Input is a high frequency sinusoidal signal whose amplitude varies with respect to a modulating signal. Is there any unsupervised neural network method to perform demodulation of this signal?
Neural networks are not needed to solve this problem. It is a classic signal processing problem. (Use frequency analysis - Fast Fourier Transforms - to demodulate the signal.)
If your situation is that you are looking for an application of neural networks, I would suggest you find a problem for which conventional methods are inadequate.
For analog amplitude modulation, where there are an 'infinite' number of waveform symbol possibilities, simple rectifier-lowpass filter methods have been used since the invention of radio communication. The most general possible method of demodulation is the Costas Demodulator invented by J. P. Costas decades ago. It does both amplitude and phase demodulation.
If you have a finite set of waveform symbols, matched filter detection can be used. I could envision that you might use a neural network in the case but it would be sub-optimal to the matched filter. In other words, you would give up some performance quality by using the neural network. However, if you have a finite set of 'unknown' waveform symbols, then the neural net is a method of training a receiver to detect and catagorize the waveform symbols.