# What's the relation between the sampling rate and FFT size in OFDM

In OFDM system,

Is there relationship between Sampling rate and FFT size? For example, if we downsample or oversample the received signal, Should we decrease or increase the FFT size accordingly?

thank you

• I don't think you fully understand the basics of OFDM – the FFT size is exactly the number of subcarriers your OFDM system has. Nothing ever changes that. And "Oversampling Pop Up Menu" is something that has to do with a specific software or so? You might be forgetting that we don't sit in front of the same computer using the same software as you... Jul 26, 2018 at 19:35
• leave the "Oversampling Pop Up Menu" and answer about the question in the fist part. Is there relationship between Sampling rate and FFT size? For example, if we downsample or oversample the received signal, Should we decrease or increase the FFT size accordingly? Jul 27, 2018 at 5:02
• Hello .. So you question is there relation between sampling rate and FFT size. Yes, there is, Let s be a data vector of length N. When oversampling is not used, the transmitted signal is x=F^H s where F is the N x N DFT matrix whose (k,l)th entry is exp(-j2¥pi k l /N). When oversampling is used, the transmitted signal is Fp^H s where Fp is the pN x N DFT matrix and p is the oversampling factor.Then, what happens if F is used is used for demodulation? .. Jul 27, 2018 at 5:16
• @MarcusMüller .. It's not allowed to evaluate people if they understand or not understand. they are here to learn and help each other. I've seen some comments for you where you evaluate people themselves by negative feedback. if they understand well, they won't come here to ask and try to understand. Eng. Badr, Keep going on, Jul 27, 2018 at 5:19

Yes, you can use different sample rates and corresponding FFT sizes to accomplish the same thing for OFDM (mod and demod). For example, 10 MHz LTE can be sampled with 15.36 Msps and modulated/demodulated with a 1024-point FFT for 15 kHz subcarrier spacing and the 600 subcarriers around DC give the 9 MHz of utilized BW. Alternatively, you can use 30.72 Msps and 2048-point FFT to mod/demod and get the same 600 subcarriers.

What is effectively happening is that the basis vectors are resampled (by 2x in this case), but they remain orthogonal and at the same subcarrier spacing.

• Thank you very much ... I really enjoy reading your comments. Jul 27, 2018 at 11:03
• @msm Many thanks for your answer, it's useful. Jul 27, 2018 at 11:16
• @msm how are you. hope you will read this comment. I actually read some papers where they mention same idea as your comment but only at receiver without changing the structure of transmitter, such as: OOFDM. It's the same idea which you mentioned in your comments but just at receiver. do you have any idea for that? I mean when oversampling by double the Frequency sampling and then 2048-point FFT how can the extract the data? I try to explore that by MATLAB but I don't get any result, do you have any idea? Aug 5, 2018 at 6:32
• Yes, you can use different sample rates at TX vs RX. As noted above, this is simply about using a orthogonal basis set for mod/demod. Not all subcarriers of the (I)FFT are used, and if you oversample by 2x, then a smaller fraction of the FFT bins are used (e.g. 1024 point IFFT/FFT at fsamp=15.36 MHz for 10 MHz LTE uses 600 subcarriers with 15 kHz spacing for 9 MHz of used BW; this is the same as using 600 of 2048 subcarriers IFFT/FFT at fsamp=30.72 MHz. In this case, TX could use 1024 and fsamp=15.36, and the receiver can use 2048 and fsamp=30.72 or vice versa for TX vs RX).
– user35336
Aug 5, 2018 at 20:40