# Pairwise Error Probability simulation versus SNR for Space-time code

I have a MIMO system using Space-time coding. I am required to produce simulation results in the form $$\text{PEP}=f(\text{SNR})$$, meaning a curve representing the Pairwise Error Probability (PEP) for each SNR value (say from 0 to 25 dB).

The PEP is the probability of mistaking a matrix $$M_a$$ with a matrix $$M_b$$ which is $$P(M_a \rightarrow M_b)$$.

Given that I have a matrix constellation in my system of cardinality 16 (16 matrices in my code book) how am I to represent $$\text{PEP}=f(\text{SNR})$$?

Should represent the result of just one pair of matrices ? (exemple $$P(M_1 \rightarrow M_2)$$ would this be fair given that I have other pairs of matrices?

Or is there a method to group the PEPs of all the pairs into one curve ?

Attached is an example of the curve I am looking to produce. thanks • You've got only 256 possible matrix combinations. Try them all out. ML decoding for but 16 options isn't really hard. – Marcus Müller Dec 9 '19 at 20:14
• i understand, but which PEP result should be represented in the graph ? since a PEP is related to a single pair. – Ibrahim DAWI Dec 9 '19 at 20:44
• I'd say it'd be the maximum PEP for each SNR, as that gives you a lower error bound. Or, you give the average PEP, because that gives you an error probability. – Marcus Müller Dec 9 '19 at 20:54
• perfect, thanks ! – Ibrahim DAWI Dec 9 '19 at 20:55
• Note that I didn't give an answer: you need to find out what data is useful to what you want to do. – Marcus Müller Dec 9 '19 at 21:26