Lab 6.5 — RF impairment calibration (DC, IQ imbalance, LO leakage)

Goal

Build a reproducible calibration flow for common RF receiver impairments:

• DC offset;
• IQ gain/phase mismatch;
• LO leakage at baseband DC.

Why this lab matters

An ideal zero-IF receiver would deliver a clean complex baseband. A real one adds three artefacts that are easy to mistake for signal: a DC offset (a spike at 0 Hz from ADC and mixer bias), LO leakage (the local oscillator itself leaking into the signal path, which for a zero-IF receiver also lands at 0 Hz), and I/Q imbalance (the two mixer arms are never exactly equal in gain or exactly 90 degrees apart), which reflects every real signal to a mirror-image copy at the negative frequency. If you do not recognise these, you will chase phantom tones, read a wrong SNR, and lose several dB of constellation quality in every later lab. This lab makes each artefact measurable so you can see it, remove it and know how much is left.

Engineering question

Can we quantify impairment metrics before/after calibration and show measurable improvement on spectrum and constellation?

Executable file

File	Purpose
blocks/block_06_rf_frontend_and_ad9363/python/lab_6_5_rf_impairment_calibration.py	impairment synthesis, calibration, metrics, plots

Run from the repository root:

python blocks/block_06_rf_frontend_and_ad9363/python/lab_6_5_rf_impairment_calibration.py

Generated artifacts

docs/assets/lab65_rf_impairment_spectrum_before_after.png
docs/assets/lab65_rf_impairment_constellation_before_after.png
docs/assets/lab65_rf_impairment_calibration_metrics.json

Metrics

Metric	Meaning
dc_offset_rms	complex mean magnitude of IQ samples
iq_gain_mismatch_db	I vs Q RMS mismatch in dB
iq_cross_correlation	residual non-orthogonality between I and Q
image_rejection_db	desired tone power vs image tone power
lo_leakage_dbfs	LO/DC leakage level relative to peak tone

Calibration stages

1. Remove complex DC component.
2. Match I/Q RMS amplitudes.
3. Orthogonalize Q against I (Gram-Schmidt style).
4. Remove residual DC again.

What to expect

With the default synthetic impairments (DC = 0.085 − j0.052, 1.7 dB I/Q gain mismatch, 6.5° phase skew, LO leakage 0.14 at −30°, noise rms 0.015, 180 kHz tone at 2.4 MS/s):

DC offset RMS before/after: 0.239629 / 0.000000
Image rejection (dB) before/after: 19.16 / 78.77
IQ cross-correlation before/after: 0.1131 / 0.0000

and, from lab65_rf_impairment_calibration_metrics.json, LO leakage improves from −10.2 dBFS to −86.1 dBFS and the I/Q gain mismatch from −1.64 dB to 0 dB.

How to read these numbers:

• Image rejection of 19 dB is what those imbalances predict. A first-order estimate is IRR ≈ 10·log10(4 / (ε² + φ²)) with amplitude error ε ≈ 0.22 (1.7 dB) and phase error φ ≈ 0.11 rad (6.5°), which gives about 18–19 dB. In practice this means a strong signal at +180 kHz also shows up at −180 kHz only ~19 dB lower: enough to fake an interferer.
• DC offset and LO leakage collapse together because in a zero-IF receiver both sit at exactly 0 Hz; removing the complex mean removes both.
• The "after" numbers are unrealistically good (78.8 dB image rejection, −86 dBFS leakage, DC at 1e-17). That is because this compact method estimates each correction from the same noiseless-enough 65 536-sample synthetic record it then corrects, so the estimate is essentially exact. On real hardware the estimate is limited by noise, by temperature and gain drift, and by the fact that imbalance varies with frequency across the band. Expect a real calibration to reach tens of dB, not 78, and to have to be repeated.

Exercises

1. Set iq_gain_mismatch_db to 0 and keep the 6.5° skew. How much of the image is left? Then do the opposite. Which impairment matters more for this tone?
2. Halve noise_rms and re-run. Does the "after" image rejection change? Why or why not?
3. Move the tone from 180 kHz to 5 kHz. What happens to the tone, the DC spike and the image, and what does that tell you about signals near 0 Hz in a zero-IF receiver?

Answers (checked by running the lab script)

1. Without the gain mismatch (skew only) the image rejection is 24.9 dB; without the skew (gain mismatch only) it is 20.2 dB. Removing the 1.7 dB gain mismatch helps more, so it is the larger contributor here, as the first-order formula predicts: ε ≈ 0.22 against φ ≈ 0.11 rad.
2. The "before" rejection does not change (19.2 dB): it is set by the impairments. The "after" rejection does: 87.9 dB with half the noise and 68.2 dB with double the noise, against 78.8 dB by default. After calibration the residual image is set by how well the correction was estimated from noisy samples and by the noise in the image bin, not by the impairment.
3. At 5 kHz the tone, the DC/LO-leakage spike and the image all sit within ±5 kHz of 0 Hz (tone at 0 dB, DC at −9.2 dB, image at −19.2 dB). The long synthetic record still separates them and the calibration still works (image −74.7 dB, DC −51.6 dB after). On real hardware this is where zero-IF hurts: a DC-removal filter that also removes 5 kHz takes the signal with it (the Block 11 DC-blocker case, Lab 11.41), and the image of anything near 0 Hz lands right next to it. That is why receivers tune the wanted signal away from 0 Hz (Lab 6.7).

Report checklist

• Show before/after spectrum and constellation.
• Report all five metrics before and after calibration.
• Explain which metric improved the most and why.
• State limits of this compact calibration method for real hardware.