Polarization Division Multiplexed Coherent Optical Orthogonal Frequency Division Multiplexing Research Articles

Joint estimation and compensation of transceiver IQ imbalance for PDM CO-OFDM system

In this paper, a frequency-domain mathematical model is deduced for polarization-division multiplexing (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) system with transceiver in-phase and quadrature (IQ) imbalances. A novel training symbol structure is designed in which the mirror-subcarriers of pilot subcarriers were modulated with zero signal so that the channel distortion with transceiver IQ imbalances can be estimated. It proves that the channel distortion and transmitter IQ imbalances cannot be separated using the training symbols; therefore, the channel equalization method was used to recover the signals. Simulation results show that at 2 dB transmitter amplitude imbalances, 15° transmitter phase imbalances, 100 Gbit/s transmission rate, 1 040 km standard signal-mode fiber link, and 1×10−3 bit error rate, 23.5 dB optical signal-to-noise ratio (OSNR) is necessary for the proposed method. However, the compared schemes cannot achieve effective transmission.

Modified constellation reshaping method for PAPR reduction of PDM CO-OFDM based on a SLM algorithm

In this paper, we propose a modified constellation reshaping method for peak-to-average power ratio (PAPR) reduction in polarization division multiplexing (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems based on the selective mapping (SLM) method. A modified quadrature amplitude modulation (M-QAM) constellation is generated that has the same minimum distance as that of the conventional QAM (C-QAM) constellation. The M-SLM method is denoted as the M-QAM constellations combining with the traditional SLM method. At the receiver side, the mean square errors between the constellations of the received data and each M-QAM rotated by different phase rotation factors are calculated. Then, the phase rotation factor with the minimum mean square error is selected to recover the original data. The advantage of the proposed method is that it does not need to send additional side information, while it possesses nearly the same PAPR reduction and bit error rate performance as the traditional SLM method.

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.

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.

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.

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.

Blind Equalization Based on JADE in PDM-CO-OFDM

Optical orthogonal frequency division multiplexing (OOFDM) significantly reduces frequency overhead in data transmission. Channel equalization (CE) is an approach used to estimate the channel state, and generally with inserting periodic training symbols (TS) to assist channel estimation. By study the technique of independent component analysis, a blind CE method based on joint approximate diagonalization of eigen-matrices with only one-tap in each subcarrier and without TS for polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) is proposed. This method has a faster convergence speed than the conventional CE technique in PDM-CO-OFDM. For the free of TS, it also enhances the spectral efficiency of the systems. The given approach may offer an efficient technique in the fields such as data transmission in high speed and burst communication, as well as OFDM system. Simulation results indicate that our method is effective for blind CE in OOFDM.

Training Symbol Assisted in-Band OSNR Monitoring Technique for PDM-CO-OFDM System

We proposed and demonstrated an in-band optical signal-to-noise ratio (OSNR) monitoring method for a polarization-division-multiplexed coherent optical orthogonal frequency-division-multiplexing (PDM-CO-OFDM) system. OSNR of the PDM signals on both polarization tributaries can be simultaneously monitored by calculating the electrical SNR with low complexity by taking advantage of the uncorrelation property between the noise and training symbol, which is used for conventional frame synchronization. This OSNR monitoring technique is verified in 103.57-Gb/s 16 quadrature amplitude modulation-based PDM CO-OFDM transmission system with 240—1440-km standard single-mode fiber (SSMF) links. Experimental results show that after calibration, the OSNR estimation error is less than 0.6 dB in a dynamic range of 12—27 dB, the estimation remains accurate even after 1440-km SSMF transmission, regardless of the chromatic dispersion and polarization mode dispersion in the fiber. To further investigate the robustness of the proposed OSNR monitoring method, additional simulation is implemented on VPI and MATLAB platform. It turned out to be insensitive to nonlinear effect within reasonable range as our monitoring technique shows good performance with launching power below −2 dBm after 500-km SSMF transmission. The proposed technique could still accurately monitor the individual OSNR of each polarization tributary of the PDM signal even in the presence of 5-dB polarization-dependent loss.

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.

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.

A code-aided carrier synchronization algorithm based on improved nonbinary low-density parity-check codes

In order to further improve the carrier synchronization estimation range and accuracy at low signal-to-noise ratio (SNR), this paper proposes a code-aided carrier synchronization algorithm based on improved nonbinary low-density parity-check (NB-LDPC) codes to study the polarization-division-multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system performance in the cases of quadrature phase shift keying (QPSK) and 16 quadrature amplitude modulation (16-QAM) modes. The simulation results indicate that this algorithm can enlarge frequency and phase offset estimation ranges and enhance accuracy of the system greatly, and the bit error rate (BER) performance of the system is improved effectively compared with that of the system employing traditional NB-LDPC code-aided carrier synchronization algorithm.

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.

Channel Equalization Using Independent Component Analysis in PDM-CO-OFDM

We propose a channel equalization method without training symbols (TSs) based on the independent component analysis (ICA) for polarization-division-multiplexing coherent-optical orthogonal-frequency-division-multiplexing (PDM-CO-OFDM) transmission systems. Compared with the conventional TS-based channel equalization method, the proposed method with 80 collected OFDM symbols shows a better transmission performance in the case of QPSK modulation format, and almost the same performance in the case of 16-quadrature amplitude modulation (QAM) format. In addition, we propose a new channel frequency response initialization method to solve the permutation indeterminacy and complex uncertain scaling problems in ICA-based channel equalization. The proposed initialization method shows faster convergence speed than the conventional random initialization method in the channel equalization process. Finally, we examine the number of OFDM symbols required for the proposed ICA-based channel equalization. This study shows that 40 and 80 OFDM symbols are sufficient for the QPSK and 16-QAM formats, respectively. Since the proposed ICA-based channel equalization method is free of TSs, the spectral efficiency of the PDM-CO-OFDM systems can be improved considerably.

Orthogonal Basis Expansion-Based Phase Noise Suppression for PDM CO-OFDM System

In this letter, we develop an orthogonal basis expansion (OBE)-based phase noise suppression method for polarization-division-multiplexed (PDM) coherent optical orthogonal frequency-division-multiplexing (CO-OFDM) systems. Compared with the conventional phase noise suppression approach, the OBE method not only significantly promotes the system tolerance of laser phase noise, but also improves the system robustness against nonlinear phase noise. The theoretical analysis is validated by numerical simulations of PDM CO-OFDM systems with 16-quadrature-amplitude-modulation format.

Joint scheme for symbol, sampling clock, and carrier frequency synchronization in PDM-CO-OFDM system beyond 100 Gb/s

We propose a joint scheme for symbol, sampling clock, and carrier frequency synchronization in a polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system. Unlike other existing algorithms designed for specific impairment, the scheme can estimate and compensate for the interactional synchronization errors effectively without extra training overhead by building a compre­hensive error model. The simulation shows that symbol synchronization error and sample timing error can be corrected by channel equalizer, and the estimation ranges of sampling frequency offset and normalized carrier frequency offset are about (-2000, 2000)ppm, and (-0.04 (-3.5), 0.04 (3.5))Ghz, respectively.

Per-symbol-based digital back-propagation approach for PDM-CO-OFDM transmission systems

For polarization-division-multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) systems, we propose a per-symbol-based digital back-propagation (DBP) approach which, after cyclic prefix removal, conducts DBP for each OFDM symbol. Compared with previous DBP, this new proposal avoids the use of inefficient overlap-and-add operation and saves one fast Fourier transform (FFT) module, therefore simplifying the hardware implementation. Transmitting a 16-QAM, 42.8-Gb/s PDM-CO-OFDM signal over 960-km standard single mode fiber (SSMF), we compare the previous and the proposed DBP approaches with different receiver's sampling rates and different step lengths in each DBP iteration, and found that the proposed DBP can achieve a similar performance as that of the previous DBP while enjoying a simpler implementation. We have also specifically introduced a small self-phase modulation (SPM) model for DBP and demonstrated its feasibility with the same experimental setup.

Mth-power-law method to compensate laser linewidth of 100 Gb/s PDM-CO-OFDM systems

Laser linewidth is the important determinant of applying coherent optical orthogonal frequency division multiplexing (CO-OFDM) in optical transmission systems. The laser linewidth impairments in 100-Gb/s polarization division multiplexing CO-OFDM (PDM-CO-OFDM) system without optical dispersion compensation are compensated by the phase drift compensator (PDC) based onMth-power-law method located at the receiver. PDC is more effective to compensate the phase drift due to laser linewidth. Simulating results show that the maximum Q factor can be increased by almost >10.0 dB for back-to-back (BtoB). For the 100-kHz linewidth system of 800-km system, a benefit of about 4.9 dB is possible for the maximum Q factor.

Improving nonlinearity tolerance of 112-Gb/s PDM OFDM systems with coherent detection using BLAST algorithm

The use of Bell Laboratories layered space-time (BLAST) architecture as a digital signal processing algorithm is proposed in this letter. It is aimed at improving the nonlinearity tolerance of a polarization division multiplexing (PDM) coherent optical orthogonal frequency division multiplexing (CO-OFDM) system. The application of this channel estimation algorithm simulates system performance under different dispersion compensation (DC) maps. Simulation results show that, compared with intra-symbol frequency-domain averaging (ISFA) algorithm, at least 5-dB Q-factor improvement is achieved for the PDM CO-OFDM system at 112-Gb/s data rate over an 800-km standard single-mode fiber (SSMF) without DC.

应用于100Gb/s长距离PDM-CO-OFDM系统中的电域补偿算法的研究

We study an electronic compensator (EC) as a receiver for a 100-Gb/s polarization division multiplexing coherent optical orthogonal frequency division multiplexing (PDM-CO-OFDM) system without optical dispersion compensation. EC, including electrical dispersion compensation (EDC), least squares channel estimation and compensation (LSCEC), and phase compensation (PC), is used to compensate for chromatic dispersion (CD), phase noise, polarization mode dispersion (PMD), and channel impairments, respectively. Simulations show that EC is highly effective in compensating for those impairments and that the performance is close to the theoretical limitation of optical signal-to-noise rate (OSNR), CD, and PMD. Its robustness against those transmission impairments and fiber nonlinearity are also systematically studied.

Improving the Nonlinear Tolerance of Polarization-Division-Multiplexed CO-OFDM in Long-Haul Fiber Transmission

We present digital signal processing techniques and algorithms for improving the tolerance of polarization-division multiplexed (PDM) coherent optical orthogonal frequency-division multiplexing (CO-OFDM) to fiber nonlinear effects, in both single-channel and wavelength-division multiplexed (WDM) transmission. For single-channel transmission, we discuss a self-phase modulation (SPM) compensation method that jointly processes two polarization components of a PDM CO-OFDM signal. For WDM transmission, we describe a novel OFDM channel estimation scheme that reduces the cross-phase-modulation (XPM) penalty among the WDM channels. The nonlinear tolerance improvements enabled by these signal processing techniques are quantified through numerical simulations for both dispersion-unmanaged and dispersion-managed long-haul optical fiber transmission with 112-Gb/s PDM CO-OFDM wavelength channels.