# Normalizing OFDM after IFFT

I had a question about normalizing OFDM transmit power after IFFT across each subcarrier. I have simulated OFDM with BPSK and according to different website I have used NFFT/sqrt(Nsubcarrier_used)*ifft(x) where x is the modulated signal and NFFT is the size of ifft and Nsubcarrier_used is total number of subcarrier that is used. This gives me the transmit power of $1$ across each subcarrier.

My question is: How to know the scaling factor, such as NFFT/sqrt(Nsubcarrier_used), of different modulation schemes?

Because I have tried the same scaling factor for 16-QAM here and it did not give me $1$ as a transmit power. Therefore I would really appreciate if anyone can explain about the method to find the scaling factor for FFT and IFFT in OFDM.

• The FFT scaling factors have been covered in numerous posts on here. The truth is that real transmit signals don't normalize for the FFT length, they just use the numbers as they come out of the FFT. The absolute amplitudes simply don't matter, since a digital number doesn't have any physical unit. – Marcus Müller Jul 3 '17 at 18:34
• Thanks. I looked at many posts but they did not explain about this scaling factor used in IFFT or FFT in OFDM. can you please guide to posts here or quickly mention what would be the scaling for different modulation ? – user59419 Jul 4 '17 at 2:33
• simple: it wouldn't apply. Scaling is just done to ensure some mathematical properties of the transform. For transmission, the absolute amplitude doesn't matter, and scaling, if at all, is done to achieve other things, totally unrelated to the length of the FFT. – Marcus Müller Jul 4 '17 at 7:31
• BUT IT WILL AFFECT THE BER. If the Transmit power is not 1 the BER would not be acceptable like the link I referred to if the scaling is not correct the theoretical and simulated curve do not match. – user59419 Jul 4 '17 at 7:37
• That's a totally different problem. It only applies to simulation/theory. And, in theory, you're doing the math yourself, so you obviously in charge of setting the average power to 1 yourself, and have to figure out, based on your own formulas, what the right normalization factor is! You've got all the math you need (i.e. mathematical definition of the FFT you're using, power of the symbols, Parseval's theorem), so you're the only one who can calculate what the right normalization factor would be! – Marcus Müller Jul 4 '17 at 8:05