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Transmitting the signal $x$ over the channel $h$ and affected by noise $n$ can be expressed:

$y = hx + n$

$h$ is the channel gain, that is known for me. I sometimes see phrases saying "when the channel gain is normalized, the performance will be different".

What is the effect of normalizing the channel gain? does that mean it cancel the effect of the channel ?

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  • $\begingroup$ What is the relationship between $s$ and $x$? $\endgroup$ Commented Jul 2, 2021 at 14:16
  • $\begingroup$ @DilipSarwate it's an error, I modified it. $\endgroup$ Commented Jul 2, 2021 at 14:28

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Normalizing $h$ means defining it so that the expected value of $|h|$ is equal to 1. The implication is that multi-path is (on average) neither taking energy from $x$ nor adding energy to it.

In an actual wireless channel several effects play out simultaneously: path loss, large-scale fading (e.g. shadowing), short-scale fading, noise, distortion, etc. Often, one wants to separate these processes and simulate them independently. The channel $y=hx+n$ ignores everything except multi-path and Gaussian noise.

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