How do I add AWGN noise to a RF Signal at the receiver ?

When we deal with the channel decoding, we add the awgn noise to the signal BPSK moduated signal "r" as

SNR_ratio = 10^(SNRdB / 10);

N0 = sqrt(1.0 / (2.0 * Rate * SNR_ratio));

r = r + N0*randn(size(r));

In the matlab example code for HARQ, the AWGN noise is added to the received Rf signal as below

• SNR = 10^(SNRdB/10);
• N0 = 1/sqrt(2.0*simLocal.NRxAnts*double(waveinfoLocal.Nfft)*SNR);
• noise = N0*complex(randn(size(rxWaveform)),randn(size(rxWaveform)));
• rxWaveform = rxWaveform + noise;

1. So, How can we relate those two things ? In the matlab example code, N0 is calculated based on the SNR, NFFT and NRx antenna but do not care about the code rate. I would be so happy if someone explain it clearly.
2. How can we calculate the Eb/No from the the demodulated/rxwaveform signal ?

Thank you.

Answer 1

[vidyesh]

Hi Narayan,

1.So, How can we relate those two things ? In the matlab example code, N0 is calculated based on the SNR, NFFT and NRx antenna but do not care about the code rate. I would be so happy if someone explain it clearly.

N0 calculation depends on your system and its implementation. You can ignore coding rate if you are using 'snr' or 'esno' and it may factor in if you are using 'ebno'. Refer to the below two pages for more details:

• StackExchange - https://dsp.stackexchange.com/questions/33731
• MATLAB Help - https://www.mathworks.com/help/comm/ref/convertsnr.html

If you are considering a simple BPSK transmission, you can calculate 'N0' as . However, since the HARQ system is a complex one, we factor in the number of Receive antennas as well as the number of FFT points.

2.How can we calculate the Eb/No from the the demodulated/rxwaveform signal ?

Instead of calculating 'ebno' from the received waveform, you can use the awgn function to add noise, and specify the 'signalpower' parameter as 'measured' which ensures that "The signal level of X is computed to determine the noise level required to achieve the specified SNR".

For more information on using the awgn function, see:

• https://www.mathworks.com/help/comm/ref/awgn.html

Hope this helps.