# OFDM demodulation, how to set the sampling rate?

I have a signal for which I know the OFDM burst length (from the autocorrelation function of the signal) T_burst and the FFT size 1024 (by measuring the channel spacing) and the guard interval (128).

• How should sample such a signal for OFDM demodulation ?
• What is the ideal sample rate for that ?
• Is it (1024+128)/T_burst?

I plan to use GNU radio for demodulation, like this (this image is from IRC channel - credit to drmpeg):

Your receiver will consist of, apart from synchronization blocks, an FFT. You want that FFT to generate one output bin for each of the subcarriers. Therefore, you should make use of the relationship between the input sample rate of a DFT to its output bin spacing:

$$\Delta f = \frac{f_s}{N_{FFT}}$$

where $\Delta f$ is the subcarrier spacing and $f_s$ is the sample rate (both in Hz). Assuming you know the subcarrier spacing and the FFT size, then it's straightforward to choose the sample rate:

$$f_s = N_{FFT} \Delta f$$

• Thanks, the problem is that I only know the subcarrier spacing approximately, not exactly. – jhegedus May 4 '16 at 12:11
• You'll need to have good knowledge of the spacing if you want to effectively demodulate the signal. One area to start looking is to note that most OFDM implementations use a power of 2 FFT size (you noted 1024), and they also often use "nice" sample rates, like 20 MHz, 25 MHz, and so on. Is your subcarrier spacing estimate somewhere close to an even-sounding number divided by 1024? – Jason R May 4 '16 at 12:13
• Yeah, it is close to 1024 but I don't know the exact spacing value, I guess I need to think about this. Can I calculate the spacing from the OFDM-FFT burst length ? – jhegedus May 4 '16 at 12:55
• I see what you mean. It is something like 11kHz, the subcarrier estimate. So 11*1024=11MHz ? My reasoning is that if I know the burst length then that is the length where I have 1024 samples if the FFT length is 1024. So the sample rate must be (FFT size)/(burst length) or not ? – jhegedus May 4 '16 at 13:07
• @jhegedus: Yes, that's just a different way of expressing the relationship that I showed above. – Jason R May 4 '16 at 13:18