This letter reports on a critical issue with the application of OFDM to a full-duplex (FD) cellular system. With small frequency offsets of uplink signals, the downlink BER increases considerably. This is attributed to the high spectral-leakage-interference from the OFDM waveforms of geographically nearby uplink users. As an alternative, we propose applying the FBMC waveform to the same FD cellular system scenario. We calculate the precise spectral-leakage-interference for OFDM and FBMC, based on which, we set up a semianalytic BER simulation framework. Analysis and numerical results confirm that spectral leakage interference from uplink signals is the critical performance limiting factor. Even with tiny frequency offsets among the users, the performance of FD with OFDM is severely degraded. Although the FDs with the other multicarrier waveforms having lower spectral leakage such as GFDM, UFMC, and f-OFDM overcome this issue to a certain extent, the degradations remain substantial. However, the FBMC-based FD cellular system achieves almost spectralleakage-interference-free performance, and thus, it substantially outperforms the counterparts with other waveforms.