Abstract

We propose and experimentally demonstrate an accurate modulation-format-indepen-dent and cascaded filtering effect (CFE) insensitive in-band optical signal-to-noise ratio (OSNR) monitoring technique enabled by Gaussian process regression (GPR) utilizing a widely tunable optical bandpass filter (OBPF) and optical power measurements. By adjusting the center frequency of a widely tunable OBPF and measuring the corresponding output optical power as the input features of GPR, the proposed OSNR monitoring technique is experimentally proven to be transparent to modulation formats and robust to CFE, chromatic dispersion (CD), polarization mode dispersion (PMD), and nonlinear effect (NLE). Experimental results for 9-channel 32Gbaud PDM-16QAM signals with 50GHz channel spacing demonstrate OSNR monitoring with the root mean squared error (RMSE) of 0.429 dB and the mean absolute error (MAE) of 0.294 dB, in the OSNR range of -1∼30 dB. Even better, our proposed technique has the potential to be employed for link monitoring at the intermediation nodes and can eliminate the necessity to know the transmission information.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

With the explosive growth of global IP traffic induced by various new applications, the capacity of optical communication systems has kept increasing rapidly and the optical network is evolving from the current fixed architecture to a flexible and adaptive architecture [1]. To satisfy a large number of bandwidth demands, dense wavelength division multiplexing (DWDM) and advanced optical modulation formats have been widely applied to expand network capacity and increase spectrum efficiency [2]. Furthermore, reconfigurable optical add-drop multiplexers (ROADMs) together with flexible transceivers also have been employed to enable elastic [3]. In such a heterogeneous optical network, optical performance monitor (OPM) is of great significance to provided fault management, optimum resource utilization and damage repair. Among various OPM parameters, the optical signal-to-noise ratio (OSNR) is the most pivotal one due to its straight-forward relationship to signal bit-error ratio (BER). Thus, OSNR monitoring plays a vital role in ensuring high quality-of-service and should be deployed ubiquitously across the network including intermediate nodes.

However, the traditional standardized out-band OSNR monitoring technique based on linear interpolation tends to be no longer accurate for DWDM transmission systems with ultra-narrow channel spacing or dynamic optical networks with ROADMs. In these scenarios, since the out-of-band noise may be highly suppressed or reshaped by cascaded optical filtering elements, its spectrum is not uniform. To alleviate this challenge, numerous of in-band OSNR monitoring techniques for coherent fiber optical transmission systems have been proposed. These techniques can be categorized into two main types. The first type can be typically enabled at the destination node by digital coherent detection systems. These include statistical moments [4], error vector magnitude [5], amplitude histograms (AHs) [6], Stokes parameters [7], amplitude noise correlation [8] and data-aided [911] based on techniques. While the second type can be typically enabled at the intermediate nodes by employing additional photonic components. These include polarization nulling [12], optical delay interferometer [13], offset filtering and optical power measurement [14], asynchronous delay-tap plots [15] and reference optical spectrum [1619] based on techniques. For the first type of techniques, due to the high sampling rate and expensive hardware cost, it will be too impractical to be deployed ubiquitously across the network including intermediate nodes. Therefore, the second type of techniques is the prime choice when the cost is a significant constraint and transmission information is unknown. However, these methods have their own disadvantages. For example, the technique in [12] is unsuitable for polarization multiplexed (PM) signals, and the technique in [13] needs to turn off the noise measurement and noise-free interference characteristics. It is unrealistic and in reality, noise cannot be turned off. In addition, the technique in [14] is sensitive to cascaded filtering effect (CFE), and the technique in [15] is unsuitable for scenarios with large transmission impairments.

In [16] and [17], a novel in-band OSNR monitoring scheme is proposed, which is transparent to modulation formats and insensitive to CFE. The monitoring accuracy depends on the offset frequencies and the bandwidth of the electrical low pass filter, and then the offset frequencies are desirable to set closer to the edge of the signal spectrum. However, these two methods only utilize the information of the single-sideband optical spectrum, and many parameters need to be calibrated to guarantee good monitoring accuracy. In [18], the authors propose an in-band OSNR estimating method from high-resolution optical spectrum information using machine learning techniques. Although very high prediction accuracy can be achieved, this method is not cost-effective and is not conducive to large-scale practical use because it uses a Brillouin optical spectrum analyzer (BOSA) with a spectral resolution of up to 0.1pm to obtain the input features. We previously proposed a cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression (GPR), which is experimentally demonstrated that it is robust to CD, NLE and optical amplifier types [19]. But in our previous work, due to the limitations of the experimental conditions, we did not verify whether the proposed method is independent of the modulation formats and insensitive to CFE. Meanwhile, the baud rate of the signal used is too low comparing to the channel spacing, which does not reflect the real characteristics of the DWDM system. So, this paper extends the previous work [19], improves the baud rate of the signal, adopts some advanced modulation formats, uses an appropriate kernel function and changes the number of cascade wavelength selective switches (WSSs) to further verify whether the proposed technique is independent of modulation formats and CFE robust. Extensive experimental results demonstrate that our proposed monitor can achieve highly accurate OSNR monitoring for various modulation formats without any calibration and tolerate CD, PMD, NLE, and CFE by adjusting the center frequency of a widely tunable optical bandpass filter (OBPF) and measuring the corresponding output optical power as the input features of GPR. Moreover, the transmission information is not necessary for our proposed monitor, which means that our proposed monitor can be deployed at the intermediate nodes for link monitoring.

2. Operation principle

2.1 GPR

In this paper, OSNR monitoring is regarded as a regression problem. GPR is a novel machine learning technique, which is based on a Bayesian nonparametric approach and can be considered as an alternative method of fitting a function [20]. Through investigation, we found that GPR is more suitable for complex regression problems with small sample sizes and high feature dimensions than neural networks. The data set samples we use in this paper just meet these characteristics. Therefore, we chose GPR as the machine learning technique in this article which is the key enabling technology for OSNR monitor.

A Gaussian process (GP) is defined as a collection of a finite number of random variables, and it is fully specified by its mean function $m({\boldsymbol x} )$ and covariance (or kernel) function $k({{\boldsymbol x},{\boldsymbol x^{\prime}}} )$.

$$\left\{ {\begin{array}{c} {m({\boldsymbol x} )= E[{f({\boldsymbol x} )} ]}\\ {k({{\boldsymbol x},{\boldsymbol x^{\prime}}} )= E[{({f({\boldsymbol x} )- m({\boldsymbol x} )} )({f({{\boldsymbol x^{\prime}}} )- m({{\boldsymbol x^{\prime}}} )} )} ]} \end{array}} \right.$$
Thus, a GP can be denoted as:
$$f({\boldsymbol x} ){\; }\sim {\; }GP({m({\boldsymbol x} ),k({{\boldsymbol x},{\boldsymbol x^{\prime}}} )} )$$
where $f({\boldsymbol x} )$ are the random variables representing the value of training points at ${\boldsymbol x}$.

The predictive distribution can be derived from this based on the marginalization property and the Gaussian assumption of GP, which indicates that the joint distribution is Gaussian. To utilize GP for regression, we need to specify a kernel function. The necessary conditions for the kernel function are that the covariance matrix is symmetric and positive semi-definite. There are several commonly used kernel functions for GPR. Each kernel function has its own most suitable application scenario. Their specific mathematical expressions are as follows:

The squared exponential kernel function is defined as:

$$k({{\textbf x},{\boldsymbol x^{\prime}}} )= \sigma _f^2\exp \left[ { - \frac{1}{2}\frac{{{r^2}}}{{\sigma_l^2}}} \right]$$
The exponential kernel function is defined as:
$$k({{\textbf x},{\boldsymbol x^{\prime}}} )= \sigma _f^2\textrm{exp}\left( { - \frac{r}{{{\sigma_l}}}} \right)$$
The rational quadratic kernel function is defined as:
$$k({{\textbf x},{\boldsymbol x^{\prime}}} )= \sigma _f^2{\left( {1 + \frac{{{r^2}}}{{2\alpha \sigma_l^2}}} \right)^{ - \alpha }}$$
The Matern 5/2 kernel function is defined as:
$$k({{\textbf x},{\boldsymbol x^{\prime}}} )= \sigma _f^2\left( {1 + \frac{{\sqrt 5 r}}{{{\sigma_l}}} + \frac{{5{r^2}}}{{3{\sigma_l}^2}}} \right)exp\left( { - \frac{{\sqrt 5 r}}{{{\sigma_l}}}} \right)$$

In all the above expressions, $\textrm{r} ={\parallel} {\boldsymbol x} - {\boldsymbol x^{\prime}}\parallel $ is the Euclidean distance between ${\boldsymbol x}$ and ${\boldsymbol x^{\prime}}$, $\mathrm{\alpha }$ is a positive-valued scale-mixture parameter of the rational quadratic kernel function and the two hyper-parameters $\sigma _f^2$ and ${\sigma _l}$ are called signal variance and length scale, respectively.

The task of the OSNR estimator is to learn a continuous mapping function between the input features and the OSNR.

2.2 Proposed OSNR monitoring scheme

We propose an OSNR monitoring scheme that can be placed ubiquitously across the transmission link including the intermediate nodes. As shown in Fig. 1, the proposed monitor consists of a widely tunable OBPF, a low-speed photodiode (PD), and a signal processor. The incoming optical signals tapped from the transmission link is filtered out by the widely tunable OBPF. Besides, the modulation formats and baud rates of incoming optical signals can also be various. Specifically, as shown in Fig. 2, we adjust the center wavelength of tunable OBPF with wavelength resolution (${\lambda _r}$) to traverse the C-band and then record the whole filtered optical power measurements. When the center wavelengths of tunable OBPF are consistent and the optical power measurements and the OSNRs are belonging to the same monitoring channel, the corresponding optical power measurements will be distinctive and unique for different OSNRs. In the signal processor, the optical power measurements are directly employed as the input features of GPR for OSNR monitoring (called GPR-OSNR).

 figure: Fig. 1.

Fig. 1. Schematic diagram of the proposed OPM. The proposed OPM can be placed after any intermediate node.

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 figure: Fig. 2.

Fig. 2. The signal optical spectrum after adjusting the center wavelength of the tunable OBPF with wavelength resolution (${\lambda _r}$) . The solid black lines represent the signal optical spectrum, and the dashed green lines represent the filter shape of the tunable OBPF.

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When the channel spacing of a DWDM transmission system is $\Delta \lambda $, the number N of optical power measurements equals $\Delta \lambda \textrm{ / }{\lambda _r}$ for OSNR monitoring of the monitoring channel, which is equivalent to taking out the N optical power measurements as input features of the monitoring channel from the widely tunable OBPF. Besides the launch power, the transmission distance and the number of cascaded wavelength selective switches (WSSs) of the signals at the monitoring nodes can also be considered alternative parameters as the input features of GPR. In this paper, the training data set consists of training examples pairs, each containing an input feature vector, and an output scalar indicating the OSNR value. During the training phase, we also introduced a 5-fold cross-validation method to prevent overfitting.

Once the training phase is complete, the performance of trained GPR-OSNR is analyzed by utilizing an independent data set called the testing data set. During the testing phase, the input features such as optical power measurements belonging to the testing data set are applied at the input of trained GPR-OSNR. Then the estimated OSNR values can be obtained from the output scalars and compared with the actual ones. Therefore, the accuracies of OSNR monitoring are determined.

3. Experimental setup

The experimental setup for the demonstration of the proposed OSNR monitoring technique is shown in Fig. 3. At the transmitter side, there are 9 channels with channel spacing 50 GHz (0.4 nm) and the center channel is under monitoring. Nine continuous-wave (CW) lights with 100-kHz-linewidth are combined by a multiplexer and then modulated by a polarization-multiplexed IQ modulator for generating PDM-QPSK, PDM-16QAM, and PDM-64QAM signals. Besides, a programmable arbitrary waveform generator (AWG, Keysight: M9502A) is used to generate 32GS/s electrical driver signals. Thus, the output of optical signals is amplified by an erbium-doped fiber amplifier (EDFA) and launched. The transmission link whose loss is compensated by Raman amplifiers contains several (from 6-24) spans of 80 km standard single mode fiber (SSMF). In this scenario, the launch power, the transmission distance, and the number of cascaded WSSs of the signals transmitted over at the monitoring node are changed to form different system conditions. Specifically, the number of cascaded WSSs is determined by a Finisar WaveShaper 4000s tunable filter loaded with various cascaded filter shapes. Each individual filter is set to 50 GHz bandwidth with 3 order super-Gaussian shape. At the monitoring node, a variable optical attenuator (VOA) followed by an amplified spontaneous emission (ASE) noise source (EXFO FLS-2300B) is employed to adjust the OSNRs of the signals. For comparison, the noisy signals are then sent into both the proposed monitor and an optical spectrum analyzer (OSA). The OSA is used to measure the true OSNR by the signal On/Off method. The proposed monitor consists of a commercially available widely tunable OBPF with a super-Gaussian shape having a 3 dB bandwidth of 0.2 nm and a wavelength resolution of 0.02 nm. We adjust the center wavelength of the tunable OBPF with the wavelength resolution to traverse the C-band and then record the corresponding optical power measurements using a low-speed PD (several GHz). We collect 5 sets of independent optical power measurements under different combinations of modulation formats and OSNRs for specified system conditions. Thereupon, we generate a large data set. In the rest part of this paper, the chunks of data set are randomly divided into training and testing data sets by selecting 70% and 30% of them, respectively. In our work, the training phase is implemented using the matlab R2019a regression learner toolbox.

 figure: Fig. 3.

Fig. 3. Experimental setup. MUX: multiplexer. Specifically, the number of cascaded WSSs is determined by a Finisar WaveShaper 4000s tunable filter loaded with various cascaded filter shapes. M represents the number of spans which ranges from 6 to 24.

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4. Results analysis

The performance of the proposed monitor is firstly demonstrated by the OSNR monitoring results of 32Gbaud PDM-16QAM signals. To ensure a wide OSNR range of the signals over long-haul transmission and verify the robustness of the proposed monitoring technique to CD, PMD, NLE and CFE, our system conditions are shown in Table 1. In the following part of the paper, we will call the transmission distance as D, the launch power as P and the number of cascaded WSSs as ${N_c}$.

Tables Icon

Table 1. System conditions for a 32Gbaud PDM-16QAM system.

The above system conditions can be divided into three categories: (I) Both D and P change and there is no WSS in the transmission link; (II) Both D and P change and there are 6 cascaded WSSs in the transmission link; (III) Either D or P does not change, but ${N_c}$ changes in the transmission link.

To investigate the effect of GPR kernel function on the OSNR monitoring performance, we compared the root mean squared error (RMSE), mean absolute error (MAE) and training time of the four commonly used GPR kernel functions mentioned in Section 2 using the first category data set to select the best kernel function for subsequent research. In this category, we generate an extensive data set encompassing 585 groups of optical power measurements along the C-band. The first category is similar to most of the currently proposed schemes that no WSS is introduced in the transmission link. When we take out the whole optical power measurements in the monitoring channel, the number N of input filtered optical power measurements is $0.4\; \textrm{nm}/0.02\; \textrm{nm}$ (i.e., $N = 20$) for the OSNR monitoring according to Section 2. Therefore, when we utilize such 20 optical power measurements, P, and D together as the input features of GPR, there are experimental results as shown in Fig. 4(a). Additionally, the optical power measurements near the center wavelength of the monitoring channel already contain certain power information. Thus, we consider just using the above optical power measurements as the input features of GPR. There are experimental results, as shown in Fig. 4(b). Considering the three performance indicators in Fig. 4, we can find that the Matern 5/2 kernel function has the smallest RMSE and MAE among them, and the training time is also quite close to the exponential kernel function. Based on this, we believe that the Matern 5/2 kernel function has the best overall performance. So, in the rest part of this paper, we will use the Matern 5/2 kernel function as our chosen GPR kernel function. In our work, the training time was obtained using an AMD Ryzen 7 3700X 8-core processor with 32 GB RAM memory.

 figure: Fig. 4.

Fig. 4. RMSE, MSE and training time for PDM-16QAM signals using different kernel functions during the testing phase in the first category. (a) With P and D among the input features; (b) Without P and D among the input features.

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In detail, the OSNR monitoring error in the first category is shown in Fig. 5. Similar to the previous comparison method, in Fig. 5(a), such 20 optical power measurements, P, and D together serve as the input features of GPR, whereas in Fig. 5(b), only the above optical power measurements serve as the input features of GPR. In Fig. 5(a), the RMSE, and the MAE are 0.484 dB and 0.386 dB, respectively, in the OSNR range of 4∼30 dB, which indicates that the OSNR monitor we proposed can work properly in the presence of CD, PMD, and NLE. In Fig. 5(b), the RMSE and MAE are 0.486 dB and 0.386 dB, respectively, which indicates that the OSNR monitoring performance has almost no change. Therefore, for this transmission scenario, although the transmission information is unknown at the monitoring nodes, the OSNR monitor we proposed is not affected and can still work effectively with high precision.

 figure: Fig. 5.

Fig. 5. OSNR monitoring error for PDM-16QAM signals during the testing phase in the first category. (a) With P and D among the input features; (b) Without P and D among the input features.

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To further investigate the effect of optical filtering elements on the OSNR monitoring performance, we fix ${N_c}$ (=6) in the transmission link. Thus, in the second category, we generate an extensive data set encompassing 625 groups of optical power measurements along the C-band. Similar to the previous comparison method, in Fig. 6(a), such 20 optical power measurements, P, and D together serve as the input features of GPR, whereas in Fig. 6(b), only the above optical power measurements serve as the input features of GPR. The RMSE of 0.315 dB and MAE of 0.2 dB are observed in Fig. 6(a), the RMSE of 0.311 dB and MAE of 0.208 dB are observed in Fig. 6(b), in the OSNR range of -1∼30 dB. The results show the OSNR monitor we proposed can work properly without knowing the transmission information in the presence of filtering effect. In comparison with the first category, the OSNR monitoring performance is improved. This is mainly due to the fact that the true OSNR range expands towards lower OSNR and the monitoring error shows less at the low OSNR than at the high OSNR.

 figure: Fig. 6.

Fig. 6. OSNR monitoring error for PDM-16QAM signals during the testing phase in the second category. (a) With P and D among the input features; (b) Without P and D among the input features.

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To further investigate the effect of CFE on the OSNR monitoring performance, only the ${N_c}$ is changed in the transmission link when the transmission distance is 960 km and the launch power is 4 dBm. Thus, in the third category, we generate an extensive data set encompassing 785 groups of optical power measurements along the C-band. Similar to the previous comparison methods, in Fig. 7(a), such 20 optical power measurements and ${N_c}$ together serve as the input features of GPR, whereas in Fig. 7(b), only the above optical power measurements serve as the input features of GPR. The RMSE of 0.393 dB and MAE of 0.284 dB are observed in Fig. 7(a), the RMSE of 0.415 dB and MAE of 0.307 dB are observed in Fig. 7(b), in the OSNR range of 2∼30 dB. The results show the OSNR monitor we proposed can work properly without knowing ${N_c}$ in the presence of CFE.

 figure: Fig. 7.

Fig. 7. OSNR monitoring error for PDM-16QAM signals during the testing phase in the third category. (a) With ${N_c}$ among the input features; (b) Without ${N_c}$ among the input features.

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Then, we further consider whether the OSNR monitor we proposed can work properly without prior knowledge of transmission information and ${N_c}$ (i.e. system conditions). Thereupon, we mix the data from the above three categories in Table 1. That is a new data set encompassing 1675 groups of optical power measurements along the C-band. Similar to the previous comparison methods, in Fig. 8(a), such 20 optical power measurements, P, D and ${N_c}$ together serve as the input features of GPR, whereas in Fig. 8(b), only the above optical power measurements serve as the input features of GPR. The RMSE of 0.418 dB and MAE of 0.3 dB are observed in Fig. 8(a), the RMSE of 0.429 dB and MAE of 0.294 dB are observed in Fig. 8(b), in the OSNR range of -1∼30 dB. It is evident that the OSNR monitoring performance is almost no degradation. We further analyze the experimental results in Fig. 8 to obtain Fig. 9. Whether or not know system conditions, Fig. 9 illustrates the OSNR monitor we proposed with high precision. Specifically, most of the results are very good, with typical deviations (e.g. $\left\langle \textrm{x} \right\rangle \pm \mathrm{\sigma }$) within ${\pm} $0.2 dB in the OSNR range of -1∼30 dB.

 figure: Fig. 8.

Fig. 8. OSNR monitoring error for PDM-16QAM signals during the testing phase including the above three categories. (a) With P, D and ${N_c}$ among the input features; (b) Without P, D and ${N_c}$ among the input features.

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 figure: Fig. 9.

Fig. 9. OSNR deviation from true OSNR for PDM-16QAM signals during the testing phase including the above three categories. (a) With P, D and ${N_c}$ among the input features; (b) Without P, D and ${N_c}$ among the input features.

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Finally, to further investigate the effect of the modulation formats on the OSNR monitoring performance, ${N_c}$ and modulation formats are both changed in the transmission link when the transmission distance is 960 km and the launch power is 4 dBm. Thus, in these system conditions as shown in Table 2, we generate an extensive data set encompassing 2270 groups of optical power measurements along the C-band. In Fig. 10(a), such 20 optical power measurements serve as the input features of GPR, whereas in Fig. 10(b), we further analyze the experimental results in Fig. 10(a) to obtain Fig. 10(b). The RMSE of 0.430 dB and MAE of 0.308 dB are observed in Fig. 10(a), typical deviations (e.g.$\; \textrm{}\left\langle \textrm{x} \right\rangle \pm \mathrm{\sigma }$) within ±0.2 dB are observed in Fig. 10(b), in the OSNR range of 2∼30 dB. Compared with the RMSE of 0.415 dB and MAE of 0.307 dB in Fig. 7(b) corresponding to the third category in Table 1, it can be found that the monitoring error of OSNR does not change significantly when OSNR is monitored simultaneously with multiple modulation formats. The results show that our proposed OSNR monitor can achieve high precision under the premise of being transparent to modulation format.

 figure: Fig. 10.

Fig. 10. (a) OSNR monitoring error for all three modulation formats during the testing phase without ${N_c}$ among the input features; (b) OSNR deviation from true OSNR for all three modulation formats during the testing phase without ${N_c}$ among the input features

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Tables Icon

Table 2. System conditions for a 32Gbaud PDM-QPSK, PDM-16QAM, and PDM-64QAM system.

From all the experimental results obtained above, it can be seen that the proposed OSNR monitor is modulation-format-independent and robust to CD, PMD, NLE, and CFE. It can be placed ubiquitously across the transmission link. Even better, the OSNR monitor can be utilized without knowing system conditions.

5. Conclusion

In this paper, a cost-effective and distributed in-band OSNR monitor is proposed and experimentally demonstrated in the fiber optical coherent transmission system. By using widely tunable OBPF and Matern 5/2 kernel function based GPR, the proposed OSNR monitoring technique has high precision. Experimental results show that in a 9 × 3Gbaud PDM-16QAM system with a 50 GHz grid, the RMSE and the MAE are below 0.47 dB and 0.32 dB, respectively, in the OSNR range of -1∼30 dB. Moreover, extensive experimental results also show that our proposed monitor is modulation-format-independent and robust to CD, PMD, and NLE. In addition, our OSNR monitor has almost no degradation in the presence of CFE, which means it has strong robustness to CFE. Even better, our proposed monitor has the potential to be applied at the intermediation nodes and can be utilized without any prior knowledge about transmission information.

Funding

National Key Research and Development Program of China (2018YFB2200900).

Acknowledgments

The authors wish to thank Dr. Shaohua Yu and Zhixue He from Wuhan Research Institute of Posts & Telecommunications for his help.

Disclosures

The authors declare no conflicts of interest.

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References

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  1. H. Khodakarami, B. Pillai, B. Sedighi, and W. Shieh, “Flexible optical networks: An energy efficiency perspective,” J. Lightwave Technol. 32(21), 3958–3969 (2014).
    [Crossref]
  2. Z. Dong, F. N. Khan, Q. Sui, K. Zhong, C. Lu, and A. P. T. Lau, “Optical performance monitoring: A review of current and future technologies,” J. Lightwave Technol. 34(2), 525–543 (2016).
    [Crossref]
  3. J. C. Cartledge, “Performance of coherent optical fiber transmission systems,” Front. Optoelectron. 11(2), 128–133 (2018).
    [Crossref]
  4. C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012).
    [Crossref]
  5. R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
    [Crossref]
  6. F. N. Khan, K. Zhong, X. Zhou, W. H. Al-Arashi, C. Yu, C. Lu, and A. P. T. Lau, “Joint OSNR monitoring and modulation format identification in digital coherent receivers using deep neural networks,” Opt. Express 25(15), 17767–17776 (2017).
    [Crossref]
  7. L. Lundberg, H. Sunnerud, and P. Johannisson, “In-band OSNR monitoring of PM-QPSK using the Stokes parameters,” in Proc. Optical Fiber Communication Conference (OFC, 2015), paper W4D. 5.
  8. Z. Dong, A. P. T. Lau, and C. Lu, “OSNR monitoring for QPSK and 16-QAM systems in presence of fiber nonlinearities for digital coherent receivers,” Opt. Express 20(17), 19520–19534 (2012).
    [Crossref]
  9. C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
    [Crossref]
  10. C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
    [Crossref]
  11. W. Wang, A. Yang, P. Guo, Y. Lu, and Y. Qiao, “Joint OSNR and interchannel nonlinearity estimation method based on fractional Fourier transform,” J. Lightwave Technol. 35(20), 4497–4506 (2017).
    [Crossref]
  12. J. H. Lee, H. Y. Choi, S. K. Shin, and Y. C. Chung, “A review of the polarization-nulling technique for monitoring optical-signal-to-noise ratio in dynamic WDM networks,” J. Lightwave Technol. 24(11), 4162–4171 (2006).
    [Crossref]
  13. Z. Huang, J. Qiu, S. Wang, X. Ji, Y. Tian, D. Kong, M. Yu, and J. Wu, “Guideline of choosing optical delay time to optimize the performance of an interferometry-based in-band OSNR monitor,” Opt. Lett. 41(18), 4178–4181 (2016).
    [Crossref]
  14. S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.
  15. M. C. Tan, F. N. Khan, W. H. Al-Arashi, Y. Zhou, and A. P. Tao Lau, “Simultaneous optical performance monitoring and modulation format/bit-rate identification using principal component analysis,” J. Opt. Commun. Netw. 6(5), 441–448 (2014).
    [Crossref]
  16. Z. Dong, K. Zhong, X. Zhou, C. Lu, A. P. T. Lau, Y. Lu, and L. Li, “Modulation-format-independent OSNR monitoring insensitive to cascaded filtering effects by low-cost coherent receptions and RF power measurements,” Opt. Express 23(12), 15971–15982 (2015).
    [Crossref]
  17. G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
    [Crossref]
  18. F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
    [Crossref]
  19. C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
    [Crossref]
  20. F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

2019 (3)

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

2018 (2)

G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
[Crossref]

J. C. Cartledge, “Performance of coherent optical fiber transmission systems,” Front. Optoelectron. 11(2), 128–133 (2018).
[Crossref]

2017 (2)

2016 (2)

2015 (1)

2014 (2)

2013 (1)

C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
[Crossref]

2012 (3)

C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012).
[Crossref]

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Z. Dong, A. P. T. Lau, and C. Lu, “OSNR monitoring for QPSK and 16-QAM systems in presence of fiber nonlinearities for digital coherent receivers,” Opt. Express 20(17), 19520–19534 (2012).
[Crossref]

2006 (1)

Akasaka, Y.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Al-Arashi, W. H.

Anderson, T.

Aoki, Y.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Becker, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Bi, Y.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Cartledge, J. C.

J. C. Cartledge, “Performance of coherent optical fiber transmission systems,” Front. Optoelectron. 11(2), 128–133 (2018).
[Crossref]

Chen, S.

Choi, H. Y.

Christodoulopoulos, K.

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

Chung, Y. C.

Cui, S.

G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
[Crossref]

Do, C.

C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
[Crossref]

Do, C. C.

Dong, Z.

Dreschmann, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Du, L. B.

Fàbrega, J. M.

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

Feng, Q.

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

Freude, W.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Guo, P.

Hewitt, D.

C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
[Crossref]

Hillerkuss, D.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Hu, C.

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

Huang, Z.

Huebner, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Hugues-Salas, E.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Ji, X.

Johannisson, P.

L. Lundberg, H. Sunnerud, and P. Johannisson, “In-band OSNR monitoring of PM-QPSK using the Stokes parameters,” in Proc. Optical Fiber Communication Conference (OFC, 2015), paper W4D. 5.

Josten, A.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Ke, C.

G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
[Crossref]

Khan, F. N.

Khodakarami, H.

H. Khodakarami, B. Pillai, B. Sedighi, and W. Shieh, “Flexible optical networks: An energy efficiency perspective,” J. Lightwave Technol. 32(21), 3958–3969 (2014).
[Crossref]

Koenig, S.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Kong, D.

Koos, C.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Lau, A. P. T.

Lee, J. H.

Leuthold, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Li, L.

Li, W.

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

Liu, D.

G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
[Crossref]

Locatelli, F.

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

Lowery, A. J.

Lu, C.

Lu, Y.

Lundberg, L.

L. Lundberg, H. Sunnerud, and P. Johannisson, “In-band OSNR monitoring of PM-QPSK using the Stokes parameters,” in Proc. Optical Fiber Communication Conference (OFC, 2015), paper W4D. 5.

Meng, F.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Meyer, J.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Moreolo, M. S.

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

Nebendahl, B.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Nejabati, R.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Nikolovgenis, K.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Oda, S.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Ou, Y.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Pillai, B.

H. Khodakarami, B. Pillai, B. Sedighi, and W. Shieh, “Flexible optical networks: An energy efficiency perspective,” J. Lightwave Technol. 32(21), 3958–3969 (2014).
[Crossref]

Qiao, Y.

Qiu, J.

Rasmussen, J. C.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Schmogrow, R.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Sedighi, B.

H. Khodakarami, B. Pillai, B. Sedighi, and W. Shieh, “Flexible optical networks: An energy efficiency perspective,” J. Lightwave Technol. 32(21), 3958–3969 (2014).
[Crossref]

Sekiya, M.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Shieh, W.

H. Khodakarami, B. Pillai, B. Sedighi, and W. Shieh, “Flexible optical networks: An energy efficiency perspective,” J. Lightwave Technol. 32(21), 3958–3969 (2014).
[Crossref]

Shin, S. K.

Simeonidou, D.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Skafidas, E.

C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
[Crossref]

C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012).
[Crossref]

Sone, K.

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Spadaro, S.

F. Locatelli, K. Christodoulopoulos, M. S. Moreolo, J. M. Fàbrega, and S. Spadaro, “Machine Learning-Based in-Band OSNR Estimation From Optical Spectra,” IEEE Photonics Technol. Lett. 31(24), 1929–1932 (2019).
[Crossref]

Sui, Q.

Sunnerud, H.

L. Lundberg, H. Sunnerud, and P. Johannisson, “In-band OSNR monitoring of PM-QPSK using the Stokes parameters,” in Proc. Optical Fiber Communication Conference (OFC, 2015), paper W4D. 5.

Tan, M. C.

Tao Lau, A. P.

Tian, Y.

Tran, A. V.

C. Do, A. V. Tran, C. Zhu, D. Hewitt, and E. Skafidas, “Data-aided OSNR estimation for QPSK and 16-QAM coherent optical system,” IEEE Photonics J. 5(5), 6601609 (2013).
[Crossref]

C. Zhu, A. V. Tran, S. Chen, L. B. Du, C. C. Do, T. Anderson, A. J. Lowery, and E. Skafidas, “Statistical moments-based OSNR monitoring for coherent optical systems,” Opt. Express 20(16), 17711–17721 (2012).
[Crossref]

Wang, R.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Wang, S.

Wang, W.

Wang, Y.

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

Winter, M.

R. Schmogrow, B. Nebendahl, M. Winter, A. Josten, D. Hillerkuss, S. Koenig, J. Meyer, M. Dreschmann, M. Huebner, C. Koos, J. Becker, W. Freude, and J. Leuthold, “Error vector magnitude as a performance measure for advanced modulation formats,” IEEE Photonics Technol. Lett. 24(1), 61–63 (2012).
[Crossref]

Wu, J.

Xie, Y.

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

Yan, S.

F. Meng, S. Yan, K. Nikolovgenis, Y. Ou, R. Wang, Y. Bi, E. Hugues-Salas, R. Nejabati, and D. Simeonidou, “Field trial of Gaussian process learning of function-agnostic channel performance under uncertainty,” in Proc. Optical Fiber Communication Conference (OFC, 2018), Paper W4F.5.

Yang, A.

Yang, Jeng-Yuan

S. Oda, Y. Aoki, M. Sekiya, Y. Akasaka, K. Sone, Jeng-Yuan Yang, and J. C. Rasmussen, “In-band OSNR monitor using an optical bandpass filter and optical power measurements for superchannel signals,” in Proc. European Conference and Exhibition on Optical Communication (ECOC, 2013), paper P.3.12.

Yin, G.

G. Yin, S. Cui, C. Ke, and D. Liu, “Reference optical spectrum based in-band OSNR monitoring method for EDFA amplified multispan optical fiber transmission system with cascaded filtering effect,” IEEE Photonics J. 10(3), 1–10 (2018).
[Crossref]

Yu, C.

Yu, M.

Zheng, H.

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

Zheng, Q.

C. Hu, W. Li, H. Zheng, Q. Feng, Q. Zheng, and Y. Wang, “A novel cost-effective and distributed in-band OSNR monitoring method using Gaussian process regression,” IEEE Photonics J. 11(4), 1–12 (2019).
[Crossref]

C. Hu, W. Li, Q. Feng, Q. Zheng, Y. Wang, and Y. Xie, “A novel in-band OSNR monitoring technique based on fractional Fourier transform of LFM signal,” Opt. Commun. 445, 36–40 (2019).
[Crossref]

Zhong, K.

Zhou, X.

Zhou, Y.

Zhu, C.

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[Crossref]

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[Crossref]

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Figures (10)

Fig. 1.
Fig. 1. Schematic diagram of the proposed OPM. The proposed OPM can be placed after any intermediate node.
Fig. 2.
Fig. 2. The signal optical spectrum after adjusting the center wavelength of the tunable OBPF with wavelength resolution (${\lambda _r}$) . The solid black lines represent the signal optical spectrum, and the dashed green lines represent the filter shape of the tunable OBPF.
Fig. 3.
Fig. 3. Experimental setup. MUX: multiplexer. Specifically, the number of cascaded WSSs is determined by a Finisar WaveShaper 4000s tunable filter loaded with various cascaded filter shapes. M represents the number of spans which ranges from 6 to 24.
Fig. 4.
Fig. 4. RMSE, MSE and training time for PDM-16QAM signals using different kernel functions during the testing phase in the first category. (a) With P and D among the input features; (b) Without P and D among the input features.
Fig. 5.
Fig. 5. OSNR monitoring error for PDM-16QAM signals during the testing phase in the first category. (a) With P and D among the input features; (b) Without P and D among the input features.
Fig. 6.
Fig. 6. OSNR monitoring error for PDM-16QAM signals during the testing phase in the second category. (a) With P and D among the input features; (b) Without P and D among the input features.
Fig. 7.
Fig. 7. OSNR monitoring error for PDM-16QAM signals during the testing phase in the third category. (a) With ${N_c}$ among the input features; (b) Without ${N_c}$ among the input features.
Fig. 8.
Fig. 8. OSNR monitoring error for PDM-16QAM signals during the testing phase including the above three categories. (a) With P, D and ${N_c}$ among the input features; (b) Without P, D and ${N_c}$ among the input features.
Fig. 9.
Fig. 9. OSNR deviation from true OSNR for PDM-16QAM signals during the testing phase including the above three categories. (a) With P, D and ${N_c}$ among the input features; (b) Without P, D and ${N_c}$ among the input features.
Fig. 10.
Fig. 10. (a) OSNR monitoring error for all three modulation formats during the testing phase without ${N_c}$ among the input features; (b) OSNR deviation from true OSNR for all three modulation formats during the testing phase without ${N_c}$ among the input features

Tables (2)

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Table 1. System conditions for a 32Gbaud PDM-16QAM system.

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Table 2. System conditions for a 32Gbaud PDM-QPSK, PDM-16QAM, and PDM-64QAM system.

Equations (6)

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{ m ( x ) = E [ f ( x ) ] k ( x , x ) = E [ ( f ( x ) m ( x ) ) ( f ( x ) m ( x ) ) ]
f ( x ) G P ( m ( x ) , k ( x , x ) )
k ( x , x ) = σ f 2 exp [ 1 2 r 2 σ l 2 ]
k ( x , x ) = σ f 2 exp ( r σ l )
k ( x , x ) = σ f 2 ( 1 + r 2 2 α σ l 2 ) α
k ( x , x ) = σ f 2 ( 1 + 5 r σ l + 5 r 2 3 σ l 2 ) e x p ( 5 r σ l )

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