual carrier frequency.

Does that depends only on noise and differences in LO? How can we handle that?

[PaKa]

So when you are calculating the phase error for each channel you use the data from the reference period to calculate the frequency of the signal represented in the I&Q data and the reference phase? Remember as all frequencies will have inaccuracies you can't use any "fixed" parameters for this as there will be differences for each channel, device, temperature+++++

Also, if you are using multiple antennas and not only one, remember that the phase shift will be different for different channels as the base frequency is different. Also note that multipath will impact different channels differently so at a given position different antenna may have multipath issues for different channels.