Frequency offset modeling in presence of ASE noise and corresponding low-complexity solution for discrete spectrum modulated nonlinear frequency division multiplexing system

For discrete spectrum modulated nonlinear frequency division multiplexing (DS-NFDM) transmission, the combined effect of laser frequency offset (FO) and amplifier spontaneous emission (ASE) noise would cause a perturbative shift of eigenvalues and corresponding spectral distortion. Moreover, the classical 4th-power feedforward frequency offset estimation (FOE) scheme is not suitable for DS-NFDM system with low baud rate. In this paper, we firstly deduce an FO impairment model with ASE noise in nonlinear Fourier domain (NFD). Meanwhile, we have proposed a training sequence-assisted FOE (TS-FOE) scheme, which effectively reduces the impact of ASE noise. The 2 GBaud DS-NFDM 16QAM simulation results illustrate that this scheme achieves an FOE error within 1 MHz using a training sequence (TS) with length of 64. Besides, its FOE range achieves [−Rs/2, +Rs/2], where Rs denotes the baud rate of signal. Furthermore, the effectiveness of TS-FOE scheme has been verified by 2 GBaud NFDM QPSK experimental system. The results demonstrate that when optical signal-to-noise ratio (OSNR) is set 13 dB, the TS-FOE scheme presents stable FO compensation performance for different FOs within 1 GHz, and the corresponding bit error rates (BERs) are all below the 7% hard decision forward error correction (HD-FEC) threshold. Meanwhile, its complexity is on the order of OL and related with the length L of TS, which is as one thousandth as that of angle search FOE scheme. •We firstly have analyzed the combined effects of FO and ASE noise on the perturbation of eigenvalue shift, and established an NFD-FO model.•The NFD-FO model reveals that the eigenvalue perturbations caused by ASE noise are transformed into amplitude noise and phase noise.•We propose a low-complexity TS-FOE scheme, which effectively reduces the impact of ASE noise on FOE accuracy.•The complexity of this scheme is reduced to the order of O(L).