BER Analysis of WFRFT Precoded OFDM and GFDM waveforms with an integer time offset

In this paper, we investigate bit error rate (BER) performances of weighted-type fractional Fourier transform (WFRFT) precoded orthogonal frequency-division multiplexing (OFDM) and generalized frequency-division multiplexing (GFDM) waveforms with an integer time offset (TO) over additive white Gaussian noise and fading channels. First of all, theoretical BER expressions of hybrid carrier systems with TO are derived according to the linear combination characteristic of WFRFT. In addition, the fusion mechanism is also employed to calculate noise enhancement factor (NEF) of WFRFT precoded GFDM waveforms, and then analytical BER expressions are derived, including the cases with TO. Basically, analytical BER expressions of WFRFT precoded OFDM and GFDM waveforms are under the same framework, and BER of the latter could be simplified to the former when GFDM systems are reduced to OFDM systems. Through WFRFT precoding, the BER performance of GFDM waveforms could be improved by about 2 dB over fading channels with timing errors. Furthermore, using derived NEF of WFRFT precoded GFDM waveforms, theoretical BER expressions could be easily extended to space-time coded systems. Finally, when interblock interference and intercarrier interference are generated due to insufficient cyclic prefix and timing errors, BER performances of WFRFT precoded OFDM and GFDM waveforms also surpass their two special cases, i.e., nonprecoded and discrete Fourier transform precoded ones.