# Pairwise error probability representation problem

i am looking to make a comparison between theoretical and simulation results for pairwise error probability data.

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

On the other hand, i have a closed form expression that produces the theoretical result of the exact PEP.

On the matter of which PEP value to choose among all the the PEP values to represent in my curve, on the theoretical side, i choose the maximum PEP in order to lower the error bound. ( example for a code book of 4 matrices, there are 12 PEP values (for each matrix pair), i produce results for those 12 values and choose the highest result). In the simulation, the transmitter sends a large number of matrices, and the receiver decodes them, i classify the results in a table, i produce each PEP for each value ( example, for $$P(M_1->M_2)$$ i divide the number of times the receiver decodes $$M_2$$ when $$M_1$$ is transmitted by the number of times $$M_1$$ is sent).

The problem is, for a low spectral efficiency of 1 bps/Hz , where the code book is composed of 4 matrices, the theoretical and simulation results are a prefect match. while for a higher spectral efficiency of 3.5 bps/Hz (128 matrices in code book), the curves converge from each other and don't match as in the figure.

i beleive the problem is with the high number of PEP values for 3.5 bps/Hz (16256 PEP values) the error margin grows when matching maximal theoretical PEP with maximal simulation PEP.

How can i solve this issue? is there another method to represent the PEP other then choosing the maximal one? am i supposed to only choose a specific PEP (example $$P(M_1->M_2)$$ ) to represent in both theoretical and simulation parts?

Thank you