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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.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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.

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.

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.

This paper considers Godard's error as signal quality metric to monitor chromatic dispersion (CD), nonlinear parameter and modulation format in the DSP module of the coherent receivers. We first review a CD monitoring based on Godard's error that can be able to accurately monitor arbitrarily large dispersion values in uncompensated transmission links in combination with frequency domain equalizer, then extend the previous nonlinear parameter monitoring method based on Godard's error by blindly obtaining the optimized value γξp to significantly improve the adaptive capability, and present a simple and effective modulation format monitoring based on Godard's error. Meanwhile, the effectiveness has been experimentally verified in 128-Gb/s PDM-QPSK, 192-Gb/s PDM-8QAM, and 256-Gb/s PDM-16QAM systems.

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.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper considers Godard's error as signal quality metric to monitor chromatic dispersion (CD), nonlinear parameter and modulation format in the DSP module of the coherent receivers. We first review a CD monitoring based on Godard's error that can be able to accurately monitor arbitrarily large dispersion values in uncompensated transmission links in combination with frequency domain equalizer, then extend the previous nonlinear parameter monitoring method based on Godard's error by blindly obtaining the optimized value γξp to significantly improve the adaptive capability and present a simple and effective modulation format monitoring based on Godard's error. Meanwhile, the effectiveness has been experimentally verified in 128-Gb/s PDM-QPSK, 192-Gb/s PDM-8QAM and 256-Gb/s PDM-16QAM systems [ABSTRACT FROM AUTHOR]

A novel symbol rate estimation (SRE) technique utilizing the clock tone (CT) obtained by Godard timing recovery algorithm is proposed. By this technique, the known sampling rate of the analog-to-digital converter (ADC) in digital coherent optical receivers can used as a reference to directly determine the unknown signal symbol rate. The impact of polarization mode dispersion (PMD) on the CT magnitude can be mitigated by using the hybrid correlation function (HCF) consisting of both auto-correlation function (ACF) and cross-correlation function (XCF) of the received signal spectrum, while the chromatic dispersion (CD) impact can be mitigated by adaptive CD compensation techniques. This technique is simple, accurate, applicable to advanced modulation formats commonly used, and robust to various link impairments. Numerical simulations and experimental results are presented to validate this technique. [ABSTRACT FROM AUTHOR]

Abstract: We propose a polynomial fitting algorithm based method for non-data-aided chromatic dispersion (CD) estimation in single carrier (SC) coherent optical systems with arbitrary modulation formats, and compare it with our previously proposed CD estimation method which is also based on the polynomial fitting algorithm but requires special modulation formats thus is a data-aided CD estimation method for systems with PDM-QPSK or other multilevel modulation formats. For the data-aided CD estimation method, an extra chirp-free OOK signal is transmitted. The curve of the average phase at the frequency± f as a function of the frequency f is measured at the coherent receiver. The accumulated CD is then estimated with a polynomial fitting algorithm. In the simulation of a 50Gbaud 50%-RZ OOK system through 12.5×80km standard single mode fiber (SSMF), the estimation errors are within±50ps/nm in 20 tests when the launch power is from −5dBm to −1dBm. 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 errors are within±200ps/nm, in a 50Gbaud PDM-QPSK system through 10×80km SSMF with the launch power from −3dBm to −1dBm. The estimation accuracy can be potentially improved by averaging multiple results. The data-aided CD estimation method has an inherently bigger estimation range than that of the newly proposed non-data-aided method, while the newly proposed non-data-aided method can tolerate a much larger frequency offset between the transmitter and the local oscillator. These methods are promising for future optical fiber networks with dynamic optical routing and coherent detection. [Copyright &y& Elsevier]

We experimentally investigate the performance of the signal power autocorrelation-based method for chromatic dispersion (CD) estimation in a polarization-multiplexing quadrature phase-shift keying (PM-QPSK) 100G coherent optical system conveying optical channel transport unit level-4 (OTU4) frames. It is shown that the typical laboratory setup, where the signal components are generated from delayed versions of the same pseudorandom binary sequence (PRBS), is inadequate for experimental validation because of artifacts in the signal auto-correlation function. This problem is circumvented by the use of a commercial line card transporting independent data sequences. The algorithm is used to estimate accumulated CD values from 0 to 50 000 ps/nm under up to 80-ps differential group delay (DGD). We further evaluate its convergence properties in terms of the length of the sample vector required for correct CD estimation and address the hardware resource requirements. The CD-shifted version of the algorithm yielded a maximum estimation error of 186 ps/nm in all tested conditions.