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Abstract
We demonstrate accurate estimation of generalized optical signal to noise ratio (GOSNR) for wavelength division multiplexed fiber communication systems using an experimentally trained multi-tasking convolutional neural network while simultaneously estimating linear and nonlinear noise contributions. Using dual-polarized 32-GBaud 16QAM DWDM links we extract learnable features from constellation density matrices and accurately estimate GOSNR while simultaneously estimating linear and nonlinear contributions. Estimation of the OSNRASE, OSNRNL and GOSNR are demonstrated with < 0.5 dB mean absolute error. We also assess the universality of our model within the regime of metro networks by cross-training with data from such links comprised of different fiber types. We demonstrate a path to a practical universal training method that includes additional link parameters. The methods do not require contiguous high-speed sampling, additional hardware nor transmission of special symbols or patterns and are readily implemented in deployed systems.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The optical signal-to-noise ratio (OSNR) is a primary optical link performance metric. Monitoring the OSNR enables network operators to validate the expected performance from the network planning stage, monitor the health of the WDM system permitting preemptive maintenance and to optimize the link capacity and/or margin, particularly when changes are made to the link. The traditional OSNR monitored by comparing the signal power to the adjacent out-of-band noise power using an optical spectrum analyzer (OSA) is the OSNRASE and it suffers from multiple challenges. First, the tight channel spacing in dense wavelength division multiplexed (DWDM) systems completely obfuscates the noise floor, Fig. 1(a). Second, the OSNRASE mostly captures the linear ASE noise and does not accurately capture the non-linear interference contribution, since nonlinear interference is predominantly found in-band, Fig. 1(b) [1]. Finally, OSNRASE measurement using an OSA often involves changes to the link, for example, removing adjacent channels. The generalized OSNR (GOSNR) ideally captures only optical impairments including linear noise and nonlinear interference and is the primary metric of interest since it reflects the BER more accurately. In the low nonlinearity regime, GOSNR is close to the OSNRASE. For all other scenarios, GOSNR is lower than the OSNRASE [2].
Fig. 1. Conceptual optical spectra demonstrating the challenges of measuring OSNRASE using OSA in a deployed environment. (a) DWDM spectrum showing inaccessible noise floor due to side channel interference; (b) a spectrum showing the difference between in-band noise and out-of-band noise floor.
The GOSNR can be estimated for a specific link by identifying the back-to-back (B2B) OSNRASE needed to achieve the same BER [3,4]. This presumes the transceiver impairments are constant for B2B and after fiber transport. In deployed links, identifying separate contributions of linear noise and non-linear interference also requires the knowledge of OSNRASE of the deployed link, which in turn generally requires adjacent channels to be turned off or the transmission of specific symbols to estimate the noise floor [5].
We previously demonstrated accurate OSNRASE estimation using machine learning (ML) techniques employing only I-Q constellation images [6,7] without separately discerning linear and nonlinear interference. ML can potentially identify unique Gaussian and non-Gaussian signatures of ASE and nonlinear interference, respectively. Nonlinear interference originates from three types of interactions via fiber nonlinearity: signal-signal, signal-ASE and ASE-ASE [8]. Such interactions can be mitigated through digital back propagation techniques or maximum a posterior joint detection of center and adjacent channels [9]. Signal-signal interactions are the most likely to produce distinct non-Gaussian signatures and are likely to be the dominant interaction. However, it is noted that in a deployed system the adjacent channels may originate at different points in the network and may have accumulated significant dispersion prior multiplexing in which case they may appear noise-like. We use the term nonlinear noise to denote the total of all nonlinear interferences in our system and the associated signal to nonlinear noise ratio as OSNRNL. Estimating the GOSNR from constellation density matrices using machine learning requires the OSNRASE of the deployed link only in the ML training phase. Nonlinear interference from fiber nonlinearity is unlike amplified spontaneous emission (ASE) noise because distortions associated with nonlinear interference noise are not necessarily circularly Gaussian symmetric [10]. This is especially true for monitoring nonlinearities within metro networks with the associated lower dispersion. These networks have generated significant interest as can be seen from the use of predistortion and probabilistic shaping for nonlinear mitigation within these systems [11,12]. The recovered I-Q constellations should therefore provide unique signatures of ASE and nonlinear noise. In fact, our results do demonstrate that the ML technique of convolutional neural network (CNN) is able to discern linear and nonlinear noise in these metro links. It remains a further challenge to examine possibilities for long-haul links, where the large accumulated dispersion tends to result in noise that is mostly “circular”, as suggested by the success of the Gaussian Noise model and other works.
Recently, it has been demonstrated that a deep neural network (DNN) ML technique based on the amplitude histogram can accurately estimate OSNR [13–15]. However, these works were typically performed at a fixed nonlinear noise power without separately identifying the relative contributions of nonlinear and ASE noise. Previous efforts have demonstrated the ability to estimate the nonlinear noise and ASE noise separately using the amplitude noise correlation characteristics and a known sequence of symbols [16,17]. However, this technique requires synchronous sampling at high sample rates and hence the availability of high-speed data from some point in the receiver DSP chain. On the other hand, constellations can be acquired asynchronously and at lower rates, dramatically easing implementation. Most importantly, none of the previous efforts have demonstrated complete or partial universality (within a regime of interest) of their models, where this refers to the ability to train on one link configuration and successfully estimate noise on a different link configuration.
In this work, we implement a multi-tasking CNN that maps constellation density features to ASE and nonlinear noise characteristics simultaneously. Given the complex nature of nonlinear noise and its dependence on various parameters such as modulation format, launch power, copropagating channels, fiber characteristics etc., it is advantageous to quantify this metric using a data driven approach such as machine learning. The use of constellations instead of waveforms enhances the practicality of the method. We begin by assessing the performance of our ML model on linear OSNRASE, nonlinear OSNRNL, and GOSNR when the model is trained and tested on data obtained from the same link.
We also consider the scenario of reduced training at a few optical launch powers spanning the data set and then predicting the noise metrics at intermediate optical powers not used in training. We then assess the universality of our model within the regime of metro networks by cross-training with data from metro links comprised of different fiber types. Linear OSNRASE, nonlinear OSNRNL and GOSNR estimation are demonstrated with ≤ 0.5 dB mean absolute error (MAE) for experimental dual-polarized 32-GBaud 16-QAM waveforms. We also verified our ML approach using data obtained from QPSK experiments, where the trends are similar to 16-QAM. Here, we focus on the 16-QAM results. It should be noted that error refers to imperfect estimation and that the training, validation as well as testing data has the typical acceptable uncertainty associated with any experimental effort.
2. Methodology
A CNN is a variant of a DNN and has proven to be highly effective in various image processing applications such as brain image analysis in medical science [18,19]. An image is a matrix of pixel values, and a CNN finds useful relations between input images and output labels through application of several kernels (filter masks) that slide across the width and the height of the pixel matrix and assign learnable parameters such as weights and biases to various parts of the image creating distinctive feature maps composed of smaller matrices. These extracted features are passed to a network of nodes with nonlinear activation functions that create a nonlinear mapping between the network’s inputs and outputs.
The symbol distributions (2D distribution around each symbol centroid) within a constellation image depend on the ASE noise and nonlinear noise with the asymmetric distortions associated with nonlinear noise being pronounced in higher modulation formats [20,21]. We anticipate that a CNN can map the constellation density features simultaneously onto the quantity of linear ASE noise and nonlinear noise, Fig. 2. Subsequently, we can also estimate the GOSNR [3,4]:
Fig. 2. CNN architecture for simultaneous OSNRASE and OSNRNL estimation. X- and Y-polarized constellations are treated as two separate channels instead of the three RGB channels in the standard CNN application [22]. Two convolutional layers and 2 corresponding pooling layers in Shared Layers and 1 extra convolutional layer and 1 corresponding pooling layer were implemented. For this first layer, the density matrix is zero-padded to enable capture of information in the periphery of the constellations. Each convolutional layer is followed by a batch normalization layer to mitigate overfitting [23] and a nonlinear rectified linear unit to extract features, (not shown). Pooling reduces the matrix size and is accomplished by averaging over a 2 × 2x2 matrix that is scanned with a 2 × 2x2 step size (i.e., stride). Kernels are initialized using the Glorot method to prevent vanishing or exploding gradients during the training process [24,25]. Dropout layers with a factor of 0.1 are implemented to further prevent overfitting. The outputs are estimated throughout CNN models trained with regression fitting. 25 selected feature maps in (i) first convolutional layer, (ii) second convolutional layer, (iii) third convolutional layer in the top branch, and (iv) third convolutional layer in the bottom branch.
The Shared Layers consist of two convolutional layers and two corresponding pooling layers for generating, via 2D convolutions with kernels, several feature maps containing low to mid-level spatial features of the constellation density matrix. Figure 2(i) shows 25 selected feature maps generated by the kernels inside the first convolutional layer. The pooling layers downsample the feature maps, while preserving features and reducing computational complexity. The widely used leaky rectified linear units (ReLUs) are the nonlinear function immediately following each convolutional layer. The conventional ReLU is a piecewise linear function that outputs the input if it is positive, and outputs zero if it is negative [26]. A leaky ReLU responds with a small slope (e.g., 0.01) for inputs in the negative region, and is known to prevent the death of neurons with negative inputs during the training. These neurons would not have played any role had a conventional ReLU been used [27]. We used average pooling to mitigate overfitting. The second convolutional layer extracts higher level spatial features.
The Job-Specific Layers have two branches, each of which have one additional convolutional layer to extract features specific to linear or nonlinear noise contributions. The feature maps after the 3A and 3B convolutional layers in the top OSNRASE and bottom OSNRNL branches, respectively, are largely abstracted by the machine learning itself, Fig. 2(iii)-(iv). However, we note that the activations are more spread out across the feature maps after convolutional layer 3A as the ASE noise is uniformly spread around all constellation points, while the activation functions are more sparsely concentrated in the feature maps after convolutional layer 3B likely because they represent the asymmetrical distortions around the constellation points. Insets (iii) and (iv) show 25 out of the 256 feature maps after the convolutional layers in the top and bottom branches, respectively. The global average pooling layer at the end computes the overall mean of the final feature maps and these are vectorized by fully-connected (FC) layers in each branch. We doubled the number of kernels in the subsequent convolutional layers following the first convolutional layer as there are more combinations of features to capture. We used appropriately small kernel sizes in the convolutional layers to ensure accurate capture of the density variations and used OSNRNL and OSNRASE in dB for target variables to avoid unstable and large gradient updates arising from the wide dynamic ranges of OSNRASE and OSNRNL [7].
The specific CNN structure was heuristically determined: 30 × 30 bin size using 30,000 symbols and CNN hyperparameters such as the number of convolutional layers (3) and kernel size (64/128/256) were designed for best performance with minimal computational complexity, Fig. 3. We explored the root-mean-squared training loss (difference between target and estimated value) for different bin sizes and number of symbols, in OSNRASE and OSNRNL estimation, Fig. 3(a) and 3(b) respectively. In this optimization phase, we measured data consisting of 104 combinations of ASE and nonlinear noises from our homogeneous link described in section 3. We also investigated the performance when the number of kernels are gradually increased from a combination of 16 (layer #1) /32 (layer #2) /64 (layer #3) to 256/512/1024 by increasing the kernels in all convolutional layers by the same factor each time, Fig. 3(c) and 3(d). We increased the number of convolution and pooling layers from 1 to 4 and chose 3 since beyond that there is no significant performance improvement. The training loss of OSNRNL was higher than OSNRASE in part due to the fewer and sparser OSNRNL target labels.
Fig. 3. RMSE training loss performance dependence on bin resolution and number of symbols in the constellation density matrix for (a) OSNRASE; (b)OSNRNL; Training loss performance for (c) OSNRASE and (d) OSNRNL versus the ratio of number of kernels where 1 indicates 16/32/64 kernels in the first, second, and third convolutional layers and increasing ratio refers to increasing the kernels in all layers by the same factor.
3. Experiment setup
3.1 DWDM setup
We examine two distinct 3-span links operating in C-band in which the center channel suffers a dispersion of either ∼4,600 ps/nm or ∼3,500 ps/nm, Fig. 4(a). For links with modest dispersion, the nonlinearities are expected to exhibit a non-Gaussian signature. In our DWDM system, adjacent channels are emulated by filtered ASE noise having the same power and spectral density as the center channel [28]. Unlike the EDFA ASE noise that is added after each span, adjacent channels emulated by filtered ASE noise are only added once at the beginning of the link. Prior to detection, the optical signal is filtered with an optical bandpass filter (3.5 order Super-Gaussian, BW = 37.5 GHz). We note that using modulated signals as adjacent channels as well as using additional adjacent channels will make the non-Gaussian signature of the nonlinear products more readily identifiable. The adjacent channels were multiplexed with a tight spacing of 37.5 GHz, Fig. 4(b). The center channel’s OSNRASE was measured by temporarily increasing the channel spacing from 37.5 GHz to 112.5 GHz, Fig. 4(c). We did not remove the adjacent channels so that the power in the spans remains constant. The OSNRASE was varied by ASE noise loading after fiber propagation but before the optical bandpass filter. We used standard PRBS-15 electrical signals to drive the QAM transmitter. The received signal is processed using standard offline digital signal processing including chromatic dispersion compensation, sampling timing recovery, polarization demultiplexing, frequency offset compensation, carrier phase recovery, and channel equalization [29].
Fig. 4. (a) Experimental DWDM link configured to have a DP-32 GBaud QAM signals copropagating through three spans of 90 km SSMF with two side channels emulated by amplified and filtered noise; (b) Optical spectrum of the tightly spaced transmitted signal; (c) optical spectrum with temporarily increased channel spacing for OSNR measurement.
First, the 16-QAM signals were transmitted across a homogeneous link of 3 spans, each of which are 90 km SSMF. In the inhomogeneous link, the last span was replaced by non-zero dispersion shifted fiber (NZDSF). The attenuation, dispersion parameter and nonlinear coefficient of the SSMF are approximately 0.19 dB/km, 17.0 ps/nm-km and 1.17 W−1km−1, respectively, while they are 0.21 dB/km, 4.5 ps/nm-km, and 2.03 W−1km−1 for the NZDSF [30].
3.2 OSNRNL extraction for training
Figure 5(a) depicts the conventional BER vs. launch power, where OSNRASE is allowed to freely vary with launch power producing the traditional “inverted bell-shaped” response with the bottom of the inverted bell representing the optimum launch power for minimum BER. The clearly defined minima reveals that any transceiver penalty does not produce a BER floor in the OSNRASE range of interest. Transceiver limitations may be significant for OSNRASE higher than those considered here [31]. In Fig. 5(b), we increased the launch power and held the OSNRASE constant at 23 dB by adjusting the noise loading to emphasize that the increasing BER at higher optical power is occurring due to fiber nonlinearity. Furthermore, the NZDSF span results in an increased nonlinearity for the inhomogeneous link resulting in higher BER for the same optical power and OSNRASE, Fig. 5(b). We note that the different links exhibit slightly different limiting BERs at low launch power [32].
Fig. 5. BER vs. Launch power (a) variable OSNRASE which corresponds to the conventional “inverted bell-shaped” curve used for determining the optimum launch power and (b) OSNRASE constant at 23 dB by adjusting the noise loading to emphasize that the increasing BER at higher optical power is occurring due to fiber nonlinearity.
The GOSNR includes both the ASE and nonlinear noise and determines the Q-factor $20lo{g_{10}}\left( {\sqrt 2 erf{c^{ - 1}}({2BER} )} \right)$ and BER for a given link, while OSNRASE only captures the in-band ASE noise using the out-of-band noise floor. To determine the GOSNR and OSNRNL used for CNN training, we compare the Q-factor vs. OSNRASE performance for the B2B and fiber link cases., Fig. 6(a). We then identify the GOSNR of the fiber link as the OSNRASE required to achieve the same BER in the B2B case. Graphically this corresponds to “tracing back” from the link performance plot to the B2B plot along a fixed BER [3,4], Fig. 6(a). The fiber link’s OSNRNL used for CNN training is measured via Eq. (1) using the measured OSNRASE and the GOSNR identified from this “tracing back” method. Figure 6(a) shows the Q-factors of the homogeneous link, while its measured OSNRNL is shown in Fig. 6(b). The stronger saturation in the Q-factor plots at higher OSNRASE for the non-B2B cases occurs primarily due to the fiber nonlinearity becoming increasingly significant as the ASE contribution reduces. As expected, higher launch powers result in lower Qs for all OSNRASE. As expected [33], there is a very small variation in measured OSNRNL for constant launch power, despite the OSNRASE varying substantially. This enables a CNN, which was trained using the average OSNRNL, to generate robust estimates. The average OSNRNL decreases with launch power due to increase in nonlinear effects as expected. The average OSNRNL for the inhomogeneous link was consistently lower than the corresponding homogeneous link, Fig. 6(c), again due to the higher nonlinear coefficient of the NZDSF fiber.
Fig. 6. (a) Q-factor of 3 spans of homogeneous link and depiction of the traceback method that identifies the GOSNR and OSNR penalty due to nonlinearities; (b) increasing OSNRNL with launch power for the 3-span homogeneous link; (c) Average OSNRNL in inhomogeneous link and homogeneous link.
The data was captured with the OSNRASE increased in steps of 0.5 dB, from 17 dB to 23 dB. Optical launch power was increased in steps of 1 dBm from 1 dBm to 8 dBm in the homogeneous link, and from 0 dBm to 7 dBm in the inhomogeneous link. Two hundred forty waveforms were captured for each unique combination of OSNRASE and launch power. The CNN training/validating/testing split was 160/40/40 waveforms per configuration.
4. ML estimation results
4.1 ML performance for training and testing on the same link
We first assess the capability of our model when trained and tested on the same link [6,7,13–17]. Testing was done for all 104 combinations of 13 measured OSNRASE and 8 launch powers. For each combination, estimation of OSNRASE, OSNRNL and GOSNR was done for 40 waveforms and the mean estimate was computed. Hence, a total of 4,160 waveforms were used for testing. However, only five launch powers spanning the low to high OSNRNL regions in the two links are shown for clarity.
The mean CNN-estimated vs. the measured OSNRASE revealed good performance, Fig. 7. Over all 4,160 waveforms tested, the maximum estimation error was 0.75 dB and the MAE was 0.11 dB in the homogenous link, while the maximum estimation error was 1.51 dB and the MAE was 0.21 dB in the inhomogeneous link. Additionally, we have shown the root mean square error (RMSE) for an example launch power in the insets. Generally, the estimation errors were slightly higher in the inhomogeneous case at higher OSNRASE. The higher nonlinear noise in the inhomogeneous case may mask changes in the constellation density at high OSNRASE. However, estimation errors ≥ 1 dB were only seen ≤ 1% of the entire testing data set.
Fig. 7. CNN performance in estimating OSNRASE when trained and tested on same link (a) homogeneous link; (b) inhomogeneous link. Markers represent mean CNN-estimated OSNRASE. Error bars indicate worst case estimate over 40 waveforms. Insets depict the RMSE for a single launch power.
OSNRNL are well estimated for all OSNRASE for both links, Fig. 8. The solid lines represent the average measured OSNRNL used as target labels for CNN training, where averaging was done over all OSNRASE at a given launch power, while the markers represent the mean estimates over the 40 waveforms at a given launch power and OSNRASE. The MAE was computed between the average measured OSNRNL and the CNN-estimated OSNRNL over the entire 4,160 test waveforms. The OSNRNL estimation has relatively higher estimation errors than OSNRASE. The inhomogeneous link exhibits a higher sensitivity to launch power due to the higher average nonlinearity. On the other hand, the homogeneous link had a slightly higher dispersion. Dispersion causes multiple effects depending on the amount of dispersion and nonlinearity. At modest dispersion, the conversion of nonlinear phase distortions to amplitude distortions is discernible. This likely caused the maximum estimation error of OSNRNL to be slightly lower in the homogenous link. However, in long-haul links, the larger accumulated dispersion tends to circularize the distortions and degrades the estimation accuracy. The MAE was ≤ 0.5 dB in both links and the maximum estimation error was ≤ 2 dB and ≤ 2.5 dB for the homogeneous and the inhomogeneous links, respectively. However, estimation errors higher than 1 dB occurred in ≤ 5% of the testing data sets.
Fig. 8. CNN-estimated OSNRNL when trained and tested on same link (a) homogeneous link; (b) inhomogeneous link. Colored solid lines represent the OSNRNL from the traceback method. Colored markers represent the CNN-estimated OSNRNL.
The CNN-estimated GOSNR computed using CNN estimates and Eq. (1) match the GOSNR determined via the measured Q and the traceback analysis, Fig. 9. The MAE and the maximum error were < 0.2 dB and < 0.7 dB for both links, demonstrating accurate estimation. The errors in the estimated GOSNR are relatively lower than OSNRASE because GOSNR is estimated from features of the total noise), thereby circumventing the need to separate the linear ASE and nonlinear noise. The estimation error histograms for the homogenous link, Fig. 10, reveal that the OSNRNL error tends to be larger than the OSNRASE error. Figure 10(a) also reveals a slight tendency to have larger OSNRASE error at higher launch powers consistent with Fig. 7. The error histograms for OSNRNL, Fig. 10(b), reveal a larger error but no simple trend. These behaviors are representative of all cases.
Fig. 9. CNN-estimated 16-QAM GOSNR when trained and tested on same link (a) homogeneous link; (b) inhomogeneous link. Dotted lines represent the GOSNR from traceback method. Insets depict the RMSE for a single launch power.
Fig. 10. Error histograms of homogeneous link for (a) OSNRASE; (b) OSNRNL. Colored solid lines represent the errors for the different launch powers.
We trained our CNN using only data with moderate to high nonlinearity and tested it in the low nonlinearity regions, Fig. 11. The threshold OSNRNL is the OSNRNL at and beyond which the data has moderate nonlinearity. Each marker represents the average of 40 CNN-estimated OSNRNL at that OSNRASE and launch power. Most of the estimated OSNRNL in the low nonlinearity region were close to or just above the measured OSNRNL threshold used in training, which represents a qualitatively accurate estimation. It is important to note that quantitative assessment outside of the machine learning training range cannot be performed. This test showed that the CNN had extracted useful features that can characterize the nonlinear noise in the constellations.
Fig. 11. CNN-estimated 16-QAM OSNRNL when trained on moderate to high nonlinear regions and tested on ASE-dominated low nonlinearity data for (a) homogeneous; (b) inhomogeneous links. Colored solid lines represent the OSNRNL from the traceback method. NR: nonlinear region; NTR: nonlinear threshold regions.
Lastly, our I-Q constellation densities were formed from 30,000 contiguous data symbols which requires high sampling rate and high bandwidth hardware in the receiver DSP, thereby increasing the implementation cost. However, the constellation density matrices can be formed using down-sampled data with equal integrity. We created new constellation images by concatenating six 5,000 symbol segments randomly selected from the waveforms at a given optical power and OSNRASE. We ensured that the same segment of symbols is not used in multiple constellation images. We used 5,000 contiguous symbols in a segment to ensure each possible symbol and symbol transitions were equally represented. We trained and tested our CNN on this data for both link cases. The accuracy of estimation was equivalent to using 30,000 contiguous symbols, thus demonstrating that our CNN performs well with drastically down-sampled acquisition of symbols.
4.2 ML performance with reduced training set
We tested using a reduced training set and found CNN to be robust and sufficiently general to accurately predict for cases not considered in the training phase but spanned by the training set. This provides two advantages, first, it increases the degree of universality of the model within the regime of metro networks and second, the speed of ML training is increased by training on a smaller data set.
For the homogeneous link, we trained using the data at 3 dBm, 6 dBm, and 8 dBm and tested on the data at 4 dBm, 5 dBm, and 7 dBm, that is only on data that has launch power within bounds of the training. For the inhomogeneous link scenario, we trained the CNN using the data at 2 dBm, 5 dBm, and 7 dBm and tested on the data at 3 dBm, 4 dBm, and 6 dBm. We included the OSNRNL extremities in the training. The mean estimated OSNRASE, OSNRNL, and GOSNR, Fig. 12, Fig. 13, and Fig. 14, respectively demonstrate that the estimation errors are comparable or only marginally higher than when training using all eight launch powers. These results demonstrate an important capability to estimate performance at intermediate launch powers not used in training in addition to performing well at launch powers used for training.
Fig. 12. CNN-estimated OSNRASE when trained on subset of launch powers and tested on the other launch powers in same link. (a) homogeneous link; (b) inhomogeneous link. Insets depict the RMSE for a single launch power.
Fig. 13. CNN-estimated OSNRNL of 16-QAM when trained on a subset of the launch power range and tested on the remaining launch powers in the same link. (a) homogeneous link; (b) inhomogeneous link. Colored solid lines represent the OSNRNL from the traceback method. Colored markers represent the CNN-estimated OSNRNL.
Fig. 14. CNN-estimated GOSNR of 16-QAM when trained on a subset of the launch power range and tested on the remaining launch powers in the same link. (a) homogeneous link; (b) inhomogeneous link. Dotted lines with markers represent the GOSNR from traceback method. Insets depict the RMSE for a single launch power.
4.3 Assessing the limits of universality: ML performance for cross-training
Although the application of ML in optical performance monitoring (OPM) is an ongoing research area, most of the reports [6,7,13–15] use a ML model that is trained and tested on the same link or set of links [16,17]. However, it is significantly more useful if one can attain a high degree of universality in which the ML is trained one link yet is applicable to any other link or links within a class. This goal is made more challenging because a particular GOSNR and BER can be associated with different symbol distributions (2D distribution around each symbol centroid) within a constellation image. Here, we assess the performance and identify sources of error, when we cross-train a CNN on a metro class link that is different from the testing link. We conducted the cross-training test for two new scenarios: training on the homogeneous link and testing on the inhomogeneous link and vice versa.
For the first cross-training scenario we trained on the homogeneous link and tested on inhomogeneous link, Fig. 15(a). Since the inhomogeneous link exhibits OSNRNL outside the range observed from the homogenous link, we only test on the inhomogeneous link with launch powers of 0 dBm to 5 dBm. Here, Fig. 15(a), the estimated OSNRASE in the low OSNR are comparable to the case when training and testing were done using the same link. However, we observe a systematic underestimation that increased with OSNRASE and with launch power. This deviation is likely caused by the different appearance of nonlinear features in the constellations of the two links. Essentially, the CNN associates the increasing nonlinear features of the inhomogeneous link with ASE and hence the OSNRASE estimate is lower than measured. The reverse behavior is observed with the opposite case when the CNN is trained on the inhomogeneous link and tested on the homogeneous link, Fig. 15(b). In Fig. 15(b), we did not train on 6 dBm and 7 dBm data as a similar OSNRNL range during training and testing ensured better OSNRASE estimation than when the training had a wider OSNRNL range. These results demonstrate that the nonlinear features appear differently for different link configurations.
Fig. 15. CNN-estimated OSNRASE when cross training with no target label normalization (a) trained on homogeneous link and tested on inhomogeneous link, (b) trained on inhomogeneous link and tested on homogeneous link.
Figure 16 shows the constellations of the inhomogeneous and homogeneous links having the same 23 dB OSNRASE and 24.4 dB OSNRNL. The observed distribution of received symbols is different. This results from the different nonlinear coefficient, dispersion, and their distributed interplay in the two links resulting in a different constellation distortion [34]. These distortions become more visible for scenarios where nonlinear noise is significant and not obscured by the ASE noise, namely at high OSNRASE and at high operating powers.
Fig. 16. Constellations of 16-QAM at 23 dB OSNRASE and 24.4 dB OSNRNL in (a) homogeneous link; (b) inhomogeneous link demonstrating that different links exhibit different constellation distributions when operated at the same OSNRASE and OSNRNL.
The estimated OSNRNL when the CNN was trained on the homogeneous link and tested on the inhomogeneous link using all launch powers are shown in Fig. 17(a) and the reverse scenario in Fig. 17(b), where we observe overestimated and underestimated OSNRNL, respectively. This is consistent with the observation of Figs. 15(a) and 15(b). Although the use of a multiple optical powers enabled the CNN to learn the overall dependence of nonlinearity on optical power, the specific features of the nonlinear signature depend on the link details including the dispersion and fiber nonlinearity of each span and the relative location of each fiber span. Without this information ML may not be able to precisely capture the dependency of OSNRNL on launch power for an arbitrary link when not trained on that link. To test this, we demonstrate a simple ad hoc normalization of the link nonlinearities although wide universality may require more link metrics be made available to the CNN. This is further motivated by the observed systematic offset of the OSNRNL estimations. Specifically, we scale the OSNRNL of the untrained link by a single parameter; the ratio of an effective nonlinear coefficient of the two links. An effective nonlinear coefficient can be estimated from a single measurement or analytically [35,36]. Both methods lead to the determination that the ratio of the effective fiber nonlinearity between the two links is approximately 1.5.
Fig. 17. CNN-estimated OSNRNL when cross training with no target label normalization (a) trained on homogeneous link and tested on inhomogeneous link; (b) trained on inhomogeneous link and tested on homogeneous link. Colored solid lines represent the OSNRNL from the traceback method. Colored markers represent the CNN-estimated OSNRNL.
We estimate an effective nonlinear coefficient for the inhomogeneous link as:
The OSNRNL estimated using this scaled approach are shown in Fig. 18 for the two cross training scenarios. All the launch powers were used during training as the OSNRNL ranges for the two links match post normalization. The systematic over/under estimations are nearly eliminated. The estimated OSNRNL in the moderately nonlinear region have errors comparable to those when training and testing is done on the same link. The errors are somewhat higher in the high nonlinearity region, most likely due to the estimation limits of the ML model, which was trained on sparse high-step size OSNRNL data in this region. There is also likely estimation error due to the difference in the chromatic dispersion map of each link. Clearly the difference in the complex distributed interplay between chromatic dispersion and nonlinearity in the two links may not be completely captured through this simple normalization. However, these results suggest that a universal model at least within a class of links such as those associated with metro links with moderate accumulated dispersion and only a few spans, may be possible with additional link information added as input to the CNN.
Fig. 18. CNN-Estimated OSNRNL using normalized target labels when (a) trained on homogeneous link and tested on inhomogeneous link; (b) trained on inhomogeneous link and tested on homogeneous link. Nonlinear coefficient of tested link is available. Colored solid lines represent the OSNRNL from the traceback method. Colored markers represent the CNN-estimated OSNRNL.
Lastly, we demonstrate that the GOSNR are still accurately estimated when the ML was trained on the homogeneous link and tested on the inhomogeneous link along with the reverse cross training, Fig. 19, although the individual contributions to the GOSNR may not be precisely estimated. We have also compared these estimated GOSNR with the estimated GOSNR when the ML was directly trained with GOSNR as the target variable and found the estimation errors to be similar. Thus, universality of GOSNR estimation within the regime of metro networks is more readily accomplished than identifying individual noise contributions using CNN. Interestingly, a study of the skew and kurtosis did not reveal any high level, easily identifiable difference between the scenarios where linear and nonlinear noise dominates.
Fig. 19. CNN-Estimated GOSNR when cross training with no target label normalization (a) trained on homogeneous link and tested inhomogeneous link; (b) trained on inhomogeneous link and tested on homogeneous link. Dotted lines represent the GOSNR using the traceback method. Insets depict the RMSE for a single launch power.
5. Conclusion
We have demonstrated that ML can be used to accurately estimate the OSNRASE and OSNRNL when training and testing are done on the same link. We implemented a multi-tasking CNN that maps the constellation density features simultaneously onto the ASE noise and nonlinear noise levels, thereby indirectly estimating GOSNR. We also demonstrated that accurate estimation of these metrics is possible even at intermediate optical powers that were not used during training, which enables real time tracking of these metrics in the event of random or systematic variation of operating power/gain in the network over time. Training using a reduced data set was shown to perform without significant increase in the estimation error.
Estimation of the OSNRASE and OSNRNL were demonstrated with < 0.5 dB MAE for 32-GBaud 16-QAM DWDM links. We demonstrated the robustness of our approach by using links comprised of two different fiber types. The GOSNR can in turn be estimated to within 0.5 dB MAE using the estimated OSNRASE and OSNRNL. We also showed that the performance was robust when training was done using noncontiguous asynchronously captured data significantly reducing hardware requirements.
Finally, we investigated the possibility of creating a universal machine learning estimation tool by considering the scenario of training on one link and testing on a link comprised of different fiber types. We identified a simple scaling approach based on an effective link nonlinearity that enables good cross trained estimation. The results suggest that including additional link metrics as inputs to the ML may enable a fully universal ML method at least within a class of links. All methods presented are readily deployed without the need for additional hardware nor transmission of special symbols or patterns.
Funding
Georgia Electronic Design Center; L3Harris Technologies, Inc.; ADVA Optical Networking, Inc..
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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