An optimized principal component-based phase estimation (OPCPE) algorithm is proposed for probabilistically shaped (PS) square-quadrature amplitude modulation (QAM) systems. The optimization method is based on mirroring and partially scaling the received constellation. Numerical simulation validation shows that the proposed phase recovery algorithm outperforms the well-known blind phase search (BPS) algorithm at low signal-to-noise ratio (SNR) and solves the incompatibility between principal component-based phase estimation (PCPE) and PS at high SNR. It's worth mentioning that the proposed algorithm retains the advantages of low cycle slip rate (CSR) and low computational complexity of PCPE. Furthermore, the performance of a hybrid implementation combining the proposed algorithm and BPS is also investigated. When the shaping parameter for a PS-64QAM system is 0.05, the proposed simple and hybrid methods can achieve performance improvements around 0.34-dB and 0.61-dB respectively benchmarking the widely used two-stage BPS (2S-BPS), considering the 0.8 normalized generalized mutual information (NGMI) threshold. To the best of our knowledge, this is the first time to robustly apply PCPE algorithm to PS systems, and the proposed design has stable NGMI performance, strong cycle slip tolerance and low computational complexity, which makes it a suitable candidate for practical probabilistically-shaped transmissions.

This paper proposes a novel method to improve the anti-dispersion ability of the all-optical orthogonal frequency division multiplexing (AO-OFDM) system. By replacing the Sinc-shaped filter with a Gauss-shaped filter for sub-carrier generation and inserting a cyclic prefix (CP), the impact of dispersion on the system can be significantly mitigated. Formula derivation and numerical analysis of the pulse-shaping function of the AO-OFDM system in the time domain for each cycle indicated that the pulse-shaping function generated by the Gauss-shaped filter was less affected by the dispersion effect than that of the Sinc-shaped filter. Meanwhile, less inter-carrier crosstalk between carriers was also observed. After carrying out system transmission simulations employing these two different filters, we found that the AO-OFDM system based on the Gauss-shaped filter could greatly improve the anti-dispersion ability compared with the system based on a Sinc-shaped filter. When the parameter settings in both schemes were identical, that is, the number of subcarriers was 32 and the power of a single subcarrier was −13 dBm, the bit error rate (BER) of the system based on the proposed Gauss-shaped filter after 60 km SMF transmission was only 1.596 × 10⁻³, while the BER of the traditional Sinc-shaped filter based system scheme was as high as 8.545 × 10⁻².

For high-speed optical communication systems, laser phase noise (LPN) stands as a pivotal factor influencing the quality of the received signal. Therefore, the employment of a highly accurate carrier phase recovery (CPR) algorithm at the receiving end is indispensable to ensure the reliability of transmission. While a CPR algorithm called principal component-based phase estimation (PCPE) has been proven to be capable of achieving low-complexity and high-performance phase recovery for even-bit quadrature amplitude modulation (QAM) (i.e., square QAM) signals, it is not compatible with traditional cross-shaped odd-bit QAM signals. To circumvent this problem, a signal constellation design scheme based on geometric shaping (GS) is proposed. The pair-wise optimization (PO) algorithm is used to optimize the constellation structure of 32QAM and 128QAM signals in order to obtain results that are compatible with the PCPE algorithm. Monte Carlo simulation results reveal that for odd-bit QAM signals utilizing PCPE for phase recovery, the proposed GS constellations enhance the mutual information (MI) performance across the entire measured signal-to-noise (SNR) range. Moreover, compared with regular 32QAM and 128QAM constellations using the well-known blind phase search (BPS) algorithm, the proposed GS and PCPE scheme can achieve SNR gains of 1.10 dB and 2.59 dB, respectively, when considering the 20% soft-decision forward error correction (SD-FEC) overhead. Verification through commercial simulation software corroborates these findings, demonstrating that the proposed GS constellations are particularly suitable for the PCPE algorithm, especially under conditions of high optical signal-to-noise ratio (OSNR). To the best of our knowledge, this is the first time that the incompatibility between the PCPE algorithm and odd-bit QAM signals has been investigated, and the proposed GS scheme has broadened the application scope of the low-complexity CPR algorithm.

In this paper, a method to suppress the impact of the nonlinear effects on an all optical orthogonal frequency division multiplexing (AO-OFDM) system is proposed. By inserting a guard interval (GI), the duty cycle of the optical signal in each symbol period of each subcarrier is decreased, thus generating a ‘zeroed’ temporal. By giving different time delays to the sub-carriers, these ‘zeroed’ temporals and optical signals of the adjacent sub-carriers are interleaved, which reduces the coincidence of the optical signals between the sub-carriers and eliminates the products of the four-wave mixing (FWM) effect to suppress the influence of the nonlinear effect on the system. The simulation results show that for an AO-OFDM system with 32 subcarriers, inserting GI and introducing different delays for each subcarrier can improve the transmission distance by 30 km or enhance the spectral efficiency by 16.7%, considering the 7% hard decision forward error correction (HD-FEC) threshold. Moreover, even when the number of subcarriers is up to 256 and the power of each subcarrier is as high as 0 dBm, our proposed signal optimization scheme can still guarantee that the BER can satisfy the 7% HD-FEC threshold.

Power unevenness, mainly induced by stimulated Raman scattering, has been a major problem in multi-band transmission systems, especially in the upcoming field-deployed 400 Gbit/s widened C band plus L band system for backbone long-haul and ultra-long-haul scenarios. To reduce the impact of power unevenness, we propose an automatic power optimization (APO) algorithm to guarantee reliable transmission for all channels, especially the channels at short wavelengths. The simulation results show that the power unevenness of output power after 5-span transmission in the C band is up to 11 dB before APO, while after APO is applied, it is greatly improved to less than 1.6 dB. To further investigate the performance of the APO scheme, we conduct a real-time 44 Tbit/s C+L transmission system over 1900 km G.654.E fiber utilizing 400 Gbit/s transponders. The experimental results show that the power unevenness has been effectively compensated from 12 dB to 4 dB in the entire 11 THz range, making the received optical signal-to-noise ratio relatively flat (3.4 dB). Moreover, the capacity and distance product of this system is 83.6 Pbit/s·km (44 Tbit/s × 1900 km), and to the best of our knowledge, this is a record capacity and distance product in the real-time single-mode fiber transmission system.