Hi , please what is the difference between randn and awgn , when adding white gaussian noise to get snr = 10dB , also I see difference in result when using snr function .

P_rms = rms(signal)^2; %

noisy_signal_1 = awgn(signal,10,'measured');

noisy_signal_2 = signal+0.1*P_rms*randn(L_t,1);

snr1=snr(signal,awgn(signal,10,'measured'))

snr2=snr(signal,noisy_signal_2)

var1=var(noisy_signal_1);

var2=var(noisy_signal_2);

Answer 1

[Meg Noah]

They are the same.

% signal is a sine wave of 2 Hz
nSamples = 10000;
f = 2; % [Hz]
time        = linspace(0, 2, nSamples+1);
signal   = sin(2*pi*f*time);

% calculate the signal power
signalPower = sum((signal).^2)./nSamples;

% SNR in db is 10log(Psignal/Pnoise)
snrDb = 10; % [dB]
 
% noise power such that signal power is 10 dB more 
% 10 = 10 log (Ps / Pn)
% Pn is variance which for zero mean gaussian noise 
% is essentially - square sum of all samples -> divided by numSamples
noiseStd = sqrt(signalPower / 10^(snrDb/10));
noiseMean = 0;

% generate the gaussian white noise
noiseValues = noiseStd*randn(nSamples,1) + noiseMean;

% verify the Signal-to-Noise value
noisePower = sum(noiseValues.^2)/numel(noiseValues);
SNR = 10*log10(signalPower/noisePower);
fprintf(1,"noiseStd: model input: %f simulation output: %f\n", noiseStd, std(noiseValues));

noiseStd: model input: 0.223607 simulation output: 0.224735

fprintf(1,"SNR: %f\n", SNR);

SNR: 9.956735

% compare to awgn
noisedSignal = awgn(signal,10,'measured');
awgnNoiseValues = noisedSignal - signal;
awgnNoisePower = sum(awgnNoiseValues.^2)/numel(awgnNoiseValues);
SNR = 10*log10(signalPower/awgnNoisePower);
fprintf(1,"awgnNoiseStd: simulation output: %f\n", std(awgnNoiseValues));

awgnNoiseStd: simulation output: 0.223148

fprintf(1,"SNR: %f\n", SNR);

SNR: 10.018253