During my research I've encountered a following issue. As an outcome of one simulation we are getting the one dimensional signal D(t) plus the white noise N(t) of unknown variance. Yet, for the number of reasons, from the simulation program we are getting the square of the signal (D(t)+N(t))^2. Since N(t) is gaussian WN N(t)^2 is chi^2 with non-zero mean. Is there any way how to disentangle the signal from noise in that case?
I've looked into the literature for over the month now, but I haven't anything useful so far.
To be honest I'm no expert in signal processing, so maybe I am missing some obvious reasoning here.
Any ideas on that?