Removing Attenuator and Real Mixer influence on the received Baseband signal in Radar IQ Transmitter - De-embedding

Question

Radar IQ Transmitter Measurement Setup:

Waveform Generator + IQ Transmitter + Attenuator + Real Downconversion mixer + Oscilloscope + Post-processing (Hilbert Transform)

With the above arrangement Radar IQ Transmitter characterization is done, I need to remove the influence of Attenuator and Real Down-conversion mixer on the received Baseband signal at the oscilloscope. At first, attenuator is characterized and corresponding S Parameter file is obtained. Similarly using RS ZVA67 VNA, the RF to IF conversion loss (b2/a1) of Real Down-conversion Mixer measurement is done.

My Understanding:

S Parameter of the attenuator shows large variation over the frequency range (It is converted to linear scale.) Since, the S Parameter refers to frequency domain, the received time domain baseband signal (Bandwidth = 250 MHz) at Oscilloscope is converted to frequency domain using 'FFT'.

Note: I have 601 sample points in S Parameter file and 20480 sample points in Baseband signal both ranging from -1 GHz to 1 GHz (which is the bandwidth of interest)

Questions: Could you please correct my following understanding:

1. Since, both are in linear scale, to obtain original signal with no attenuation i) should I perform subtraction of 2 signals (i.e FFT of the Baseband signal and S21 of attenuator, both magnitude and phase) OR ii) should I take inverse of S parameter matrix of Attenuator and Mixer and then multiply wih the original signal.

• However in both the cases number of sample points of baseband signal and S parameter is not same!

2. The BW of interest is -1 GHz to 1 GHz. Therefore only 40 points (340 to 381) out of 601 in attenuator is considered. However, I have 20480 sample points of the Baseband signal which is also ranging from -1 GHz to 1 GHz. Since, 2 arrays of different shape (20480, 40), subtraction is not possible. Could you please let me know how can I proceed in this case?

3. I would be glad to know if there is any suggestion for change in measurement setup for the above scenario (Note: The BB signal is measured using Oscilloscope because later I need time domain signals for IQ TX modelling)

Fig1. FFT of BB signal Fig2. S21 of Attenuator Fig 3. Superimposed BB and S21 signal (https://i.stack.imgur.com/qlxNv.jpg)

Edit: As the IQ Receiver is yet to be characterized, the real down-conversion mixer is used and the digital IF concept is used to avoid folding of the image onto desired signal. The real baseband signal at oscilloscope is Hilbert-transformed (in the post-processing step) to obtain the Inphase and Quadrature components.

Answer 1

Waveform Generator + IQ Transmitter + Attenuator + Real Downconversion mixer + Oscilloscope

Here are some initial comments and considerations and I can add more details once these points are clarified / confirmed:

Your approach is a valid way to capture the signal if you are down-converting a real digital IF frequency, and that IF frequency is ideally centered at 250 MHz to simplify the "anti-alias" filter that should be ahead of the scope and centered on the bandwidth of your signal of interest. From this you can digitally down-convert in quadrature to create the baseband complex samples you are ultimately interested in.

If you are using a real mixer to translate the higher frequency microwave/RF carrier directly to baseband, then the upper and lower sidebands of your modulated signal will fold / alias, corrupting the signal. To do this properly if your bandwidth can't support a digital IF would require quadrature down-conversion and then use two channels of the scope, one for "I" and one for "Q" referring to the in-phase and quadrature components of your complex baseband signal.

If you are trying to compensate for wideband distortion effects of your attenuator, then you must also pay close attention to the phase distortion as well as the amplitude distortion. You could feasibly compensate both with a careful network analyzer measurement of the attenuator and mixer, but doing such a dual frequency measurement (RF in to IF out) with a network analyzer is a little more complicated. Another approach that I like to do is to use a sounding sequence (transmit a known PRN modulated signal) and then from that determine the least squares estimate of the channel. This will include everything in the path and is fairly straight forward with a few lines of code. It is important that any such sounding sequence spectrally fill the bandwidth of interest (the bandwidth the radar signal would fill). It's quite feasible the radar signal itself could work well as the sounding sequence (for instance FMCW would be perfect in sweeping the channel), you would just need to have a time aligned copy of what was actually transmitted. I demonstrate that approach in detail here:

How determine the delay in my signal practically

Finally when capturing a signals with the scope, also make a capture with the scope set up the exact same way (vertical scale etc) but with no input connected. This is a capture showing your measurement noise floor. Confirm that this is well below (>15 dB) your signal. Also confirm that you are not clipping your signal with the scope in the same configuration.