What happens if I ignore Nyquist? I have a 16.368MHz digital signal coming out of a GPS front-end chip. My microcontroller (which is reading that digital stream of data) operates at a maximum of 32MHz so sampling at ~16MHz seems unlikely. If I undersample my signal with say M = 3, then I have a 5.456MHz signal which I can sample.
The Intermediate Frequency of the digital signal coming from the GPS chip is at 4.092MHz, it has a bandwidth of about 2MHz but there does seem to be noise at all frequencies. So clearly, downsampling shouldn't destroy my signal. When I simulate the downsampling, even values of M seem to completely corrupt the data (frequency domain looks like pure noise) however odd values of M give a recoverable spectrum.
So what if I do undersample my signal without filtering it first? Is there any way to quantify the extra loss this will add to my signal without ever recovering the full 16.368MHz digital signal? Also, are there any tricks I could use here to avoid this problem completely?
UPDATE: Here is a frequency domain representation of the 16.368MHz signal (and yes it's a Real signal, despite me plotting both sides of the spectrum): 
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