Comparison between fractional Fourier transform-based single carrier and OFDM systems

In this paper, we compare fractional Fourier transform orthogonal frequency division multiplexing (FrFT-OFDM) system and a single carrier (SC) system whose equalization is performed in the fractional Fourier domain which is called FrFT-SC. We first derive a tight upper bound for the interference power of the FrFT-SC signal in the fractional Fourier domain. Then, by obtaining the angle of transform which minimizes this tight upper bound, we derive a close approximation of the optimal angle of transform and show that it is similar to that of FrFT-OFDM system. Furthermore, we perform a comparative performance evaluation between the FrFT-OFDM and FrFT-SC systems from the bit error rate and peak to average power ratio (PAPR) point of views. The simulation results indicate that in a doubly dispersive channel, the FrFT-SC system significantly outperforms the FrFT-OFDM system when both systems utilize the near optimal angle of transform. Our comparison also shows that the PAPR of FrFT-OFDM system is significantly higher than that of FrFT-SC systems for all angles of transform between 0 and π.