I want to add complex wgn to a signal for a specified SNR. I have been using the following lines:

SNR = -10:5:50;
for l = 1:length(SNR)
   SignalN = awgn(Signal, SNR(l),'measured','dB');

where $Signal$ is the actual complex damped signal and the $SNR$ is in dB. I want to replace the above line with $randn$ function in MATLAB that considers the definition of WGN and SNR in dB. can someone help me with this?

  • $\begingroup$ just type edit awgn.m and you access to the source code of the awgn() function. $\endgroup$
    – AlexTP
    Jun 14 '21 at 10:50
  • $\begingroup$ Do you want to noise to be complex as well ? $\endgroup$
    – Hilmar
    Jun 14 '21 at 11:09
  • $\begingroup$ Thank you AlexTP. I do not want to continue using awgn, instead I want to use randn function that fulfils the same requirement as awgn. $\endgroup$
    – Neuling
    Jun 14 '21 at 11:10
  • $\begingroup$ Hi Hilmar. Yes I want it to be complex WGN, but without using the awgn or wgn functions from MATLAB. I want it to be with randn function in MATLAB $\endgroup$
    – Neuling
    Jun 14 '21 at 11:11
  • $\begingroup$ @Neuling well, if you ever look at the implementation of awgn(), it does use randn(). $\endgroup$
    – AlexTP
    Jun 14 '21 at 12:35
%  create complex white normal noise 
noise = randn(size(Signal)) + 1i*randn(size(Signal));
% calculate the gain for the noise
noiseGain = rms(Signal)./rms(noise)*exp(-SNR(i)*log(10)/20);
% add it
SignalN = Signal + noiseGain*noise;
  • $\begingroup$ Thank you Hilmar. I was not aware of the noise gain formula. Could you please correct the logarithmic function in the second line.. the brackets are missing. $\endgroup$
    – Neuling
    Jun 14 '21 at 11:39
  • $\begingroup$ Done. Should have been $log(10)$. It's just turning dB into a linear gain $\endgroup$
    – Hilmar
    Jun 15 '21 at 13:14

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