Symbol Error Probability Analysis of DFrFT-Based OFDM Systems With CFO and STO in Frequency Selective Rayleigh Fading Channels

In this paper, we derive exact symbol error probability (SEP) expressions for orthogonal frequency-division multiplexing (OFDM) based on discrete fractional Fourier transform (DFrFT) when symbol timing offset (STO) and carrier frequency offset (CFO) are present together. Closed form expressions are derived for binary phase shift keying, quadrature phase shift keying, and 16-ary quadrature amplitude modulation in the case of transmission over a frequency selective Rayleigh fading channel. As it is well known, in OFDM the presence of CFO destroys the orthogonality between the sub-carriers, generating inter-carrier interference (ICI), while the presence of STO introduces intersymbol interference, between successive symbols, and phase rotations in frequency domain, within the same symbol. It is well recognized that an OFDM system based on DFrFT is more robust to ICI introduced by CFO than that based on discrete Fourier transform (DFT). Motivated by this, the combined effect of CFO and STO on the SEP of a DFrFT-based OFDM system is analyzed. Our results show that the DFrFT-based OFDM system outperforms that based on the DFT for different values of the DFrFT “angle parameter.” Monte Carlo simulations are used to demonstrate the correctness of the derived analytical expressions.