AM modulation index

This is not the most exciting topic, but on the KiwiSDR forum there were repeated questions on how to measure the AM modulation index.

The best reference which I have found for that is an report from the ITU, R-REP-BS.2433-2018-PDF-E, where the "RMS modulation depth", i.e., the RMS ratio of side-bands and the carrier is being used as a proxy for the modulation index.

GNURadio flowgraph for measuring AM RMS modulation depth 

First, synchronous AM demodulation is performed using a PLL which locks onto the carrier. Then the RMS power in the carrier and in the side-bands is computed and their ratio is formed. Smoothed versions of this variable are shown a number and as a histogram. Note that the "RMS AM modulation depth" block consists of just a few lines of python.

The grayed out, i.e., disabled portions of this flowgraph were used to verify that the normalization is correct.

For the BBC transmitter on 198 kHz, the RMS modulation depth was found to be about 12% at the time of measurement which is consistent with the value quoted in the ITU report mentioned above. However, this number can vary by a factor of 1.5 or more (9-18%) depending on whether the program consists of speech or of music at the time of measurement. Furthermore,  the measured modulation depth indicates that dynamic carrier suppression is being used, see again the ITU report for details.

AM RMS modulation depth for BBC on 198 kHz