Given an unknown OFDM symbol consisting of 9144 samples, interested to know the size of the FFT used in the TX/Number of bins.

Downsampling to 512,256,128,64,32 yields the following.

Do not see how can this information be derived based on this data.

As a result, have tried to analyze the time domain of the downsampled vectors, and detect samples that were removed by the downsampling process.

Seems that the third graph represents the original FFT size – 128, as the sample at 277 has not been witnessed before(fft=64,32), and is witnessed at higher sampling rates.

Wonder if this is correct and whether there is a more accurate approach to determine the FFT size used?

little bit of an odd question the modem design is normally predetermined, i.e. you know the transmitters IFFT size. You also haven't provided any information on what it is you are receiving -standard WiFi packets? Typically its 64. Also unclear why you are downsampling at the possible FFT size, not sure what this would tell you, especially if you are not sample aligned to the start of a symbol to begin with and not sampling at the correct bandwidth.

If this is a standard WLAN packet as described by https://www.mathworks.com/help/wlan/ug/wlan-packet... then you can note the cyclic prefix will have some predetermined length in time. Try sampling at the max channel bandwidth possible for WLAN (160MHz, but probably only need to go up to 20-80MHz) and note the cyclic prefix duration which should give you the channel bandwidth being used, which should be using a standard sub-carrier spacing and from that fact you can solve for N, the fft size from:

$$\Delta_t = \frac{1}{N T}$$

This is a propriety video link being BLINDLY demodulated.

No parameters are given/known.

There was however a progress with the problem, no bits yet though. Will update when there will be.

As, spetcavich pointed typically FFT size is already decided during modem design. 

But would be interested to know how your blind demodulation turns out.

May be you can use the cyclic prefix as your flag. For example correlate the stream in a sliding manner with a sliding delayed version and see if you get peaks of correlation where cyclic prefix is aligned with end of symbol then it will tell you how many samples are between peaks. Next you need to identify where samples are equal or so i.e. end of symbol Vs cyclic prefix.