Very often the high gain electronic amplifiers at the front end of such a measurement system will "demodulate" and "down-convert" strong high frequency signals that make their way into the amplifier front end, much like an AM radio. The sub-harmonic signals seen are the down-converted AM signal from the mobile phone carrier frequency. The frequency of the sub-harmonic signal is the frequency of the amplitude modulation.This happens because the semiconductor junctions in the amplifiers front end are acting as rectifiers, similar to how a simple AM radio envelope detector works. Once the demodulation has happened, it is near impossible to remove the artifact signal unless it is fixed in a narrow frequency band and can be post filtered out. The best way is to prevent this from happening to begin with, by providing front end filtering at the high sensitivity amplifiers to keep the RF signals seen at the amplifier inputs below the threshold of rectification/demodulation. You need to find out what this threshold is, by feeding an RF AM (amplitude modulated) signal into the analog front end (typically through a small capacitor) and sweep it's amplitude/carrier frequency until you begin to see an output due to this signal. Then you design and implement front end low pass filters to eliminate or keep the RF level below this threshold at the front end. This is a basic and simplified explanation, but it is indeed the typical source of major problems with low level high gain analog signal processing...

Wow! That's such a nice and detailed answer which I honestly didn't expect. Thank you very much dear Perry Bakalos! I need time to digest all the details you said here but I am sure they are very useful.