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?

[SwRa]

Hi,

Kindy refer this document: https://www.pe0sat.vgnet.nl/sdr/iq-data-explained/. The formulas for calculating with IQ signals translating between polar and rectangular forms can be found here.

Peak Amplitude A = (I²+Q²)½

Phase Angle ϕ = tan⁻¹(Q/I)

I = A⋅cos(ϕ)

Q = A⋅sin(ϕ)

Converting IQ Data to a plain signal: I is the original signal.

Euler form: A⋅eiϕ = A⋅(cos(ϕ) + i⋅sin(ϕ)) = I + Qi

Best Regards,

Swathy

[g.cutri]

Hi, thank you for your answer.

I already know iq sampling, but that formulation does not match my experiment results. I and Q should be two sine waves. Instead this is what I obtain when I plot I(t) of one antenna:

The color changes at every packet. This looks like more to an AM modulated signal than a pure sine wave. So I thought that maybe I and Q where not what I suppose.

Where am I wrong?