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In my research work regarding wireless communication, I came across many research papers wherein AWGN is assumed to be modelled as "complex Gaussian with zero mean and unit variance".

I understood why we model noise as Gaussian, but I am not getting why we model noise with zero mean and unit variance only.

Also, what effect the noise will make if mean is non-zero and variance is more than unity ?

Any help in this regard will be highly appreciated.

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2 Answers 2

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The zero-mean assumption rests on empirical validation. You can do it yourself: turn on an oscilloscope and set it to the minimum amplitude. You'll see noise with roughly zero mean. Intuitively, this is the case because Gaussian noise is made up of billions of separate, independent actions (from heated electrons), which on average cancel each other out.

The variance of the noise indeed changes from case to case. Keep in mind, though, that what matters in communications is the signal-to-noise ratio, not the individual signal or noise powers. When studying or simulating a system, it is often convenient to set the noise variance to one, and then vary the signal power to obtain different SNRs. You may as well set the signal power to one and vary the noise -- the result is the same.

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    $\begingroup$ Thank u sir.... $\endgroup$ Dec 12, 2023 at 23:41
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Additive White Gaussian Noise (AWGN) is typically assumed to be zero mean as this adds random fluctuations around the original signal without biasing it in some way. If there is a non-zero mean in additive noise, it will impart a bias on the signal. This is opposed to Multiplicative White Gaussian Noise, which is typically assumed to be unit mean. This is because multiplicative noise scales the signal, and implies that on average, the signal's scale is not changed. If multiplicative noise is not unit-mean, there will be some bias in the scaling. The signal will on average be amplified if the mean is >1, and on average attenuated if the mean is <1.

For AWGN with assumed zero mean, noise power = noise variance. So, setting the noise to have unit variance normalizes the noise power. In the case where the noise is non unit mean, noise power can be expressed more generally as noise variance plus noise mean squared. If you assume unit variance and add the mean square of the noise, you can calculate the power.

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  • $\begingroup$ Thank u sir.... $\endgroup$ Dec 12, 2023 at 23:41
  • $\begingroup$ You are welcome, glad to help! $\endgroup$
    – Baddioes
    Dec 13, 2023 at 0:14

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