Applying implicit training to polarization-division-multiplexed coherent optical systems

Polarization dependent loss (PDL) causes imbalanced optical signal to noise ratio (OSNR) of the two polarizations, thus remains one of the major bottlenecks for next-generation polarization-division-multiplexed (PDM) coherent optical transmission systems. In this paper, we investigate Pairwise Coding for adaptive PDL mitigation in PDM coherent optical systems. By pre-coding across two polarizations, the PDL-induced performance degradation can be largely mitigated without any coding overhead. We present details of the coding and de-coding design, and also derive the analytical symbol/bit error rate of the Polarization Pairwise Coding scheme, which can be used to predict the performance gain as well as for optimal rotation angle calculation. Simulation results verify that Pairwise Coding achieves substantial system performance gains over a wide range of PDL values. Compared with other digital coding techniques, Polarization Pairwise Coding shows improved performance than Walsh-Hadamard transform since it maximizes the coordinate diversity; and also Pairwise Coding is computationally much simpler to decode compared with the Golden and Silver Codes, therefore is practical for current 100-Gb/s and future 400-Gb/s and 1-Tb/s digital coherent transceivers.

A maximum likelihood sequence detection (MLSD) receiver is used to detect data sequences in single-carrier coherent optical systems in the presence of laser phase noise. It requires no explicit phase estimation and involves only linear operations. It consistently shows improvement in the OSNR penalty (e.g., 1.1 dB at BER = 10⁻⁴ with memory length L =3) and the laser linewidth tolerance (e.g., around 4 times that of DAML at 1dB OSNR penalty at BER = 10⁻⁴ with memory length L =3) over the well-known DAML and Mth power approaches in laser phase noise (LPN)-impaired coherent optical systems.

We propose an optical signal-to-noise ratio (OSNR) estimation technique using self-equalized complementary Golay sequences for both QPSK and 16-QAM coherent optical systems. The training sequences have complementary spectra, which enable accurate channel estimation and equalization, and have length-independent constellation for high-performance estimation. Estimation performances are verified through 100- and 40-Gb/s QPSK and 200- and 80-Gb/s 16-QAM coherent polarization-multiplexed optical systems, with an accuracy of 0.4 and 0.7 dB, in both simulations and experiments, respectively.

In coherent optical communication systems, where multiple modulation formats are mixed and variable, the correct identification of signal modulation formats provides the foundation for subsequent performance improvement using digital algorithms. A modulation format identification (MFI) scheme based on signal constellation diagrams and support vector machine (SVM) is proposed. Firstly, the signal constellation diagrams are divided by the fractal dimension of the weighted linear least squares (WLS-FD) algorithm, and the fractal dimension (FD) in each region is calculated, which is regarded as one of the image features. Then, the feature values of the image in different directions are extracted by the gray-level co-occurrence matrix (GLCM), and their mean and variance are calculated, which is regarded as another feature. Finally, the two features are input into the modulation format classifier constructed by the SVM to achieve MFI in coherent optical communication systems. To verify the feasibility and superiority of the scheme, we compare it with the MFI scheme based on higher-order statistical (HOS) features, GLCM features, and FD features, respectively. Further, we built a 30 GBaud coherent optical communication system with fiber lengths of 80 km and 120 km, where the optical signal-to-noise ratio (OSNR) ranges from 0 dB to 30 dB. The proposed MFI scheme identifies seven modulation formats: QPSK, 8QAM, 16QAM, 32QAM, 64QAM, 128QAM, and 256QAM. The results show that compared with the other three schemes, our proposed scheme has a better identification accuracy at low OSNR. In addition, the identification accuracy of this scheme can reach 100% when the OSNR ≥ 10 dB.

Theory of Optical Communications. Fiber Devices for Optical Communication Systems. Integrated Devices for Optical Communication Systems. Direct Detection Optical Communication Systems. Coherent Systems: Structure and Ideal Performance. Performance Degradation Sources in Coherent Optical Systems. Multilevel Coherent Optical Systems. Multichannel Optical Systems. Present--Day Systems Implementations. Appendices. Index.

Deep learning-based nonlinear phase shift estimation in coherent optical communication systems

The high speed rotation of state of polarization (RSOP) is a key issue for 16 quadrature amplitude modulation (QAM) coherent optical polarization division multiplexing (PDM) communication systems in strong lightning weather. To reduce the bit error rate (BER) caused by the high speed of RSOP, the historical information is first proposed to correct the demodulation process in coherent optical communication systems. By adding the time reverse error term into the cost function, a new equalization algorithm is proposed for coherent optical communication systems. Compared with the conventional Multi-modulus Algorithm (MMA), simulation results show that the average BER and steady-state error (SSE) of the new algorithm is reduced by 33.47% and 4.08%, respectively. Moreover, the average tolerance of RSOP of the new algorithm is increased by 28.57% compared with the MMA in 16 QAM coherent optical PDM communication systems.

Cost-effective OSNR monitoring with large chromatic dispersion tolerance using random forest for intermediate nodes

In this study, we proposed an improved Minimum Mean Square Error (MMSE) channel estimation algorithm for the coherent wireless underwater optical OFDM system aiming to improve parameters such as dispersion, attenuation and optical noise. The simulation results of the proposed algorithm was compared with the performance of Discrete Fourier Transform (DFT) based and time based Least Square (LS) and MMSE channel estimation techniques. The results demonstrated that the proposed approach improved the underwater wireless channel estimation performance and offers a promising alternative for the OFDM systems with less complexity and high efficiency.

The problem of joint channel estimation, equalization, and multiuser detection for a multiantenna DS/CDMA system operating over a frequency-selective fading channel and adopting long aperiodic spreading codes is considered in this paper. First of all, we present several channel estimation and multiuser data detection schemes suited for multiantenna long-code DS/CDMA systems. Then, a multipass strategy, wherein the data detection and the channel estimation procedures exchange information in a recursive fashion, is introduced and analyzed for the proposed scenario. Remarkably, this strategy provides, at the price of some attendant computational complexity increase, excellent performance even when very short training sequences are transmitted, and thus couples together the conflicting advantages of both trained and blind systems, that is, good performance and no wasted bandwidth, respectively. Space-time coded systems are also considered, and it is shown that the multipass strategy provides excellent results for such systems also. Likewise, it is also shown that excellent performance is achieved also when each user adopts the same spreading code for all of its transmit antennas. The validity of the proposed procedure is corroborated by both simulation results and analytical findings. In particular, it is shown that adopting the multipass strategy results in a remarkable reduction of the channel estimation mean-square error and of the optimal length of the training sequence.

The increasing shortage of spectrum resources makes researchers pay much attention to how to improve the spectral efficiency. Faster-than-Nyquist (FTN) coherent optical transmission is one of the most promising techniques to improve the spectral efficiency achieved by duobinary shaping. In this work, a FTN coherent optical transmission system is constructed containing transmitting side and receiving side. On the transmitting side, signals are transmitted after QPSK or 16QAM modulation with duobinary shaping. On the receiving side, the laser phase noise is eliminated by a pilot aided blind phase search (BPS) algorithm. Then the duobinary-shaped 16QAM or QPSK signal is processed by the maximum likelihood sequence estimation (MLSE). The constellation diagrams prove the effectiveness and convergence of the proposed algorithms. Moreover, the numerical results verify the relationship between the optical signal to noise ratio (OSNR) and the bit error rate (BER). Meanwhile, it is obvious that the FTN coherent optical transmission with duobinary shaping can improve the spectral efficiency effectively for signals of different modulation formats.

We propose a novel bit error rate (BER) estimation scheme based on a k-means clustering algorithm assisted Gaussian approach (GA). This method can implement accurate BER estimation within a short symbol sequence and is applicable for arbitrary modulation formats. First, after carrier phase recovery (CPR), the k-means clustering algorithm is used to partition clusters and find the respective centroids of each cluster. The means and variances are calculated from the symbols of each cluster. Compared with the decision-directed method based on power normalization, our method can find more precise means and further obtain more accurate variances. Subsequently, with the accurate means and variances, the resultant probability density function (PDF) of each symbol under Gaussian assumption is integrated over the respective decision zone to calculate symbol error rate (SER). Finally, the general conversion factor from SER to BER is introduced by taking into account the coding information of adjacent symbols. Therefore, the accurate BER estimation is attributed to the more accurate statistical parameter calculation and general SER-to-BER conversion schemes. The proposed scheme is verified in 34 GBaud polarization division multiplexing (PDM)-QPSK/8-QAM/16-QAM experiments. Compared with error vector magnitude (EVM)-to-BER conversion and GA+ common approximation (CA) scheme, the better estimation accuracy in the BER range from 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> -10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> is achieved successfully with only 10000 symbols. More specifically, our method has a significant improvement in estimation accuracy for non-Gray-mapped signals under low optical signal-to-noise ratio (OSNR). The BER estimation error can be reduced from 60 to 14% with PDM-8-QAM signal considered when actual BER is around 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> .

Joint modulation format identification and OSNR estimation method based on trajectory information analysis

As one of the three major scenarios of fifth-generation (5G) communication system, massive machine type communications (mMTC) raises more challenges for development of new radio access technology. Unlike the human-to-human communications, the mMTC typically exhibit features such as massive number of devices, small-sized packets and sporadic transmission, which requires novel solutions to satisfy these features. In this paper, we propose a novel grant-free compressive sensing based solution with system level design to jointly conduct the active devices detection, channel estimation and data recovery without knowing the number of active devices. Specifically, in proposed solution, we integrate the sparsity information of channel coefficients and data symbols and exploit the constellation information of modulation and the data diversity of different devices to enhance the performance of receiver. Simulation results demonstrate that the proposed solutions have improve the performance of active device detection, channel estimation, data recovery and the throughput of the system.

Data Dependent Superimposed Training (DDST) scheme outperforms the traditional superimposed training by fully canceling the effects of unknown data in channel estimator. In DDST, however, the channel estimation accuracy and the data detection or channel equalization performance are affected significantly by the amount of power allocated to data and superimposed training sequence, which is the motivation of this research. In general, for DDST, there is a tradeoff between the channel estimation accuracy and the data detection reliability, i.e., the more accurate the channel estimation, the more reliable the data detection; on the other hand, the more accurate the channel estimation, the more demanding on the power consumption of training sequence, which in turn leads to the less reliable data detection. In this paper, the relationship between the Signal-to-Noise Ratio (SNR) of the data detector and the training sequence power is analyzed. The optimal power allocation of the training sequence is derived based on the criterion of maximizing SNR of the detector. Analysis and simulation results show that for a fixed transmit power, the SNR and the Symbol Error Rate (SER) of detector vary nonlinearly with the increasing of training sequence power, and there exists an optimal power ratio, which accords with the derived optimal power ratio, among the data and training sequence.