I have read many online materials and journal paper where the equation for MMSE equalizer is given as:

$G_{MMSE}$ = $H^H(HH^H+\nu^2I )$

where $H$ is the channel, $H^H$ is its hermitian. $\nu^2$ is noise variance (a statistical property) and $I$ is a identity matrix.

I know how to compute the channel $H$, my question is how to find $\nu^2$ will it be simply a scalar from Gaussian distribution of mean 0 and variance 1 ? If so, how is it taking care of the real channel noise, as the real channel noise can be anything?

  • $\begingroup$ Could you write out what "MMSE" is for, please? Does that answer the last sentence in your question? $\endgroup$ Commented Jun 25, 2021 at 22:53

1 Answer 1


First, regarding $v^2$, yes it's simply a scalar value. For example, you can get it in Matlab using $v^2$ = 1/10.^(SNR/10); where you SNR is a known scalar too.

In real channels, you usually receive real signal and the noise usually becomes ambient specially with difficult environments. It's hard to estimated the $v^2$ in real communication channels. I personally performed some real tests long time ago with high SNR and I used to set it as the simulation value mentioned above. That was working well.

Is that what you are asking about? I hope I got what you mean.

  • $\begingroup$ Noise variance should be inversely propotional to SNR. Also, be careful that by setting noise variance $\nu^2 = 10^{-\frac{\mathrm{SNR}}{10}}$, you are assuming that $\mathbf{H}$ is normalized. $\endgroup$
    – AlexTP
    Commented Jun 29, 2021 at 8:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.