# SNR in AWGN

251 views (last 30 days)
oblivious on 10 Jun 2012
Answered: Darel on 4 Aug 2021
Hello,
i am trying to do some simulation of AWGN channel. matlab has a function awgn(x,snr). what kind of snr does it use here? is it Eb/No (average bit energy/power spectral density)? If so, then i know the awgn has a PSD equal to No/2. does that psd in the snr term implies No/2?
-OBLI

Darel on 4 Aug 2021
The function awgn does not use EbNo. It uses SNR, defined in the same manner as the snr() function from the Signal Processing Toolbox: sum of the squared samples of the signal over sum of the squared samples of the noise, where that ratio is converted to dB. Thus, if you created noisy data according to
y = awgn(x, SNR);
you should be able to check that
mySNR = snr(x, y-x)
is about the same as SNR in the first call.

Wayne King on 10 Jun 2012
With the syntax
y = awgn(x,snr);
You generate a white noise vector with a variance of
variance = 10^(-snr/10);
noise = sqrt(variance)*randn(size(x));
If you use 'measured', then awgn actually measures the signal power.
For example:
x = cos(pi/4*(0:99));
y = awgn(x,5,'measured');
In this case the variance of the additive white noise is:
sigp = 10*log10(norm(x,2)^2/numel(x));
snr = sigp-5;
noisep = 10^(snr/10);
noise = sqrt(noisep)*randn(size(x));
Mrutyunjaya Hiremath on 13 Sep 2020
Meaningful Explanation