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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. thanksenter image description here

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  • $\begingroup$ You've got only 256 possible matrix combinations. Try them all out. ML decoding for but 16 options isn't really hard. $\endgroup$ – Marcus Müller Dec 9 '19 at 20:14
  • $\begingroup$ i understand, but which PEP result should be represented in the graph ? since a PEP is related to a single pair. $\endgroup$ – Ibrahim DAWI Dec 9 '19 at 20:44
  • $\begingroup$ 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. $\endgroup$ – Marcus Müller Dec 9 '19 at 20:54
  • $\begingroup$ perfect, thanks ! $\endgroup$ – Ibrahim DAWI Dec 9 '19 at 20:55
  • $\begingroup$ Note that I didn't give an answer: you need to find out what data is useful to what you want to do. $\endgroup$ – Marcus Müller Dec 9 '19 at 21:26

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