Equalization Enhanced Phase Noise Research Articles

Impact of pump-phase noise in PPLN-based optical parametric amplifier and wavelength converter for digital coherent transmission

Wideband signal amplification and optical signal processing with a high gain using an optical parametric amplifier based on a periodically poled LiNbO3 (PPLN) waveguide is attractive for constructing wideband optical fiber networks. We experimentally investigate the transfer characteristics of the phase noise of a pump laser in χ(2)-based optical parametric amplification and wavelength conversion on the basis of second-harmonic-generation and differential-frequency-generation processes. We also evaluate the effect of the transferred phase noise on signal quality in dispersion-unmanaged digital coherent fiber transmission systems. We show that the phase noise is transferred only to the wavelength-converted idler and does not affect the amplified signal even by using a pump laser with a MHz-order linewidth. We also show that the phase noise transferred to the idler light can have a similar impact on signal quality as equalization-enhanced phase noise (EEPN) in digital coherent transmission. The signal penalty including EEPN was evaluated with several pump lasers and at symbol rates of 32, 64, and 96 Gbaud. We also propose a method of using correlated pump lights between a wavelength converter pair to cancel out the transfer of phase noise.

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).

Analytical Study and Noise Mitigation for Complex-Valued Optical DSB Transmission With Carrier-Assisted Differential Detection Receiver

A thorough analysis of the system model for complex-valued optical double-sideband (DSB) transmission with carrier-assisted differential detection (CADD) receiver under the influence of laser phase noise and fiber chromatic dispersion (CD) is presented. It is shown that the interaction of laser phase noise and CD leads to the phenomenon of phase-to-amplitude (P2A) noise and equalization-enhanced phase noise (EEPN). The achievable performance of the complex-valued optical DSB transmission with CADD receiver under the influence of EEPN and P2A noise is estimated by a closed-form expression, and it is verified by simulation that the results show an inaccuracy of less than 1 dB for a wide range of system parameters. In addition, in order to mitigate the EEPN and P2A noise, we propose a pre-decision aid-based simplified blind phase search (BPS) algorithm, commonly referred to as PDA-BPS algorithm. The PDA-BPS algorithm allows for reduced complexity by decreasing the number of symbols entering the BPS algorithm. Theoretical derivation and simulation verification illustrate that the PDA-BPS algorithm can achieve similar mitigation performance to the BPS algorithm with lower complexity. Specifically, under the condition that classification decision threshold R is equal to 0.25, the complexity can be reduced by 40%/16.6% with 1 MHz/7 MHz linewidth for 16-QAM and 29%/10.9% with 0.5 MHz/3 MHz linewidth for 64-QAM.

Extended Study on Equalization-Enhanced Phase Noise for High-Order Modulation Formats

Coherent optical receivers with electronic dispersion compensation (EDC) become ubiquitous for high-capacity and long-distance transmissions. However, their performance can be decimated by equalization-enhanced phase noise (EEPN). The existing reports have shown some unique features that deserve further studies, especially for high-order modulation formats. In this paper, we firstly show that the intra-symbol EEPN is dominated by the phase noise. Therefore, the probability density function (PDF) due to intra-symbol EEPN and inter-symbol EEPN are quite different. We derive the variances of EEPN-induced phase and amplitude noise for QPSK signals, and fully explain the elliptical PDF. Secondly, we show that the intra-symbol EEPN is scaled with the power of the different modulus, but the inter-symbol one, the average power of the constellation. Subsequently, we elucidate that for higher-order constellations with multiple moduli, the total EEPN, the EEPN-induced phase noise and amplitude noise, all distribute differently on the different moduli. Finally, we analyze the EEPN after the practical carrier phase recovery algorithms, also with a closed-form prediction. Our analysis of EEPN is readily extended to arbitrary modulation formats.

Intra-Channel Nonlinearity Mitigation in Optical Fiber Transmission Systems Using Perturbation-Based Neural Network

In this work, a perturbation-based neural network (P-NN) scheme with an embedded bidirectional long short-term memory (biLSTM) layer is investigated to compensate for the Kerr fiber nonlinearity in optical fiber communication systems. Numerical simulations have been carried out in a 32-Gbaud dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM) transmission system. It is shown that this P-NN equalizer can achieve signal-to-noise ratio improvements of ∼1.37 dB and ∼0.80 dB, compared to the use of a linear equalizer and a single step per span (StPS) digital back propagation (DBP) scheme, respectively. The P-NN equalizer requires lower computational complexity and can effectively compensate for intra-channel nonlinearity. Meanwhile, the performance of P-NN is more robust to the distortion caused by equalization enhanced phase noise (EEPN). Furthermore, it is also found that there exists a tradeoff between the choice of modulation format and the nonlinear equalization schemes for a given transmission distance.

Nonlinear Coherent Optical Systems in the Presence of Equalization Enhanced Phase Noise

Equalization enhanced phase noise (EEPN) occurs due to the interplay between laser phase noise and electronic dispersion compensation (EDC) module. It degrades significantly the performance of uncompensated long-haul coherent optical fiber communication systems. In this work, a general expression accounting for EEPN is presented based on Gaussian noise model to evaluate the performance of multi-channel optical communication systems using EDC and digital nonlinearity compensation (NLC). The nonlinear interaction between the signal and the EEPN is analyzed. Numerical simulations are carried out in nonlinear Nyquist-spaced wavelength division multiplexing (WDM) coherent transmission systems. Significant performance degradation due to EEPN in the cases of EDC and NLC are observed, with and without the consideration of transceiver (TRx) noise. The validation of the analytical approach has been done via split-step Fourier simulations. The maximum transmission distance and the laser linewidth tolerance are also estimated to provide important insights into the impact of EEPN.

Impact of Equalization-Enhanced Phase Noise on Digital Nonlinearity Compensation in High-Capacity Optical Communication Systems.

Equalization-enhanced phase noise (EEPN) can severely degrade the performance of long-haul optical fiber transmission systems. In this paper, the impact of EEPN in Nyquist-spaced dual-polarization quadrature phase shift keying (DP-QPSK), dual-polarization 16-ary quadrature amplitude modulation (DP-16QAM), and DP-64QAM optical transmission systems is investigated considering the use of electrical dispersion compensation (EDC) and multi-channel digital backpropagation (MC-DBP). Our results demonstrate that full-field DBP (FF-DBP) is more susceptible to EEPN compared to single-channel and partial-bandwidth DBP. EEPN-induced distortions become more significant with the increase of the local oscillator (LO) laser linewidth, and this results in degradations in bit-error-rates (BERs), achievable information rates (AIRs), and AIR-distance products in optical communication systems. Transmission systems using higher-order modulation formats can enhance information rates and spectral efficiencies, but will be more seriously degraded by EEPN. It is found that degradations on AIRs, for the investigated FF-DBP schemes, in the DP-QPSK, the DP-16QAM, and the DP-64QAM systems are 0.07 Tbit/s, 0.11 Tbit/s, and 0.57 Tbit/s, respectively, due to the EEPN with an LO laser linewidth of 1 MHz. It is also seen that the selection of a higher-quality LO laser can significantly reduce the bandwidth requirement and the computational complexity in the MC-DBP.

Impact of laser flicker noise and linewidth on 64 to 96 Gbaud/DP-nQAM metro coherent optical links.

We experimentally investigate the impact of laser flicker noise and linewidth on 64 Gbaud/DP-64QAM, 96 Gbaud/DP-32QAM and 64 or 96 Gbaud/DP-16QAM links. To give a more practical viewpoint, the examined flicker noise closely follows that of an industry forum (OIF 400ZR). We have found that higher modulation order (e.g., 64QAM) is sensitive to phase noise from the linewidth and flicker noise, even in the back to back case. Significant optical signal to noise ratio (OSNR) and cycle slip rate penalties can also be observed with a transmission distance $ {\gt} {200}\;{\rm km}$>200km for both 64QAM and 32QAM signals, which mainly comes from equalization-enhanced phase noise. Moreover, with the increasing of transmission distances, the effective linewidth of a tunable laser with a higher flicker noise and higher linewidth (210 KHz) increases significantly, while it remains unchanged for an external cavity laser (ECL) with 47-kHz linewidth. The result indicates the importance of more stringent flicker noise and linewidth requirement for future ultrabaud rate transmissions.

Phase Noise Characterization and EEPN of a Full C-Band Tunable Laser in Coherent Optical Systems

We perform phase noise characterization of a tunable laser source that is capable of tuning to 103 channels between 1527.6-1568.36 nm with 50 GHz grid spacing between the channels. The measured frequency modulation (FM) noise power spectral density (PSD) is reproduced by simulations in order to investigate the impact of equalization-enhanced phase noise (EEPN) in a coherent transmission system. The simulations are performed on a 30 Gbaud channel with 16 quadrature amplitude modulation (16QAM) and using pilot-based carrier phase estimation with 3% overhead. By performing extensive system simulations, we show the impact of different accumulated dispersion. Furthermore, we show the possibility to overcome EEPN related penalties by using a local oscillator (LO) with reduced low frequency phase noise or flat FM-noise PSD profiles with lower linewidths.

Phase Noise Cancellation in Coherent Communication Systems Using a Radio Frequency Pilot Tone

Long-haul optical fiber communication employing digital signal processing (DSP)-based dispersion compensation can be distorted by the phenomenon of equalization-enhanced phase noise (EEPN), due to the reciprocities between the dispersion compensation unit and the local oscillator (LO) laser phase noise (LPN). The impact of EEPN scales increases with the increase of the fiber dispersion, laser linewidths, symbol rates, signal bandwidths, and the order of modulation formats. In this work, the phase noise cancellation (PNC) employing a radio frequency (RF) pilot tone in coherent optical transmission systems has been investigated. A 28-Gsym/s QPSK optical transmission system with a significant EEPN has been implemented, where the carrier phase recovery (CPR) was realized using the one-tap normalized least-mean-square (NLMS) estimation and the differential phase detection (DPD), respectively. It is shown that the RF pilot tone can entirely eliminate the LPN and efficiently suppress the EEPN when it is applied prior to the CPR.

Research on Carrier Recovery Algorithm in Coherent Optical Communication System

In coherent optical communication system, the random deviation of optical phase which is caused by the spontaneous emission of laser leads to phase noise, resulting in a random rotation of signal constellation. In order to ensure the reliability of the communication system, carrier phase estimation and recovery are required at the receiver. In this paper, we investigate two traditional carrier phase recovery (CPR) algorithms, including Viterbi&Viterbi phase estimation (VVPE) and blind phase search (BPS) algorithm. On this basis, we also discuss seven improved algorithms. Then we compare and analyze the hardware complexities of eight different CPR algorithms. In addition, the cause of equalization enhanced phase noise (EEPN) and its impact on the carrier phase recovery algorithm are also discussed.

Equalization Enhanced Phase Noise in Coherent Receivers: DSP-Aware Analysis and Shaped Constellations

We revisit the analysis of equalization-enhanced phase noise (EEPN) arising in coherent receivers from the interaction between the chromatic dispersion compensation by an electronic equalizer and the phase noise of the local oscillator. Through numerical simulations we highlight EEPN characteristics and investigate its impact on the behavior of the carrier phase recovery algorithm. We show that the blind phase search, which is usually used in practice to recover the carrier phase, partially mitigates the EEPN. We detail a numerical approach to predict the system performance including the phase recovery algorithm, and show that taking into account EEPN characteristics relaxes the constraint on the system laser phase noise given by previous pessimistic analytical models. We present experimental validations of our claims, and address future advanced transoceanic systems using 98 GBd probabilistically shaped QAM formats.

Influence of EEPN and P2A noise with CD pre- and post-compensation in optical SSB transmission and Kramers-Kronig receiver system.

We present a comparative study of equalization-enhanced phase noise (EEPN) and phase to amplitude (P2A) noise with chromatic dispersion (CD) pre- and post-compensation in single side-band (SSB) transmission and direct-detection (DD) systems, respectively. We analyze the interplay of laser phase noise and fiber dispersion on an optical SSB Nyquist shaped four-level pulse amplitude modulation (PAM-4) signal in a Kramers-Kronig (KK) receiver. Our main results show that the EEPN in a DD-KK receiver dominates the system noise with the relaxed signal-to-noise ratio (SNR). The P2A noise in CD post-compensation scheme is relaxed due to the complex filed recovery with KK receiver. The numerical simulations are implemented to illustrate the interplay of laser linewidth and fiber dispersion in both CD pre- and post-compensation scenarios. Compared with CD pre-compensation, 3-dB reduction of power spectral density (PSD) of P2A noise at the peak is alleviated with CD post-compensation. The laser linewidth has ~1 MHz release with CD post-compensation for a 56-Gbaud PAM-4 signal over 100-km standard single-mode fiber (SSMF) transmission.

Low complexity carrier phase estimation for m-QAM optical communication systems

A low complexity carrier phase estimation (CPE) algorithm for M-ary quadrature amplitude modulation (m-QAM) optical communication systems is investigated in this paper. In the proposed CPE algorithm, a two-stage CPE method is adopted. In the first stage, the QPSK points of the constellation are picked out to achieve a coarse phase estimation using the traditional Viterbi and Viterbi algorithm. In the second stage, all the points of the constellation are used for a fine phase estimation. In addition, the fourth-power operation is replaced by the 4-level absolute operation for the removal of modulated data phase, which greatly reduced the complexity. The proposed method was investigated through simulation, with 16-QAM, 32-QAM and 64-QAM modulation formats, respectively. The simulation results show that the proposed algorithm has both good linewidth tolerance and amplified spontaneous emission noise tolerance as well as low complexity. Moreover, when the equalization enhanced phase noise is considered, the proposed method also has better performance than traditional algorithm.

A Closed-Form Expression for Direct Detection Transmission Systems With Kramers-Kronig Receiver

In recent years, direct detection (DD) transmission with Kramers–Kronig (KK) receiver has attracted a lot of attention as a promising technology for short reach and metro applications due to its capability of electronic chromatic dispersion compensation and the possibility of canceling completely the signal–signal beat interference resulted from the nonlinearity of the photodiode. However, the achievable performance of DD transmission with KK receiver is still not well understood, especially in the presence of the laser phase noise which would strongly interact with both optical carrier and chromatic dispersion during propagation. In this letter, for the first time, we derive a closed-form expression for estimating the achievable performance of DD transmission with KK receiver under the influence of laser phase noise, taking into account the phase-to-amplitude noise conversion and equalization-enhanced phase noise phenomena. In comparison with Monte Carlo simulation, our model shows less than 0.2-dB discrepancy for a wide range of systems parameters, indicating its high accuracy.

Numerical Investigation of the Equalization Enhanced Phase Noise Penalty for M-Quadrature Amplitude Modulation Formats in Short-Haul Few-Mode Fiber Transmission Systems with Time-Domain Equalization

The equalization enhanced phase noise (EEPN), caused by the interaction of the chromatic dispersion (CD) with the phase noise of the local oscillator (LO), has been extensively studied for single-mode optical communication systems. Few-mode fiber (FMF) transmission systems introduce a new channel impairment, the differential mode delay (DMD), which also creates EEPN and hence limits the maximum transmission distance of those systems. In this work, we numerically investigate the optical signal to noise ratio (OSNR) penalties caused by the EEPN in a 3-mode FMF transmission system at 25 GBd for quadrature phase-shift keying (QPSK), 16-quadrature amplitude modulation (QAM), 32-QAM and 64-QAM modulation formats when using the blind phase search (BPS) carrier phase recovery (CPR) algorithm, which has been demonstrated to be both robust and suitable for optical communication systems. Our numerical study assumes a short-span of FMF, modeled in the weakly-coupled regime, and includes two cases; the use of ideal mode-selective de/multiplexers at both ends of the FMF span (model A), and the use of ideal non-mode-selective de/multiplexers (model B). The results show that the EEPN has almost no effect in model A. However, EEPN produces a severe penalty in model B with the onset of the OSNR degradation starting for a DMD spread of the impulse response of about 100 symbols for all modulation formats investigated. The distribution ratio of the amount of phase noise between the transmitter and receiver lasers is also assessed for model B and we confirm that the degradation is mainly due to the phase noise of the LO.

Optical single side-band Nyquist PAM-4 transmission using dual-drive MZM modulation and direct detection.

We present the design and optimization of the optical single side-band (SSB) Nyquist four-level pulse amplitude modulation (PAM-4) transmission using dual-drive Mach-Zehnder modulator (DDMZM)modulation and direct detection (DD), aiming at the C-band cost-effective, high-speed and long-distance transmission. At the transmitter, the laser line width should be small to avoid the phase noise to amplitude noise conversion and equalization-enhanced phase noise due to the large chromatic dispersion (CD). The optical SSB signal is generated after optimizing the optical modulation index (OMI) and hence the minimum phase condition which is required by the Kramers-Kronig (KK) receiver can also be satisfied. At the receiver, a simple AC-coupled photodiode (PD) is used and a virtual carrier is added for the KK operation to alleviate the signal-to-signal beating interference (SSBI).A Volterra filter (VF) is cascaded for remaining nonlinearities mitigation. When the fiber nonlinearity becomes significant, we elect to use an optical band-pass filter with offset filtering. It can suppress the simulated Brillouin scattering and the conjugated distortion by filtering out the imaging frequency components. With our design and optimization, we achieve single-channel, single polarization 102.4-Gb/s Nyquist PAM-4 over 800-km standard single-mode fiber (SSMF).

Analysis of chromatic dispersion compensation and carrier phase recovery in long-haul optical transmission system influenced by equalization enhanced phase noise

The performance of long-haul coherent optical fiber transmission system is significantly affected by the equalization enhanced phase noise (EEPN), due to the interaction between the electronic dispersion compensation (EDC) and the laser phase noise. In this paper, we present a comprehensive study on different chromatic dispersion (CD) compensation and carrier phase recovery (CPR) approaches, in the n-level phase shift keying (n-PSK) and the n-level quadrature amplitude modulation (n-QAM) coherent optical transmission systems, considering the impacts of EEPN. Four CD compensation methods are considered: the time-domain equalization (TDE), the frequency-domain equalization (FDE), the least mean square (LMS) adaptive equalization are applied for EDC, and the dispersion compensating fiber (DCF) is employed for optical dispersion compensation (ODC). Meanwhile, three carrier phase recovery methods are also involved: a one-tap normalized least mean square (NLMS) algorithm, a block-wise average (BWA) algorithm, and a Viterbi-Viterbi (VV) algorithm. Numerical simulations have been carried out in a 28-Gbaud dual-polarization quadrature phase shift keying (DP-QPSK) coherent transmission system, and the results indicate that the origin of EEPN depends on the choice of chromatic dispersion compensation methods, and the effects of EEPN also behave moderately different in accordance to different carrier phase recovery scenarios.

Laser Phase Noise Effects and Joint Carrier Phase Recovery in Coherent Optical Transmissions With Digital Subcarrier Multiplexing

In this paper, we numerically and experimentally investigate the impairments related to laser phase noise in coherent digital subcarrier multiplexing (SCM) systems. Based on the evaluation in both back-to-back and transmission scenarios and the performance comparison between single carrier (SC) and SCM systems, we show that even though SCM systems suffer from degraded performance of carrier phase recovery (CPR) algorithms, they can potentially achieve an improved laser linewidth tolerance compared with SC systems after long-haul transmission attributed to the mitigation of equalization-enhanced phase noise. In addition, the effect of dispersion-enhanced phase noise is discussed in digital SCM systems, and a joint CPR (J-CPR) algorithm is proposed for cycle slip detection and correction. The effectiveness of the proposed J-CPR algorithm is then demonstrated in a 16-quadrature amplitude modulation (QAM) digital SCM system by both simulations and experiments.

Equalization-Enhanced Phase Noise in Stokes-Vector Direct Detection Systems

In this work, we provide both numerical and experimental investigations of equalization-enhanced phase noise (EEPN) in Stokes-vector direct detection (SV-DD) systems. We show that the influence of EEPN cannot be neglected in high symbol rate SV-DD systems after transmission over several hundred kilometers of fibers when electronic chromatic dispersion compensation and lasers with linewidths of the order of Megahertz are employed. Simulation results are presented to evaluate the dependence of EEPN effects on laser linewidth, transmission distance, and symbol rate. Experiments are then conducted in a 56-Gbaud 16-quadrature amplitude modulation (QAM) SV-DD system to demonstrate the EEPN-induced performance degradation after 320-km transmission over standard single mode fiber (SSMF).