Under singularity conditions, the S-curve slope of timing recovery algorithms based on signal power approaches zero, hindering the timing error detector’s ability to extract timing errors accurately and establish an effective timing synchronization loop. Additionally, impairments from inter-symbol interference (ISI), residual chromatic dispersion (CD), differential group delay (DGD), and sample clock offset increase the convergence cost of establishing the timing synchronization loop. Previous research indicates that timing recovery algorithms suitable for faster-than-Nyquist (FTN) systems struggle to establish effective timing synchronization loops under singularity conditions. This paper addresses these challenges by proposing an anti-singularity and low convergence scheme for polarization demultiplexing and timing recovery based on orthogonal training sequences, analyzing the underlying principles of clock recovery algorithm limitations under singularity conditions.

This paper presents a joint scheme for polarization demultiplexing and timing recovery utilizing orthogonal training sequences, designed for low convergence cost and anti-singularity performance. The scheme calculates the channel matrix representing polarization crosstalk using orthogonal training sequences to mitigate singularity effects on the timing recovery algorithm. An adaptive equalization algorithm integrated within the timing loop compensates for inter-symbol crosstalk, residual chromatic dispersion, and differential group delay impairments before timing error calculation, enabling accurate determination of timing error adjustment direction. This approach reduces the convergence cost for establishing timing synchronization. The loop filter module generates control words based on timing errors, while the control unit calculates basic pointers and fractional intervals to guide the interpolation filter’s timing recovery process. Through continuous iteration of the timing feedback loop, the fractional interval stabilizes into periodic changes, and the root mean square of timing error detection converges to zero, indicating synchronization.

To validate the proposed scheme, a triple-carrier 64 Gbaud polarization-multiplexed 16-ary quadrature amplitude modulation (PM-16QAM) FTN-WDM wavelength-division multiplexing (WDM) simulation platform was established in this paper. The simulation results demonstrate that the proposed algorithm could achieve timing recovery under singularity conditions [Fig. 5(f)]. Under 800 km transmission distance and 0.90 and 0.85 acceleration factor, the proposed scheme could reduce the convergencecost at least 39%/41%, respectively, comparedto conventional scheme (Fig. 6). Furthermore, under the same conditions, the proposed scheme improves the OSNR tolerance by 0.4 dB and 0.6 dB (@64 Gbaud PM-16QAM FTN, B_BER=2×10^-2) compare with the conventional scheme (Fig. 7). Additionally, offline experimental results for a triple-carrier 40 Gbaud PM-16QAM FTN system reveal that under 0.90 and 0.85 acceleration factor, the proposed scheme could reduce the convergence cost required forestablish timing synchronization loop by at least 37%/38%, respectively, compared to the conventional scheme (Fig. 10). Moreover, under 800 km transmission and 0.90 and 0.85 acceleration factor, the proposed scheme achieves OSNR tolerance improvements of 0.50 dB and 0.75 dB (@40 Gbaud PM-16QAM FTN B_BER=2×10^-2) compare with the conventional scheme (Fig. 11).

The proposed scheme demonstrates reduced computational complexity, approximately 28% lower than the conventional scheme (which includes adaptive equalization, polarization demultiplexing algorithm, and squared Gardner phase detector timing recovery algorithm), while requiring only 2.9% training sequences under identical acceleration factor, DGD, and azimuth conditions (Table 1).

This research presents an anti-singular and low convergence cost scheme for polarization demultiplexing and timing recovery based on orthogonal training sequence (TS). The proposed approach effectively achieves polarization demultiplexing under singularity conditions using orthogonal TS. The integration of adaptive equalization before timing error detection compensates for DGD, ISI, and residual CD impairments, significantly reducing convergence cost. The scheme requires approximately 2.9% TS overhead while achieving 28% reduction in computational complexity compared to conventional methods. Simulation results for 64 Gbaud PM-16QAM FTN-WDM demonstrate convergence cost reductions of 39%/41% at 0.90 and 0.85 acceleration factors over 800 km transmission, with OSNR tolerance improvements of 0.4 dB and 0.6 dB (@64 Gbaud PM-16QAM FTN B_BER=2×10^-2). Offline experiments with triple-carrier 40 Gbaud PM-16QAM FTN-WDM show OSNR tolerance improvements of 0.50 dB and 0.75 dB (@40 Gbaud PM-16QAM FTN B_BER=2×10^-2) at 800 km transmission with 0.90 and 0.85 acceleration factors. These results confirm the proposed scheme’s effectiveness in achieving low convergence cost and anti-singular polarization demultiplexing and timing recovery in FTN systems.