How to determine the FFT size of LTE downlink receiver?
You don't need to sample at cell FFT rate. Just shifted the received signal to the desired subcarrier and take a lowpass filtering, then sample at user-specific bandwidth (see attached image). The shifting operation can be implemented by a multiplication with phase ramp in the time domain.



However samping at cell specific FFT rate is optimal because the lowpass filter needs some kind of roll-off.