# Calculation of Eb/N0 in OFDMA

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Foxy Seif Eddine on 23 Jul 2011
Answered: Drew on 20 Oct 2021
Hello,
I'm working on OFDMA performances, i'm a little bit confused between SNR & Eb/N0 because of the presence of many definitions in the Internet,in some books,and in Matlab help!
In my simulation,i generate an OFDMA signal X,i use the Matlab function awgn to add AWGN noise to my signal X:
awgn(X,snr,'measured');
SNR: [0:1:20] [dB]
Then i demodulate my OFDMA signal & calculate BER vs SNR.
My next task was to try to get BER vs Eb/N0. I searched how is it calculated,i found many definitions.I found that:
1) In AWGN channels,Eb/N0 is part of the calculation of the variance (sigma^2) of the additional noise n.Linear equation:
sigma = sqrt(2)*sqrt(1./(2*Rm*Rc*EbN0));
Rm = log2M: Modulation rate
Rc: Code rate
2) I found then SNR[dB] is calculated from Eb/N0[dB]! found many equations in dB format:
a) From Matlab help:
snr = EbNo + 10*log10(Rc) + 10*log10(Rm); [in dB]
b) From Matlab help:
snr = Eb/N0 + 10*log10(Rc) + 10*log10(Rm) - 10*log10(Tsymb/Tsampl);
I'm really confused.My questions is:
1) What's difference between Eb/N0 & SNR? Which is important on performances basis?
2) Do i have to program my own awgn function to simulate Eb/N0 or is it possible to use awgn Matlab function knowing it requires snr in entry not eb/b0?
3) Equation 2)a) & 2)b) are different knowing it's both on matlab help,wich one is adequate? and how using them?
Regards,

Neels on 25 Jul 2011
1. Eb/No is normalized SNR. ie, if you consider SNR for individual bit Eb/No. If you generally consider FEC during transmission or for comparison of various modulation schemes Eb/No is used. In your case SNR appears to be best(my opinion).
2. I am not sure what you are trying to do. if you post your entire code, it will be clear. But if possible, its better you write your own AWGN
3. 2 a looks fine, i hope you have the parameters
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Foxy Seif Eddine on 27 Jul 2011
1. In your opinion,SNR appears to be the best suitable to my case,can you clarify please?
2. To clarify my second question,i use awgn matlab function as channel model,this function require as entry parameters SNR in dB not Eb/N0,so by that i mean, can i use this function to study BER vs Eb/N0,or do i have to program a linear function to add a gaussian white noise in Eb/N0 not in SNR in function of Eb/N0 (equations 2)a) &b)) ?
Thanks again.

### More Answers (1)

Drew on 20 Oct 2021
1) ) Eb/No is energy per bit to noise power ratio, while SNR is signal to noise power ratio.
The two are related as:
SNR = EbNo+ 10*log10(Rc) + 10*log10(Rm) -10*log10(Tsymb/Tsamp) (dB)
Either can be used for the performance comparison.
2) awgn can be used with SNR as an input, adjusted as per the relation above.
3) 2a assumes Tsymb/Tsamp =1, so either can be used based on the link parameters.