Denoising a signal using a known carrier modulation

Hi,

this is a rather theoretical question, yet. Maybe one could point me to the right toolboxes or keywords.

For example purpose let´s consider this as a simulation:

I have a Signal (S) from a source. In reality this signal would be super noisy (S_n). Now I would like to modulate my signal on top of its intrinsic changes with a known modulation function (M). Giving me a convolution of Signal, noise and Modulation (S_n_M). Now I would like to use my knowledge on the modulation function to best extract the original Signal S from the modulated signal S_n_M. The approach is a bit like locked-in-amplifier but I am sure there are also answers from machine learning and other information-theory approaches.

Thanks