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Let me simplify the question: assuming a PAM-4 signal {-3,-1,1,3} with noise added. I focus on the BER for the signal 1. My question is: with same noise power, does Gaussian noise have the minimum SNR?

DanielB
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  • You are asking a different question in your title and in your text (BER in the title, SNR in the text). Please edit your question so that they do not conflict -- the answers are different. Note that in the BER case the answer is "it depends on the noise and the detector", and for the right kind of noise and signal processing you could design a detector where the BER vs. SNR ratio is almost arbitrarily small compared to Gaussian noise. – TimWescott Dec 15 '23 at 16:47
  • While you are clarifying your question -- is the receiver allowed to have a bandwidth greater than the signal bandwidth (i.e., is it anticipated that there will be a clear channel around the signal) and will the signal have clear bands around it? Also, what sort of non-Gaussian noise are you considering? Gaussian noise is one type of noise in a space of noise types that is uncountably infinite -- if you leave the type of noise unrestricted, then you can pretty much decide on the answer you want, then invent a noise characteristic that'll get you that answer. – TimWescott Dec 15 '23 at 20:52
  • I think the question is ill-defined. The BER depends also on the demodulator used. What we can say is that for Gaussian noise the ML estimator is efficient. – Yair M Dec 16 '23 at 06:40

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