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Abstract
An approach for simultaneous modulation format identification (MFI) and optical signal-to-noise ratio (OSNR) monitoring in digital coherent optical communications is proposed based on optoelectronic reservoir computing (RC) and the signal’s amplitude histograms (AHs) obtained after the adaptive post-equalization. The optoelectronic RC is implemented using a Mach-Zehnder modulator and optoelectronic delay feedback loop. We investigate the performance of the proposed model with the number of symbols, bins of AHs and the hyperparameters of optoelectronic RC. The results show that 100% MFI accuracy can be achieved simultaneously with accurate OSNR estimation for different modulation formats under study. The lowest achievable OSNR estimation mean absolute errors for the dual-polarization (DP)-quadrature phase-shift keying signal, the DP-16-ary quadrature amplitude modulation (16QAM) signal, and the DP-64QAM signal are 0.2 dB, 0.32 dB and 0.53 dB, respectively. The robustness of the proposed scheme is also evaluated when the optoelectronic RC is in presence of additive white Gaussian noises. Then, a proof of concept experiment is demonstrated to further verify our proposed method. The proposed approach offers a potential solution for next-generation intelligent optical performance monitoring in the physical layer.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical communication networks become more cognitive and flexible with the rapid development of new data services [1]. Elastics optical network (EON) has been considered a promising solution to meet unpredictable and heterogeneous traffic demands [2]. The modulation formats, line rates, and spectrum assignments in EON are expected to be adaptively adjustable based on the varying channel conditions and traffic demands [3].
Due to the transmission performance being primarily determined by the optical signal-to-noise ratio (OSNR) [4], OSNR is commonly used to evaluate the quality of transmission and has an extremely important relation with automatic fault detection and diagnosis in optical communication networks. Meanwhile, for the trade-off between transmission distance and spectrum efficiency, the modulation format and line rate should also be adaptively adjusted according to OSNR [5]. With the reconfigured modulation formats in the transmitter, the digital signal processing (DSP) modules should also be dynamically configured to handle the modulation format-dependent impairments, such as adaptive equalization and carrier phase recovery [1]. Consequently, both OSNR and modulation format should be monitored in advance to enable an adaptive optical transceiver in the efficient and intelligent EON [5,6].
Recently, machine learning techniques have attracted extensive attention and achieved significant research progress in optical communication networks. Many reports have shown that machine learning techniques, such as feedforward neural network (FFNN) [7–11], recurrent neural network (RNN) [8,12], convolutional neural network (CNN) [3] and reservoir computing (RC) [13,14], can be applied in optical communication systems for optical performance monitoring (OPM), channel equalization, and quality of transmission enhancement, etc. Especially for OPM, the feature-based FFNN has been used to achieve joint and accurate OSNR estimation and modulation format identification (MFI) [8]. A long short-term memory network is a special RNN architecture, which was proposed to simultaneously estimate OSNR and nonlinear noise power. A method of OSNR monitoring and MFI based on a binarized CNN was proposed and experimentally demonstrated in a coherent receiver [3]. However, these methods based on FFNN, CNN and RNN usually take up a lot of memory resources. In addition, the backpropagation algorithm used for updating the weights needs large-scale float valued operations in the training phase, which are time and power-consuming [15]. Subsequently, RC has attracted increasing research attention because it has many conspicuous advantages by the virtue of its unique structure. In the RC system, only the weights of the linear output layer need to be trained, indicating that RC is potentially amenable for large-scale practical configurations. The RC is suitable for different kinds of tasks and has lower implementation complexity [16]. With the development of photonic machine learning, hardware implementations of photonic RC with error rates comparable to the state-of-the-art digital algorithms have been realized as another breakthrough in optical information processing [16–19]. In [20], photonic RC was used to achieve MFI based on an optically injected semiconductor laser with self-delay feedback and the proposed technique utilized very simple devices, thus offered a resource-efficient alternative approach.
In this paper, we propose a method for simultaneous MFI and OSNR monitoring in digital coherent communication systems based on an optoelectronic RC. The amplitude histograms (AHs) of dual-polarization (DP)-quadrature phase-shift keying (QPSK), DP-16-ary quadrature amplitude modulation (16QAM), and DP-64QAM signals are collected after the constant modulus algorithm (CMA)-based adaptive equalization. A Mach-Zehnder modulator (MZM) and optoelectronic delay feedback loop are used to configure the optoelectronic RC. The influence of different optoelectronic RC parameters on OPM performance is investigated. For the OSNR estimation, The mean absolute errors (MAEs) of 0.2 dB, 0.32 dB and 0.53 dB are achievable for the DP-QPSK, the DP-16QAM and the DP-64QAM signals, respectively. In the meantime, we could also achieve 100% MFI accuracy for these three modulation formats under study. Then, the performance of the optoelectronic RC in presence of different levels of additive white Gaussian noise (AWGN) is quantified to show the robustness of the proposed scheme. Finally, a proof of concept experiment is also demonstrated to verify our proposed method.
2. Operation principle
Figure 1(a) shows the schematic diagram of a conventional RC, which generally consists of an input layer, a reservoir, and an output layer. In the input layer, an input signal u(n) is multiplied by mi (i = 1, 2, …, N) for preprocessing. mi is the mask value corresponding to the ith virtual node where N is the number of virtual nodes. Then the masked signal v(n) = miu(n) is injected into the reservoir. The reservoir states x(n) can be written as:
where f is the nonlinear transformation and A is the connection matrix. In the output layer, the output signal y(n) is obtained by taking a linear combination of virtual node states and can be expressed as where xi(n) is the state of the ith virtual node at time (n = 0, 1, 2,…) in the reservoir, and Wi is the readout weight of ith virtual node in the output layer which is determined during the training phase and fixed in the testing phase.
Fig. 1. (a) Schematic diagram of RC. NL denotes the nonlinear transformation. (b) Structure of the optoelectronic RC. LD, laser diode; MZM, Mach-Zehnder modulator; OC, optical coupler; PD, photodetector; DSO, digital storage oscilloscope; EA, electrical amplifier; EDFA, erbium-doped fiber amplifier; AWG, arbitrary waveform generator.
To achieve the optoelectronic RC, a single nonlinear node consisted of the MZM with an optoelectronic time-delayed feedback loop is applied as the reservoir [21]. Figure 1(b) shows the envisioned structure of an optoelectronic RC configuration, which is implemented numerically in this work. The optoelectronic feedback loop is composed of MZM, optical coupler (OC), photodetector (PD), electronic combiner, erbium-doped fiber amplifier (EDFA) and electrical amplifier. A laser diode with optical power I0 provides the optical carrier for the MZM. Assuming that an electrical signal V(t) drive the MZM, the intensity of the MZM output signal can be expressed as
where Vπ is the half-wave voltage of MZM and φ is the bias-induced phase difference between the upper and lower arms of the MZM. The output signal of MZM is divided into two parts by an OC. One part is sent to PD2 and recorded by a digital storage oscilloscope (DSO) while the other is amplified by an EDFA and is sent to PD1 to perform the optical-to-electrical conversion.The output signal of PD1 is combined with a masked signal v(t) which is generated by arbitrary waveform generator (AWG). Then the combined signal is amplified by an electrical amplifier (EA) to drive the MZM. It can be expressed as
where G1 and G2 are the gains of EA and EDFA, κ is the coupling ratio of OC, R is the responsivity of PD1, and ρ is the scaling factor for v(t). In our proposed time-delayed reservoir, the x(t) can be considered as the light intensity or electrical signal amplitude. In this case, we define x(t) to be I(t)/I0. For the description’s simplicity, the optoelectronic RC’s behaviours can be considered in discrete time. The roundtrip time of the optoelectronic feedback loop is defined as T’. Considering N + p virtual nodes in the feedback loop, the roundtrip time T’= (N + p)θ can be obtained, where θ denotes the time interval between the virtual nodes. We choose p equal to 1 to make the RC work at the unsynchronized regime, where the state equations become coupled, yielding a much richer dynamic [22]. The reservoir states in optoelectronic RC can be approximated by3. Numerical simulation configuration
3.1 Coherent transmission system
To verify the feasibility of our proposed joint MFI and OSNR monitoring scheme based on the optoelectronic RC, we adopt three commonly used modulation formats, i.e., DP-QPSK, DP-16QAM and DP-64QAM, for digital coherent optical communications. The simulation setup of the coherent transmission system and the DSP routine are shown in Fig. 2. The signals of the three modulation formats are generated at a symbol rate of 28 Gbaud, and transmitted over a 100 km single-mode fiber (SMF, dispersion coefficient: 16.75 ps/nm/km; attenuation: 0.2 dB/km; nonlinear coefficient: 2.6 × 10−20 m2/W) link. An EDFA is used to compensate the fiber loss and an optical bandpass filter (OBPF) is used to filter out the out-of-band noise. Coherent detection is performed at the coherent frontend with a local oscillator (LO) laser. The detected signals are sent to the DSP module after analog-to-digital conversion. After down-sampling to 2 samples per symbol, in-phase quadrature imbalance compensation, chromatic dispersion compensation and an adaptive equalizer (T/2-space, T is the symbol period) based on the constant modulus algorithm (CMA), the amplitudes of the signal symbols are represented in amplitude histograms (AHs). Figure 3 shows selected examples of 30-bin AHs for all three modulation formats captured at three different OSNR values, each generated with 1800 symbols. The overall dataset consists of in total 1050 AHs, with 30 different AHs for each modulation format at each OSNR point. The selected modulation formats, the corresponding label vectors and the OSNR values are illustrated in Table 1. Therefore, the dataset consists of in total 1050 AHs of 30-bin each, in total where we randomly mess up the dataset and use a five-fold cross method to evaluate the performance of the proposed joint MFI and OSNR monitoring scheme.
Fig. 2. Simulation setup of the coherent transmission system and the DSP procedure. SMF: single-mode fiber, EDFA: erbium-doped fiber amplifier, LO: local oscillator, CD: chromatic dispersion, OBPF: optical bandpass filter, DSO: digital storage oscilloscope, CMA: constant modulus algorithm, MMA: multi-modulus algorithm.
Fig. 3. AHs with different modulation formats, OSNRs and bins. AHs with 30 bins for three different OSNRs for QPSK (first row), 16-QAM (second row), and 64-QAM (third row) signals after CMA equalization.
Table 1. Labels for modulation formats and ONSRs
3.2 Optoelectronic reservoir computing
The optoelectronic RC is constructed numerically in our time-domain simulation platform according to the configuration in Fig. 1(b). The masked signal in the input layer of optoelectronic RC is generated with an AWG and combined with the output of PD1. There are four types of masks including binary, random, six-level and chaos sequences in our proposed optoelectronic RC system [23]. The binary mask is composed of a random binary sequence {−1, 1}. The six-level mask is composed of a random sequence {±1, ± 0.6, ± 0.3}. The random mask is uniformly distributed over the interval [-1,1]. A simple non-linear dynamical equation is used to generate the chaos mask [24]. In the reservoir, the roundtrip time of feedback loop T’ is set to be 7.65 µs. Considering θ = 150 ns and p = 1, there are 50 virtual nodes in the optoelectronic RC. The input gain β can be adjusted by the AWG, whereas an EDFA is used to control the feedback gain α. The output signal of the reservoir is recorded by a DSO. To achieve the joint MFI and OSNR monitoring, the procedure of optoelectronic RC is configured as shown in Fig. 4. The input of the optoelectronic RC is the AHs collected in our coherent transmission system described in the previous sub-section. In the output layer, there are six outputs which connect to the all-virtual nodes of the reservoir.
In the training phase, the readout weights Wj,i (j = 1, 2, … 6; i = 1, 2,…50) are generated by ridge regression. The outputs [y1 y2 y3] and [g1 g2 g3] represent the labels of the modulation formats and OSNR, respectively. The g1, g2, and g3 represent the estimated OSNRs of QPSK, 16QAM, and 64QAM signals, respectively. For OSNR estimation, we regress reservoir states in optoelectronic RC with OSNR labels of each modulation format. Note that the outputs [g1 g2 g3] for estimating OSNR are designed to avoid a large number of virtual nodes to approximate the complex relationship between the OSNRs and reservoir states. In the test phase, the target modulation format and OSNR can be estimated simultaneously. Although three OSNRs g1, g2 and g3 can be obtained, only the OSNR corresponding to the target modulation format is selected by using the location “1” of the label.
4. Simulation results and discussion
4.1 Influence of the number of received symbols and bins
The influence of the bins and the number of received symbols for the overall performance of joint OSNR monitoring and MFI is investigated. We evaluate the OSNR estimation performance by using the total MAE which is an average value of QPSK, 16QAM and 64QAM MAE. The MFI accuracy is calculated by the Nerr/Ntotal, where Nerr is the number of erroneous identification AHs and Ntotal is the total AHs of three modulation formats. The chaos sequence-based mask is used in optoelectronic RC. For this specific evaluation we set the feedback gain α = 1.6, input gain β = 0.65, bias angle φ = 0°, and regularization parameter k = 1 × 10−6 . Figure 5(a) shows the total MAE and MFI accuracy as a function of the number of received symbols on 30-bin AHs test datasets. One can clearly observe that when the number of post-CMA symbols is increasing, the joint MFI and OSNR monitoring performance of RC is improved as we expected. With above 1500 symbols in the dataset, < 0.3 dB total MAE can be achieved simultaneously with 100% MFI accuracy. Figure 5(b) shows the relationship between the number of bins and the joint OSNR monitoring and MFI performance with 1800-symbol dataset. It can be observed that the optimized performance of joint OSNR monitoring and MFI is obtained with 30-bin AHs. Note that we focus on the parameters sweeping to optimize the MFI and OSNR monitoring performance without considering noise in the optoelectronic loop. The influence of noise on the optoelectronic RC performance is discussed in the Sec. 4.4. With the increase of bins, the performance is slightly degraded. We attribute such performance to the sparse distribution of symbols among bins with limited dataset size, which degrades the extraction of AH features. A more stable amplitude distribution can be expected by the use of a larger bin number with a larger amount of received symbols, which in turn increases the cost of MFI and OSNR monitoring. Therefore, we employ the configuration of 1800 symbols and 30-bin AHs for our studies.
4.2 Optimization of key parameters of optoelectronic RC
We then move to the optimization of the input gain and feedback gain of optoelectronic RC to improve the joint MFI and OSNR monitoring performance. The remainder parameters of optoelectronic RC are identical to Sec. 4.1. Figure 6 shows the total MAE and MFI accuracy dependency on feedback gain and input gain. According to the definition of α = πG1G2κR/Vπ and β = πG1ρ/Vπ, the sweeping of input gain α or feedback gain β can be achieved by adjusting the EA gain G1 and EDFA gain G2 or the scaling factor ρ at AWG. When the feedback gain α and input gain β ranges from 0 to 2, we obtain a lower total MAE and 100% MFI accuracy around the region of α = 1.45 and β = 0.6. After the optimization of the feedback gain α and input gain β, the influence of the bias angle and the regularization parameter k for joint MFI and OSNR monitoring are studied as shown in Fig. 7. The optimized bias angle φ and regularization parameter k are 0° and 7.7 × 10−7, respectively. Figure 8 shows the joint MFI and OSNR monitoring performance based on optoelectronic RC with four types of mask signals. It is observed the performance can be improved by using a chaos mask due to the complex dynamical response [25], particularly in terms of OSNR monitoring. Therefore, these optimized parameters of optoelectronic RC are used to obtain the detailed performance of joint OSNR monitoring and MFI in the next sub-section.
Fig. 6. (a) Total MAE as a function of the parameters feedback gain α and input gain β, (b) MFI accuracy as a function of the parameters feedback gain α and input gain β.
Fig. 7. (a) Total MAE and MFI accuracy as a function of bias angle φ. (b) Total MAE and MFI accuracy as a function of regularization parameter k.
4.3 Joint MFI and OSNR monitoring performance
We study numerically the system-level performance of joint OSNR monitoring and MFI with the optimal configuration of the datasets and the optoelectronic RC as we described in Sec. 4.1 and Sec. 4.2. Figure 9(a)-(c) shows the OSNR monitoring results for QPSK, 16QAM and 64QAM signals, respectively. One can see that high OSNR estimation accuracy can be achieved for the majority of the estimated values within a 1-dB deviation. The performance for the 64QAM signal is slightly worse than the other two modulation formats. Such degraded performance may be attributed to the distribution of multi-level symbols in the AHs for the 64QAM signal, which may have blurred the features. Figure 9(d) summarizes the joint performance of OSNR monitoring and MFI for all three modulation formats, i.e., QPSK, 16QAM and 64QAM signals. For MFI, it can be observed that 100% MFI accuracy can be achieved for all three modulation formats across the investigated OSNR ranges. For OSNR monitoring, the MAEs of QPSK, 16QAM and 64QAM signals are below 0.2 dB, 0.32 dB and 0.53 dB, respectively. The OSNR estimation error can potentially be reduced by employing relatively large training datasets. These results indicate the capability of joint OSNR and modulation formats monitoring of the proposed RC approach.
Fig. 9. True versus estimated OSNRs for (a) QPSK, (b) 16 QAM and (c) 64 QAM signal. (d) The MAE and MFI accuracy versus OSNR of QPSK, 16 QAM and 64 QAM signal.
4.4 Influence of noise on the optoelectronic RC performance
AWGN is considered to study the robustness performance of the optoelectronic RC. Then, the reservoir state in optoelectronic RC can be expressed as
Fig. 10. (a) The MAE and MFI accuracy versus OSNR of QPSK, 16QAM and 64 QAM signal considering the 25 dB SNR in the optoelectronic loop. (b) Total MAE and MFI accuracy versus SNR on the effects of the feedback loop in the optoelectronic RC.
Figure 10(b) shows the joint OSNR monitoring and MFI performance versus SNR on the effects of the feedback loop in the optoelectronic RC. The performance can be improved by increasing the SNR of the optoelectronic system. Without the feedback loop, the constructed OPM module is achieved by simple ridge regression. One can observe that the performance degrades dramatically with the decreased SNR. Therefore, the optoelectronic feedback loop with higher SNR is important in our proposed joint MFI and OSNR monitoring scheme. The performance of the proposed system is comparable to the existing joint MFI and OSNR monitoring technique based on FFNN [26]. There are more than 130 neurons and two hidden layers applied in the previous FFNN scheme, yet only 50 virtual nodes in our proposed optoelectronic RC method.
We have also summarized a detailed computational complexity comparison between different approaches in Table 2. The performance of the optoelectronic RC is comparable with that of photonic RC and random forest (RF), but it lags behind the methods based on CNN and FFNN [33]. The implementation complexity of FFNN and CNN schemes is higher than the RC- and RF-based approaches. For the FFNN and CNN, the connection weights of each layer are required to update in the training phase. Due to complex convolution operations, CNN has a heavier training time and implementation complexity. Owing to the random and fixed connections in RC, the calculation of the RC is a simplified recurrent neural network, so the training time of the RC is greatly reduced. Although the RF method has a lower implementation complexity and training time, the RF scheme needs to create two separate tasks for classification (MFI) and regression (OSNR monitoring) [4]. Although the processing speed may be limited by the “electronic bottleneck”, our proposed optoelectronic RC scheme has two distinct advantages compared to the photonic RC [34]. (i) The optoelectronic RC can be modelled with high accuracy: the optoelectronic RC is composed of mature devices and the MZM provides the sinusoidal function in the RC loop [21]. (ii) The optoelectronic RC can be integrated with field-programmable gate arrays (FPGAs) to train the readout weights online. Owing to the rapid development of electronics, we can process the signal with the accurate operation and high interrogation speed in the electrical domain. Therefore, our proposed scheme is potentially attractive and viable for future optical communication networks.
Table 2. Comparison of different approaches for MFI and OSNR monitoringa
5. Proof of concept experiment
We further experimentally study the system-level performance of joint OSNR monitoring and MFI. Figure 11 shows the experimental setup for dataset collection. Firstly, 215-1 pseudo-random bit sequence (PRBS) pattern is generated as the input bits. The PRBS pattern is mapped to the symbol to form 28 Gbaud 16-ary circular QAM (16C-QAM), 16QAM and 64QAM signals. Such a selection of modulation formats covers both constellation shape and constellation order to evaluate the performance of the proposed RC scheme. The Nyquist pulse shaping is used to generate bandwidth-limited signals and then resampling of the signal sequences is performed to match the sampling rate of the AWG. After that, the output electrical signals of AWG are amplified by electrical amplifiers and loaded on a an in-phase and quadrature modulator. An external cavity laser (ECL) with 100 kHz linewidth is used to generate a CW optical carrier. We use an EDFA to amplify the signal at the transmitter. After 33.6 km SMF transmission, the OSNR of the received signal is adjusted by the use of a variable optical attenuator (VOA) and an amplified spontaneous emission (ASE) noise source. After that, we place an OBPF to filter out the out-of-band noise. In the receiver, coherent detection is performed at the coherent frontend with an LO laser. The detected signals are then sampled by an 80 GSa/s DSO and then sent to the DSP module. As before, we collect the symbols which are used to generate the AHs.
Fig. 11. Experimental setup for dataset collection. PRBS, pseudorandom bit sequence; ECL, external cavity laser; EA, electrical amplifier; IQM, in-phase and quadrature modulator; VOA, variable optical attenuator; ASE, amplified spontaneous emission; OBPF, optical bandpass filter; DSO, digital sampling oscilloscope.
According to the dataset optimization we described in Sec. 4.1, the configuration of 3000 symbols and 40-bin AHs is selected. We also optimize the key parameters and consider a 25 dB SNR in our proposed optoelectronic RC. Figure 12 shows the OSNR monitoring and MFI results for 16C-QAM, 16QAM and 64QAM signals, respectively. For MFI, it can be observed that 100% accuracy can be achieved for 16C-QAM, 64QAM and 16QAM across the investigated OSNR range. For OSNR monitoring, the MAEs of 16C-QAM, 16QAM and 64QAM signals are below 0.5 dB, 0.9 dB and 1.45 dB, respectively. The selected AHs are shown in the inset of Fig. 12. Therefore, these experimental results also indicate our proposed RC approach can be adopted in future optical communication networks.
Fig. 12. The MAE and MFI accuracy versus OSNR of 16C-QAM, 16 QAM and 64 QAM signal in the experiment considering the 25 dB SNR in the optoelectronic loop. Inset is the selected AHs of 16C-QAM, 16 QAM and 64 QAM signal.
6. Conclusion
In this paper, we have proposed and demonstrated a simultaneous MFI and OSNR monitoring scheme based on optoelectronic RC. The AHs were collected in 28 Gbaud DP-QPSK, DP-16QAM and DP-64QAM coherent transmission systems. We have studied the influence of the bins and the number of received symbols for the overall performance of joint OSNR monitoring and MFI. The estimation MAEs of DP-QPSK, DP-16QAM and DP-64QAM signals are 0.2 dB, 0.32 dB and 0.53 dB, respectively. The accuracy of MFI for these three modulation format signals can reach 100%. In addition, AWGN was taken into consideration in an optoelectronic feedback loop to show the robustness of our proposed scheme. The results showed the performance of our proposed scheme was slightly degraded and could also verify the feasibility of our proposed scheme in practical applications. Besides, experimental validation was performed using the 28 Gbaud 16C-QAM, 16QAM and 64QAM configuration. 100% MFI accuracy and total MAEs of OSNR estimation below 1 dB were achieved simultaneously. Therefore, due to the OPM performance and its conceptual simplicity, it can be expected that optoelectronic RC may provide a promising solution for realizing the intelligent OPM in next-generation optical communication networks.
Funding
National Natural Science Foundation of China (U2006217, 61775015); China Scholarship Council (202107090113); the Swedish Research Council (VR) (2019-05197, 2022-04798); the Latvian Council of Science (lzp-2022/1-0497).
Disclosures
The authors declare no conflicts of interest related to this paper.
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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