How to determine the original size of the FFT used in unknown OFDM symbol

1. Solve for the useful period, Tu. The easiest way to blindly estimate Tu in OFDM is via autocorrelation. You can peak pick the output of the autocorrelation (or visually inspect) to get Tu.

2. Estimate the number of used carriers. Once you have Tu you can estimate the total used carriers with: Used Carriers = Measured BW * Tu, where measured BW is the observed from the power spectral density (PSD) of the signal of interest.

3. Next highest power of 2. Assuming the DFT size is a power of 2, which is true for nearly any commercial OFDM signal I can think of, you can infer the FFT size by taking the next highest power of 2 from the number of used carriers (step 2).

If you use an FFT size to generate a PSD estimate far longer than the IFFT used to generate the OFDM signal, then you'll see the "valleys" between the sinc maxima in the spectrum, and then it's easy to just go in there and count subcarriers, and their spacing.

This will, however, require a high degree of frequency stability in your system, and won't work well with OFDM systems where small number of consecutive symbols are bursted out.

You can make that a little more robust and work on longer autocorrelation functions, like here.

You probably want one of the more advanced methods of OFDM parameter estimation, like those implemented in gr-inspector (hint: that's free&open source; don't reinvent the wheel).

The relevant blog post of the author of that software would be https://grinspector.wordpress.com/2016/07/08/week-7-ofdm-prototype/ .

You basically want to read

Bouzegzi, A., Ciblat, P., & Jallon, P. (2010). New algorithms for blind recognition of OFDM based systems. Signal Processing, 90(3), 900–913. doi:10.1016/j.sigpro.2009.09.017

They propose clever (as in: outperforming above roughly sketched autocorrelation-based methods) ways to synchronize and estimate OFDM parameters.

Your symbols should all have a cyclic prefix of length M such that the entire symbol is M+N(FFT Size). You could correlate the start of a symbol and see how many samples later (length L) it shows up, such that L+M = N. This works if you are entirely certain that you are sampling at the same rate (OFDM bandwidth) as your transmitter. This is easy to do though, just spectrum analyze at a much higher sampling rate and see the bandwidth of the signal in question then set your receiver to match this bandwidth.