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?
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.