Joint equalization of frequency offset and phase noise using two-stage cascaded extended Kalman filter for discrete spectrum 16/64APSK NFDM systems.

For the discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) 16/64 amplitude phase shift keying (APSK) system, the inevitable laser impairments including frequency offset (FO) and carrier phase noise (CPN) would cause different rotations of the received signal constellations. In addition, the combined effect of FO and amplifier spontaneous emission (ASE) noise induces the eigenvalue shift, accordingly the residual channel impairment (RCI) is inevitably yielded. To address the above problems, we deduce the joint impairment model of FO, CPN and RCI, and then propose a joint equalization scheme using two-stage cascaded extended Kalman filter (TSC-EKF) for these impairments. It performs frequency offset compensation in the first stage, subsequently carries out joint equalization of CPN and RCI in the second stage. Meanwhile, the minimum Euclidean distance and phase difference between the received symbols and the ideal 16/64APSK constellations are ingeniously fused to calculate the innovations of TSC-EKF. The effectiveness has been verified by 2 GBaud DS-NFDM 16/64 APSK simulations and DS-NFDM 16APSK transmission experiments. The results demonstrate that when performing the joint equalization of FO, CPN and RCI, the maximum FOE range of TSC-EKF scheme achieves 1.2 and 9.6 times as that of nonlinear frequency domain (NFD) scheme and fast Fourier transform -Like (FFT-Like) scheme, respectively. Furthermore, its maximum LW tolerance reaches 3.3 times as that of the M-th power scheme. Importantly, the complexity of TSC-EKF is 63.4% as that of NFD scheme and on an order of O(N).

ASE noise mitigation with digital frequency offset loading for discrete spectrum nonlinear frequency division multiplexing systems.

We propose an amplified spontaneous emission (ASE) noise mitigation scheme utilizing digital frequency offset loading (DFO-loading) for discrete spectrum nonlinear frequency division multiplexing (DS-NFDM) systems. Firstly, based on the one-to-one mapping relationship between frequency offsets and eigenvalue positions, the transmitter side encodes 4-bit information onto 16 kinds of different digital frequency offsets. Then, a sliding window-assisted eigenvalue position (SWA-EP) decoding technology is further proposed to substitute the classical channel equalization and carrier phase recovery processes, with the purpose of recovering the original information. The numerical and experimental results demonstrate that, compared with b-coefficient 16 quadrature amplitude modulation (QAM) scheme, Q-factor gains are 2.1 dB under 15 dB optical signal-to-noise ratio (OSNR) and 1.8 dB after 800 km fiber transmission, respectively. Moreover, its complexity is only 0.6% of the b-coefficient scheme. The DFO-loading scheme offers an effective and low-complexity way to mitigate ASE noise of DS-NFDM system.