Hello

I have a question about finding the FFT duration for 802.11a preamble. According to standards when the bandwith is 20MHz and for N=64 we have 20 MHz/64 =312.5 KHz and it says FFT duration to be 1/delta F=1/(312.5 KHz)=3.2 microseconds. My question is why FFT duration should be 1 over subcarrier spacing ? and generally how to calculate time for N point FFT that repeats itself for example it says A 64 points FFT can create a pattern which repeats itself four times for short preamble. why? should I observe the sequence to know this or is there any way to figure this out by looking at the sequence itself?

To the first question; it is about the nature of multicarrier schemes. Each subcarrier conveys a different data and time domain representation of each subcarrier is transmitted in parallel. Assume that you are only using one subcarrier. Then, having an FFT-duration as 1/(subcarrier BW), makes sense right? No matter how many subcarriers you are using in multicarrier, the symbol duration (fft size) remains the same as the ifft of each subcarrier are summed up.

Hope it helps

The system is designed so that the fading will be flat for each subcarrier, so, in general, this restricts the subcarrier spacing.   Once that is determined and the width of the channel is determined, then the size, N, and duration of the FFT is known, because there are no more unknowns, basically.

The reasons that portions of the preamble are repeated for multiple FFT lengths is so that they can be averaged for noise reduction.   Typically, take the FFT of the first one, take the FFT of the second one, add them together to get a 3dB increase in SNR before further processing.