2.1.2. Linear optical sampling for amplitude histograms

In the literature, optical sampling proved necessary for a variety of experiments. Optical signals are sampled by means of optical or even opto-electrical gates. This technique covers LOS systems that enable the measurement of amplitude histograms and eye diagrams.

Some publications in this field date back to the mid-1990s, when the first optically sampled eye diagrams of 10 Gbps optical data signals were published [2, 3]. The LOS technique allows us the processing of signals at high speeds, like in our case when using WDM-Nyquist system. Received signals are asynchronously oversampled to generate amplitude histograms. These histograms define the own signature or traces of the five used modulation formats. Figure 3 shows an example of cleaned histogram on back-to-back (a) and an impaired one after a fiber transmission (b,c). Correspondent eye diagram is also showed in the figure (2nd column).

It is clear from the histograms that the location of each peak correspond to a particular intensity level of the formats constellations. By definition, amplitude histograms are the empirical distribution of the received signal power. Therefore, they are sensitive to changes in optical signal-to-noise ratio (OSNR), CD and polarization mode dispersion (PMD) of the transmission

Figure 3. Generated amplitude histograms on back-to-back (b), after fiber transmission (c), and in the presence of DGD (c) [4].

link. As given in Figure 3(c), histogram characteristics changes significantly regarding the optical link impairments and distances.

### 2.2. Simulation design

The architecture of ANN for recognition problems requires some guidelines. More neurons need more computation and they have a tendency to overfit the data when the number is set

In the literature, optical sampling proved necessary for a variety of experiments. Optical signals are sampled by means of optical or even opto-electrical gates. This technique covers

Some publications in this field date back to the mid-1990s, when the first optically sampled eye diagrams of 10 Gbps optical data signals were published [2, 3]. The LOS technique allows us the processing of signals at high speeds, like in our case when using WDM-Nyquist system. Received signals are asynchronously oversampled to generate amplitude histograms. These histograms define the own signature or traces of the five used modulation formats. Figure 3 shows an example of cleaned histogram on back-to-back (a) and an impaired one after a fiber transmission (b,c). Correspondent eye diagram is also showed in

It is clear from the histograms that the location of each peak correspond to a particular intensity level of the formats constellations. By definition, amplitude histograms are the empirical distribution of the received signal power. Therefore, they are sensitive to changes in optical signal-to-noise ratio (OSNR), CD and polarization mode dispersion (PMD) of the transmission

Figure 3. Generated amplitude histograms on back-to-back (b), after fiber transmission (c), and in the presence of DGD

LOS systems that enable the measurement of amplitude histograms and eye diagrams.

too high, which justifies the choice of MLP3 architecture.

2.1.2. Linear optical sampling for amplitude histograms

14 Advanced Applications for Artificial Neural Networks

the figure (2nd column).

(c) [4].

In Figure 4, the simulation design of the proposed method for automatic MFR is shown. Five different transmitters generates NRZ-OOK at 10 Gbps, NRZ-DQPSK at 40 Gbps, NRZ-DP-QPSK at 100 Gbps, DP-16QAM at 160 Gbps and WDM-Nyquist NRZ-DP-QPSK at 1 Tbps. The pseudorandom binary sequence (PRBS) is of length 214 – 1. Then, using a variable optical attenuator (VOA), generated output signals are decreased, which affects the gain of the optical amplifier (OA). The latter is used to emulate the effect of optical signal-to-noise ratio (OSNR) by tuning the noise figure and add a variable amount of ASE noise into the signals. As a result, the OSNR values are adjusted in the range between 10 and 30 dB with steps of 2 dB and are then transmitted over a single mode fiber (SMF). By using the CD/PMD (polarization mode dispersion) emulator, the accumulated CD of the link varied in the range of 0–510 ps/nm (steps of 17 ps/nm) to reach 30 km fiber transmission, while the DGD is introduced in the range of 0– 14 ps with steps of 2 ps. An optical filter optical band pass filter (OBPF) is used to select the carrier whose modulation format need to be recognized.

Using an optical switch (SW) in the detection stage, the NRZ-OOK signal is directly detected with single photodetector, while coherent receivers detect other formats. Using polarization beam splitter (PBS), the detected signal is split into two orthogonal polarization states. Each output is coupled with the signal derived from the local oscillator (LO). A single-polarization is detected in the case of NRZ-DQPSK signal. In the MFR block, signals are asynchronously oversampled with a rate of 16 samples/bit to have 262,144 amplitude samples. The amplitude histograms of the five used modulation formats are shown in Figure 5 (2nd and 3rd columns). Besides, when considering the OSNR equal to 16 dB, DGD at 10 ps for 10 km fiber length (3rd column), these histograms stay again different from each other. Typical eye diagrams are also showed in the 1st column of the figure. Later, these histograms are used in the ANN module for formats classification, as described in the previous section. The number of neurons in hidden layer is optimized to be 30 neurons using the incremental-constructive approach [1].

With n input and m output neurons, the training set is given as {(X1; t1), …, (Xp; tp)}, where P = 27,280 is the size of the entire data corresponding to different OSNR (11 values), CD (31 values), DGD (8 values) and modulation types at two polarization states, n = 100 is the number of histograms bins. More precisely, we want to minimize the error function of the network, the MSE, defined as ||<sup>y</sup> <sup>t</sup>||<sup>2</sup> . When training multilayer networks, the overall data set is randomly divided, with 60% used for training, 15% for validation and 25% for testing. On the other side, the results of the simulations indicate that the Levenberg-Marquardt (LM) training algorithm provides high correct recognition ratios [5].

Figure 4. Outline of simulation setup.

Figure 5. Link impairments variation effect to amplitude histograms and eye diagrams, for the five used modulation formats: (a) 10 Gbps NRZ-OOK, (b) 40 Gbps NRZ-DQPSK, (c) 100 Gbps NRZ-DP-QPSK, (d) 160 Gbps DP-16QAM and (e) 1 Tbps WDM-Nyquist NRZ-DP-QPSK with OSNR = 16 dB (2nd column) and OSNR = 16 dB, DGD = 10 ps, CD = 170 ps/ nm (3rd column).

Using our previous settings, we reach the minimum of MSE on 3.67 <sup>10</sup><sup>7</sup> for 27 epochs leading to abort the training process, as illustrated in Figure 6. This amelioration reduces the required time for ANN training process, which depends on ANN size, type of learning algorithm, size of the training data set and the desired degree of accuracy.

#### 2.3. Modulation formats recognition

The previously described system of MFR has validated with test cases comprising five modulation formats. Training data sets are arranged into 16,368 input vectors x<sup>i</sup> (60%), and then numerous simulations using different combinations of OSNR, CD and DGD are performed.

Modulation Format Recognition Using Artificial Neural Networks for the Next Generation Optical Networks http://dx.doi.org/10.5772/intechopen.70954 17

Figure 6. Effect of epoch's number on MSE variation for training (black), validation (grey) and testing (silver) data sets.

The results of the testing data sets (6820 input vectors xi) are depicted in Figure 7 and five elements of ANN output vectors y<sup>i</sup> are shown. Each output represents a particular modulation type among 10 Gbps NRZ-OOK, 40 Gbps NRZ-DQPSK, 100 Gbps NRZ-DP-QPSK, 160 Gbps DP-16QAM and 1 Tbps WDM-Nyquist NRZ-DP-QPSK.

Indeed, one output y<sup>i</sup> reaches a maximum value than the others, as clearly shown in the figure, which represents the modulation format. For that, there is no ambiguity in the classification process because of this large separation. The five-used modulation formats are well recognized with good accuracies, as given in the all cases represented in Figure 7.

After ANN training, the recognition accuracy is validated with different set of testing data. Table 1 shows the obtained results, and it is apparent that 100% accuracy is obtained for 10 Gbps NRZ-OOK, 40 Gbps NRZ-DQPSK and 160 Gbps DP-16QAM with small differences in recognition probabilities (i.e., 99.99% and 99.98%) for the other formats.

Using our previous settings, we reach the minimum of MSE on 3.67 <sup>10</sup><sup>7</sup> for 27 epochs leading to abort the training process, as illustrated in Figure 6. This amelioration reduces the required time for ANN training process, which depends on ANN size, type of learning

Figure 5. Link impairments variation effect to amplitude histograms and eye diagrams, for the five used modulation formats: (a) 10 Gbps NRZ-OOK, (b) 40 Gbps NRZ-DQPSK, (c) 100 Gbps NRZ-DP-QPSK, (d) 160 Gbps DP-16QAM and (e) 1 Tbps WDM-Nyquist NRZ-DP-QPSK with OSNR = 16 dB (2nd column) and OSNR = 16 dB, DGD = 10 ps, CD = 170 ps/

The previously described system of MFR has validated with test cases comprising five modulation formats. Training data sets are arranged into 16,368 input vectors x<sup>i</sup> (60%), and then numerous simulations using different combinations of OSNR, CD and DGD are performed.

algorithm, size of the training data set and the desired degree of accuracy.

2.3. Modulation formats recognition

16 Advanced Applications for Artificial Neural Networks

nm (3rd column).

An unannounced precision ambiguity between 100 Gbps NRZ-DP-QPRK and 1 Tbps WDM-Nyquist NRZ-DP-QPSK modulation formats has observed. This is due to the use of the same coding scheme, which is the QPSK. As previously stated at the outset, our simulations are performed under various impairments of ASE noise, CD and PMD but the recognition accuracy remains high up to 99.99%. This result is an improvement compared to other works presented in the literature (99.6%, 99.95%) [6, 7].

Figure 7. The ANN outputs y<sup>i</sup> for 5 used modulation formats in response to the 6200 test cases representing input vectors xi.


Table 1. Recognition accuracies of the five used modulation formats using the proposed automatic MFR technique.
