Fig. 1. (a) Coherent Rx DSP; (b) FFT-based FOE relying on Mth power operation; (c) DA-FOE; (d) conventional adaptive equalizer. ICR, integrated coherent receiver; RTO, real-time oscilloscope; GSOP, Gram–Schmidt orthogonalization procedure.

Fig. 2. Schematic of (a) data frame, (b) coarse FOE, and (c) AEQ to compensate RFO and linear impairment.

Fig. 3. Experimental setup.

Fig. 4. NFV of coarse FOE (N = 20, 50, 100).

Fig. 5. Comparison of (a) frequency offset estimates and (b) MSE between FSS-LMS and VSS-LMS algorithms.

Fig. 6. Relation curve between step-sized parameters and e(n).

Fig. 7. (a) NFV of the proposed algorithm with different N (N = 20, 50, 100); (b) performance comparison between the proposed scheme (N = 50, 100), the 2048-FFT-based FOE, and the DA-FOE using 50\100\600 training symbols.

Fig. 8. (a) Convergence process of the proposed AEQ (N = 100); (b) residual phase noise at the output of the AEQ (N = 100). The constellation diagrams of the signals (c) before equalization, after equalization at (d) N = 50 and (e) N = 100, and (f) after phase recovery (N = 100).

Fig. 9. (a) N versus NFV in the DA-FOE and the proposed scheme; (b) MSE curves using DA-FOE and conventional NDA equalization; DA-FOE and conventional DA equalization; and the proposed scenario (N = 100, M = 11, and frequency offset = 5 GHz).