1. Introduction

The next-generation fiber-optic communication networks are envisioned to be more elastic and cognitive, which could adjust signal bandwidth, data rate, modulation format, transmission wavelength, signal power etc. adaptively based on time-varying channel conditions, network resources and capacity demand from customers with the objective of maximizing the network resource efficiencies (e.g. bandwidth, energy, and wavelength) and assuring the quality of service [1,2]. Consequently, the knowledge of these kinds of adaptive parameters, the quality of transmission links and the health of optical signals should be available in such optical networks. OSNR is one of the most important parameters that should be monitored due to its direct relation with bit-error ratio (BER) and signal quality after linear impairments equalization in digital coherent receivers [2]. Over the last few years, numerous of OSNR monitoring techniques for digital coherent detection systems have been proposed. These include amplitude histograms [2], interferometer [3], optical filtering and optical power measurement [4], RF spectrum [5,6], statistical moments [7,8], error vector magnitude [9], Stokes parameters [10], Golay sequences [11], amplitude noise correlation [12] and cyclostationarity [13] based techniques.

Besides OSNR monitoring, it is also essential for receivers in the elastic and cognitive optical networks to identify or classify the modulation formats of the received signals autonomously. As mentioned before, modulation formats is one of the key adaptive parameters in feature elastic and cognitive optical networks, which means that the modulation format at the receiver side is likely various at different moments. Meanwhile, the carrier phase recovery, frequency offset compensation, polarization demultiplexing etc. DSP module used in the receiver must be suitable for the received modulation format. Therefore, the real-time information about modulation formats of received signals (obtained through MFI) can enable the receivers to adopt algorithms most appropriate for these formats types to achieve the optimum performance [2,14–16]. All these suggest that MFI is indispensable for digital coherent receivers used in future elastic and cognitive optical networks. Recently, several MFI techniques for digital coherent receivers have been demonstrated in literatures, including peak-to-average-power ratio (PAPR) evaluation [14], Stokes-space representation [15–21], data-aided [22,23], nonlinear power transformation [24], k-means algorithm [25], and machine learning based techniques [26–30].

The above-mentioned techniques for OSNR monitoring and MFI focus on either OSNR monitoring or MFI. However, joint estimation of both parameters might be required for modulation format independent signal quality characterization and automatic fault detection in the end receivers or optical performance monitoring devices installed at the intermediate network nodes in future elastic and cognitive optical networks [2]. Recently, F. N. Khan et al. firstly demonstrated a joint MFI and OSNR monitoring technique for digital coherent receivers by employing DNNs to extract features of signals’ amplitude histograms, and great MFI and OSNR monitoring accuracies were achieved with moderate computational complexity and low cost [2]. In this paper, we propose a new joint MFI and OSNR monitoring technique based on the Stokes-space representation. In the proposed scheme, first a single DNN is utilized to perform MFI by extracting modulation format dependent futures of the first-order derivation of the density distribution fitting curves in $s_1$ and $s_2$axes. Subsequently, a customized DNN is selected based on the MFI information for OSNR monitoring of identified signal type. Experimental results for 28Gbaud/s PDM-QPSK, PDM-8QAM, PDM-16QAM, and 21.5Gbaud/s PDM-32QAM signals demonstrate OSNR monitoring over back-to-back transmission with mean SEs of 0.21dB, 0.48dB, 0.35dB and 0.44dB, respectively. 100% MFI accuracies for all these four modulation formats are achieved both over back-to-back transmission at the OSNR values lower or equal to their respective 7% FEC thresholds and after long-haul transmission within practical launching optical power ranges. All the results show that the performance of the proposed technique is superior or comparable to the noes reported either OSNR monitoring [5–13] or MFI techniques [15–30], from the perspective of monitoring range, accuracy and kinds of modulation formats. Similar to [2], this technique requires neither additional hardware nor any modification of transmitters, and also does not sacrifice the system’s spectral efficiency as it is completely non-data-aided. Additionally, since this technique is based on the Stokes-space representation, it is inherently insensitive to carrier phase noise, frequency offset and polarization mixing.

2. Operation principle

The DSP configuration for digital coherent receiver including the proposed MFI and OSNR monitoring block is depicted in Fig. 1(a). First, standard modulation format independent chromatic dispersion (CD) compensation, timing recovery and constant modulus (CMA) equalization algorithms are utilized to compensating the linear transmission impairments. Then, the proposed MFI and OSNR monitoring technique is employed after CMA equalization as shown in Fig. 1(a) (right part). It is worth noting that this CMA is format modulation independent which is used for compensating the linear transmission impairments (such as PMD, residual CD).The details of proposed technique are as follow:

 

Fig. 1 (a) DSP configuration in the receiver with the proposed MFI and OSNR monitoring; (b) The first-order derivation of the density distributions fitting curves ($s_1^{\text{'}}$ and$s_2^{\text{'}}$) for (i) various formats and (ii) PDM-QPSK with different OSNRs.

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First, the samples after CMA equalization is converted to the Stokes space, by [16]

Where X = I_x + jQ_x and Y = I_y + jQ_y represent the two orthogonal polarizations, while Re{·} and Im{·}stand for the real and the imaginary parts of a complex number, respectively. Then, the samples are projected onto $s_1$ and $s_2$axes with 80 bins for obtaining the corresponding density distributions, respectively. The features of the density distributions in $s_1$ and $s_2$axes are sensitive to the modulation format and OSNR. Actually, in order to improve the probability of format correct identification and OSNR estimation accuracy, we utilize the first-order derivation of the density distributions fitting curves ($s_1^{\text{'}}$ and$s_2^{\text{'}}$) for MFI and OSNR monitoring. Figure 1(b)-(i) shows the first-order derivation curves of $s_1$ and $s_2$for four different modulation formats (PDM-QPSK, PDM-8QAM, PDM-16QAM and PDM-32QAM), and Fig. 1(b)-(ii) shows the results for PDM-QPSK signals with various OSNRs (11.3dB, 13.3dB, 15.3dB, and 17.3dB). It is obvious from Fig. 1(b) that the curves of $s_1^{\text{'}}$ and$s_2^{\text{'}}$exhibit unique and distinctive characteristics for various modulation formats and OSNRs with given modulation format. Finally, the modulation format and OSNR sensitive features of $s_1^{\text{'}}$ and$s_2^{\text{'}}$ are extracted by DNNs for MFI and OSNR estimation. Here, we perform both MFI and OSNR monitoring after CMA equalization from the aspect of reducing the complexity of hardware structure and decreasing the computational complexity at the intermediate network nodes or end receivers for practical applications [2].

Figure 2 shows the procedure of the proposed MFI and OSNR monitoring by utilizing the DNNs. A single DNN (referred as DNN-MFI) is employed firstly for MFI. After MFI, the format information is subsequently utilized to select the OSNR monitoring DNN (referred as DNN-OSNR) which is customized for OSNR monitoring of the identified modulation format. Some key network parameters of DNN-MFI and DNN-OSNR are given in Fig. 2 as well. In order to train the DNNs, numerous data sets are generated and processed using the procedure described above-mentioned for obtaining the curves of $s_1^{\text{'}}$ and$s_2^{\text{'}}$ corresponding to four modulation formats and various OSNRs. Each set of $s_1^{\text{'}}$ and$s_2^{\text{'}}$ is represented by 160 × 1 input vector$s^{\text{'}}$. The first 80 elements of $s^{\text{'}}$are$s_1^{\text{'}}$, while the rest elements are $s_2^{\text{'}}$ (Seen in Fig. 2). Similarly, corresponding to each set of $s^{\text{'}}$, a 4 × 1 binary vector label y and a scalar label x are obtained as well. Vector y includes only one non-zero element whose location indicates the modulation format type, e.g. [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0] and [0, 0, 0, 1] corresponding to PDM-QPSK, PDM-8QAM, PDM-16QAM, and PDM-32QAM, respectively. While, scalar x indicates the actual OSNR value corresponding to that set of $s^{\text{'}}$. Then, the DNN-MFI is trained by utilizing input vectors$s^{\text{'}}$and label vectors y, and the DNN-OSNRs are trained by utilizing input vectors$s^{\text{'}}$ and label scalars x pertaining to respective signal types.

 

Fig. 2 The DNNs structures for MFI and OSNR monitoring with some key network parameters.

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As shown in Fig. 2, two hidden layers DNN with activation function of sigmoid is used for MFI (DNN-MFI) in this work. The output layer’s activation function and cost function are chosen to be softmax and cross-entropy, respectively, as they are well adapted for multiclass classification. The DNN-OSNRs structure and key network parameters for all the four modulation formats are selected the same in this work. They include one input layer, one output layer, and three hidden layers. The first and second hidden layers’ activation function are both sigmoid while the third hidden layer’s activation function is linear. The output layer activation function and cost function of the DNN-OSNRs are chosen to be linear and logcosh, respectively, which are suitable for regression and estimation. Once the DNNs are well trained, their performances are evaluated by using the testing data sets. During the testing procedure, input vectors $s^{\text{'}}$of the testing data set are first imported to the trained DNN-MFI and corresponding output vectors y are obtained. Subsequently, the modulation format types are identified by taking argmax (y). After MFI, based on the identified modulation format information, the input vector $s^{\text{'}}$are imported to their respective DNN-OSNR and the estimated OSNR value is obtained from the output scalar x.

3. Experiment setup and results

The experimental setup for demonstrating the proposed MFI and OSNR monitoring technique is shown in Fig. 3. An optical carrier signal provided by an external cavity laser (ECL) is modulated by an integrated polarization-multiplexed (PM) IQ (PM-IQ) modulator for generating 28Gbaud/s PDM-QPSK, PDM-8QAM, PDM-16QAM and 21.5Gbaud/s PDM-32QAM signals. The center wavelength of ECL is 1549.3nm and its linewidth is about 100kHz. The electronic signals driving four different ports of the PM-IQ modulator are generated by two arbitrary waveform generators (AWG1 and AWG2). The word length of four pseudo-random bit sequence (PRBS) signals are all 2¹⁵-1. Before driving the PM-IQ modulator, the PRBS signals are pre-processed by utilizing off-line DSP program, including mQAM modulation format coding, pulse shape filtering with roll-off factor of 1.0 square root raised cosine filter, pre-distorting for compensation the frequency roll-off in AWGs. Two scenarios, back-to-back and fiber transmission, are demonstrated the proposed MFI and OSNR monitoring technique. In back-to-back case, an OSNR setting block consisting of an amplified spontaneous emission (ASE) noise source and variable optical attenuator (VOA) is utilized to alter OSNR value of the input optical signal. Following the OSNR setting block, the actual OSNR value is monitored by an optical spectrum analyzer (OSA). While in fiber transmission case, the transmission link is composed of multi-spans SMF whose dispersion parameter D, attenuation coefficient α, and nonlinear coefficient γ are 16.9ps/nm/km, 0.2dB/km, and 1.27km⁻¹∙W⁻¹, respectively. Fiber loss of each span is compensated using an EDFA with noise figure of ~5dB. At the receiver side, an optical band-pass filter (OBPF) with 0.8nm bandwidth is firstly utilized in front of the receiver to reject the out-of-band ASE noise. Subsequently, the received signals are detected by an integrated coherent receiver, and then sampled by a real-time digital oscilloscope with 80GSamples/s sampling rate and 33GHz electrical bandwidth. Finally, the samples are processed offline using a DSP core including the proposed MFI and OSNR monitoring technique.

 

Fig. 3 Experimental setup for the proposed MFI and OSNR monitoring. ECL: external cavity laser, AWG: arbitrary waveform generator, PBS: polarization beam splitter, PBC: polarization beam coupler, ASE: Amplified spontaneous emission noise source EDFA: Erbium-doped fiber amplifier, VOA: variable optical attenuator, OSA: optical spectrum analyzer, SMF: single mode fiber, OBPF: optical bandpass filter, LO: local oscillator, B-t-B: back-to-back.

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The performance of the proposed MFI and OSNR monitoring technique is firstly evaluated in the back-to-back transmission system. A VOA (shown in Fig. 3) is utilized to alter OSNRs of PDM-QPSK, PDM-8QAM, PDM-16QAM, and PDM-32QAM signals in the ranges 9.3~16.8dB, 12.5~22.5dB, 17~27dB, and 18~30dB, respectively, in steps of 0.5dB. We generated 100 data sets for each modulation format at a given OSNR value, e.g. 16 × 100 sets of data generated for PDM-QPSK in the OSNR ranges of 9.3~16.8dB. To ensure that the collected data sets are as random as possible, the polarization state of the signals at the transmitter are continuously scrambled by a polarization scrambler and the storage time interval of the 100 data sets are random chosen as well in the real-time digital oscilloscope. Each data set encompasses 8000 symbols whose sample rate is resampled down to one sample per symbol after timing recovery and modulation format independent CMA equalization. In the proposed MFI and OSNR monitoring technique procedure, every 100 data sets are projected onto $s_1$ and $s_2$axes with 80 bins for obtaining the corresponding density distributions and first-order derivation of the density distributions fitting curves ($s_1^{\text{'}}$ and $s_2^{\text{'}}$, respectively) firstly (Seen in Fig. 1). Subsequently, every 100 data sets of $s_1^{\text{'}}$ and $s_2^{\text{'}}$ are divided into 80 training data sets and 20 testing data sets by randomly selected. Then, the DNNs input vector as well as labels for every 100 data sets of $s_1^{\text{'}}$ and $s_2^{\text{'}}$ are obtained in these training and testing data sets, which are finally employed for training or testing for the DNNs mentioned-before. Figure 4 shows the MFI identification accuracy versus OSNRs for PDM-QPSK, PDM-8QAM, PDM-16QAM and PDM-32QAM signals over back-to-back transmission. As shown in Fig. 4, 100% identification accuracies of all these four modulation formats are achieved at the OSNR values lower or equal to their corresponding 7% FEC thresholds. Additionally, 100% identification accuracies of PDM-QPSK and PDM-8QAM can be obtained even at the OSNR values lower to their respective 20% FEC thresholds.

 

Fig. 4 MFI identification accuracies versus OSNRs for PDM-QPSK, PDM-8QAM, PDM-16QAM and PDM-32QAM. The dot lines (same color with the corresponding data curves) represent OSNR thresholds corresponding to FEC correcting BER of 3.8 × 10⁻³ of the corresponding modulation formats.

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After MFI, a customized DNN-OSNR is selected based on the identified modulation format for OSNR monitoring. The estimated OSNR resutls and coressponding estimated SEs for five modulation formats over back-to-back transimission are shown in Fig. 5. Here, the SE is defined as:

 

Fig. 5 Actual OSNRs versus estimated OSNRs (left) and estimated SEs (right) for (a) PDM-QPSK, (b) PDM-8QAM, (c) PDM-16QAM and (d) PDM-32QAM.

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To further verify the feasibility of proposed method, we carry out a series of long-haul transmission experiments under different launching optical powers. The launching optical powers of 28Gbaud/s PDM-QPSK over 2000km SMF, 28Gbaud/s PDM-8QAM over 2000km SMF, 28Gbaud/s PDM-16QAM over 1040km SMF, and 21.5Gbaud/s PDM-32QAM over 400km SMF are varied in the ranges of −4~6dBm, −3~6dBm, −3~7dBm, and −2~7dBm, respectively. Figure 6 shows the MFI identification accuracies versus launching optical powers results. As shown in this figure, nearly 100% correct identification can be realized for all these four modulation format signals within practical optical power ranges launched to the fiber, which indicates that the proposed technique is resilient towards fiber impairments. As a 0.8nm bandwidth OBPF is integrated in the fiber loss compensating EDFA (Seen in Fig. 3), the actual OSNR is hard to accurately measure by the OSA after fiber transmission. Thus, OSNR monitoring is not carried out in fiber transmission case.

 

Fig. 6 MFI identification accuracies versus launching optical power for PDM-QPSK over 2000km SMF transmission, PDM-8QAM over 2000km SMF transmission, PDM-16QAM over 1040km SMF transmission and PDM-32QAM over 400km SMF transmission, respectively.

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4. Discussion and conclusion

In this paper, we experimentally demonstrated a MFI and OSNR monitoring technique for digital coherent receivers by utilizing the specific features of received signals’ density distributions in Stokes axes in combination with DNNs. The effectiveness of the proposed technique has been successfully confirmed in 28GBaud PDM-QPSK, PDM-8PSK, PDM-8QAM, PDM-16QAM, and 21.5GBaud PDM-32QAM systems over both back-to-back and long-distance transmission link. Experimental results show that mean estimation SEs of about 0.21dB, 0.48dB, 0.35dB and 0.44dB for OSNR monitoring are achieved for these four modulation format, respectively. Meanwhile, 100% MFI accuracies for all these four modulation formats are achieved both over back-to-back transmission at the OSNR values lower or equal to their respective 7% FEC thresholds and after long-haul transmission within practical launching optical power ranges. As this technique is based on the Stokes-space representation, it is inherently insensitive to carrier phase noise, frequency offset and polarization mixing. Therefore, it might have potential application in future elastic and cognitive optical networks.