Robustness of fractional order for FRFT-OFDM systems

Fractional Fourier transform (FRFT) has been widely used in orthogonal frequency division (OFDM) systems to combat the doubly dispersive channels. The sensitivity of the fractional order is a serious problem. In this paper, we derive the closed form of the variable order and its optimal value based on the mathematical expression in the FRFT-OFDM systems. The theoretical results prove that the fractional order p = 0.5 is the global optimal fractional order for the FRFT-OFDM system in doubly dispersive channels. Furthermore, simulation results verify the robustness of fractional order 0.5 in the FRFT-OFDM systems.