Joint, accurate and robust optical signal-to- noise ratio and modulation format monitoring scheme using a single Stokes-parameter-based artificial neural network

Qian Xiang; Yanfu Yang; Qun Zhang; Yong Yao

doi:10.1364/OE.415138

1. Introduction

To meet the rapid traffic demand driven by smart devices and cloud computing, an intelligent optical switching network with the features of adaptive modulation format and bit rate configuration is considered as the potential solution to address dynamic traffic demand [1–3]. Specifically, the spectral and link resources in an intelligent optical switching network are dynamically allocated to transmission nodes according to the monitored optical performance parameters. Among those parameters, optical signal to noise ratio (OSNR) and modulation format are directly related to the quality of the transmission system. OSNR, the accumulated amplified noise from cascaded erbium-doped fiber amplifier (EDFA), is directly related to the transmission quality and used as the criterion for evaluating the quality of fiber link [4,5]. Meanwhile, it is also imperative to monitor modulation format for assisting system resource allocation, because the required OSNR for the desired forward error correction (FEC) threshold is also a function of modulation format. Therefore, a joint monitoring scheme for both OSNR and modulation format is highly desired for the next-generation dynamic optical network.

Various schemes, based on the combination of artificial intelligent techniques and optical performance-dependent features, have been proposed to estimate OSNR and identify modulation format simultaneously [6–17]. These schemes can be classified as two technology routines: (1) the monitoring schemes in Jones space and (2) the monitoring schemes in Stokes space. Jones space-based monitoring schemes using the machine learning algorithm, based on the features of the constellation diagram [9,17], amplitude histograms [10], and high order statistics [12], are widely investigated to monitor OSNR and modulation format. However, those schemes in Jones space cannot distinguish m-PSK signals, because of their similar distribution in the complex plane before the carrier recovery. Compared with the monitoring scheme in Jones space, the monitoring scheme in Stokes space is more attractive, because the constellation distribution in Stokes space is immune to the common phase noise between X and Y polarization. Clustering algorithm such as K-means is employed to identify the modulation format by finding the centroid constellation in Stokes space, but it shows a limited monitoring accuracy at low OSNR condition [13,14,18]. To monitor modulation format and OSNR simultaneously, different Stokes parameter’s gray images are used to train the convolutional neural network (CNN) [15]. However, the constellation diagram-based scheme using CNN suffers from high time complexity than simple neural network such as an artificial neural network (ANN) and deep neural network (DNN) [19,20]. Meanwhile, a two-stages DNN was also used to extract the features from the fitting curve of the first-order derivation of the Stokes parameters for both OSNR and modulation format identification [16]. Compared with the monitoring scheme using Stokes-parameters-based CNN, it needs less computational resources and shows comparable estimation accuracy. However, there exists a large OSNR estimation error if the modulation format is misclassified. Moreover, those monitoring schemes in Stokes space do not consider the phase-related polarization rotation caused by fiber birefringence, which always leads to the phase difference between orthogonalized polarization. To be specific, the constellation distribution in Stokes space changes over time, especially under dynamic polarization rotation conditions such as lightning strikes [21]. Consequently, the existing schemes fail to monitor the optical performance parameter directly in the presence of fast polarization rotation. Therefore, a joint and robust OSNR and modulation format identification scheme is indispensable to be explored for future optical network, especially under reconfigurable modulation format transmission condition.

Based on our previous work [12], we propose to use a simple ANN to predict OSNR and modulation format from cumulative distribution function (CDF) using a single Stokes parameter. Before ANN, a simple carrier recovery scheme using the power iteration method in Stokes space is used to eliminate the influence of phase difference between X and Y polarization on constellation distribution in Stokes space. Then, CDF bins of S₂parameter are calculated. Subsequently, a simple ANN with three layers is used to extract the potential relationship between CDF bins and target OSNR and modulation format directly. Compared with those feature-based schemes in Jones space, the proposed scheme can identify both m-PSK and m-QAM signals easily, because constellation distributions of signals in Stokes space are dependent on its modulation type. 28GS/s polarization division multiplexing (PDM) QPSK, 8PSK, 8QAM, and 16QAM as well as 64QAM are employed to evaluate the monitoring performance over wide OSNR ranges. Simulation results indicate that the proposed scheme can obtain 100% modulation format identification accuracy and small OSNR estimation error over wide OSNR ranges. Meanwhile, the proposed scheme also shows high OSNR estimation accuracy and acceptable OSNR estimation error after long-haul fiber transmission. The experimental results show that the mean OSNR estimation errors in our scheme are around 0.13 dB, 0.29 dB, and 0.41 dB for 28GS/s PDM QPSK, 8PSK, and 16QAM, respectively. Meanwhile, high modulation format identification accuracy can also be obtained for the tested formats over wide OSNR and launched power ranges. Meanwhile, compared with the monitoring scheme enabled by DNN and CNN, our scheme also has the advantages of low computational complexity due to the simple structure of ANN.

2. Operating principle

In the PDM transmission system, the received signal can be expressed mathematically as follows:

(1)$${\boldsymbol{R}} = \left[ {\begin{array}{{c}} {{{\boldsymbol R}_{\boldsymbol x}}}\\ {{{\boldsymbol R}_{\boldsymbol y}}} \end{array}} \right] = {\boldsymbol H} \otimes \left[ {\begin{array}{{cc}} {\cos \theta {e^{j{\kappa_1}}}}&{ - \sin \theta {e^{j{\kappa_2}}}}\\ {\sin \theta {e^{ - j{\kappa_2}}}}&{\cos \theta {e^{ - j{\kappa_1}}}} \end{array}} \right]\left[ {\begin{array}{{c}} {{{\boldsymbol T}_{\boldsymbol x}}}\\ {{{\boldsymbol T}_{\boldsymbol y}}} \end{array}} \right]{e^{j\varphi }} + \mathrm{\xi }{= \boldsymbol H} \otimes {\boldsymbol J} \cdot {\boldsymbol T} \cdot {e^{j\varphi }} + \mathrm{\xi }.$$

in which R and T denote the received and transmitted signals, ${\otimes}$ is the convolution operator, subscript “x” and “y” present X and Y polarization, and H denotes the total system response. J is a three parameters polarization rotation matrix, and f₁, f_2, and f₃ are the rotation rate of θ, κ_1, and κ₂, respectively. $\varphi$ is the total phase noise induced by both frequency offset and phase noise, $\xi$ represents the additive white Gaussian noise with zero mean, respectively.

After chromatic compensation by statistic equalizer and channel pre-equalization by constant modulus algorithm (CMA), the pre-equalized signals Z can be expressed as below:

(2)$${\boldsymbol Z} = \left[ {\begin{array}{{c}} {{{\boldsymbol Z}_{\boldsymbol x}}}\\ {{{\boldsymbol Z}_{\boldsymbol y}}} \end{array}} \right] = {{\boldsymbol H}_{\boldsymbol{res}}} \otimes \left[ {\begin{array}{{cc}} 1&0\\ 0&{{e^{j\Delta \phi }}} \end{array}} \right]\left[ {\begin{array}{{c}} {{{\boldsymbol T}_{\boldsymbol x}}}\\ {{{\boldsymbol T}_{\boldsymbol y}}} \end{array}} \right]{e^{j\varphi }} + \mathrm{\xi } = {{\boldsymbol H}_{\boldsymbol{res}}} \otimes {\boldsymbol G}\left[ {\begin{array}{{c}} {{{\boldsymbol T}_{\boldsymbol x}}}\\ {{{\boldsymbol T}_{\boldsymbol y}}} \end{array}} \right]{e^{j\varphi }} + \mathrm{\xi }.$$

where H_res is the residual chromatic dispersion, $\Delta \phi$ is the phase difference between X and Y polarization, which is induced by polarization rotation. G is the phase difference matrix.

Obviously, before carrier recovery, the distribution of square QAM signals varies with modulation level, which is always used as a useful feature for modulation format identification. However, it is noticed that m-PSK signals show a similar distribution in Jones space, which means that m-PSK signals cannot be classified directly. One possible solution for this problem is to map signals in Jones space into 3-dimension Stokes space.

The Stokes parameters in Stokes space can be expressed as follows [18]:

(3)$${\boldsymbol S} = \left\{ {\begin{array}{{c}} {{{\boldsymbol S}_0}}\\ {{{\boldsymbol S}_1}}\\ {{{\boldsymbol S}_2}}\\ {{{\boldsymbol S}_3}} \end{array}} \right.{ = }\left\{ {\begin{array}{{c}} {{{\boldsymbol Z}_x}{\boldsymbol Z}_x^\ast { + }{{\boldsymbol Z}_y}{\boldsymbol Z}_y^\ast }\\ {{{\boldsymbol Z}_x}{\boldsymbol Z}_x^\ast { - }{{\boldsymbol Z}_y}{\boldsymbol{Z}}_y^\ast }\\ {{{\boldsymbol Z}_y}{\boldsymbol Z}_{x}^{\ast }{ + }{{\boldsymbol Z}_x}{\boldsymbol Z}_y^\ast }\\ { - j{{\boldsymbol Z}_y}{\boldsymbol Z}_{x}^{\ast }{ + }j{{\boldsymbol Z}_x}{\boldsymbol Z}_y^\ast } \end{array}} \right.{ = }\left\{ {\begin{array}{{c}} {{\boldsymbol a}_x^2{ + {\boldsymbol a}}_y^2}\\ {{\boldsymbol a}_x^2{ - {\boldsymbol a}}_y^2}\\ {2{\boldsymbol a}_x^{}{\boldsymbol a}_y^{}\cos \Delta \phi }\\ {2{\boldsymbol a}_x^{}{\boldsymbol a}_y^{}\sin \Delta \phi } \end{array}} \right.$$

where S₀ is the total power, S₁, S₂ and S₃ denote the Stokes parameters. Superscript “*” is the conjugation operation. a_x and a_y is the amplitude of the complex signal. After power normalization, the constellations in Stokes space are located at the Poincare sphere and it varies with signal type, as shown in Fig. 1 (a1)-(d1). Moreover, Fig. 1 (a2)-(d2) indicates that the distribution in (S₂,S₃) plane also varies with modulation type, which means that S₂ or S₃ parameter can be used as an alternative feature for signal classification. In this paper, S₂ parameter is used as the feature for signal classification. However, it is noticed that the constellation distribution in both the Stokes space and (S₂, S₃) plane suffers from phase difference $\Delta \phi$, as shown in Fig. 1 (a4)- (d4). Notably, the phase difference $\Delta \phi$ is mainly caused by fiber birefringence. Therefore, before optical performance-dependent feature extraction, it is necessary to estimate phase difference firstly.

Fig. 1. Constellation diagram in Stokes space and Stokes parameter projection in (S₂, S₃) plane. (a) PDM QPSK, (b) PDM 8PSK, (c) PDM 8QAM and (d) PDM 16QAM. (1) and (2) with polarization rotation rate f₂=0 kHz, (3) and (4) with polarization rotation rate f₂=100 kHz, OSNR is set to 30 dB.

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To estimate $\Delta \phi$, we construct a complex signal Uusing the S₂ and S₃ parameters, given as U = S₂+jS₃. Obviously, the phase difference $\Delta \phi$ can be considered as the phase noise of the constructed signal U, and the phase noise estimation scheme can be used to estimate the phase difference.

The power iteration method (PIM), a simple and useful first principal component (PC) tracking scheme, has been demonstrated for phase noise estimation for m-QAM signal [22]. After 2^nd power operation of the signal, the square m-QAM signals show elliptical distribution, and its first PC varies with phase noise. Phase noise can be calculated according to the tracked first PC. As mentioned above, the phase difference can be modeled as phase noise in Stokes space, which means that PIM can also be used to track the phase difference in Stokes space.

It is also worthy to notice that different N^th power operation should be used for m-PSK and m-QAM signals to estimate the phase difference angle correctly. Specifically, there only needs 2^nd power for m-QAM signals, because constellation in (S₂, S₃) plane shows elliptical distribution after 2^nd power, its first PC can be easily determined. However, N^th (N>2) power operation must be used for m-PSK signal, because its constellation in (S₂, S₃) plane must be transformed into a QPSK signal firstly. To estimate the phase difference accurately, paralleled PIM using different N^th power is used to estimate the phase difference simultaneously. Notably, only with the corrected N^th power, the phase difference can be estimated accurately, and the MSE between the corrected phase difference and the initial one is maximized. Consequently, after paralleled implementation of PIM, the corrected phase difference can be determined by finding the estimated phase with the largest MSE in the phase analysis module. The mean square error between the estimated phase angle $\mathrm{\sigma }_k^N$ and its initial value ${\mathrm{\sigma }_0}$ is calculated according to $MSE = E\{ {(\mathrm{\sigma }_k^N - {\mathrm{\sigma }_0})^2}\}$. E denotes the expectation operation.

Figure 2 illustrates the schematical diagram of paralleled PIM for phase estimation in Stokes space, it consists of 3 parts: (1) N^th power and covariance calculation, (2) first PC tracking and phase estimation and (3) phase analysis.

Fig. 2. The schematical diagram of paralleled PIM for phase difference estimation in Stokes space.

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After N^th power operation, the covariance of the input vector with L elements is calculated, given as follows:

(4)$${{\boldsymbol A}_k} = \left[ {\begin{array}{{c}} {\textrm{Re} \{ {\boldsymbol U}_k^N(1)\} ,\ldots ,\textrm{Re} \{ {\boldsymbol U}_k^N(L)\} }\\ {{\mathop{\textrm {Im}}\nolimits} \{ {\boldsymbol U}_k^N(1)\} ,\ldots ,{\mathop{\textrm {Im}}\nolimits} \{ {\boldsymbol U}_k^N(L)\} } \end{array}} \right].$$

(5)$${{\boldsymbol C}_k} = {{\boldsymbol A}_k}{\boldsymbol A}_k^T.$$

where A is a 2 ${\times}$ L real matrix, superscript “T” denotes the transposition operation.

Next, the vector of the first PC ${\boldsymbol{v}_k}$ and phase angle $\boldsymbol{\sigma}$ can be iteratively estimated according to the covariance matrix ${\textrm{C}_k}$, given as below:

(6)$${{\boldsymbol v}_k} = {{\boldsymbol C}_k}{{\boldsymbol v}_{k - 1}}.$$

(7)$${{\boldsymbol v}_k} = {{\boldsymbol v}_k}/|{{\boldsymbol v}_k}|.$$

(8)$${\boldsymbol{\sigma}_k} = {\boldsymbol{arctan}}({{\boldsymbol v}_k}(2)/{{\boldsymbol v}_k}(1))/N$$

where |.| is norm operation, and the initial vector of the first PC is always chosen as ${{\boldsymbol v}_0}$=[1 0]^T.

Finally, the estimated phase angle is sent into the phase analysis module to select the corrected phase angle according to its MSE between the estimated phase and the initial one.

Consequently, the de-rotated ${\boldsymbol S}_2^{\prime}$ can be expressed mathematically as follows:

(9)$${\boldsymbol S}_{2,k}^{\prime} = {\textrm {Re}} \{ {{\boldsymbol U}_k}{e^{ - 1i{\boldsymbol{\sigma}}_k^N}})\}.$$

where ${\boldsymbol{\sigma}}_k^N$ is the estimated phase angle with the largest MSE.

After phase difference elimination, the empirical CDF of the absolute amplitude of ${\boldsymbol S}_2^{\prime}$ is used to characterize the distribution of ${\boldsymbol S}_2^{\prime}$, given as follows [8]:

(10)$${\boldsymbol F}(s) = \frac{1}{N}\sum\limits_{i = 1}^l {f({|{\boldsymbol S}}_2^{\prime}(i)|< s)}.$$

where f () is the specially designed function, which equals to one when the input is true, otherwise equals to zeros. l and s denote the length of ${\boldsymbol S}_2^{\prime}$ and the normalized absolute amplitude, respectively.

As shown in Fig. 3, CDF varies with both OSNR and modulation format, which indicates that CDF bins can be used as a useful feature for both OSNR and modulation format monitoring. To achieve modulation format and OSNR monitoring with low computational complexity, a simple ANN is employed here to map the potential relationship between CDF and modulation format as well as OSNR, as shown in Fig. 4.

Fig. 3. Cumulative distribution function of ${\boldsymbol S}_2^{\prime}$ parameter for different modulation formats, (a) PDM QPSK, (b) PDM 8PSK, (c) PDM 8QAM and (d) PDM 16QAM.

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Fig. 4. The schematic diagram of the OSNR and modulation format identification scheme using ANN.

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Before the training stage, the received signals of all combinations of modulation format and OSNR are pre-equalized by CMA with 5 taps. Then, the pre-equalized signals are mapped into Stokes space and phase difference is estimated by PIM. Next, CDF is calculated according to Eq. (10), and the corresponding modulation format for each CDF is labeled by the binary sequence as shown in Table I. Next, 50 bins of CDF are sent into ANN to approximate the potential relationship between the input features and target optical performance parameters. After weight optimization of ANN, the trained ANN is employed to predict modulation format and OSNR from the corresponding CDF bins. Then, the predicted modulation format and OSNR can be used as a reference for optimizing the spectrum and links resource allocation in the established optical transmission network.

3. Numerical simulation and discussion

In this section, 28GS/s PDM QPSK, 8PSK, 8QAM, 16QAM, and 64QAM are used to verify the effectiveness of our scheme regarding the estimation accuracy, chromatic dispersion tolerance and phase-related polarization rotation tolerance. The frequency offset and linewidth are 1 GHz and 100kHz. The polarization azimuth angle is π/5. The tap number and step size in CMA are set to 5 and 1e-3 for channel pre-equalization and polarization demultiplexing. To estimate the phase difference correctly, PIM with N of 2 and 4 is applied for the same signal, and the optimized block length in PIM is found to be 1024 under a fixed phase difference. 200 datasets, sampled for each OSNR and modulation format, are used to train and test the performance of the proposed ANN-based monitoring scheme. OSNR ranges are set to 10dB∼18 dB, 12dB∼20 dB, 12dB∼20 dB, 16dB∼24 dB, and 22dB∼28 dB for QPSK, 8PSK, 8QAM, 16QAM, and 64QAM, respectively. 75% of datasets are used to train the used ANN with 60 neurons in the hidden layer, and the rest are employed to evaluate the monitoring accuracy of our scheme.

As shown in Fig. 5, the proposed scheme shows high OSNR estimation accuracy over wide OSNR ranges for the employed modulation format. It is observed that the probability of OSNR estimation error within 1 dB is 100%, 99.78%, 100%, 99.78% and 98.89% for QPSK, 8PSK, 8QAM, 16QAM, and 64QAM respectively. The maximum OSNR estimation errors are 0.88 dB, 2.41 dB, 2.04 dB, 1.14 dB and 2.07 dB for the employed modulation format respectively. OSNR mean square error (MSE) in our scheme is 0.086 dB, 0.125 dB, 0.038 dB, 0.17 dB and 0.40 dB for QPSK, 8PSK, 8QAM, 16QAM and 64QAM respectively. The mean OSNR estimation error increases with modulation level, and 64QAM shows a larger mean estimation error than others. This phenomenon is attributed to the fact that CDF of 64QAM shows similar shapes under different OSNR conditions, which degrades the estimation accuracy. Moreover, the proposed scheme shows a comparable mean estimation error in comparison with the existing OSNR monitoring schemes [8,10,11,16]. Therefore, the proposed scheme also can be considered as an alternative scheme for high accuracy OSNR estimation.

Fig. 5. OSNR estimation error probability versus estimation error, (a) QPSK, (b) 8PSK, (c) 8QAM, (d) 16QAM and (e) 64QAM.

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As shown in Fig. 6 (a), the modulation format identification accuracy varies with the epoch in the neural network. QPSK and 8PSK need few epochs to achieve 100% MFI accuracy, whereas 16QAM needs around 60 epochs to achieve the same accuracy threshold. This phenomenon is attributed to the fact that different modulation format shows different CDF over wide OSNR ranges, high order modulation format shows similar CDF over wide OSNR ranges bins because of their dense distribution. With epochs of 90, the proposed scheme can classify both m-PSK and m-QAM signals correctly, as depicted in Fig. 6 (b). Compared with the existing methods, the proposed scheme shows comparable MFI accuracy. Moreover, to the best of our knowledge, it is the first time that a simple ANN is demonstrated to monitor both m-PSK and m-QAM signals simultaneously.

Fig. 6. (a) MFI accuracy versus epoch and (b) the detailed information about MFI accuracy with the epochs of 90.

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Moreover, the performance of trained ANN in the BTB case is also investigated under different phase-related polarization rotation rate. The phase-related polarization rotation rate is managed by changing the rotation rate of phase-related polarization rotation parameter κ₁ in Eq. (1). With the required OSNR for 7% FEC, 100 datasets for each modulation format and polarization rotation rate are sampled to test the trained ANN in the BTB case. As shown in Fig. 7(a), within 1 dB OSNR estimation error, the proposed scheme can tolerate the polarization ration rate up to 380kHz, 80kHz, 230kHz, 100kHz and 50kHz for QPSK, 8PSK, 8QAM, 16QAM, and 64QAM, respectively. Moreover, the trained ANN also shows 100% modulation identification accuracy when the polarization rotation rate is smaller than 100kHz. It is also noticed that the polarization rotation tolerance of our scheme is strictly dependent on the block length of PIM, which is similar to the performance of the phase noise estimation scheme in the Jones space. With a slow phase-related polarization rotation rate, the proposed scheme can obtain stable modulation identification accuracy and small OSNR estimation error. To the best of our knowledge, it is the first time that the phase-related polarization rotation problem is considered and solved by Stokes parameter based OSNR and modulation format monitoring scheme. Moreover, the estimated phase difference using PIM in Stokes space can also be used to compensate the fixed phase angle between orthogonalized polarization, which can simplify the carrier recovery module in the following digital signal processing (DSP) [23].

Fig. 7. (a) OSNR estimation errors versus phase-related polarization rotation rate and (b) modulation monitoring accuracy versus phase-related polarization rotation rate.

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In the following, modulation format identification and OSNR estimation accuracy of our scheme are investigated in detail after fiber transmission. The length of single fiber span and fiber loss are 80km and 0.2dB/km, and EDFA with a noise figure of 6dB is to compensate for fiber loss. The chromatic dispersion and nonlinear coefficient are 16ps/nm/km, and 1.3 km^-1·W^-1. The span number is set to 30, 20, 20, 12 and 8 for QPSK, 8PSK, 8QAM, 16QAM and 64QAM, respectively. The launched power is adjusted with the step size of 1dBm within the range of [-5∼5] dBm. As depicted in Fig. 8(a), the proposed scheme shows around 100% MFI accuracy for the tested modulation format over a wide launched power range, whereas OSNR mean estimation error varies with launched power. The main reason for this phenomenon is that nonlinear noise induced by the nonlinear Kerr effect cannot be ignored under the scenarios of large launched power [24,25]. Definitely, nonlinear noise and linear ASE noise should be monitored separately for further optimizing system parameters, but it is out of the scope of this work. Meanwhile, with 1dB OSNR estimation error, the proposed scheme can tolerate the residual chromatic dispersion up to ±100ps/nm in the presence of a moderate nonlinear Kerr effect. Although the residual chromatic dispersion tolerance is limited, it is still larger than the mean estimation error of the existed chromatic dispersion monitoring scheme [26]. Therefore, after coarse chromatic dispersion compensation and channel pre-equalization by multi-taps CMA, the proposed scheme is applicable for monitoring modulation format and OSNR after long-haul fiber transmission even in the presence of a moderate nonlinear Kerr effect.

Fig. 8. Performance evaluation after fiber transmission (a) monitoring accuracy versus launched power and (b) monitoring accuracy versus residual chromatic dispersion with launched power of -1dBm.

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4. Experimental result and discussion

The performance of our scheme is investigated in detail under the scenarios of both BTB and fiber transmission, and the experimental setup and DSP flow are illustrated as Fig. 9. Four channels 28GS/s electronic signals generated by arbitrary waveform generator (Keysight: M9502A) are fed into dual-polarization I and Q modulator. In the BTB case, the modulated optical signals are sent into fiber and coupled with the noise signals by a coupler with a ratio of 7:3. In the fiber transmission scene, the loss parameter, chromatic dispersion coefficient and nonlinear coefficient in fiber are 0.2 dB/km 17ps/nm/km, and 1.3 km^-1·W^-1, respectively. After single-span fiber transmission, EDFA is used to compensate for the fiber loss. The launched power is adjusting with the step size of 1dBm within a range of [-5∼5]dBm. The total fiber length is around 940 km. Subsequently, an optical bandpass filter is used to filter the out-of-band noise, and a narrow linewidth laser is used as the local oscillator to beat with a signal light in polarization diversity coherent receiver. Next, an 80 GS/s real-time oscilloscope (Keysight: DSA-X 96204Q) is employed to sample the signals, and the following DSP flow processes the sampled signals. Specifically, the timing recovery is obtained by the square-law nonlinear scheme. IQ imbalance is compensated by the Gram-Schmidt orthogonalization procedure (GSOP). After pre-equalization by CMA with 5 taps, the pre-equalized signals are mapped into Stokes space, and the phase difference between X and Y polarization is estimated by PIM in Stokes space. Then, the CDF of S₂ parameter is calculated, and it is used to train and verify the performance of our scheme. Consequently, the proper channel equalization scheme and carrier recovery scheme is employed to demodulate the signal. To train and verify the proposed scheme, 200 datasets are sampled for each OSNR and modulation format, and 60 datasets are sampled for each format after fiber transmission. OSNR ranges are set to 9.8dB ∼16.8dB, 12dB∼19dB and 16dB∼23dB for QPSK, 8PSK and 16QAM, respectively. Moreover, 75% of datasets are used to train the proposed ANN, and the rest datasets are employed to verify its performance.

Fig. 9. The experimental setup and digital signal processing flow.

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As shown in Fig. 10, with 1 dB OSNR error, the probability of OSNR estimation error is 99.75%, 99.50%, and 98.75% for QPSK, 8PSK, and 16QAM, respectively. The maximum OSNR estimation error is 1.06 dB, 1.04 dB, and 1.43 dB for the tested modulation format under the scenarios of low OSNR. Meanwhile, it is also worthy to notice that the mean OSNR estimation error is 0.13 dB, 0.29 dB, and 0.41 dB for QPSK, 8PSK and 16QAM, which is comparable to the results of the existing schemes. Moreover, the proposed scheme also shows 100% modulation format identification accuracy over wide OSNR ranges, as shown in Fig. 10(d). The experimental results further confirm that our scheme can obtain high modulation format identification and OSNR estimation accuracy for both m-PSK and m-QAM signals, which is consistent with the theoretical analysis and simulation results.

Fig. 10. The monitoring performance of our scheme, (a), (b) and (c) the OSNR estimation error probability for QPSK, 8PSK and 16QAM, and (d) the modulation format identification accuracy.

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After trained in BTB case, the trained ANN is used to monitor the modulation format and OSNR after 940 km fiber transmission. Kerr nonlinear effect and residual chromatic dispersion are emulated by adjusting the launched power and chromatic dispersion compensation coefficient. As shown in Fig. 11 (a), the proposed scheme shows high MFI accuracy for QPSK, 8PSK and 16QAM over wide launched power ranges. It is also noticed that OSNR estimation error increases with the launched power when the launched power is larger than a certain value. This phenomenon is caused by the fact that linear ASE noise plays a dominant role in the weak nonlinear region, but it is opposite under large launched power. As shown in Fig. 11 (b), with 1 dB OSNR estimation error, the proposed scheme can tolerate the residual chromatic dispersion up to ±160 ps/nm. With the case of large residual chromatic dispersion, the degradation of monitoring accuracy is mainly attributed to the fact that CMA with only 5 taps cannot achieve polarization demultiplexing and chromatic dispersion compensation completely. Additionally, it is also unacceptable to continually increase the launched power to obtain high OSNR, because the signal quality after transmission link is determined by both linear ASE and nonlinear noise, Therefore, the proposed scheme can also be integrated into the practical transmission link for optical performance monitoring.

Fig. 11. Monitoring performance after 940 km fiber transmission, (a) monitoring accuracy versus launched power and (b) monitoring accuracy versus residual chromatic dispersion with launched power of 0dBm.

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5. Conclusion

In this paper, we proposed and demonstrated a joint and accurate OSNR estimation and modulation format identification scheme using a single Stokes parameter-based ANN. Before the CDF calculation, PIM in Stokes space is employed to estimate the phase difference between X and Y polarization. Subsequently, the estimated phase difference is used to de-rotate the constellation in Stokes space to its ideal position. Then, the CDF of de-rotated S₂ parameter is used to train and verify the performance of our scheme. The numerical simulation result indicates that OSNR means estimation error in our scheme is around 0.5 dB, which is comparable with the existed scheme. Meanwhile, with 1 dB OSNR estimation error, the proposed scheme can tolerate the residual chromatic dispersion and phase-related polarization rotation rate up to 100ps/nm and 50kHz for 28GS/s 64QAM, which indicates the proposed scheme has the potential to be deployed into a real-time transmission system. Experimental results further confirm the high OSNR estimation and MFI accuracy of our scheme for QPSK, 8PSK, and 16QAM signal under the scenarios of BTB and fiber transmission link. With 1 dB OSNR estimation error, the proposed scheme can tolerate the residual chromatic dispersion up to ±160ps/nm after 940 km fiber transmission. To the best of the author’s knowledge, it is the first time that a simple ANN is used to monitor OSNR and m-PSK and m-QAM simultaneously. Therefore, with the attractive monitoring performance, the proposed monitoring scheme is a competitive solution for optical performance monitoring in future EONs.

Funding

Shenzhen Municipal Science and Technology Plan Project (20190806142407195); Hong Kong Polytechnic University (H-ZG7E, H-ZG8P).

Disclosures

The authors declare no conflicts of interest.

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Joint, accurate and robust optical signal-to- noise ratio and modulation format monitoring scheme using a single Stokes-parameter-based artificial neural network

Abstract

1. Introduction

2. Operating principle

3. Numerical simulation and discussion

4. Experimental result and discussion

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (11)

Equations (10)

Optics Express