Nyquist-WDM Systems Research Articles

Training strategies to minimize interchannel interference effects using supervised learning in gridless Nyquist-WDM systems.

The dynamism envisioned in future high-capacity gridless optical networks requires facing several challenges in distortion mitigation, such as the mitigation of interchannel interference (ICI) effects in any optical channel without information of their adjacent channels. Machine learning (ML)-based techniques have been proposed in recent works to estimate and mitigate different optical impairments with promising results. We propose and evaluate two training strategies for supervised learning algorithms with the aim to minimize ICI effects in a gridless 3×16-Gbaud 16-quadrature amplitude modulation (QAM) Nyquist-wavelength-division multiplexing (WDM) system. One strategy, called updating strategy, is based on symbol training sequence, and the other one, called characterization strategy, is based on an offline training using a previous system characterization. Artificial neural networks (ANN), support vector machine (SVM), K-nearest neighbors (KNN), and extreme learning machine (ELM) algorithms are explored for both training strategies. Experimental results showed a bit error rate (BER) improvement at low training lengths for both training strategies, for instance, gains up to ∼4dB in terms of optical signal-to-noise ratio were achieved in a back-to-back scenario. Besides, the KNN and ELM algorithms showed significant BER reduction in transmission over 250 km optical fiber. Additionally, we carried out a brief computational complexity analysis where ELM presented only 1.9% of ANN processing time. Hence, the use of ML-based techniques could enhance the optical gridless networks performance and consequently fulfill future traffic demands.

Inter-Channel Fiber Nonlinearity Mitigation in High Baud-Rate Optical Communication Systems

Kerr nonlinearity in long distance fiber-optic link imposes a fundamental limitation to the capacity of wavelength division multiplexed (WDM) optical communication systems. Solving the inverse-propagating nonlinear Schrodinger equation (NLSE) is in principle a fundamental methodology to mitigate fiber nonlinear impairments. However, solving multi-channel coupled NLSE is too complexed to be implemented commercially. It is of great importance to compensate for nonlinear distortions in high baud-rate WDM systems based on the information of one single target channel. In this article, we experimentally study fiber nonlinearity mitigation in an 8 × 512 Gb/s (64Gbaud) polarization division multiplexed (PDM) 16-ary quadrature amplitude modulation (16-QAM) Nyquist-WDM system with 960 km standard single mode fiber (SSMF) loop transmission. The digital back-propagation (DBP) algorithm based on the target channel is applied, which can compensate for intra-channel nonlinearity. The inter-channel nonlinearity of cross phase modulation (XPM) induces nonlinear polarization scattering and nonlinear phase noise, which are partially correlated over adjacent pulses in high baud-rate systems. We propose an advanced nonlinear polarization crosstalk canceller (NPCC) with a novel decision feedback (DF) update strategy that is called the DF-NPCC, which incorporates the iterative process of the least mean square (LMS) algorithm and can thus mitigate the correlated nonlinear polarization crosstalk and nonlinear phase noise. Through nonlinearity mitigation, the DBP together with the DF-NPCC can achieve a 0.77 dB Q2 factor promotion. The DF-NPCC can suppress the remaining nonlinear distortions after the single channel DBP, which corresponds to a 0.36 dB Q2 factor improvement due to inter-channel nonlinear mitigation. Our work indicates XPM distortions can be mitigated with low complexity digital signal processing such as the DF-NPCC based on the single channel information, which provides an attractive solution to compensate inter-channel fiber nonlinearity in high baud-rate Nyquist-WDM systems.

Fiber Nonlinearity and Tight Filtering Impairments Mitigation of DP-16QAM Nyquist-WDM Systems Using Multiplier-Free MAP Detection

Tight filtering and fiber Kerr effect both cause severe pattern-dependent distortions that need to be combated to achieve higher spectral efficiency (SE), larger capacity and greater achievable transmission distance in the next generation wavelength division multiplex (WDM) optical transmission system. In this paper, a novel multiplier-free maximum-a-posteriori-probability (MAP) detection scheme is proposed and verified in dual-polarization (DP) 16-ary quadrature amplitude modulation (16-QAM) Nyquist-WDM systems. Based on the innovative technique of approximate calculation of Euclidean distance, the competitive performance is obtained in terms of pattern-dependent impairments mitigation. Besides, the computational complexity (CC) is drastically reduced to about 34%, as the multiplier of the proposed MAP detection is completely removed. Comprehensive simulation results of triple-carrier Nyquist DP 16-QAM demonstrate that the MAP scheme could effectively mitigate the tight filtering and fiber nonlinearity impairments with much lower CC, i.e., achieve desirable SE and nonlinearity tolerance in long-haul transmissions. In addition, a 1.1 dB reduction of the required OSNR and 2.6 dB launch power range extension are observed in the triple-carrier 480 Gb/s Nyquist DP 16-QAM back-to-back and 700 km transmission experiments, respectively. The advantages of the proposed low-complexity MAP scheme make it a preferable impairment mitigation technique for practical Nyquist-WDM systems.

Impact of InterChannel Interference in gridless nyquist-wdm systems with and without nonlinear impairments compensation


 
 
 
 This paper presents a characterization of interchannel interference (ICI) effects in gridless Nyquist-wdm systems due to two contributions, namely, overlapping among optical carriers and stimulation of nonlinear optical fiber impairments. ICI is assessed regarding bit error rate (BER) at 16 and 32 Gbaud, as a function of several system parameters. Nonlinear impairment compensation based on the digital back-propagation algorithm is implemented in the DSP-based coherent receiver. Results demonstrated that ICI due to channels overlapped has a higher impact concerning BER than nonlinear optical fiber impairments. Besides, the use of the back-propagation algorithm improves system performance, reducing up to 3 and 0.7 orders of magnitude of BER in QPSK and 16QAM cases, respectively. It means that this algorithm can minimize nonlinear effects under varying system parameters, but its performance is limited in sub-Nyquist cases.
 
 
 

Semi-analytic modeling of FWM noise in QAM Nyquist-WDM system with phase-conjugated twin waves

Abstract Nonlinear models previously reported for coherent optical fiber transmission have been used to explain the mechanism of nonlinear noise squeezing by phase-conjugated twin waves (PCTW) scheme, but the reduction of four-wave-mixing (FWM) noise by the nonlinearity mitigation method cannot be directly derived from these models for a quasi-symmetric dispersion map, especially when the effect of walk-off between channels is included. Semi-analytic models based on a statistical method are derived herein order to quantify the reduction of FWM noise for quadrature amplitude modulation (QAM) PCTW Nyquist-WDM systems. Our models derived here show that the variance of non-degenerate FWM noise is irrelevant to the number of signal points within a QAM constellation diagram, as is different from the degenerate FWM case. Numerical results by using our models show that even though the effect of walk-off is included, the PCTW scheme is still greatly effective to reduce the impact of FWM noise for a quasi-symmetric map. The performances of central channel for two cases of 16QAM PCTW Nyquist-WDM systems with same total spectral bandwidth and spectral efficiency, 16-channel 32-Gbaud/ch and 32-channel 16-Gbaud/ch, are numerically compared by using our models

Fiber Nonlinearity Mitigation in Single Carrier 400 G and 800 G Nyquist-WDM Systems

Fiber Kerr nonlinearity limits the achievable transmission distance and channel capacity of high speed optical communication systems. In this paper, we study the performance of C-band single carrier 400 G and 800 G 16-ary quadrature amplitude modulation (16 QAM) or 64-ary quadrature amplitude modulation (64 QAM) Nyquist wavelength division multiplexed (WDM) systems with emphasis on fiber nonlinearity and its mitigation. The nonlinearity mitigation methods of digital back-propagation (DBP) and coupled-equation digital back-propagation (CE-DBP) are discussed for single channel and multi-channel systems, respectively. The DBP algorithm is a general approach suitable for compensating intra-channel nonlinearity. The CE-DBP is an extension of the DBP, which can deal with both intra- and inter-channel nonlinearity by solving the coupled multi-channel Manakov equations. Based on the first order perturbation theory, we also analyze the application of Kalman filter (KF) to nonlinearity compensation, which utilizes correlation between adjacent symbols to compensate for Kerr nonlinearity. With numerical simulations, the performance of three nonlinearity equalization schemes of CE-DBP, DBP + KF, and CE-DBP + KF are compared. For nonlinearity mitigation in single carrier 400 G and 800 G WDM systems, the DBP + KF is more efficient than the CE-DBP considering five coupled channels. The CE-DBP + KF method has slightly better performance than the DBP + KF. However, the CE-DBP is quite complex due to multi-channel Manakov equation calculation, which demands broad-band joint detection with a single coherent receiver or several individual coherent receivers with time synchronization. In contrast, the DBP + KF only need the information of the target channel. We thus conclude that the DBP + KF is an attractive solution to mitigate fiber nonlinearity for single carrier 400 G and 800 G Nyquist-WDM systems. With the combination of the DBP and the KF, the transmission distance extensions are achieved as 12.5%, 14.3%, 22.6% and 28% for 400 G_64 QAM, 800 G_64 QAM, 400 G_16 QAM and 800 G_16 QAM WDM systems, respectively.

Mitigation of time-varying distortions in Nyquist-WDM systems using machine learning

We propose a machine learning-based nonsymmetrical demodulation technique relying on clustering to mitigate time-varying distortions derived from several impairments such as IQ imbalance, bias drift, phase noise and interchannel interference. Experimental results show that those impairments cause centroid movements in the received constellations seen in time-windows of 10k symbols in controlled scenarios. In our demodulation technique, the k-means algorithm iteratively identifies the cluster centroids in the constellation of the received symbols in short time windows by means of the optimization of decision thresholds for a minimum BER. We experimentally verified the effectiveness of this computationally efficient technique in multicarrier 16QAM Nyquist-WDM systems over 270 km links. Our nonsymmetrical demodulation technique outperforms the conventional QAM demodulation technique, reducing the OSNR requirement up to ∼0.8 dB at a BER of 1 × 10−2 for signals affected by interchannel interference.

Analytical FWM Expressions for Coherent Optical Transmission Systems

Simplified, closed-form, mathematical expressions for four wave mixing (FWM) in coherent optical systems are derived. FWM is an important limitation in both coherent OFDM (CO-OFDM) and Nyquist-WDM systems. The effect is also important in networks deploying dispersion shifted fiber and/or based on very narrow channel spacing. In this work, 1) we improve the accuracy of the formalism in CO-OFDM systems by taking into account not only the contribution due to the power of the central carrier but also the contribution due to the spectral flanks as well as the guard band between channels and 2) we extend the formalism to work for flexgrid systems. The derived expressions can be used for a quick estimation of system performance and/or can be incorporated in routing algorithms that account for physical layer effects. The formalism for flexgrid systems is estimating the power of FWM with improved accuracy compared to existing models in the literature so it can be a key asset in dynamic resource allocation operations. Finally, the derived expressions are valid for both, uncompensated and dispersion managed systems.

An improved model for estimating the impact of FWM in coherent optical systems

Four Wave Mixing is the main source of nonlinearity in coherent optical OFDM systems that degrades the system performance. In this paper, based on a previously introduced model, we derive a closed form expression that calculates the FWM power. This model can be used for a fast estimation of system performance within a broad range of system parameters and/or can be also used as an integral part of physical layer aware algorithms. The proposed model is in very good agreement with the exact model as well as with numerical results and provides significant lower mismatch than the previously published model. Moreover, this expression is also expanded in Nyquist-WDM systems showing very good accuracy with numerical results while is modified to take into account dispersion compensation, something that was neglected in the previous work.

Combined Optical and Electrical Spectrum Shaping for High-Baud-Rate Nyquist-WDM Transceivers

We discuss the benefits and limitations of optical time-division multiplexing (OTDM) techniques based on the optical generation of a periodic train of sinc pulses for wavelength-division multiplexing (WDM) transmission at high baud rates. It is shown how the modulated OTDM spectrum bandwidth is related to the optical comb parameters and the pulse shaping of the modulating waveforms in the electrical domain. Such dependence may result in broadening of the modulated spectra, which can degrade the performance of Nyquist-WDM systems due to interchannel crosstalk penalties. However, it is shown and experimentally demonstrated that the same technique of optical pulse train generation can be allied with digital pulse shaping to improve the confinement of the modulated spectrum toward the Nyquist limit independently of the number of OTDM tributaries used. To investigate the benefits of the proposed approach, we demonstrate the first WDM Nyquist-OTDM signal generation based on the periodic train of sinc pulses and electrical spectrum shaping. Straight line transmission of five 112.5-Gbd Nyquist-OTDM dual-polarization quadrature phase-shift keying (QPSK) channels is demonstrated over a dispersion uncompensated link up to 640 km, with full-field coherent detection at the receiver. It is shown that such a design strategy effectively improves the spectral confinement of the modulated OTDM signal, providing a minimum intercarrier crosstalk penalty of 1.5 dB in baud-rate-spaced Nyquist-WDM systems.

Feed-forward carrier phase recovery for offset-QAM Nyquist WDM transmission.

Due to the half symbol delay between in-phase and quadrature components for offset quadrature amplitude modulation (OQAM) signal, phase noise cannot only lead to constellation rotation but also introduce additional crosstalk. Therefore, OQAM signal has very poor tolerance to the laser linewidth. Here, we carry out a semi-analytical investigation of phase noise induced crosstalk during OQAM Nyquist WDM transmission, and find that the carrier phase recovery (CPR) has to be implemented prior to the inter-symbol-interference (ISI) equalization. Then, after a function separation of polarization de-multiplexing and ISI equalization, we propose a new DSP flow with a linewidth-tolerant blind feed-forward CPR scheme for OQAM signal. Its effectiveness is verified under the scenario of 5-channel 28-Gbaud polarization multiplexing (PM) OQAM Nyquist WDM systems. A tolerance of linewidth and symbol duration products of 6.5×10(-4) and 1.1×10(-4) is secured for 4-OQAM and 16-OQAM, respectively, given 1-dB required-OSNR penalty at BER = 10(-3).

Analytical expressions for the nonlinear interference in dispersion managed transmission coherent optical systems

Closed-form expressions of nonlinear interference of dense wavelength-division-multiplexed (WDM) systems with dispersion managed transmission (DMT) are derived. We carry out a simulative validation by addressing an ample and significant set of the Nyquist-WDM systems based on polarization multiplexed quadrature phase-shift keying (PM-QPSK) subcarriers at a baud rate of 32Gbaud per channel. Simulation results show the simple closed-form analytical expressions can provide an effective tool for the quick and accurate prediction of system performance in DMT coherent optical systems.

In-Band Estimation of Optical Signal-to-Noise Ratio From Equalized Signals in Digital Coherent Receivers

We propose a novel method of in-band estimation of optical signal-to-noise ratio (OSNR) using a digital coherent receiver, where OSNR is determined from second- and fourth-order statistical moments of equalized signals in any modulation format. Our proposed method is especially important in recently-developed Nyquist wavelength-division multiplexed (WDM) systems and/or reconfigurable optical-add/drop-multiplexed (ROADM) networks, because in these systems and networks, we cannot apply the conventional OSNR estimation method based on optical-spectrum measurements of the in-band signal and the out-of-band noise. Effectiveness of the proposed method is validated with computer simulations of Nyquist-WDM systems and ROADM networks using 25-Gbaud quadrature phase-shift keying (QPSK) and 16 quadrature-amplitude modulation (16-QAM) formats.

Matched Filter Design for RRC Spectrally Shaped Nyquist-WDM Systems

We investigate the matched filter design for root-raised-cosine (RRC) spectrally shaped Nyquist wavelength-division-multiplexed (WDM) systems. We show that the complexity of the receiver-side adaptive butterfly equalizer can be significantly reduced by incorporating a matched filter in the static chromatic dispersion equalizer for RRC Nyquist spectrally shaped signals. We find that the Nyquist-WDM system with a matched filter is sensitive to the laser frequency offset between the local oscillator at the receiver and the laser at the transmitter, and show that the frequency offset induced penalty decreases with increased RRC roll-off factor. With a roll-off factor of 0.1, the optical signal-to-noise ratio penalty at BER 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> from 1 GHz frequency offset is for 28-Gbaud polarization division multiplexed quadrature phase shift keying and for 28-Gbaud polarization division multiplexed 16-ary quadrature amplitude modulation.

Optimization of DSP to Generate Spectrally Efficient 16QAM Nyquist-WDM Signals

We investigate transmitter-side digital signal processing to generate 16-ary quadrature-amplitude-modulation (16QAM) Nyquist wavelength-division-multiplexing (WDM) signals by simulations. We first study required digital finite-impulse response (FIR) filter tap numbers and optimum roll-off factors to generate Nyquist 16QAM WDM signals. We show that a root-raised cosine spectrum with a roll-off factor of 0.1 is optimal for Nyquist 16QAM signals considering the tradeoff between the system performance and complexities, and a digital FIR filter with 37 taps is sufficient to generate such signals. Then we look into the effects of digital-to-analog converter (DAC) sampling speeds on the performance of Nyquist-WDM systems. We show that the electrical filter shape and spectral pre-emphasis have a big impact on the system performance. With a fourth-order super-Gaussian electrical filter and spectral pre-emphasis, DACs with 1.2 samples/symbol sampling speed can generate 16QAM Nyquist-WDM signals at 1.05-symbol-rate channel spacing, with an OSNR penalty below 0.2 dB compared with 2 samples/symbol DACs.

Joint digital signal processing for superchannel coherent optical communication systems

Ultra-high-speed optical communication systems which can support ≥ 1Tb/s per channel transmission will soon be required to meet the increasing capacity demand. However, 1Tb/s over a single carrier requires either or both a high-level modulation format (i.e. 1024QAM) and a high baud rate. Alternatively, grouping a number of tightly spaced "sub-carriers" to form a terabit superchannel increases channel capacity while minimizing the need for high-level modulation formats and high baud rate, which may allow existing formats, baud rate and components to be exploited. In ideal Nyquist-WDM superchannel systems, optical subcarriers with rectangular spectra are tightly packed at a channel spacing equal to the baud rate, thus achieving the Nyquist bandwidth limit. However, in practical Nyquist-WDM systems, precise electrical or optical control of channel spectra is required to avoid strong inter-channel interference (ICI). Here, we propose and demonstrate a new "super receiver" architecture for practical Nyquist-WDM systems, which jointly detects and demodulates multiple channels simultaneously and mitigates the penalties associated with the limitations of generating ideal Nyquist-WDM spectra. Our receiver-side solution relaxes the filter requirements imposed on the transmitter. Two joint DSP algorithms are developed for linear ICI cancellation and joint carrier-phase recovery. Improved system performance is observed with both experimental and simulation data. Performance analysis under different system configurations is conducted to demonstrate the feasibility and robustness of the proposed joint DSP algorithms.

Inter-Channel Crosstalk Cancellation for Nyquist-WDM Superchannel Applications

Superchannel WDM systems employ narrow channel spacing to achieve high spectral efficiency and increase channel capacity. Additionally, these systems attempt to avoid inter-channel interference (ICI) and inter-symbol interference (ISI), by creating and maintaining both spectral and temporal orthogonality. This in turn imposes a strong requirement on the spectral amplitude and phase of the received signals. For Nyquist-WDM systems, the temporal shapes are Nyquist pulses, requiring uniform spectral density with flat phase. In practice, these requirements are only partially achieved, resulting in non-ideal Nyquist systems with inter-channel interference (ICI). We propose and demonstrate two joint ICI cancellation methods based on our new “super receiver” architecture, which jointly detects and demodulates multiple subchannels simultaneously. The maximum a posteriori (MAP) algorithm is most readily implemented for systems with channel spacing equal to the baud rate, and the adaptive linear equalizer is effective for all channel spacings. Simulation results show that both joint ICI cancellation schemes outperform conventional linear equalization, approaching the performance of an isolated single channel.

The validity of “Odd and Even” channels for testing all-optical OFDM and Nyquist WDM long-haul fiber systems

We investigate experimentally the validity of testing all-optical OFDM and Nyquist WDM systems using interleaved test channels derived from only two data sources. These "odd and even" channels are insufficiently decorrelated, so experiments underestimate the inter-carrier interference (ICI). Additionally, numerical simulations demonstrate that using odd and even channels generates stronger nonlinear distortions during transmission, causing an unrealistically large penalty in the nonlinearity-limited region.