Assuming QAM symbols (or OFDM system) with AGWN, I found that the use of ML detector does not enhance the BER but only enhances (reduces) error vector magnitude (EVM) because of symbol decision and matching each received (corrupted) QAM constellation point to the nearest ideal QAM constellation point.

I am a bit confused as I expected the ML detector to enhance both BER and EVM not just EVM? Thanks

  • $\begingroup$ "Enhances" compared to what? If something else is as good as the ML detector, congratulations, you have found an ML detector. $\endgroup$
    – mmmm
    Jun 12, 2021 at 9:50
  • $\begingroup$ compared with the theoretical BER calculation, or simply compared with the case where ML detector is not applied. Note: I am using matlab command (biterr) for BER simulation result $\endgroup$ Jun 12, 2021 at 9:53
  • $\begingroup$ What do you mean with "theoretical BER calculation"? What decider do you assume while calculating? Or are you referring to Shannon capacity? $\endgroup$
    – mmmm
    Jun 12, 2021 at 10:17
  • $\begingroup$ I will post matlab code to help to understand my question $\endgroup$ Jun 12, 2021 at 10:33
  • $\begingroup$ Assuming the transmitted symbols are independent and equally likely, the matched filter followed by a threshold detector is ML and therefore it's also optimum. $\endgroup$
    – MBaz
    Jun 12, 2021 at 14:39

1 Answer 1


If your error vector magnitude is below the decision threshold between adjacent symbols then there would be no impact on the BER. Thus there will be a point where you can continue to reduce the error vector while not see a change in BER.

Ultimately our objective is to minimize the error vector regardless, to maximize performance in lower SNR conditions. Also we will have cases where an error vector is due to other factors besides the additive noise floor, which would then add to the error vector in lower SNR conditions, creating a higher threshold at which the bit error rate is noticeably impacted. A typical error vector is a statistical quantity with theoretically infinitely long tails in the distribution such that given an rms error vector magnitude , if we wait long enough we will achieve an error an thus a bit error rate. I suspect the OP is operating at levels far below the threshold where it is feasible to wait long enough, or working with an error distribution that itself is limited to be below a symbol error threshold, in which case it makes sense that a decrease in error vector magnitude can be measured with no change in BER.

When data is equiprobable and the noise is zero mean and equally distributed on I and Q (real and imaginary), the the ML decision threshold would be mid-way between the ideal symbol locations. The error vector is just the vector from the actual sample location to the nearest symbol and is typically given as an rms quantity due to it being a noise quantity.



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