Coherent Optical OFDM Systems Research Articles

Robustness analysis of a parallel two-box digital polynomial predistorter for an SOA-based CO-OFDM system

The linearization performance of various digital baseband pre-distortion schemes is evaluated in this paper for a coherent optical OFDM (CO-OFDM) transmitter employing a semiconductor optical amplifier (SOA). In particular, the benefits of using a parallel two-box (PTB) behavioral model, combining a static nonlinear function with a memory polynomial (MP) model, is investigated for mitigating the system nonlinearities and compared to the memoryless and MP models. Moreover, the robustness of the predistorters under different operating conditions and system uncertainties is assessed based on a precise SOA physical model. The PTB scheme proves to be the most effective linearization technique for the considered setup, with an excellent performance-complexity tradeoff over a wide range of conditions.

Receiver IQ mismatch estimation in PDM CO-OFDM system using training symbol

Abstract Receiver in-phase/quadrature (IQ) mismatch is hard to mitigate at the receiver via using conventional method in polarization division multiplexed (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. In this paper, a novel training symbol structure is proposed to estimate IQ mismatch and channel distortion. Combined this structure with Gram Schmidt orthogonalization procedure (GSOP) algorithm, we can get lower bit error rate (BER). Meanwhile, based on this structure one estimation method is deduced in frequency domain which can achieve the estimation of IQ mismatch and channel distortion independently and improve the system performance obviously. Numerical simulation shows that the proposed two methods have better performance than compared method at 100 Gb/s after 480 km fiber transmission. Besides, the calculation complexity is also analyzed.

An Iterative Frequency Offset Estimation Method for Coherent Optical OFDM System

In this letter, we propose and experimentally investigate a training-aided iterative frequency offset estimation (IFOE) method, which can track dynamic frequency offset (FO) drift in coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. In contrast to existing FO estimation algorithms that compute specific FO values, in IFOE, only the sign value of FO is judged and recorded without any phase calculation. The estimated FO is updated once for every data block based on FO signs obtained from multiple previous blocks, which helps combat noise and allows the shortening of the employed training symbol. We experimentally investigate the performance of IFOE in a 160-km CO-OFDM system. The results show that IFOE achieves superior bit error rate performance to a one-time FO estimator (without FO tracking) and approaches the performance of multiple separate FO estimators that use longer training symbols.

A novel timing synchronization for CO-OFDM systems using CAZAC sequences

A novel symbol timing synchronization algorithm based on constant amplitude zero auto correlation (CAZAC) sequences is proposed for coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. The training symbol of the proposed algorithm is comprised of four different parts, utilizing even symmetry property of each part to accomplish timing synchronization. The performance of the proposed algorithm is demonstrated by means of simulations in OFDM and CO-OFDM systems. The proposed algorithm is shown to eliminate the timing sidelobes of Park’s algorithm and has a more accurate timing estimation. In the condition of chromatic dispersion (CD), the timing metric of the proposed method still maintains its peak value at the correct timing point, while the values are almost 0 at all the other positions. Meanwhile, the timing mean square error (MSE) of the proposed algorithm remains around 10-6.

Unbiased Channel Estimation Based on the Discrete Fresnel Transform for CO-OFDM Systems

In this letter, the deviation of the channel estimator based on intra-symbol frequency-domain averaging (ISFA) for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) is investigated. The deviation-induced estimation error is derived analytically as a function of pulse broadening caused by chromatic dispersion and averaged noise power, and thereby the optimum averaging window size can be determined. To avoid the deviation, we propose an unbiased channel estimation algorithm based on the discrete Fresnel transform (DFnT) for CO-OFDM systems, utilizing the convolution-preservation property of DFnT for intra-symbol averaging. It is shown that the DFnT-based channel estimator converges to the actual channel response under estimation, and achieves better performance than the ISFA estimator, especially in highly dispersive channels. Finally, numerical results are provided to confirm the analysis and its advantages.

CFO compensation method using optical feedback path for coherent optical OFDM system

Abstract We investigate feasibility of carrier frequency offset (CFO) compensation method using optical feedback path for coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. Recently proposed CFO compensation algorithms provide wide CFO estimation range in electrical domain. However, their practical compensation range is limited by sampling rate of an analog-to-digital converter (ADC). This limitation has not drawn attention, since the ADC sampling rate was high enough comparing to the data bandwidth and CFO in the wireless OFDM system. For CO-OFDM, the limitation is becoming visible because of increased data bandwidth, laser instability (i.e. large CFO) and insufficient ADC sampling rate owing to high cost. To solve the problem and extend practical CFO compensation range, we propose a CFO compensation method having optical feedback path. By adding simple wavelength control for local oscillator, the practical CFO compensation range can be extended to the sampling frequency range. The feasibility of the proposed method is experimentally investigated.

A novel improved SLM scheme of the PAPR reduction technology in CO-OFDM systems

The higher peak-to-average power ratio (PAPR) is a major shortcoming of coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. Selective mapping (SLM) technology can effectively reduce the probability of high PAPR, but it has higher computational complexity, and requires additional bandwidth to transmit the side information, which will affect the transmission efficiency of the system. In response to these shortcomings, a novel improved SLM (NI-SLM) scheme with low complexity and without side information is proposed. Simulation results show that the proposed scheme can exponentially reduce the computational complexity, and the bit error rate (BER) performance can greatly approach the original signal. What’s more, it shows the better PAPR reduction performance.

Phase Noise Estimation and Suppression for PDM CO-OFDM/OQAM Systems

Phase noise induced common phase error and inter-carrier-interference are serious impairments for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. As have been discussed in previous publications, extra signal-to-noise-ratio (SNR) penalty is required to maintain the system performance under the interference of laser phase noise. The SNR penalty is proportional to the laser linewidth, the time duration of an OFDM symbol, and the system SNR. Therefore, the phase noise induced interference remains the bottleneck for CO-OFDM systems, especially for those systems employing high-order modulation formats, or with long fast Fourier transform window. Thanks to the usage of specially designed filter banks, CO-OFDM/offset quadrature amplitude modulation (CO-OFDM/OQAM) systems demonstrate lower out-of-band leakage and higher spectral efficiency compared with conventional CO-OFDM systems. Recently, both theoretical studies and experimental demonstrations for CO-OFDM/OQAM systems have been widely reported. With the relaxation of orthogonal condition from the complex field to the real field, phase noised induced interference in CO-OFDM/OQAM systems is more complicated than that in conventional CO-OFDM systems. To our best knowledge, there have been no studies on the phase noise estimation and suppression methods for CO-OFDM/OQAM systems. In this paper, we systematically study and analyze phase noise induced interference for CO-OFDM/OQAM systems. Based on the theoretical analysis and the concept of orthogonal basis expansion, we develop a time-domain phase noise estimation and suppression method for polarization-division-multiplexed CO-OFDM/OQAM systems. As shown in numerical Montel Carlo simulations, the proposed method can improve the system robustness against phase noise effectively.

Investigation of Tolerable Laser Linewidth for Different Modulation Formats in CO-OFDM Systems

The ideal behavior of communication system requires a single frequency carrier. In optical communication system, light is used as a carrier. Practical laser source has a finite linewidth due to variations in the frequency of operation, hence, resulting in undesired phase perturbations in the signal whereas the ideal requirement is the delta function spectral shape at the carrier frequency. The spectral shape gets broadened due to phase noise and is modeled as lorentzian shape. Linewidth is a measure of stability of laser phase noise with time. Coherent Optical Orthogonal frequency division multiplexing (CO-OFDM) along with the spectrally efficient Quadrature Amplitude Modulation (QAM) formats is emerging as one of the best solutions for future high speed fiber transmission systems. Though the coherent, receivers have advantages in terms of sensitivity and selectivity, laser phase noise is the main limitation of such systems as the laser phase noise further causes common phase rotation of all the subcarriers per symbol and also results in inter carrier interference. QAM formats are also susceptible to laser phase noise. Phase noise in coherent systems is governed by laser linewidth. Hence, it is very important to investigate the impact of laser linewidth in CO-OFDM systems. This paper investigates the tolerable laser linewidths for different QAM formats in a 40 Gbps COOFDM system.

Joint timing/frequency offset estimation and correction based on FrFT encoded training symbols for PDM CO-OFDM systems.

A joint timing offset (TO) and frequency offset (FO) estimation algorithm is proposed for polarization division multiplexing (PDM) coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. It is realized by taking the advantage of the time-frequency property of the fractional Fourier transformation (FrFT) encoded training symbols. Compared with the classical Schmidl & Cox method, the proposed algorithm exhibits robust estimation result of timing offset with poor optical signal-to-noise ratio (OSNR) and nonlinear interference. For the frequency offset estimation, a quite large FO estimation ranges of [-5GHz + 5GHz] can be achieved. The mean normalized estimation error can be kept under 0.002 and the max normalized estimation error is no more than 0.008. The feasibility and effectiveness of the proposed joint estimation algorithm has been verified by experiments. The transmission performances with [-5GHz + 5GHz] FO are compared under the OSNR range from 14 to 27dB in a 106.8Gbit/s 16-ary quadrature amplitude modulation (16-QAM) PDM CO-OFDM transmission system. The proposed TO/FO estimation algorithm performs robustly and accurately without any induced BER degradations.

Study on performance of coherent orthogonal frequency division multiplexing system in exponential atmospheric turbulent channel

We analyze the performance of a coherent orthogonal frequency division multiplexing (OFDM) system and a serial decode and forward relay transmission multihop coherent free-space optical OFDM system using an exponential distribution atmospheric turbulence model under the circumstance of strong atmospheric turbulence. The attenuation of the atmospheric channel fading model mainly considers the light intensity scintillation caused by atmospheric turbulence and interaction between the path consumption, the transmitter and the receiver. The OFDM signal mapping method uses quadrature amplitude modulation. We also derive the formulas of the outage probability and symbol error rate of the coherent OFDM and multihop system, respectively, under the conditions described above. In addition, a simulation is performed, which is essential to evaluate the influence of key factors including coherent detection in a number of relay nodes, the mapping orders, and the number of subcarriers, which have a significant effect on the outage performance and the bit error performance of the OFDM-FSO system under the strong atmospheric turbulence.

Novel Training Symbol Structure for Transmitter IQ Mismatch Estimation for PDM Coherent Optical OFDM System

In this paper, two novel training symbol structures are proposed to mitigate transmitter IQ mismatch and channel distortion for polarization division multiplexed (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. Accordingly, two corresponding estimation methods are proposed. Compared with the conventional estimation approach, the advantage of the first method is that IQ mismatch and channel distortion are estimated independently, and the benefit of the second method is that the overhead of training symbols is reduced. The theoretical analysis is validated by numerical Monte Carlo simulations of PDM CO-OFDM system. Under the simulation conditions: the phase mismatch 15°, the amplitude mismatch 3 dB, the transmission bit rate 100 Gb/s, the standard signal-mode fiber link 480 km, and bit error rate 1e-3, 24 dB optical signal-to-noise ratio (OSNR) is necessary for the first method, and 28 dB OSNR for the second one.

Common phase error estimation in coherent optical OFDM systems using best-fit bounding box.

In this paper, we investigate and characterize a new approach of adopting best-fit bounding box method for common phase error estimation in coherent optical OFDM systems. The method is based on the calculation of the 2-D convex hull of the received signal constellation, which is generally adopted in image processing area to correct the skew of images. We further perform detailed characterizations including root mean square error analysis, laser linewidth tolerance, noise tolerance, and computation complexity analysis, via numerical simulations and experiments. The results show the proposed method achieves much improved spectral efficiency and comparable system performance than the pilot-aided method, while it exhibits good estimation accuracy and reduced complexity than the blind phase searching method.

SPM Supression in Long Haul CO-OFDM System using SPWR-OPC Modules

Objective: The main aim of this research paper is to enhance the reach of Long-haul Coherent Optical Orthogonal Frequency Division Multiplexing (CO-OFDM) communication system. Methods/Statistical Analysis: The purpose of SPWR and OPC in CO-OFDM system is to palliate dispersion and (Non-linearity) SPM respectively. In this proposed system Symmetrical Pulse Width Reduction (SPWR) and Optical Phase Conjugate modules (OPC) are used. The CO-OFDM system is investigated to compensate SPM by using up to 6 OPCs. Findings: While analyzing results it reveals that with the increase in the number of OPCs up to 6 enhances the transmission distance of CO-OFDM system and improves the Bit Error Rate (BER) performance but if increased beyond 6 OPCs deteriorates its performance. When using six OPCs in comparison to a single OPC, the system reach extends six times. Application/Improvement: The proposed system is simulation based and in future can be implemented commercially in Digital Terrestrial Television (DTT) and real-time audio and video communication.Keywords: Coherent Optical Orthogonal Frequency Division Multiplexing, Optical Phase Conjugate, Self Phase Modulation, Symmetrical Pulse Width Reduction

Efficient joint timing and frequency synchronization algorithm for coherent optical OFDM systems.

A joint timing and frequency synchronization algorithm is proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) systems. The timing and frequency synchronization is realized by using only one training symbol which is composed of conjugated symmetric sequence. The timing estimation of the proposed algorithm has the advantage of being robust to poor optical signal-to-noise ratio (OSNR) and chromatic dispersion (CD), and the frequency estimation range of fractional subcarrier spacing can be achieved. The feasibility and effectiveness of the proposed joint synchronization algorithm is verified in both simulations and a 47.3 Gbit/s 16-ary quadrature amplitude modulation (16-QAM) CO-OFDM system.

Comparison of the compensation effects of fiber nonlinear impairments with mid-span optical phase conjugation between PDM CO-OFDM system and PDM QPSK system**Project supported by the National Natural Science Foundation of China (Grant Nos. 61271192, 61427813, and 61331010) and the National Basic Research Program of China (Grant No. 2013AA013401).

The compensation effects of fiber nonlinearity in 112 Gb/s polarization division multiplexing (PDM) coherent optical systems by mid-span optical phase conjugation (OPC) based on four wave mixing (FWM) effect are studied. Comparisons of the compensation results between PDM coherent optical-orthogonal frequency division multiplexing (CO-OFDM) system and the single carrier (SC) PDM quadrature phase shift keying (QPSK) system are provided as well. The results demonstrate that nonlinear compensation effect with mid-span OPC in PDM CO-OFDM system is much more obvious than that in SC PDM QPSK system.

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.

Fiber Nonlinearity Equalizer Based on Support Vector Classification for Coherent Optical OFDM

A support vector machine (SVM)-based classification nonlinear equalizer (NLE) is demonstrated, for the first time, in coherent optical orthogonal frequency-division multiplexing (CO-OFDM). For a 40-Gb/s 16 quadrature amplitude modulated (16QAM) CO-OFDM system at 400 km of transmission, SVM-NLE reduces the fiber-induced nonlinearity penalty by about 1 dB in comparison to the benchmark artificial-neural-network (ANN)-based and inverse-Volterra-series-transfer-function-based NLEs.

Experimental Demonstration of a 16.27 Gb/s 2-D Coherent Optical OFDM System With 3-D Signal Mapper and 2-D IFFT Modulator

We propose a coherent optical OFDM (CO-OFDM) system based on 3-dimensional (3-D) OFDM technique in this paper. By using the 3-D signal mapper and 2-D IFFT module, the minimum Euclidean distance (MED) in constellations is increased by 8.7%, and the peak-to-average power ratio of the generated OFDM signal is reduced by 4 dB. The experimental results show that the 3-D OFDM method can improve nonlinearity tolerance by 2 dB for 100-km standard single mode fiber in a 16.27-Gb/s 2-D coherent optical OFDM system without polarization modulation. Theoretical analysis and simulation results show that the OSNR penalty could be attributed to the increased MED, the extended decision boundaries and the coding gain. To further analyze the performance in long haul transmission system, the simulation setup of 1000-km SSMF CO-OFDM system is built up. The results verify that the proposed method could effectively enhance nonlinearity tolerance and transmission performance of the CO-OFDM system.

Phase Noise Effects on Phase-Modulated Coherent Optical OFDM

One of the primary drawbacks of orthogonal frequency-division multiplexing (OFDM) is the large peak-to-average ratio (PAPR). It continues to contribute nonlinear degradations after it was introduced into optical fiber transmissions. However, phase-modulated OFDM can reduce the PAPR to the minimum, since its amplitude can be constant. In this paper, we conduct the theoretical and experimental study on the laser phase noise effect in phase-modulated coherent optical OFDM systems. Due to the laser phase noise, the phase transformation at the receiver is prone to errors due to phase wrapping. Consequently, we propose a mean-phase-compensation (MPC) method, which compensate for the mean phase offset for each OFDM symbol that has a Gaussian-distributed histogram. This method can avoid the problematic unwrapping function in phase transformation. We derive the closed-form expressions for the phase noise spreading and the corresponding signal-to-noise ratios (SNRs) based on the Wiener phase noise model. Unlike conventional coherent optical OFDM, the phase noise spreading to each OFDM subcarrier is decided by the reciprocal of the square of the subcarrier frequency, and the SNR can be improved by using a stronger PM modulation. We also discuss the SNR improvement by discarding a few affected subcarriers closing to dc. In a simulation, we demonstrate that our closed-form expressions are accurate. Finally, we experimentally verify our MPC method and our analysis.