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In digital communication systems there are plenty metrics used in various systems, MER,EVM,SER,BER,SNR...
They are all related. SNR is not that helpful but is certainly related to error rates. For example SNR relates to EVM as follows:
SNR = - [4.23 + 20 * log10 (EVM / 100)]
for 256QAM with some conditions
I am not sure about formula for SNR to SER but there plenty papers around.
May be you better measure than use equations. To measure SER you need a working model to measure the errors relative to expected symbols.
To measure SNR you can check noise floor assuming it is regular enough from dc to Nyquist. This is a bit hard as it depends on system filters/sampling rate...but with practice you can get some graphs between SNR and SER. The alternative is to inject known random noise and work from there making allowance for filtering effect and quantisation noise.