Coherent Optical OFDM Research Articles

Compensation of filter cascading effects and non‐linearities in flexible multi‐carrier‐based optical networks using a complex‐kernel‐based support vector machine

Filter cascading effects are identified and compensated in flexible coherent multi-carrier optical networks using, for the first time, a complex-valued support vector machine (C-SVM) non-linear equaliser which is compared to phase-conjugated subcarrier-coding (PC-SC)-based non-linearity compensation. The transmission performance of super-channel-based dual-polarisation coherent multi-band optical OFDM (DP-MB-OFDM) is analysed in a flexible network with two-stage wavelength selective-switch reconfigurable optical add-drop multiplexer for coarse and fine switching granularity. It is shown that filter cascading effects have significant impact only on edge OFDM sub-bands. On the other hand, C-SVM outperforms PC-SC resulting in an extension of the transmission-reach, for instance, by 420 km when employing 32-quadrature amplitude modulation at a targeted bit-error-rate of 10−3. This occurs since C-SVM can compensate more effectively stochastic-induced nonlinear cross-talk effects. Moreover, the interplay between polarisation-mode dispersion (PMD) and fibre non-linearity is also investigated in DP-MB-OFDM, revealing that a high PMD causes time fluctuation on the non-linear interaction affecting the balance of the ‘twin-subcarriers’ in PS-SC.

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.

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.

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.

Unsupervised Support Vector Machines for Nonlinear Blind Equalization in CO-OFDM

A novel blind nonlinear equalization (BNLE) technique based on the iterative re-weighted least square is experimentally demonstrated for single- and multi-channel coherent optical orthogonal frequency-division multiplexing. The adopted BNLE combines, for the first time, a support vector machine-learning cost function with the classical Sato or Godard error functions and maximum likelihood recursive least-squares. At optimum launched optical power, BNLE reduces the fiber nonlinearity penalty by ~1 (16-QAM single-channel at 2000 km) and ~1.7 dB (QPSK multi-channel at 3200 km) compared to a Volterra-based NLE. The proposed BNLE is more effective for multi-channel configuration: 1) it outperforms the “gold-standard” digital-back propagation and 2) for a high number of subcarriers the performance is better due to its capability of tackling inter-subcarrier four-wave mixing.

Non‐Gaussian statistics of CO‐OFDM signals after non‐linear optical fibre transmission

In this study, the statistical distribution of the received signal in a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system with quadrature-phase shift keying modulation in the orthogonal frequency-division multiplexing (OFDM) subcarriers is investigated, and the accuracy and correctness of the Gaussian probability density function (pdf) assumption is analysed. The well-known Anderson-Darling test is utilised to measure the deviation extent of the statistical distribution of the received signal from the Gaussian pdf. Finally, the Johnson S U -distribution is suggested as a more exact distribution for the statistical modelling of the received signal. After non-linear propagation, its accuracy is assessed through comparison with Monte-Carlo simulations, based on the time-domain split-step Fourier method.

Performance analysis of Wilcoxon-based machine learning nonlinear equalizers for coherent optical OFDM

In the recent research on the mitigation of nonlinearities in CO-OFDM systems, it has been seen that various types of non-robust algorithms (based on minimization of least square error principle) are used for learning of nonlinear equalizer. Moreover, it is well known that performance of nonlinear equalizer learned by robust algorithms is not easily affected by the outliers. In this paper, some robust algorithms such as Wilcoxon Multilayer Perceptron (WMLP), Wilcoxon Generalized Radial Basis function (WGRBF) and Wilcoxon Robust Extreme Learning Machine (WRELM) for the performance enhancement of CO-OFDM system have been analyzed. Subsequently, the performance enhancement capability of both the algorithms i.e., robust and non-robust has been compared in this study. It has been observed that the nonlinear equalizers trained with Wilcoxon approach based learning algorithm offer improved performance in terms of Q-Factor as compared to non-robust algorithms. In this study K-means machine learning based training algorithm is used to cluster the points at their desired locations. From obtained numerical results, it has been observed that the improvement in Q-Factor with Wilcoxon multilayer perceptron algorithm w.r.t its non-robust solution is ~ 0.65 dB which is significantly higher than the value ~ 0.2 dB with both the other mentioned robust algorithms w.r.t their non-robust counterparts. From the comparison of robust algorithms performance on the basis of convergence rate, it has been professed that the WRELM converges 100 and 7 times faster than WMLP and WGRBF respectively.

Terabit optical OFDM superchannel transmission via coherent carriers of a hybrid chip-scale soliton frequency comb.

We demonstrate seamless channel multiplexing and high bitrate superchannel transmission of coherent optical orthogonal frequency division multiplexing (CO-OFDM) data signals utilizing a dissipative Kerr soliton (DKS) frequency comb generated in an on-chip microcavity. Aided by comb line multiplication through Nyquist pulse modulation, the high stability and mutual coherence among mode-locked Kerr comb lines are exploited for the first time, to the best of our knowledge, to eliminate the guard intervals between communication channels and achieve full spectral density bandwidth utilization. Spectral efficiency as high as 2.625bit/Hz/s is obtained for 180 CO-OFDM bands encoded with 12.75Gbaud 8-QAM data, adding to the total bitrate of 6.885Tb/s within a 2.295THz frequency comb bandwidth. This Letter confirms that high coherence is the key superiority of Kerr soliton frequency combs over independent laser diodes, as a multi-spectral coherent laser source for high-bandwidth high-spectral-density transmission networks.

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.

Carrier Frequency Offset Estimation for CO-OFDM: The Matched-Filter Approach

This paper proposes a novel carrier frequency offset (CFO) estimator for the coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems using the matched-filter (MF) concept. We consider an OFDM symbol with $N$ subcarriers so that the receiver takes $N$ time samples of the received noisy CO-OFDM signal. Our idea is to first append these $N$ received samples with $(L-1)N$ zeros at the end to get a sequence of $LN$ time samples. By taking the discrete Fourier transform of these $LN$ samples, we compute the spectrum of the CO-OFDM symbol at $LN$ discrete frequency points. We think of this spectrum as being made up of $L$ sets of $N$ points each, each set consisting of the frequency points $\lbrace \frac{2\pi }{LN}l, \frac{2\pi }{LN}l+\frac{2\pi }{N}, \ldots, \frac{2\pi }{LN}l+\frac{2\pi (N-1)}{N}\rbrace$ , for each value of $l$ , where $l=0,1,\ldots,L-1$ . Each set of $N$ points for one value of $l$ can be considered as the spectrum of the CO-OFDM symbol corresponding to one hypothesized value $\frac{2\pi }{LN}l$ of the CFO. The receiver can now obtain the maximum likelihood (ML) CFO estimate by determining the hypothesized value that best matches the spectrum of the CO-OFDM symbol received from the channel. In the case of data-aided (DA) ML estimation, we treat the OFDM symbol as a pilot symbol in which we know the data in all the subcarriers, and this pilot symbol is used as the reference signal for the MF. In the case of blind (BL) ML estimation, the data in all the subcarriers are unknown, and the receiver uses an OFDM symbol with no data modulation in all the subcarriers as the reference signal. After making the ML decision of the hypothesized value of the CFO, a fine search will be carried out to determine the actual value more accurately. It turns out only one step is necessary to locate the actual value of the CFO. The DA MF ML algorithm can achieve full-range (integral and fractional part) CFO estimation with high accuracy, while the BL MF ML algorithm has low computational complexity but focuses on the fractional CFO estimation only. We discuss the complexity and performance of this MF ML algorithm, and present simulation results to demonstrate the estimation error variance for 16-PSK/QAM modulations. The simulation results show that the estimation error variance of the DA MF ML algorithm can achieve the Cramer–Rao lower bound in the absence of the laser phase noise.

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.

A time and frequency synchronization method for CO-OFDM based on CMA equalizers

In this paper, an efficient time and frequency synchronization method based on a new training symbol structure is proposed for polarization division multiplexing (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The coarse timing synchronization is achieved by exploiting the correlation property of the first training symbol, and the fine timing synchronization is accomplished by using the time-domain symmetric conjugate of the second training symbol. Furthermore, based on these training symbols, a constant modulus algorithm (CMA) is proposed for carrier frequency offset (CFO) estimation. Theoretical analysis and simulation results indicate that the algorithm has the advantages of robustness to poor optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD). The frequency offset estimation range can achieve [−Nsc2ΔfN,+Nsc2ΔfN] GHz with the mean normalized estimation error below 12×10−3 even under the condition of OSNR as low as 10 dB.

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.

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 .