Under some special environments in China, there exist moving radio radiations with high transmission powers that can degrade the performance of the power line communications systems significantly. Such radiations overlap with the OFDM-based signals in time and frequency domains, and hence, it is very difficult to mitigate directly if not possible. The paper introduced the fractional Fourier transform trying to deal with such moving radio interferences. When using the fractional Fourier transform to separate signals and noises/interferences, the fractional order plays a key role, but there is no method to obtain its optimal value in the published papers. In the paper, like for the time-frequency representations, we defined the second moments of the fractional Fourier transform of the signal. The fractional order, corresponding the maximum of the second moments, is the one used to separate the OFDM signals and the moving radio interferences, which is modelled as the Doppler signals in our scheme. The proposed method can mitigate the moving radio interferences significantly by applying the proposed method to the simulated OFDM signals and the measurements data. The results also show that the system's BERs can be improved from 10 2 to 10 5 for lower signal-noise-rate (SNR), and from 10 4 to 10 9 for high SNRs.