# How awgn add white noise on complex envolope signal

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Chen on 16 Jan 2020
Answered: Kaashyap Pappu on 21 Jan 2020
Hello
An I/Q baseband signal goes through Tx, the wave received by Rx at carrier (fc) with condisering receiver noise should be "rx_noise"
noise=0.1*rand(length(t),1)
rx = [I(t)*cos(2*pi*fc*t) - Q(t)*sin(2*pi*fc*t)]
rx_noise=rx.*noise
then use Matlab snr, we can get the SNR
SNR=snr(rx,noise);
the complex envolope of the rx is
RX=[I(t) + 1i*Q(t)].*exp(1i*2*pi*fc*t)
My question are:
1. how "RX_noise=awgn(RX,SNR,'measured') " add noise to the RX?
2. does real(Rx_noise) = rx_noise?
Chen

Kaashyap Pappu on 21 Jan 2020
1. awgn(RX,SNR,'measured') adds noise to each sample of RX. If RX is a real vector, only the real component has noise added to it. If RX is a complex vector, noise with complex representation ‘a + ib’ is added to each element of RX. The values of ‘a’ and ‘b’ are generated using a gaussian distribution, where the magnitudes are dependent on the SNR value provided. The 'measured' option takes the current received signal power in consideration to generate the noise samples.
2. As mentioned, this is valid only if the input RX samples are real. If it is complex IQ samples, then this may not be a valid assumption.
You can learn more about how the noise samples are generated by typing the following command in the command console:
edit awgn
The documentation for awgn can also provide more information regarding the function.
Hope this helps!

R2019a

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