Chromatic Dispersion Estimation Research Articles

Joint CD, DGD, and PDL Estimation Enabled by FrFT based Time-Frequency Reconstruction

A high-precision optical performance monitoring (OPM) scheme is proposed to achieve chromatic dispersion estimation (CDE), differential group delay (DGD) estimation, and polarization-dependent loss (PDL) estimation simultaneously for the long haul coherent optical fiber communication system. A time-frequency analysis method based on the fractional Fourier transformation (FrFT) is applied to the optical signal under different channel impairments to reconstruct the two-dimensional distribution images. Multi-task convolutional neural network (MT-CNN) is then adopted to extract the corresponding features of impairments and establish a solid relationship between the images and impairment quantities, thus can jointly estimate CD, DGD, and PDL. We validate in simulation the proposed estimation using 50GBaud PDM-16QAM, the mean absolute error (MAE) for CD, DGD, and PDL estimation is 114ps/nm, 0.26ps, and 0.072dB, and the monitoring window ranges from 1600∼48000ps/nm, 4∼100ps, and 0∼2dB, respectively. Simulation verification indicates that the proposed estimation method achieves high precision and robustness to ASE noise and fiber nonlinearity of self-phase modulation (SPM).

Training Free In-Service Chromatic Dispersion Estimation Using Power Spectrum Analysis for MZM Based IM/DD Optical Communication Systems

In high-speed optical fiber communications, chromatic dispersion (CD) estimation is essential for the monitoring and compensation of CD-induced impairments. Compared with coherent detection, in short-reach optical communication systems, intensity modulation/direct detection (IM/DD) is more widely used, and the existing dispersion estimation techniques usually require training signals or a large amount of data for curve fitting or machine learning. However, these methods cannot provide in-service estimation. This paper presents a novel technique for in-service CD estimation in IM/DD short-reach optical communication systems based on our derived analytical model. With the analytical model, the in-service CD estimation is realized via the direct power spectrum analysis of the received signal. Unlike previous studies that only work with single-frequency sinusoidal signals, the practical random data with the rectangular type of base waveform is considered in our model. Therefore, our method can be applied to the dispersion estimation of various pulse amplitude modulation (PAM) based systems. Our proposed training free in-service CD estimation method is verified and investigated, where results show that better than 0.5% accuracy in dispersion estimation can be achieved in optical communication systems with up to 40 GBaud data rate and 100 km transmission distance.

Low-Complexity and Highly-Robust Chromatic Dispersion Estimation for Faster-than-Nyquist Coherent Optical Systems

Faster-than-Nyquist (FTN) coherent optical transmission technology is considered to be an outstanding solution to achieve higher spectral efficiency (SE), larger capacity, and greater achievable transmission by using advanced modulation formats in concert with highly efficient digital signal processing (DSP) to estimate and compensate various impairments. However, severe inter-symbol interference (ISI) caused by tight FTN pulse shaping will lead to intractable chromatic dispersion (CD) estimation problems, as existing conventional methods are completely ineffective or exhibit unaffordable computational complexity (CC). In this paper, we propose a low-complexity and highly robust scheme that could realize accurate and reliable CD estimation (CDE) based on a designed training sequence (TS) in the first stage and an optimized fractional Fourier transform (FrFT) in the second stage. The training sequence with the designed structure helps us to estimate CD roughly but reliably, and it further facilitates the FrFT in the second stage to achieve accurate CDE within a narrowed searching range; it thereby results in very low CC. Comprehensive simulation results of triple-carrier 64-GBaud FTN dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) systems demonstrate that, with only overall 3% computational complexity compared with conventional blind CDE methods, the proposed scheme exhibits a CDE accuracy better than 65 ps/nm even under an acceleration factor as low as 0.85. In addition, 60-GBaud FTN DP quadrature phase shift keying (DP-QPSK)/16QAM transmission experiments are carried out, and the results show that the CDE error is less than 70 ps/nm. The advantages of the proposed scheme make it a preferable candidate for CDE in practical FTN coherent optical systems.

A Fast and Blind Chromatic Dispersion Estimation Based on Stepwise Optimal Order Search Method in Fractional Domain

A fast and low-complexity blind chromatic dispersion (CD) estimation method is proposed by a stepwise optimal order search of fractional Fourier transform (FrFT) in coherent optical communications. The method can track the cumulative dispersion over time in future dynamic and flexible scenarios. The validity of the FrFT method is verified by analogy to the field of CD estimation from the energy concentration property of the chirp signal, and the estimation equation of the CD value is obtained by parameter transformation. Numerical simulations have been carried out in the CD range of 1600 ps/nm to 32,000 ps/nm for 28 GBaud PM-QPSK and 14 GBaud PM-16QAM signals. The results show that the proposed algorithm achieves a high CD estimation accuracy with an average estimation error of less than 50 ps/nm within the 4096 sampling points and an order search interval of 0.0001. The effects of the polarization mode dispersion, optical signal-to-noise ratio and nonlinearity on CD estimation performance are discussed. In addition, the stepwise optimal order search method can achieve the purpose of greatly reducing the computational complexity under the premise of ensuring the accuracy of CD estimation.

Fast and blind chromatic dispersion estimation with one sample per symbol.

We propose a fast and blind chromatic dispersion (CD) estimation method by one sample per symbol after coherent detection. The CD estimation process is non-data aided, without the iterative scanning to obtain the CD values. Moreover, we identify that the proposed CD estimation method is transparent to the used modulation format and robust to the transmission impairments, including amplified spontaneous emission (ASE) noise and fiber nonlinearity. When the 35-GBaud DP-16QAM signal with a roll-off factor of 0.1 is transmitted over standard single mode fiber (SSMF) with a range from 320-km to 560-km, the error of CD estimation is less than 150-ps/nm under the condition of 8192 symbols used.

Joint Estimation of Symbol Rate and Chromatic Dispersion Using Delayed Multiplier for Optical Performance Monitoring

Symbol rate and chromatic dispersion (CD) are very important for optical performance monitoring. The CD, however, hinders the symbol rate detection. In this paper, we proposed a joint estimation of symbol rate and chromatic dispersion. We show that, when the signal conjugates and multiplies with the delayed replica, the spectral line can be restored. The proposed method provides a fast and simple solution for joint estimation as traditional tentative CD scanning is time consuming. The simulation shows that the root-mean-squared error (RMSE) for CD was 39.5 ps/nm and the symbol rate was 2.4 MHz. For the squared-root-raised-cosine (SRRC) pulse shape with a roll-off factor of 0.1, the experimental results show that 25,000 input samples were needed for an error-free estimation. The RMSE is 105.6 ps/nm and 63.5 kHz for CD and symbol rate, respectively.

Accurate Estimation of Chromatic Dispersion for Non-Degenerate Phase-Sensitive Amplification

A phase-sensitive amplifier (PSA) has the potential of low-noise optical amplification and nonlinear phase noise mitigation. For PSA operation, the chromatic dispersion (CD) that causes gain ripple must be compensated before amplification. We propose an accurate CD estimation method for non-degenerate PSAs (ND-PSAs). We experimentally demonstrated its effectiveness by using periodically poled LiNbO3 waveguides as amplification mediums. We first modified the conventional formula for the gain spectrum under residual CD conditions to be applicable to ND-PSAs by considering phase locking. We then experimentally described the effect of passband narrowing due to the gain ripple on the signal quality using a probabilistically shaped 64QAM signal. Furthermore, we applied the modified formula to CD estimation and compensation. As a result, accurate CD estimation on the sub-ps/nm order and gain-flattened spectrum over 3.5 THz were demonstrated with our method. We also propose a method for estimating residual CD from the gain variation among wavelength division multiplexing (WDM) channels. The possibility of adaptive compensation for CD was shown by carrying out WDM amplification.

Delay-Tap-Sampling-Based Chromatic Dispersion Estimation Method With Ultra-Low Sampling Rate for Optical Fiber Communication Systems

A cost-effective chromatic dispersion (CD) estimation method is proposed, which is based on the delay-tap sampling (DTS) technique in combination with periodic training sequences (PTS). By performing equivalent sampling of PTS, DTS-based CD estimation at ultra-low sampling rate can be realized, significantly reducing the cost and high-speed requirements of analog to digital converters (ADCs). In contrast to the existing Nyquist DTS-based CD estimation method, we construct the CD lookup table in the CD over-compensated region, which can be suitable for a dynamic range of OSNR conditions. The CD lookup table built from the simulation can be used in the experimental system with similar configurations directly, indicating that the suggested method is reasonable and highly feasible. Besides, with only 1.25 GSa/s sampling rate of ADCs (about 1/30 of the Nyquist sampling rate which is 40.28 GSa/s), both 20.14 GBaud quadrature-phase-shift-keying (QPSK) simulation and experimental systems demonstrate the feasibility of the method, with a 28 ps/nm maximum CD estimation error for the simulation and a 35 ps/nm maximum CD estimation error for the experiment when OSNR is fixed to 18 dB. Furthermore, we also investigate the robustness of our method under the condition of different amplifier spontaneous emission (ASE) noise and nonlinear noise. The proposed method shows great potential for making a remarkable cost reduction in CD monitoring.

Low-Complexity Adaptive Chromatic Dispersion Estimation Scheme Using Machine Learning for Coherent Long-Reach Passive Optical Networks

In the coherent long-reach passive optical networks (LRPON), it is crucial to propose cost-effective digital signal processing (DSP) technologies to reduce the overall complexity and power consumption. This paper has proposed a low-complexity chromatic dispersion (CD) estimation scheme based on deep neural networks (DNN) and the error vector magnitude (EVM). To add comparisons, the performances of CD estimation schemes using other two well-known machine learning algorithms including the k-nearest neighbor (KNN) and the decision tree (DT) have also been investigated. The simulation results show that the proposed CD estimation scheme is effective in the coherent LRPON with the quadrature phase shift keying (QPSK) and 16-ary quadrature amplitude modulation (QAM) systems at 14Gbaud rate, 28Gbaud rate and 56Gbaud rate. The comprehensive performances of the DNN outperform those of the KNN and the DT. The mean estimation error of the DNN is less than 20ps/nm within the 100 km access distance in the 28Gbaud QPSK/16QAM systems. What's more, compared with classical methods using the CD scanning and frequent domain equalizers (FDE), the computation complexity of the proposed CD estimation scheme based on the DNN-EVM has been respectively reduced by 72.3 times, 86.7 times and 2.8 times about the amount of multipliers, adders and comparators.

Chromatic Dispersion Estimation Based on CAZAC Sequence for Optical Fiber Communication Systems

We propose a chromatic dispersion (CD) estimation method based on constant amplitude zero-autocorrelation (CAZAC) sequence and fractional Fourier transform (FrFT) algorithm for optical fiber communication systems, which extends the application of CAZAC sequence. By applying FrFT on the CAZAC sequence signal, the optimal order is searched and employed to estimate the accumulated CD because that the CAZAC sequence shares similar properties with chirp signal. We demonstrate the feasibility of the proposed method by the simulation of a 28 GBaud polarization-division-multiplexed (PDM) quadrature phase-shift keying (QPSK) optical fiber communication system. The error of CD estimation is less than 70 ps/nm for the standard single mode fiber (SSMF) link of 2000 km with OSNR in the range of 10–20 dB and the launch power in the range of 0–4 dBm per channel in a five channel system. It shows that the method is robust to ASE noise and optical fiber nonlinearity. Furthermore, the proposed method has been experimentally verified with the error of CD estimation less than 50 ps/nm after 100–900 km fiber link transmission.

Deep Neural Network Based Chromatic Dispersion Estimation With Ultra-Low Sampling Rate for Optical Fiber Communication Systems

Fast and low-cost chromatic dispersion (CD) estimation is very important for fiber link that is dynamically reconfigurable in the next-generation optical networks. In this paper, a novel CD estimation method based on the deep neural network (DNN) with ultra-low sampling rate is proposed for the optical fiber transmission systems. The method can estimate CD for under-sampled signals by the trained DNN with a weighted average. To demonstrate the feasibility of the method, the simulation of a 28-GBaud five-channel optical fiber transmission system with 100–2000-km SSMF transmission is carried, where the sampling rate of the analog-to-digital converter (ADC) at the receiver is only 500 MHz. The results show that the maximum mean absolute error (MAE) of the estimated CD is less than 75 ps/nm with the reference cumulative CD from 1600 to 32000 ps/nm for QPSK and 16QAM signals. Meanwhile, the robustness of the proposed method is verified for amplifier spontaneous emission (ASE) and nonlinear (NL) noise. Furthermore, we experimentally demonstrated that the maximum MAE is less than 75 ps/nm when the transmission distance varies from 100 to 800 km in 20-GBaud QPSK optical fiber transmission system. In conclusion, the proposed DNN-based CD estimation method shows great potential for the cost-effective under-sampled systems.

Training Sequence-Based Chromatic Dispersion Estimation With Ultra-Low Sampling Rate for Optical Fiber Communication Systems

We present a novel method to estimate chromatic dispersion with ultra-low sampling rate based on training sequence. The under-sampling can be equivalent to over-sampling by splicing points with periodic sequence. The functional relationship between equivalent over-sampling rate and symbol rate, actual sampling rate and sequence period is deduced. To demonstrate the feasibility of the method, the simulation of a 28 GBaud QPSK optical fiber communication system is carried, in which 76 MSa/s sampling rate is equivalent to 66.5 GSa/s sampling rate. The results show that maximum estimation error is less than 160 ps/nm after 100 km to 2300 km SSMF transmission. We also demonstrate the robustness of the proposed method to amplified spontaneous emission and nonlinear noise in a three-channel optical fiber communication system. Moreover, the proposed method has been experimentally verified with a 20.5 GBaud QPSK system, 1.25 GSa/s sampling rate is equivalent to 51.25 GSa/s sampling rate, and estimation error is less than 100 ps/nm and 150 ps/nm after 100 km and 200 km SSMF transmission, respectively. The proposed method eliminates the requirement of high speed ADC and is cost effective, which can be used for optical performance monitoring.

Joint Time/Frequency Synchronization and Chromatic Dispersion Estimation With Low Complexity Based on a Superimposed FrFT Training Sequence

We design a new kind of fractional Fourier transform superimposed training sequence (TS) to simultaneously estimate linear distortions including chromatic dispersion (CD), timing offset (TO), and frequency offset (FO), etc. Without sacrificing additional spectrum efficiency, the scheme can reduce the computational complexity sharply compared to a regular estimation method. The feasibility of the proposed scheme is verified by simulations of 28 GBaud dual polarization quadrature phase-shift keying (DP-QSPK) and 16-ary quadrature amplitude modulation (DP-16 QAM) system. Simulation results show that the superimposed TS has negligible negative effects on the transmission performance considering 7% forward error correction while the TO, FO, and rough CD estimation perform well after a long distance transmission. The max TO estimation (TOE) errors are, respectively, eight samples and 12 samples for QPSK and 16 QAM, and the max FO estimation errors are, respectively, 5.7 and 3.6 MHz for QPSK and 16 QAM. The rough CD estimation (CDE) error is below 946 ps/nm. The TOE and rough CDE separately decrease the complexity of frame synchronization and CDE. In total, the computation complexity of the estimations decreases by 91.8% compared to a regular blind estimation method.

Chromatic dispersion estimation based on heterodyne detection for coherent optical communication systems

We propose an accurate and nondata-aided chromatic dispersion (CD) estimation method involving the use of the cross-correlation function of two heterodyne detection signals for coherent optical communication systems. Simulations are implemented to verify the feasibility of the proposed method for 28-GBaud coherent systems with different modulation formats. The results show that the proposed method has high accuracy for measuring CD and has good robustness against laser phase noise, amplified spontaneous emission noise, and nonlinear impairments.

Fractional Fourier Transformation-Based Blind Chromatic Dispersion Estimation for Coherent Optical Communications

In this paper, we propose and demonstrate a blind chromatic dispersion (CD) estimation method based on fractional Fourier transformation (FrFT). Through numerical simulations, the proposed CD estimation method is shown to be robust against the amplified spontaneous emission noise and nonlinear interference. Only 2048 samples are required for reliable CD estimation for single-carrier 28 GBd DP-QPSK or 32 GBd DP-16QAM signals, and the standard deviation can be as low as 98.9 and 103.6 ps/nm, respectively. The feasibility of the proposed CD estimation method has been experimentally verified using 28 GBd DP-QPSK and 14 GBd DP-16QAM signals over various transmission distances with CD ranges of 46 332–77 220 ps/nm and 5148–51 480 ps/nm, respectively. Compared with some other CD estimation methods, the method based on FrFT has advantages in the aspects of less computation complexity and robustness to transmission impairments.

Analogue‐to‐digital converter phase insensitive dispersion search method with large search step size for low computational cost

Accumulated chromatic dispersion (CD) estimation is crucial for frequency-domain equalisation in an optical coherent digital receiver. To solve the problems of small search step size and analogue-to-digital converter (ADC) sampling phase sensitivity from conventional CD searching algorithm, a CD searching method with modified shift parameters and waveforms is proposed in this study. The modified CD searching method allows a much larger search step size and can achieve faster CD estimation with low computational complexity. The performance of the modified CD searching method is also insensitive to ADC sampling phase. On the basis of simulation results, a very low search error probability is confirmed with a search step size of 50 km. About 1 K symbols are found to be enough for dispersion estimation. After the frequency-domain equaliser (FDE) with the estimated dispersion value, the residual dispersion length <30 km can be well compensated with a 9-tap adaptive time-domain equaliser (TDE) with fast convergence. The overall error rate performance of the tunable electrical dispersion compensation is also studied and compared with lumped and distributed optical dispersion compensation for dynamically switched optical networks.

Fast and adaptive chromatic dispersion compensation scheme for digital coherent systems utilizing two-stage estimation.

A two-stage fast and adaptive chromatic dispersion (CD) estimation algorithm is proposed and demonstrated for coherent polarization-division-multiplexed (PDM) systems. The first stage uses signal power auto-correlation function for the coarse estimation while the second stage utilizes a modified constant modulus algorithm (MCMA) to obtain much more accurate accumulated CD. Simulation results show that the proposed algorithm is sufficient for CD estimation in non-dispersion-managed optical transmission of 112-Gb/s PDM-QPSK or 224-Gb/s PDM-16QAM signals. The concept is further experimentally verified in a 40-Gb/s PDM-QPSK system. Only ~7% estimation time is required to achieve similar accuracy compared to previous MCMA algorithm.

Fast and robust chromatic dispersion estimation based on temporal auto-correlation after digital spectrum superposition.

We investigate and experimentally demonstrate a fast and robust chromatic dispersion (CD) estimation method based on temporal auto-correlation after digital spectrum superposition. The estimation process is fast, because neither tentative CD scanning based on CD compensation nor specific cost function calculations are used. Meanwhile, the proposed CD estimation method is robust against polarization mode dispersion (PMD), amplified spontaneous emission (ASE) noise and fiber nonlinearity. Furthermore, the proposed CD estimation method can be used for various modulation formats and digital pulse shaping technique. Only 4096 samples are necessary for CD estimation of single carrier either 112 Gbps DP-QPSK or 224 Gbps DP-16QAM signal with various pulse shapes. 8192 samples are sufficient for the root-raised-cosine pulse with roll-off factor of 0.1. As low as 50 ps/nm standard deviation together with a worst estimation error of about 160 ps/nm is experimentally obtained for 7×112 Gbps DP-QPSK WDM signal after the transmission through 480 km to 9120 km single mode fiber (SMF) loop using different launch powers.

Coded-subcarrier-aided chromatic dispersion monitoring scheme for flexible optical OFDM networks.

A simple coded-subcarrier aided scheme is proposed to perform chromatic dispersion monitoring in flexible optical OFDM networks. A pair of coded label subcarriers is added to both edges of the optical OFDM signal spectrum at the edge transmitter node. Upon reception at any intermediate or the receiver node, chromatic dispersion estimation is performed, via simple direct detection, followed by electronic correlation procedures with the designated code sequences. The feasibility and the performance of the proposed scheme have been experimentally characterized. It provides a cost-effective monitoring solution for the optical OFDM signals across intermediate nodes in flexible OFDM networks.

Experimental evaluation of chromatic dispersion estimation method using polynomial fitting

We experimentally validate a non-data-aided, modulation-format independent chromatic dispersion (CD) estimation method based on polynomial fitting algorithm in single-carrier coherent optical system with a 40Gb/s polarization-division-multiplexed quadrature-phase-shift-keying (PDM-QPSK) system. The non-data-aided CD estimation for arbitrary modulation formats is achieved by measuring the differential phase between frequency f±fs/2 (fs is the symbol rate) in digital coherent receivers. The estimation range for a 40Gb/s PDM-QPSK signal can be up to 20,000ps/nm with a measurement accuracy of ±200ps/nm. The maximum CD measurement is 25,000ps/nm with a measurement error of 2%.