is using both Nyquist's and Shannon's Theorem possible?
Your Nyquist formula has a trivial error: it's Mbps, not Bps. It also says that you have a symbol rate (baud rate) of 2x the bandwidth, which I don't think is right -- you need 2x the data rate as sample rate, but that's already considered in the &quot;MHz bandwidth&quot; measurement, so the &quot;bandwidth&quot; in your description is the &quot;baud rate&quot; AFAICT.
Your Shannon limit description doesn't include the requirement that you only use 4 levels. The Shannon limit tells you how much information you can jam through if you were to use &quot;all levels possible&quot; (given the S/N ratio.)
You can think of 4 levels as a two-bit &quot;word&quot; and the 1 MHz bandwidth as the ability to modulate/demodulate one 2-bit word every microsecond, leading to 2 Mbps throughput.