# Noise with a positive or negative mean

I am working on calculating the SNR for my network model.

Considering AWGN at the receiver with zero means, the SNR can be presented as $$\text{SNR} = \cfrac{P \cdot|h|^2}{\sigma ^2}$$ where $$P$$ and $$h$$ are the transmitted power and the channel coefficients, respectively.

I understand for a zero-mean signal, the variance is equal to the power of the signal. However, how do I update the SNR equation when there is a positive or negative mean? Thank you very much, any direction will be much appreciated.

• If the signal cannot have energy at DC, then you just include a DC blocking filter in the channel and you're done. If DC can interfere with the with the signal, then in general you'd extend your analysis to noise plus interference, and separate the "noise" into zero-mean noise and a DC interfering signal. Oct 19, 2022 at 0:54
• i dunno. i suppose that if you had a really good DC blocking filter, The SNR might be $$\text{SNR} = \cfrac{P \cdot(|h|^2-\bar{h}^2)}{\sigma ^2}$$ Oct 19, 2022 at 5:07

1.- The SNR is a parameter attributed to signals, not systems

Although often one may read 'this system has this or that SNR', in general such expression is referred to a system with a known input output signals.

2.- SNR is a power ratio : SIGNAL / NOISE

There's no such thing as 'negative' (linear) power values of signals.

I mention 'linear' because when using dBW dBmW then obviously there may be positive or/and negative dBW dBmW values.

Some people, I've worked with, shorten dBmW to dBm and then started mixing signal amplitude values with power values, not a good idea.

3.- DC is not noise

AWGN or interferring signals are ususally unknown, apart from statistical moments or direct measurements that are usually samples.

For noise, given the random nature, that is what goes to the denominator of SNR.

In analog cellular CIR measurements were/are common Carrier to Interference, obviating that the signal power contents is small compared to the carrier power, because the Interferrer has a similar value to the signal carrier, both carrier and Interferrer >> signal, without carrier.

What signal information is being conveyed by a DC level anyway?

Constellations for modulation/demodulation do not include DC.

Something related but out of context here is the (modulation constellation) Error Vector Measurement, EVM and there may be constellation points that on purpose or by noise/interference are biased, but it's all referred to the constellation coordinates origin, that doesn't include DC.

You may want to consider that a transistor bias is getting into the signal path or a power supply leaking DC, or a slightly rippled DC.

4.- Added negative mean implies increasing power

the DC sign doesn't matter when calculating power.

Let s be zero mean signal. Then s+S0 is the DC-ed signal.

P(s+S0)=P(s)+P(S0)


P() power operator cancells DC sign.