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In this paper we present a novel technique, based in what we have called Parametric Asynchronous Eye Diagram (PAED). We have used a simulation scheme, which includes a differentiator and an Artificial Neural Network to monitor simultaneously several impairments such as Chromatic Dispersion, Polarization Mode Dispersion and Optical Signal to Noise Ratio. A number of modulation formats, including NRZ, RZ and QPSK is used in the computation of results. This paper also demonstrates the effectiveness of this technique in monitoring with one single device, mixed traffic, with different bit rates and On-Off Keying (OOK) modulation formats traveling through the network.
© 2012 Optical Society of America
1. Introduction
Optical Performance Monitoring (OPM) has been a widespread research topic in the field of optical fiber communications. Several solutions have been proposed to evaluate the performance of optical networks. Performance parameters include Chromatic Dispersion (CD) [1–3], 1st order Polarization Mode Dispersion (PMD) [4,5], or Optical Signal To Noise Ratio (OSNR) [5,6], among other. One or more of these techniques are based in at least one of the following methods: Radio Frequency (RF) spectrum analysis, nonlinear optical effects detection and statistical signal processing using synchronous or asynchronous sampling. Despite the usefulness of these techniques for specific applications, the demand for a low cost, multi-impairment Optical Performance Monitor is significant.
The methods addressed above may be classified by the capability to monitor simultaneously all the parameters with one single device. Statistical signal processing by synchronous or asynchronous sampling, seems to be the best candidate [7–10]. RF spectrum analysis and nonlinear optical effects detection collides with the interdependence between different impairments [11], which requires additional techniques to solve this issue [12].
Recently, techniques using machine learning and artificial neural networks have been proposed in conjunction with very well known optical performance diagrams. These optical performance diagrams are based on asynchronous amplitude histograms [13], delay-tap asynchronous diagrams [7–9] or synchronous eye diagrams [10].
Jargon et al. [8] have reported an optical performance technique using artificial neural networks, which monitors simultaneously CD, PMD and OSNR for an NRZ-OOK modulation format at 10 Gbit/s. The monitoring window ranges from 0 to 700 ps/nm, 0 to 35 ps and 18 to 30 dB respectively. The authors do not report the errors obtained in these computations [8–10]. Machine learning with delay-tap asynchronous sampling (DTAS) histograms has also been used to compute OSNR, CD and PMD [9]. The monitoring windows reported, range from 0 to 1600 ps/nm, 0 to 50 ps and 15 to 27 dB, for CD, PMD and OSNR, respectively, using 10 Gbit/s NRZ-OOK modulation format. The patent application [9] uses several algorithms to predict CD, PMD and OSNR, including a linear and a nonlinear kernel algorithm, for pattern recognition. It demonstrates good estimates for CD and PMD, although the monitoring accuracy for OSNR is reported as not so positive.
A novel technique has been developed in [10] using parameters extracted from synchronous eye diagrams, presenting a monitoring range of 18 to 30 dB, 0 to 700 ps/nm and 0 to 35 ps for OSNR, CD and PMD, respectively. This results are shown for a 10 Gbit/s NRZ-OOK modulation format.
In [14] delay tap asynchronous sampling is used to monitor a 100 Gbit/s QPSK modulation format signal. Two different direct detection receivers have been tested (i.e single ended detection and balanced detection). Superior accuracy is achieved with balanced detection.
In [15] synchronous eye diagrams with ANN, have been used to compute several impairments using 40 Gbit/s RZ-OOK and 40 Gbit/s RZ-Differential Phase Shift Keying (DPSK). The errors reported are 2.53 ps/nm for CD and 0.58 dB for OSNR, when using 40 Gbit/s RZ-OOK signal. The OSNR is 1.85 dB and CD is 3.18 ps/nm for 40 Gbit/s RZ-DPSK. The errors reported for CD using RZ-OOK modulation format are about 5 % of the maximum range of the monitoring window used (50 ps/nm).
In this paper a novel technique so called Parametric Asynchronous Eye Diagram (PAED) [16] in conjunction with Artificial Neural Networks (ANN) is presented o monitor simultaneously several impairments. The PAED uses samples of the signal (y) and of the differentiated signal (x), to form the diagram (where and y=y(t), hence the name Parametric). The technique is completely transparent to modulation format and bit rate, in terms of hardware and signal processing. This means that no change in hardware or processing algorithm is required when the bit rate and modulation format change. Results demonstrate the effectiveness of this technique when dealing with NRZ, RZ and QPSK modulation formats and bit rates of 10 Gbit/s, 20 Gbit/s and 40 Gbit/s. We report results showing that with a simple receiver comprising only single ended detection, the optical performance technique presented in this paper is capable to monitor a signal modulated with 40 Gbit/s NRZ-QPSK.
The PAED captures the information of the first order derivative, which is strongly affected by CD and PMD, due to the pulse broadening caused by those effects. The differentiator increases the sensitivity of the monitor at high frequency components of the signal, which for instance may be beneficial for chromatic dispersion, where the components with higher frequency, have higher delay, and suffer higher fading due to chromatic dispersion. When dispersion is too high the fading at high frequencies increases to a point where it is not possible to distinguish between one level of dispersion and the other. The differentiator allows to increase the range of the monitoring window. PAED is focused on rise and fall edges and treats them separately. DTAS is focused on transitions. The impact of dispersion in PAED effects occurs mainly on rise and fall edges, while the impact of noise is mainly concentrated in the center of PAED. These three regions are represented on PAED in an easy and understandable manner. The visual analysis of DTAS depends on the delay used, modulation format and bit rate. The visual and processing analysis of PAED is completely independent of these parameters (ie. no need to change the optical performance monitoring algorithm). Asynchronous amplitude histograms fall in a different category. They are based in the evaluation of histograms, which gives an averaged measurement of Q-factor, which is affected by middle level samples.
2. Artificial neural networks
“Artificial neural networks (ANNs) are neuroscience inspired computational tools that are trained by the use of input-output data to generate a desired mapping from an input stimulus to the targeted output” [10]. The input-output pairs are grouped in two different sets, the training set and the test set. Both are taken from the input and output of a physical device or physical model. They are different in the sense that they have different input-output combinations. This is essential to test the validity of the model. The training set and the test set are composed by n + m columns, where n is the number of inputs and m is the number of outputs. Each row represents one training or test data example.
In a first phase the ANN is trained with the training set. The training applies to adjust the weights of the ANN in each training epoch, until a specified Mean Square Error, between the m outputs of the training set and the m output values obtained during the training process, has been met, or a defined number of epochs has been achieved. In Fig. 1, the weights of the ANN are illustrated by the arrow lines. They are just multipliers. The neurons in the hidden and output layer, first sum all its inputs, and then pick the result of this sum, as the coordinate x of a sigmoid (hidden layer), or linear (output layer) function. The output of each neuron is the ordinate y = f(x) of such functions. It may occur that low errors are achieved with the training sets, due to the effect known as overtraining in ANNs, but that does not mean that the ANN is well modeled. To test if the ANN is well modeled it must be validated with the test set. If the errors between the test values and the ones predicted by the ANN are sufficiently low, the ANN is well modeled, and the training process is completed. The results shown in figures presented in this paper, when related with ANNs output, are always based on the test data.
Fig. 1 Artificial Neural Network. Qn represents the nth subset of the diagram of PAED (see 5), σ the standard deviation, and , represents the mean of the amplitude and derivative of the subset of the diagram, respectively.
3. Simulation setup
In Fig. 2 the setup of the novel technique using an electrical differentiator is shown. The technique captures samples from the signal and from the differentiated signal, and plots them, one against the other, in X–Y mode. The power of the signal is splitted in two equal (not mandatory) parts. One part is sent to the differentiator and the other is sent directly to a signal processor.
Fig. 2 Setup of the novel technique using an electrical differentiator. SMF-Single Mode Fiber, DCF-Dispersion Compensating Fiber.
The setup of Fig. 2 comprises a laser centered at 1550 nm, one pattern generator, providing 10 Gbit/s NRZ-OOK modulation format, transmitting pulses with 35% of the bit duration spent in the rise time and 35 % in the fall time (ITU recommendation G.957), a Mach-Zhender modulator, a CD and a PMD emulator. Shorter rise and fall times, produce less accurate results, due to the spreading of dispersion to higher frequencies, which are not available for monitoring purposes due to the limited bandwidth of the photodetector. The PMD emulator has a depolarization rate of 10.8 degrees/GHz. This takes into account the rotation of the Principal States of Polarization (PSP). The EDFA emulates the effect of OSNR by tuning the Noise Figure. An optical gaussian filter centered at 1550 nm and bandwidth higher than 20 GHz, filters the optical signal. Higher bandwidths are possible without significant decrease in the monitor performance. Although the bandwidth of the filter and the photodetector should not be much higher than the bandwidth of the signal. High frequency noise will degrade PAED. The OSNR was measured after the optical gaussian filter. One 1st order Gaussian electrical filter, included in the receiver, simulates the PIN photo-diode passband of 10 GHz bandwidth. The propagation delay of the electrical differentiator shall be compensated in the simulation, to synchronize the electrical differentiated signal, and the modulated signal.
The differentiator is intended to be an analog filter with proper bandwidth. A digital differentiator may also be used, although it would require the Nyquist sample rate to work properly. Therefore in essence if we would like to take advantage of asynchronous undersampling we shall not use a digital differentiator at least for optical performance monitoring applications. It would be contradictory in terms of cost and philosophy of this work. We run the simulations using different PRBS and with random sample offset, relatively to the beginning of the PRBS, for each combination of impairments.
In Fig. 3 the amplitude and phase transfer function of the differentiator is shown. It was implemented in the frequency domain with one zero at −3.14x109 rad/s and one pole at −2.51x1011 rad/s. The differentiator is a high pass filter, rising the amplitude transfer function by 20 dB/decade, between 500 MHz and the cut-off frequency of 40 GHz. Millimeter-wave monolithic microwave integrated circuits technology can go up to 100 GHZ frequencies [17], and there are already companies in the market that are producing high pass filters at 40 GHz bandwidths and beyond (for example Millitech).
Fig. 3 (a) Amplitude and (b) phase transfer function of the electrical differentiator, represented in the simulation setup of Fig. 2.
The alternative to the electrical differentiator is one optical differentiator. The purpose of using an optical differentiator is that it gives the possibility to optically sample the signal, after the differentiator, enabling superior bandwidths. We tested succesfully in the simulator the optical differentiator proposed by Velanas et al. [18]. It has high transparency to the wavelength, and so it is suitable for Optical Sampling Oscilloscopes. In [16] we presented an experimental demonstration of PAED using a similar scheme, however instead of a DSF we have used a Semiconductor Optical Amplifier (SOA) for modulated signals up to 40 GHz bandwidth. We did not use one amplitude optical differentiator to compute the optical performance monitoring results, because we will have to deal with strong nonlinearities, which consume high processing time, specially when several combinations of PMD, CD and OSNR are to be computed. Computer memory and reasonable time to compute the results in this situation can be overcome.
Optical field differentiators can also be used with additional techniques. The one proposed by Kulishov et al. [19], which uses a long period fiber grating, is appropriate for applications in which the wavelength is known, for instance, on-line OPM. Its potential low cost is also an advantage. In [20] an optical multichannel differentiator with 45 channels is presented, using fiber Bragg gratings, ideal for WDM applications. In [21] an interferometer is proposed as a first order temporal differentiator. It also can be implemented as multichannel differentiator for WDM applications.
From Fig. 4 one can see that despite using two OOK modulation formats and two different bit rates, the PAED remains with similar shape, across Figs. 4(a), 2(b), 2(d) and 2(e). Figures 4(c) and 4(f) show a NRZ and RZ signal degraded with the same level of impairments. One can see that the PAED tends to close when facing signal degradation, having a behavior similar to the Synchronous Eye Diagram. The effect of CD is evident, it tends to decrease the derivative in the lower part of the bit, due to pulse broadening. The decrease of OSNR tends to spread the samples along the contour of PAED due to the increase of added noise. PMD tends to distort PAED, turning it antisymmetrical due to different rising and falling edges caused by the impact of PMD.
Fig. 4 Diagrams generated by the novel technique, using different modulation formats and bit rates. (a)-10 Gbit/s RZ signal, (b)-10 Gbit/s NRZ signal, (d)-20 Gbit/s NRZ signal and (e)-20 Gbit/s RZ signal with CD=0 ps/nm, PMD=0 ps, OSNR=30 dB. (c)-10 Gbit/s NRZ signal and (f)-10 Gbit/s RZ signal with CD=500 ps/nm, PMD=7 ps, OSNR=20 dB.
4. Simulation results and discussion
We have used ANN to model the optical performance monitor. The software used to train the ANN was the software package neuromodeler 1.5 by Zhang et al. [22], also used in [10] and [14].
In the training process the eye is splitted in 6 subsets of the diagram as shown in Fig. 5. For each subset of the diagram the mean and standard deviation of the derivative and amplitude are computed which leads to 24 inputs to the ANN, as is represented in Fig. 1. Qn represents the nth subset of the diagram, σ the standard deviation, and , represents the mean of the amplitude and derivative of the subset of the diagram, respectively.
Fig. 5 Parametric Asynchronous Eye Diagram splitted in 6 subsets of the diagram for training procedure.
The center subsets of the diagram are better, evaluating OSNR, because is there where the Noise is mainly concentrated. The outer subsets of the diagram are better evaluating dispersion effects such as PMD and CD, because dispersion enlarges the bit duration, reducing the derivative at the rising and falling edges.
We run the simulation setup with Optisystem 10.0, and simultaneously, Matlab® code also ran with the simulation. The ANN was tested with 40 and 10 hidden neurons (NRZ only), 24 inputs and 3 outputs. The ANN was trained, with the Quasi-Newton(MLP) method. The inputs are preprocessed using the mapstd and processpca Matlab® functions. This is a simulation example for the best performance possible, in terms of the minimal root mean squared error, that can be achieved. Increasing the number of hidden neurons, above 40, will not provide better performance, although in practice the number of hidden neurons can be decreased if speed is the demanding factor. A decrease in performance may occur when we set the number of hidden neurons from 40 to 10 as shown in Fig. 6.
There are some hardware implementations of ANNs that can implement them, even using optical components. An extensive review of hardware implementations of ANN can be found in [23]. Field Programmable Gate Arrays (FPGA), give a relatively cost effective, reconfigurable implementation of an ANN [23].
4.1. NRZ-OOK 10 Gbit/s
The results plotted in Figs. 6(a)–6(c), show the CD, PMD and OSNR obtained (CD out, PMD out, OSNR out) against the desired values (CD in, PMD in, OSNR in). The RMSE is calculated for each value of CD, PMD and OSNR and the error bars shown are based on this calculation. In the case that the ANN has 40 neurons CD RMSE remains bellow 60 ps/nm until about 3000 ps/nm, above that it starts to increase. PMD RMSE is higher at the borders of the monitoring window, remaining steady, with small fluctuations, along the center of the monitoring window. The RMSE of OSNR increases gradually with the increase of the value of OSNR. Better results are achieved for the ANN with 40 neurons.
4.2. NRZ-QPSK 40 Gbit/s
In Fig. 7, the results for a signal modulated with 40 Gbit/s QPSK are shown. The setup used is the same as in Fig. 2, except that the transmitter must be a QPSK transmitter and the receiver must have a bandwidth higher than 40 GHz. The number of neurons used in the ANN hidden layer was 40, and the training process is the same as the one used before. We tried several options for the receiver, although a 20 GHz receiver does not allow sufficient accuracy, despite the bandwidth of a QPSK modulated signal is 20 GHz. An alternative to this scheme with increased complexity was tested using a coherent receiver. However it does not provide a significant increase in accuracy, when compared with the former option. Therefore we only show the results, when it is considered a receiver comprising a 40 GHz photodetector. Although costs may justify one option or the other. The coherent receiver uses two 20 GHz receivers and requires 4 analog-digital converters and two differentiators. The quadrature and in-phase signals are handled as two intensity modulated signals and therefore, the signal can be represented in similar diagrams as the ones shown in Fig. 4, which is not possible with the former option. The quadrature and phase samples are superimposed, generating a PAED.
Fig. 7 40 Gbit/s NRZ-QPSK. RMSE as a function of CD, PMD and OSNR test data. (a)-CD, (b)-PMD and (c)-OSNR.
The results in Fig. 7, show RMSE as a function of the values of each impairment. CD RMSE and PMD RMSE are below 20 ps/nm and 1.3 ps. OSNR RMSE is near 1.5 dB at about 11 dB, but decreases rapidly and then starts to increase gradually, with a small fluctuation at 25 dB.
This technique can also be used to quadrature amplitude modulation, using a single ended detection scheme. For 4-QAM the technique will present the two amplitude levels clearly described in the diagram.
4.3. Mixed traffic
To the best of our knowledge, so far the performance monitoring in optical networks, showed no technique that have had the capability to monitor, mixed traffic, with a single monitor. We call mixed traffic, when the networks support traffic with several modulation formats and bit rates, traveling in the network (OBS networks for example). In Fig. 8, we present results that demonstrate the capability of this optical performance technique, to make the output of the ANN follow the test data examples, by making use of several types of modulation and bit rates, mixed in a training data set. Due to the relative complexity of the problem, the number of neurons in the hidden layer were increased from 40 to 50. The training process is identical to that used previously. The ANN comprises 24 inputs and 5 outputs. The outputs give the predictions of CD, PMD, OSNR, bit rate and modulation format. Table 1, summarizes the results obtained. Different monitoring windows were used for each modulation format and bit rate, due to the intrinsic nature, of each one of these types of traffic. The RMSE values for CD, PMD and OSNR are presented in the same table. PAED in conjunction with ANNs give the possibility to integrate all these types of traffic, due to the intrinsic nature of PAED, which gives similar diagrams for all kinds of OOK traffic. This eases considerably the learning of ANNs.
Fig. 8 Predictions of CD, bit rate, PMD, modulation format and PMD as a function of number of the test data examples, when mixed traffic is in the network. (a)-CD and bit rate,(b)-PMD, modulation format and (c)-OSNR.
Table 1. Monitoring Windows for each Impairment - RMSE-Root Mean Square Error
The predictions for bit rate and modulation format, correspond to an almost perfect match. The derivative is higher for higher bit rates, due to faster rise and fall times. This allows to distinguish between bit rates and OOK modulation formats. Information about bit rate and modulation format will be important in future optical networks in the scope of optical performance monitoring.
4.4. Discussion of results
Our results for 40 Gbit/s QPSK, show better accuracy than [14], for a single ended detection scheme, which decrease cost relatively to the balanced detection scheme proposed by that paper. The 10 Gbit/s NRZ results show higher monitoring window for CD, PMD and OSNR than [8–10]. The paper presented in [8] presented a correlation coefficient of 0.97, between the test data examples and the output of the ANN. We obtained a correlation coefficient of 0.99. The results using mixed traffic present lower accuracy and also lower monitoring range for 10 Gbit/s NRZ signal, mixed with other modulated signals, than the results presented in sections 4.1. This is due to the fact that above a certain level of impairments the ANN cannot give accurate predictions for the bit rate and modulation format, turning out difficult the learning of ANN.
5. Conclusions
Parametric Asynchronous Eye Diagram (PAED) is a straightforward and cost-effective alternative to synchronous eye diagram, when the purpose is to visually evaluate the quality of the signal. PAED, together with artificial neural networks showed to be a valid solution in the monitoring of different types of traffic with different modulation formats and bit rates, including 10 Gbit/s NRZ, 40 Gbit/s NRZ-QPSK and mixed traffic with different OOK modulation formats and bit rates traveling through the network, such as 10 Gbit/s NRZ, 10 Gbit/s RZ, 20 Gbit/s RZ and 20 Gbit/s NRZ.
Acknowledgments
The grant SFRH/BD/69577/2010 from the Portuguese Foundation for Science and Technology is acknowledged.
We would like to acknowledge Prof. Jos Azaa, from the Institut National de la Recherche Scientifique Energie, Matriaux et Tlcommunications (INRS-EMT), for valuable information provided about optical differentiators.
The authors would like also to acknowledge Prof. Fernando Morgado Dias, from the University of Madeira, for fruitful discussions about FPGA implementations of Artificial Neural Networks.
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