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?

[gdaquila]

Hi SwRa

I would like to add some additional info to the original post.

According to what is report here: https://infocenter.nordicsemi.com/topic/nwp_036/WP/nwp_036/phase_samples.html if the chip implements an IQ modulator then the plot of the IQ signals cannot be a pure cosine and/or a pure sine (as you plot them in the above images) but must be another function very similar to a mixed signal made by a sin*cos (for the I component) and sin*sin (for the Q component):

I(t) = A sin(ω t + φ) cos(ω_LO t)

Q(t) = A sin(ω t + φ) sin(ω_LO t)

If, according to the above equations, this is true, then the phase angle cannot be calculated using the formula you provided:

Phase Angle φ = tan⁻¹(Q/I).

Our opinion is that you provided a relationship that is valid for IQ sampling but not for IQ modulation and in this case, but, if our undestanding is correct and according to what nordic reports in the link provided above, we are talking about IQ Modulation.

At least, this is our understanding and we cannot figure out what we are doing wrong.

Could you please provide your opinion?

Thanks

[SwRa]

Hi,

The signals does look like an AM modulated signal. Have you based your application on the examples provided by Nordic ? Bluetooth: Direction finding connectionless beacon and Bluetooth: Direction finding connectionless locator.?

Regards,

Swathy

[g.cutri]

Hi,

At first we have tried the nRF52833 DK with the 12 array antenna (received by Nordic) but we are now using MineW AoA G2 kit since it is simpler to setup multiple anchors. This kit is based on nRF52833 and simply provide I\Q via MQTT.

Anyhow, as gdaquila pointed out, the documentation states that the input signal is mixed with the local oscillator (with a frequency of 250KHz) so it should not be strange to see a modulated signal.

Is that correct?