Restore real signal from its complex representation if sampled under Nyquist frequency Assume we have:

real signal: $s(t)$
its analytic representation: $s^+(t) = s(t) + j*H(t)$,
where $H(t)$ - Hilbert transform of $s(t)$

Spectrum of $s^+(t)$ has only positive part, so may be sampled with frequency $f_p = F_n/2$ (without aliasing); where $F_n$ - Nyquist frequency for real signal. Its for example LTE20 case which IQ representation is sampled with $f_p=30.72MHz$.
The question is: how to restore real signal from analytic representation if sampled under $F_n$?
(Typical literature response is that just imaginary part can be discarded, but they silently assumes that $f_p &gt;= F_n$.)
You simply can't.
The analytic signal contains the exact same amount of information as the original real-valued signal, and if either is undersampled, you get the loss of information that undersampling gets you.
That's it. Unless you've got any secondary information about the signal that you forgot to mention, there's nothing you can do.