Coherent Optical OFDM Systems Research Articles

A Joint OSNR and Nonlinear Distortions Estimation Method for Optical Fiber Transmission System

In this paper, we propose and demonstrate a joint optical signal-to-noise ratio (OSNR) and a nonlinear distortions estimation method. The OSNR is calculated by considering either the link parameters or the correlation operations of the training symbols. The nonlinear distortions estimation in this calculation comes from different nonlinear sensitivities of these two methods. The indicator of NL penalty is defined as the ratio of nonlinear distortion power to the signal power. As the estimation method, based on link parameters, has low computational complexity, and the training symbol used for the OSNR estimation is inherently indispensable for frame synchronization, this nonlinear distortion estimation method introduces a few complexities and no extra overhead. Experimental results obtained by using a 200 Gb/s 16 QAM DWDM system establish the accuracy of the proposed OSNR estimations method, with errors less than 1 dB. The nonlinear distortions were also measured under different simulation conditions, using a coherent optical OFDM system, and the results are in accordance with the expectations.

Experimental Demonstration of a Low-Complexity Phase Noise Compensation for CO-OFDM Systems

In this letter, a low-complexity phase noise compensation scheme based on Kalman filtering theory is experimentally demonstrated for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) transmissions. The proposed scheme can operate in two modes, pilot-aided mode and blind mode, resulting in a variety of phase noise tracking configurations upon particular transmission scenario. At a bit error rate of $3.8\times 10^{-3}$ and for 40 GBaud 16-QAM 64 subcarriers CO-OFDM systems, the proposed method operating in the pilot-aided mode reduces the pilot overhead by a factor of 2 in comparison with the conventional pilot-aided scheme, while in the blind mode, our scheme’s complexity is far superior to one of the state-of-the-art computational efficient decision-direct-free blind approach by a factor of 20.

Receiver IQ mismatch and phase noise suppression in PDM CO-OFDM system

Abstract Receiver in-phase/quadrature (IQ) mismatch as well as phase noise are hard to mitigate at the receiver in polarization division multiplexed (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) system and so far this problem hasn’t been properly solved yet. In this paper, a novel scheme is proposed to suppress receiver IQ mismatch and phase noise. In this scheme, through combining the pilot structure with Gram Schmidt orthogonalization procedure (GSOP) algorithm we can estimate the phase noise as well as channel distortion and eliminate the effect of part of the residual IQ mismatch. Numerical simulation shows that the proposed method has better performance than compared method at 100 Gb/s after 480 km transmission. What’s more, the calculation complexity is also analyzed.

Incorporating SDC Module for ISI Compensation for a Long-Haul Co-OFDM System

Abstract With the increase in demand of bandwidth hungry applications, it is recommended to develop a high data rate system for long-haul coherent optical orthogonal frequency division multiplexing (CO-OFDM). At a very high data rate, CO-OFDM signal experiences deterioration. At 50 Gbps, the signal experiences ISI effect and in order to overcome this ISI effect, a prolonged system has been developed to reach optimal ISI compensation technique. One of the prominent and competent techniques to enhance system performance is (SDCM) symmetrical dispersion compensation module. In order to make system more bandwidth efficient 4-QAM (Quadrature Amplitude Modulation) with gray coding is applied and manual adjustments are done at receiver phase to decrease error vector magnitude (EVM). OFDM data stream is successfully transmitted over a distance of 4,000 km to compete the demand of long-haul CO-OFDM system. With different launch powers and laser linewidths, the performance of the system is enhanced in terms of Q-factor, SNR and EVM.

Non-orthogonal basis expansion based laser phase noise suppression in CO-OFDM systems

A laser phase noise suppression approach, based on non-orthogonal basis expansion (NOBE), is proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. In the NOBE approach, the time-varying laser phase noise is (sub-) optimally reconstructed using a bank of non-orthogonal expansion bases. Theoretical derivation of the non-orthogonal basis expansion matrices using the minimum mean-square error (MMSE) criteria is presented analytically. Compared with the conventional inverse discrete Fourier transform (IDFT)-based orthogonal basis expansion (OBE) method, the proposed NOBE approach, with the same expansion order L, offers higher accuracy in carrier phase estimation. Numerical analysis shows that the system’s tolerance to laser phase noise is significantly enhanced by the new method thanks to the lower modeling error. For example, the laser linewidth-symbol period product in an ∼ 100-Gbps 16QAM CO-OFDM system at an optical signal-to-noise-ratio (OSNR) of 22 dB achieves 3.87×10−2 with the NOBE (L=3), which is approximately twice that with the OBE. The impact of residual carrier frequency offset (CFO) on the NOBE is also semi-analytically investigated, which shows that the NOBE has robust performance for the residual CFO up to 2 MHz under a subcarrier spacing of 31.25 MHz. By taking advantage of the elaborately-designed comb-type pilot subcarriers pattern, the computational complexity of NOBE is also lower than that of the OBE. Since the NOBE with a sub-optimal basis expansion matrix does not require a priori knowledge of the product of laser linewidth and symbol period, it is well-suited for practical implementations.

Novel transmitter IQ imbalance compensation algorithm using training symbols in PDM CO-OFDM system

We systematically deduce the optical fiber channel transmission mathematical model with in-phase/quadrature (IQ) imbalance and channel distortion for polarization division multiplexed (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. With the analysis of model, we propose two novel algorithms using training symbols, which can well realize channel distortion and IQ imbalance estimation. This study shows the proposed algorithms performed significantly better than the commonly used approaches. We examine the two proposed methods with simulation via analyzing the bit error rate in the case of different optical signal to noise ratio (OSNR), transmission distance and IQ mismatch at 80Gb/s and 100Gb/s.

PAPR reduction in CO-OFDM systems using IPTS and modified clipping and filtering

Aiming at the problem of the peak to average power ratio (PAPR) in coherent optical orthogonal frequency division multiplexing (CO-OFDM), a hybrid PAPR reduction technique of the CO-OFDM system by combining iterative partial transmit sequence (IPTS) scheme with modified clipping and filtering (MCF) is proposed. The simulation results show that at the complementary cumulative distribution function (CCDF) of 10-4, the PAPR of proposed scheme is optimized by 1.86 dB and 2.13 dB compared with those of IPTS and CF schemes, respectively. Meanwhile, when the bit error rate (BER) is 10-3, the optical signal to noise ratio (OSNR) are optimized by 1.57 dB and 0.66 dB compared with those of CF and IPTS-CF schemes, respectively.

Performance Analysis of Nonlinear Fiber-Optic in CO-OFDM Systems With High Order Modulations

In this letter, the Johnson $S_{U}$ distribution is utilized for modeling the linear and nonlinear impairments of coherent optical orthogonal frequency-division multiplexing (CO-OFDM) over the fiber-optic channel with higher order modulations. An analytical expression to evaluate the performance of CO-OFDM systems with n-PSK and n-QAM modulations is proposed. The statistical moments of this additive Johnsonian noise are calculated analytically for a dual-polarization system as a function of the input signal and channel parameters. Finally, the symbol error rate is evaluated, comparing it with the estimations obtained through Monte-Carlo simulations.

OLS-Based RBF Neural Network for Nonlinear and Linear Impairments Compensation in the CO-OFDM System

For the first time, we propose and experimentally verify a novel low-complexity orthogonal least square (OLS) based radial basis function (RBF) neural network (NN) nonlinear equalizer for high-speed coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. Its ability to compensate nonlinear impairments as well as linear impairments is comprehensively evaluated and compared with the linear equalizer. The impact of training overhead on system performance is also investigated. Results show that in a single-channel 40-Gb/s 16-quadrature amplitude modulation CO-OFDM system, with the training overhead of 4%, the maximum transmission distance is extended to 800 km at Q threshold of 8.7 dB, and RBF-NN outperforms the linear equalizer by 2.8 and 5.6 dB Q -factors after 800 and 600 km transmissions, respectively.

Experimental demonstration of a 16.9 Gb/s link for coherent OFDM PON robust to frequency offset and timing error

Due to its merits of flexible bandwidth allocation and robustness towards fiber transmission impairments, coherent optical orthogonal frequency division multiplexing (CO-OFDM) technology draws a lot of attention for passive optical networks (PON). However, a CO-OFDM system is vulnerable to frequency offsets between modulated optical signals and optical local oscillators (OLO). This is particularly serious for low cost PONs where low cost lasers are used. Thus, it is of great interest to develop efficient algorithms for frequency synchronization in CO-OFDM systems. Usually frequency synchronization proposed in CO-OFDM systems are done by detecting the phase shift in time domain. In such a way, there is a trade-off between estimation accuracy and range. Considering that the integer frequency offset (IFO) contributes to the major frequency offset, a more efficient method to estimate IFO is of demand. By detecting IFO induced circular channel rotation (CCR), the frequency offset can be directly estimated after fast Fourier transforming (FFT). In this paper, circular acquisition offset frequency and timing synchronization (CAO-FTS) scheme is proposed. A specially-designed frequency domain pseudo noise (PN) sequence is used for CCR detection and timing synchronization. Full-range frequency offset compensation and non-plateau timing synchronization are experimentally demonstrated in presence of fiber dispersion. Based on CAO-FTS, 16.9 Gb/s CO-OFDM signal is successfully delivered over a span of 80-km single mode fiber.

Adaptive Subspace Method for Phase Noise Estimation in CO-OFDM Systems

In this paper, a blind phase noise estimation method for a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system is considered. Based on the subspace approach, a simple and robust method is proposed to adaptively estimate and track phase noise in CO-OFDM systems. The idea behind this novel technique is to estimate the singular vectors that correspond to the smallest singular values of the noise subspace. A weighting parameter, which is derived based on the forward–backward linear prediction technique, is subsequently constructed using the obtained singular vectors of the noise subspace to adaptively estimate the phase noise in the system. Also, a variable step size is introduced to ensure an improved performance as well as stable convergence. Simulation results are shown to demonstrate the effectiveness as well as the efficiency of the proposed algorithm, which is implemented in a polarization multiplexed CO-OFDM system stressed by polarization mode dispersion, chromatic dispersion, and other polarization-dependent losses along the fiber link.

基于广义回归神经网络的CO-OFDM系统非线性均衡

基于广义回归神经网络的CO-OFDM系统非线性均衡

A novel transmitter IQ imbalance and phase noise suppression method utilizing pilots in PDM CO-OFDM system

In this paper, we develop a novel pilot structure to suppress transmitter in-phase and quadrature (Tx IQ) imbalance, phase noise and channel distortion for polarization division multiplexed (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. Compared with the conventional approach, our method not only significantly improves the system tolerance of IQ imbalance as well as phase noise, but also provides higher transmission speed. Numerical simulations of PDM CO-OFDM system is used to validate the theoretical analysis under the simulation conditions: the amplitude mismatch 3 dB, the phase mismatch 15°, the transmission bit rate 100 Gb/s and 560 km standard signal-mode fiber transmission. Moreover, the proposed method is 63% less complex than the compared method.

A novel joint timing/frequency synchronization scheme based on Radon–Wigner transform of LFM signals in CO-OFDM systems

A joint timing and frequency synchronization method has been proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system in this paper. The timing offset (TO), integer frequency offset (FO) and the fractional FO can be realized by only one training symbol, which consists of two linear frequency modulation (LFM) signals with opposite chirp rates. By detecting the peak of LFM signals after Radon–Wigner transform (RWT), the TO and the integer FO can be estimated at the same time, moreover, the fractional FO can be acquired correspondingly through the self-correlation characteristic of the same training symbol. Simulation results show that the proposed method can give a more accurate TO estimation than the existing methods, especially at poor OSNR conditions; for the FO estimation, both the fractional and the integer FO can be estimated through the proposed training symbol with no extra overhead, a more accurate estimation and a large FO estimation range of [−5 GHz, 5GHz] can be acquired.

Cyclic prefix‐aided linear trajectory search for phase‐noise mitigation in coherent optical‐OFDM systems

Estimating and mitigating the phase noise (PHN) in orthogonal frequency-division multiplexing (OFDM) greatly improves the system performance. Recently, a PHN mitigation method using the best match trajectory (BMT) method was proposed, and it outperformed the conventional inter-carrier interference (ICI) compensation methods in both bit error rate and computational complexity. The authors propose a modified version of the BMT method in order to further improve the computational performance when mitigating the PHN in coherent optical OFDM systems. Their simulations show that the proposed linear PHN trajectory achieves better PHN estimation than the conventional PHN trajectory, and the proposed scheme reduces the computational complexity compared with the BMT method.

Blind Nonlinearity Equalization by Machine-Learning-Based Clustering for Single- and Multichannel Coherent Optical OFDM

Fiber-induced intra- and interchannel nonlinearities are experimentally tackled using blind nonlinear equalization (NLE) by unsupervised machine-learning-based clustering (MLC) in ∼46-Gb/s single-channel and ∼20-Gb/s (middle-channel) multichannel coherent multicarrier signals (orthogonal frequency-division multiplexing (OFDM) based). To that end, we introduce, for the first time, hierarchical and fuzzy-logic C -means (FLC)-based clustering in optical communications. It is shown that among the two proposed MLC algorithms, FLC reveals the highest performance at optimum launched optical powers (LOPs), while at very high LOPs, hierarchical can compensate more effectively nonlinearities only for low-level modulation formats. When employing binary phase-shift keying and quaternary phase-shift keying, FLC outperforms K-means, fast-Newton support vector machines, supervised artificial neural networks, and NLE with deterministic Volterra analysis. In particular, for the middle channel of a QPSK wavelength-division multiplexing coherent optical OFDM system at optimum −5 dBm of LOP and 3200 km of transmission, FLC outperforms Volterra-NLE by 2.5 dB in Q-factor. However, for a 16-QAM single-channel system at 2000 km, the performance benefit of FLC over inverse Volterra-series transfer function reduces to ∼0.4 dB at a LOP of 2 dBm (optimum). Even when using novel sophisticated clustering designs in 16 clusters, no more than additional ∼0.3-dB Q-factor enhancement is observed. Finally, in contrast to the deterministic Volterra-NLE, MLC algorithms can partially tackle the stochastic parametric noise amplification .

Channel Equalization and Phase Noise Compensation Free DAPSK-OFDM Transmission for Coherent PON System

Channel equalization and phase noise compensation are required in coherent optical orthogonal frequency-division multiplexing (CO-OFDM) transmission systems for reliable performance. In general, redundant data such as training symbols and pilot tones are necessary for channel and phase noise estimation in quadrature amplitude modulation (QAM) based CO-OFDM systems, which reduces the spectral efficiency of the system. Especially, in the coherent passive optical network (PON), the redundancy increases as the number of subscribers increases. In this letter, we propose a differential amplitude shift keying (DAPSK)-based CO-OFDM transmission for PON system, which does not require channel equalization and phase noise compensation processes. The proposed DAPSK-based CO-OFDM transmission was experimentally demonstrated, and the performance according to receiver launched power and the number of subcarriers was compared with QAM-based CO-OFDM.

Performance Evaluation of High-Speed Polar Coded CO-OFDM System with Nonlinear and Linear Impairments

In this paper, the performance of polar code in high-speed coherent optical orthogonal frequency division multiplexing (CO-OFDM) system with nonlinear and linear impairments is comprehensively investigated for the first time. Results show that soft decision-based polar code is slightly affected by nonlinearity-induced non-Gaussian noise but still performs strong robustness. In the nonlinear domain of single-channel 40-Gb/s CO-OFDM at 320-km of transmission, with the help of polar code, the nonlinear tolerance is extended by 4 dB and a maximum code gain (in Q-factor) of 5.9 dB is achieved under symmetric dispersion compensation. Meanwhile, polar code significantly resists linear impairment in both nonlinear and linear domains.

Iterative algorithm for phase noise estimation in coherent optical DFT-S OFDM systems

An iterative algorithm is proposed and investigated for phase noise estimation of discrete Fourier transform spread (DFT-S) orthogonal frequency division multiplexing (OFDM). Compared with common phase estimation (CPE), significant improvement of tolerance to laser bandwidth is obtained and 2.7 dB improvement at BER of 3.8×10−3 is found using the CPE-iter scheme in 103.3 Gb/s coherent polarization-division-multiplexed DFT-S OFDM system over 480-km transmission through simulation.

Eigenvector Basis Expansion-Based Phase Noise Suppression Method for CO-OFDM Systems

Coherent optical orthogonal frequency division multiplexing (CO-OFDM) system is known vulnerable to the laser phase noise. In this letter, we propose a novel phase noise suppression method based on eigenvector basis expansion (EBE) for CO-OFDM systems. With the help of the proposed method, the induced phase noise effects can be mitigated efficiently. Numerical results show that compared with the orthogonal basis expansion-based phase noise suppression method, by performing an EBE to the phase noise, a more accurate description of the phase noise can be achieved, and hence leads to a better system performance. Besides, the additional computational complexity is limited, since the eigenvector basis only depends on the laser linewidth.