This problem is related to wideband spectrum sensing. The wideband spectrum sensing approaches are applicable only when the signal has a higher bandwidth as compared to the channel's coherence bandwidth.
the Sub-Nyquist-based WBSS detect spectral opportunities over wide-band with sampling rates lower than the Nyquist rate. So, can we identify the unused frequency bands when the Nyquist rate is less than the sampling rate?
Yes, first find frequency domain analysis or frequency spectrum (Fourier transform), plot graphically. You can get frequency slot for unused or overlapped bands
Yes, but there will be an ambiguity in the sampled signal (aliasing), unless you have other prior information that can fill in with that tells which alias is the correct one. In other words, there will be pairs of frequency bands that cannot be separated. But if your samples say that a particular band is empty, then that means that all the bands that are connected through aliasing are empty.
there is a new technique called faster than Nyquist
best regards