State Of Polarization Rotation Research Articles

Joint equalization of RSOP and PMD fused probability-aware with square-root cubature Kalman filter for the PDM PCS-64QAM system under extreme scenarios.

Extreme scenario of lightning strikes would generate ultra-fast rotation of state-of-polarization (RSOP) up to 5.1 Mrad/s and large polarization mode dispersion (PMD) in optical ground wire (OPGW). Unfortunately, the conventional multiple modulus algorithm (MMA) cannot equalize these polarization impairments in polarization division multiplexing (PDM) probabilistic constellation shaping (PCS)-64QAM system. Moreover, due to unavoidable linearization errors and higher modulation order, the extended Kalman filter based on measurement equations of concatenated multiplication (EKF-CM) is highly unstable and fails under such scenarios. To address the above issues, we have proposed a joint equalization scheme of PMD and RSOP, which fuses probability-aware with square-root cubature Kalman filter (PA-SCKF). Firstly, according to the characteristic that the amplitude of PCS signals obeys mixed Rician distribution, the scheme combines maximum a posteriori criterion to obtain the optimal radius of constellation ring which the received symbol belongs to, for the sake of calculating the innovations of SCKF. Secondly, it performs joint equalization of PMD and RSOP impairments based on SCKF and time-frequency conversion architecture. 28GBaud PDM PCS-64QAM simulation results demonstrate that our scheme can jointly equalize maximum impairments of 8.34 Mrad/s RSOP and 90ps DGD under entropy of 4.5bits/symbol. Additionally, only 0.9 dB OSNR penalty is obtained after joint equalization of 6 Mrad/s RSOP with 70ps DGD impairments. Even under entropy of 5.5bit/symbol, it can still jointly equalize impairments of 6.05 Mrad/s RSOP with 60ps DGD. Furthermore, 16GBaud PCS-64QAM experimental results indicate that the maximum joint equalization performances of PA-SCKF scheme under entropy of 4.5bit/symbol and 5bit/symbol are 17 Mrad/s RSOP with 52ps DGD, and 9 Mrad/s RSOP with 52ps DGD, respectively. These results manifest that our PA-SCKF scheme outperforms both MMA and EKF-CM schemes. Importantly, its complexity is on an order of O(Llog2 L), which is comparable to that of EKF-CM scheme.

Physical layer encryption for coherent PDM system based on polarization perturbations using a digital optical polarization scrambler.

In this paper, a security enhanced physical layer encryption scheme is proposed for coherent optical polarization division multiplexing (PDM) systems. The concept of a digital optical polarization scrambler (DOPS) is introduced to apply high speed rotation of state of polarization (RSOP) to the transmitted signal, which enables encryption based on polarization perturbations and offers superior flexibility in polarization management. By utilizing different combinations of digital polarization device matrices and adjusting their key parameters, four encryption modes are designed. The proposed encryption scheme is successfully implemented in a PDM-QPSK system at the data rate of 32 Gbps. Experimental results demonstrate that authorized users can successfully decrypt the received signal, while the eavesdroppers cannot derive useful information with a bit error rate (BER) at approximately 0.5. To enhance system security, a 5-D chaotic system is introduced with superior properties of high sensitivity to initial values and improved uniform distribution, which guarantees the large entropy and further the system's security. This scheme can effectively prevent against brute attacks with the expanded key space of 1060.

Joint PMD Tracking and Nonlinearity Compensation With Deep Neural Networks

Overcoming fiber nonlinearity is one of the core challenges limiting the capacity of optical fiber communication systems. Machine learning based solutions such as learned digital backpropagation (LDBP) and the recently proposed deep convolutional recurrent neural network (DCRNN) have been shown to be effective for fiber nonlinearity compensation (NLC). Incorporating distributed compensation of polarization mode dispersion (PMD) within the learned models can improve their performance even further but at the same time, it also couples the compensation of nonlinearity and PMD. Consequently, it is important to consider the time variation of PMD for such a joint compensation scheme. In this paper, we investigate the impact of PMD drift on the DCRNN model with distributed compensation of PMD. We propose a transfer learning based selective training scheme to adapt the learned neural network model to changes in PMD. We demonstrate that fine-tuning only a small subset of weights as per the proposed method is sufficient for adapting the model to PMD drift. Using decision directed feedback for online learning, we track continuous PMD drift resulting from a time-varying rotation of the state of polarization (SOP). We show that transferring knowledge from a pre-trained base model using the proposed scheme significantly reduces the re-training efforts for different PMD realizations. Applying the hinge model for SOP rotation, our simulation results show that the learned models maintain their performance gains while tracking the PMD.

A Novel Pilot-Aided Timing Recovery Algorithm With High Tolerance to Impairments for OQAM-Based Digital Multi-Band Systems

Timing recovery (TR) plays an important role in the digital signal processing (DSP) of coherent receivers. In TR, timing error (TE) is extracted by the timing recovery algorithm (TRA) and fed back to adjust the clock sampling phase. However, widely-used Gardner and Godard TRAs are sensitive to spectral roll-off factor and differential group delay (DGD), and more importantly, are inapplicable to the offset quadrature amplitude modulation (OQAM) system. In this paper, we propose a novel pilot-aided TRA for the OQAM-based digital multi-band (OQAM-DMB) system, which is robust to different impairments including rotation of state of polarization (RSOP), DGD, spectral roll-off, residual chromatic dispersion (rCD), residual carrier frequency offset (RFO), and laser linewidth. 1.12-Tbit/s simulations and 320-Gbit/s experiments show that OQAM-DMB based on the proposed algorithm works properly for all spectral roll-off factors and exhibits excellent tolerance against DGD, RSOP, rCD, RFO, and laser linewidth, and outperforms QAM-DMB using conventional TRAs. The digital phase-lock loop can be locked for the clock frequency offset within ±80 ppm and all initial sampling phase offsets. Although investigated in OQAM-DMB, the proposed algorithm is also applicable to conventional QAM-DMB.

Joint equalization of EEPN, RSOP, and CD with the sliding window assisted extended Kalman filter for a high baud rate Stokes vector direct detection system.

Equalization-enhanced phase noise (EEPN) has emerged as one of the major impairments that cannot be ignored for a high baud rate Stokes vector direct detection (SVDD) system. When EEPN interacts with the rotation of state-of-polarization (RSOP) and chromatic dispersion (CD), the joint impairment effects become even more complicated. To achieve the joint equalization of EEPN, RSOP, and CD impairments of a high baud rate SVDD system, this paper first derives a joint impairment model of these three kinds of impairments, and then proposes a joint equalization scheme of EEPN, RSOP, and CD with a sliding window assisted extended Kalman filter (SWA-EKF). The SWA-EKF scheme first tracks RSOP in the time domain, subsequently compensates CD in the frequency domain, and finally performs EEPN mitigation in the time domain again. The effectiveness of the proposed scheme has been verified by a 60 GBaud SVDD-16QAM simulation system. The results show that when these three impairments are jointly equalized, the SWA-EKF scheme can track RSOP as fast as 3Mrad/s, cumulative dispersion up to 1600ps/nm, and EEPN caused by laser linewidth up to 3MHz. In addition, with an optical signal-to-noise ratio penalty of 0.3dB, it could increase 35G baud rate under 3MHz laser linewidth for the SVDD system. More importantly, its total complexity can be reduced to an order of O(N log N).

60 Gb/s coherent optical secure communication over 100 km with hybrid chaotic encryption using one dual-polarization IQ modulator

We propose and experimentally study a coherent optical secure transmission system based on one dual-polarization in-phase and quadrature modulator (IQM). One beam of the polarized light is used to generate broadband chaos by configuring a nonlinear opto-electronic oscillator while the other beam carries the encrypted signal. The encrypted signal is obtained through sequential encryption of the analog and digital chaos. The mutual mask of the hybrid chaotic signals can effectively enhance the security performance. Moreover, by varying the encryption depth of analog and digital vectors, the transmission performance can be flexibly adjusted. A commercial dual-polarization IQM could simultaneously generate a chaotic signal and a load message, which provides a high-integration solution. A fast independent component analysis (ICA) algorithm is adopted to compensate for the rotation of state of polarization (RSOP). 60 Gb/s encrypted quadrature phase shift keying (QPSK) signal transmission over 100 km single-mode fiber is realized, and the decrypted bit error rate (BER) performance is below the 7% forward error correction (FEC) threshold (BER = 3.8 × 10-3).

Integrated communication and polarization sensing in self-homodyne coherent systems.

We propose and demonstrate an integrated polarization sensing technique by fully exploiting the adaptive polarization controller (APC) in a self-homodyne coherent (SHC) communication system. By analyzing the APC control signal, the input state of polarization (SOP) can be fully restored. The effect of the polarization tracking results on sensing accuracy is carefully studied in simulation to determine the acceptable SOP rotation speed. We experimentally restore the SOP rotation trajectory using an APC, conduct a comparison with a polarization analysis instrument, and verify its potential as a polarization measurement. Finally, without additional components or burdening digital signal processing (DSP), in-service detections of up to 400-Hz vibration and 2.4-nε micro-strain are achieved in the operated SHC system with 400-Gb/s DP-16QAM transmission.

Joint estimation of dynamic polarization and carrier phase with pilot-based adaptive equalizer in PDM-64 QAM transmission system

A pilot-based adaptive equalizer is investigated for high cardinality polarization-division-multiplexing quadrature amplitude modulation transmission systems. Pilot symbols are periodically inserted for joint estimation of the dynamic state of polarization (SOP) and carrier phase, in a least mean square (LMS) sense. Compared to decision-directed least mean square (DDLMS) equalization and radially-directed equalization, the proposed equalizer can achieve robust equalization and phase estimation, especially in low optical signal-to-noise ratio (OSNR) scenarios. In an experiment on 56 GBaud PDM-64 QAM transmission over 400 km standard single-mode fiber, we obtained at least 0.35 bit per symbol generalized mutual information (GMI) improvement compared with other training symbol-based equalization when tracking 600 krad/s dynamic SOP. With the joint estimation scheme, the equalization performance will not be compromised even if the SOP speed reaches 600 krad/s or the laser linewidth approaches 2 MHz. For the first time, it is demonstrated that the pilot-based equalizer can track dynamic SOP rotation and compensate for fiber linear impairments without any cycle slips under extreme conditions.

Retarded field model for fast polarization rotations caused by lightning events

We study the fast state of polarization (SOP) rotation of lightwaves propagating in the fiber of optical ground wire under lightning-induced events because of the Faraday effect. Theoretical descriptions have been completed previously based on an instantaneously established uniform magnetic field time-profile. Here we describe more accurately the SOP rotation time-profile, using the retarded field model, taking into account the finiteness of the speed of light both in vacuum and in fiber. An expression for SOP rotation angle is found using the isotropic fiber approximation. Comparison of the retarded field model with the instantaneous field model is given for both sharp (pulse rise time ∼1 μs) and slow (∼10 μs) current pulses.

Fast tracking of polarization impairments using DSP algorithms in fiber for a coherent optical communication system

AbstractIn a 100G coherent optical fiber communication system, the equalization algorithm of polarization effects in fibers is generally integrated in digital signal processing (DSP) using a multiple input/multiple output (MIMO) equalizer to overcome the impairment due to the polarization effects in fiber. However, it was found in some extreme scenarios, such as the lightning strikes near the fiber cables, the Kerr effect and Faraday effect would induce very fast time‐varying state‐of‐polarization (SOP) and transient variation of principal‐state‐of‐polarization (PSP) of polarization mode dispersion (PMD) which would result in the coherent receivers unlocking. Faced with the difficulty, we propose a 3‐parameter RSOP model and design a window‐split structured Kalman filter equalization scheme instead of conventional MIMO equalizer to cope with this extreme scenario of large PMD combined with ultra‐fast rotation of SOP in presence of residual chromatic dispersion (RCD). The proposed equalization method has an excellent performance and can cope with RCD in the range of ±820 ps/nm under RSOP from 100 krad/s to 3 Mrad/s and DGD = 200 ps.

Joint equalization of CD and RSOP using a time–frequency domain Kalman filter structure in Kramers–Kronig system

Kramers–Kronig (KK) system is a direct detection (DD) optical short-reach interconnection system which is suitable for high capacity data center interconnect (DCI) applications. For this kind of short-reach high capacity polarization-division multiplexing (PDM) optical transmission system, the fiber channel impairments contain chromatic dispersion (CD) and rotation of state of polarization (RSOP) will lead to a severe signal distortion and need to be equalized. This paper proposed a time–frequency domain Kalman filter scheme for joint equalization of CD and RSOP simultaneously in KK system. The proposed scheme is capable of tracking the fast RSOP in time domain and equalizing CD in frequency domain using a window-split structure. The performance of the Kalman scheme is investigated in a 28GBaud PDM 16QAM DD system with KK receivers. The simulation results prove that the proposed Kalman scheme exhibits a good performance of RSOP tracking ability up to speed of 2.5 Mrad/s, with a large accumulated CD tolerance as large as 2040 ps/nm at a low OSNR penalty. The results also show the proposed scheme has a comparable computational complexity compared with a generally used scheme which includes a CD compensation, combined with polarization demultiplexing algorithm constant modulus algorithm (CMA) and multiple modulus algorithm (MMA).

Experimental Investigation on Low-Complexity Adaptive Equalizer Including RSOP Tracking and Phase Recovery for 112 Gb/s PDM-QPSK Transmission System

A low-complexity adaptive equalizer including equalization, rotation of state of polarization (RSOP) tracking, and phase recovery is proposed for coherent optical polarization-division-multiplexing (PDM) quadrature phase-shifting keying (QPSK) transmission system. A conventional N-tap 2 × 2 butterfly finite impulse response filter is simplified to two N-tap filters and a 1-tap 2 × 2 filter. Two N-tap filters could compensate for inter-symbol interference and residual chromatic dispersion based on the same error cost function from the power sum of two polarization coupling constant modulus signals. 1-tap 2 × 2 filter which works on the nonlinear principal component analysis (NPCA) criterion is designed for joint polarization demultiplexing and phase recovery. NPCA is proved to not only void the singularity problem in the constant modulus algorithm (CMA) but also has faster tracking capability. Two kinds of adaptive equalizers using least mean squares NPCA (LMS-NPCA) and recursive least squares NPCA (RLS-NPCA) are compared in our simulation and experiment. In an experiment of 112 Gb/s PDM-QPSK transmission over 50 km standard single-mode fiber, the proposed two schemes have better transmission performance at RSOP speed of 1 Mrad/s and 5 Mrad/s compared to the conventional CMA and Viterbi-Viterbi phase estimation (VVPE) scheme. The reduced complexity of the proposed schemes is more than 40%.

Ultra-fast RSOP tracking via 3 pilot tones for short-distance coherent SCM systems.

We propose an algorithm to track the rotation of state of polarization (RSOP) for short-distance coherent subcarrier-multiplexing systems. 3 pilot tones are used to estimate RSOP matrices on a block-by-block basis and recover phase noise as well. An ultra-fast RSOP tracking ability using the proposed algorithm is demonstrated by experiment. Specifically, the bit error rate increases from 2.3×10-3 to 5.6×10-3 when the RSOP speed increases from 0 rad/s to 50 Mrad/s. We also demonstrate the robustness of the algorithm against polarization mode dispersion and polarization dependent loss.

Out-of-band pilot-tone-based SOP tracking in polarization diversity optical access network transmission

A polarization diversity-based PON system can be an attractive network solution for the future PON system that requires high data capacity with both a large number of subscribers and longer transmission-reach. However, the state-of-polarization (SOP) inevitably rotates during the transmission through the single-mode fiber (SMF). Therefore, this system cannot ensure high data capacity owing to the SOP rotation. In this paper, we propose the out-of-band pilot-aided SOP rotation tracking technique for in the polarization diversity-based PON transmission system. The proposed technique tracks the SOP rotation by measuring the variance of the power ratio of the inserted pilot-tone at the reference polarization axis. This technique offers the advantages of a low overhead and dynamic update for SOP variation; further, it is optical control-free and transparent for data format. For the experimental demonstration of the SOP rotation compensation, the pilot insertion was firstly optimized and the correctable range of the SOP rotation was analyzed. The results of the emulation of the uplink transmission indicated that the SNR at both polarization axes could be successfully retained by compensating the SOP rotation. Under the target forward error correction limit, the SE up to 8 bit/s/Hz within single-wavelength was obtained for 60 km PON transmission.

SOP Change Robust Optical Modulation Based on Dual Polarization Modulation for Multi-Dimensional Optical Transmission

In optical transmission technique using optical polarization, the change of state of polarization (SOP) and the rotation of SOP (RSOP) during optical transmission has a significant impact on the transmission performance. We propose polarized intensity rotational frequency shift keying (PIR-FSK) as a novel modulation technique in change of SOP and RSOP-tolerant optical transmissions. The proposed PIR-FSK signal does not affect the entire intensity of the optical carrier by modulating the sinusoidal signals on each X and Y-polarized optical carrier. Therefore, the proposed PIR-FSK modulation and optical carrier intensity modulation can operate at the same time. Moreover, since the proposed technique does not modulate the signal using the SOP unlike the PolSK, PIR-FSK is not affected by SOP changes that occur during transmission, and the signal does not be degraded even with RSOP. We demonstrated that the signals modulated using the proposed PIR-FSK modulation have higher signal capacity and efficiency compared to the signal modulated using PolSK modulation.

Time Reverse Equalization Algorithm for 16 QAM Coherent Optical Communication Systems

The high speed rotation of state of polarization (RSOP) is a key issue for 16 quadrature amplitude modulation (QAM) coherent optical polarization division multiplexing (PDM) communication systems in strong lightning weather. To reduce the bit error rate (BER) caused by the high speed of RSOP, the historical information is first proposed to correct the demodulation process in coherent optical communication systems. By adding the time reverse error term into the cost function, a new equalization algorithm is proposed for coherent optical communication systems. Compared with the conventional Multi-modulus Algorithm (MMA), simulation results show that the average BER and steady-state error (SSE) of the new algorithm is reduced by 33.47% and 4.08%, respectively. Moreover, the average tolerance of RSOP of the new algorithm is increased by 28.57% compared with the MMA in 16 QAM coherent optical PDM communication systems.

Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200 km transmission link.

A deep learning (DL) based digital backpropagation (DBP) method with a 1 dB SNR gain over a conventional 1 step per span DBP is demonstrated in a 32 GBd 16QAM transmission across 1200 km. The new DL-DPB is shown to require 6 times less computational power over the conventional DBP scheme. The achievement is possible due to a novel training method in which the DL-DBP is blind to timing error, state of polarization rotation, frequency offset and phase offset. An analysis of the underlying mechanism is given. The applied method first undoes the dispersion, compensates for nonlinear effects in a distributed fashion and reduces the out of band nonlinear modulation due to compensation of the nonlinearities by having a low pass characteristic. We also show that it is sufficient to update the elements of the DL network using a signal with high nonlinearity when dispersion or nonlinearity conditions changes. Lastly, simulation results indicate that the proposed scheme is suitable to deal with impairments from transmission over longer distances.

Performance of momentum-based frequency-domain MIMO equalizer in the presence of feedback delay.

A frequency-domain multiple-input multiple-output (FD-MIMO) equalizer employing a momentum-based gradient descent update algorithm is proposed for polarization multiplexing coherent receivers. Its performance in operation with dynamically varying optical channels is investigated and the impact of filter update delays, arising from the latency of the fast Fourier transforms (FFTs) and other digital signal processing (DSP) operations in the feedback loop, is assessed. We show that the proposed momentum-based gradient descent algorithm used to control the equalizer response has significantly greater tolerance to feedback delay than the conventional gradient descent algorithm. We considered a 92 Gbaud dual-polarization 64 QAM receiver, with DSP operating at two samples per symbol, and with the equalizer operating on blocks of 512 and 1024 samples (i.e., 512/1024-point FFT). We found that at an optical signal-to-noise power ratio (OSNR) of 35 dB, the momentum-based gradient descent algorithm can successfully track state-of-polarization (SOP) rotation at frequencies of up to 50 kHz and with filter update delays of up to 14 blocks (39 ns). In comparison, using the conventional gradient descent algorithm in an otherwise identical receiver, the equalizer performance starts to deteriorate at SOP rotation frequencies above 20 kHz.

True Equalization of Polarization-Dependent Loss in Presence of Fast Rotation of SOP

In an optical fiber communication system, polarization-dependent loss (PDL), referring to polarization-dependent optical power attenuation, might be a main system performance limiting factor. PDL causes a difference in signal power and imbalance of optical signal-to-noise ratio (OSNR) between the two polarization branches. The OSNR asymmetry will eventually deteriorate the overall system performance. At present, most of the equalization methods of PDL in the literature can only accomplish power imbalance equalization and are, thus, not the true equalization of PDL. Besides, in some extreme environments, like lightning strikes, Kerr and Faraday effects would generate ultra-fast rotation of state of polarization (RSOP), as fast as mega-radian per second. The fast RSOP in combination with PDL makes the eigenmodes of the PDL randomly time-varying, which will put a heavy burden on the equalization module of the receiver. Faced with this dilemma, in this paper, we propose a scheme for the true equalization of PDL in the presence of fast RSOP through an approach based on the combination of the polarization-time code and Kalman filter. The proposed approach is proved to be very effective and provides significant performance. With a 1.2 dB OSNR penalty, it can jointly equalize large PDL (7 dB) and fast RSOP (up to 1 Mrad/s).

Adaptive Blind Stokes-Space Based Equalizer for RSOP in SV-DD Systems With High Chromatic Dispersion Tolerance

Polarization de-multiplexing becomes challenging in Stokes vector-direct detection (SV-DD) systems, especially when the rotation of state of polarization (RSOP) and fiber chromatic dispersion (CD) are induced. To address this issue, an adaptive blind RSOP equalizer based on Stokes space is proposed. After theoretical analysis, it is found that the distribution of transmitted signals in Stokes space keeps a paraboloid. Based on this analysis, an adaptive scheme is proposed to track the symmetry axis of paraboloid for the first time. It is worth noticing that not only CD but also high-order modulation formats could not change the paraboloid distribution. Therefore, our algorithm has strong robustness to CD and good suitability for SV-DD systems with different modulation formats. In our simulation, the conventional Stokes space-based method and the training sequences (TS) method are both evaluated for comparison. The results show that our scheme can track RSOP of 20 Mrad/s and 8 Mrad/s at hard-decision forward error correction threshold in 28 Gbaud 4-level quadrature amplitude modulation (4-QAM) and 16-QAM SV-DD systems after 100 km fiber transmission, respectively. No additional computational complexity is required compared to the conventional Stokes space-based method. Moreover, compared to the TS-based method, there is no need to know the actual channel information, contributing to good flexibility.