NEW APPLICATIONS OF ARTIFICIAL NEURAL NETWORKS IN MODELING & CONTROL

Comparison of optical performance monitoring techniquesusing artificial neural networks

Vıtor Ribeiro • Mario Lima • Antonio Teixeira

Received: 28 February 2013 / Accepted: 5 April 2013

� Springer-Verlag London 2013

Abstract In this paper, we make an overview of three

techniques that have used artificial neural networks

(ANNs) to model impairments in optical fiber. A compar-

ison between a linear partial least squares regression

algorithm and ANN is also shown. We demonstrate that

nonlinear modeling is required for multi-impairment

monitoring in optical fiber when using Parametric Asyn-

chronous Eye Diagram (PAED). Results demonstrating the

accuracy of PAED are also shown. A comparison between

PAED and Synchronous Eye Diagrams is also demon-

strated, for NRZ, RZ and QPSK modulated signals. We

show that PAED can provide comprehensible diagrams for

QPSK modulated signals, under a certain range of chro-

matic dispersion.

Keywords Optical performance monitoring � Artificial

neural networks � Partial least squares � Parametric

asynchronous eye diagram � Delay-Tap Asynchronous

Sampling � Asynchronous amplitude histograms

1 Introduction

Optical performance monitoring (OPM) is a widespread

research topic in optical communications. Its research

started in the early 1990s and the term itself has taken

several definitions [1]. OPM is devoted to the monitoring

of the signal quality in the physical layer, for the purpose of

providing information about the signal integrity in the

optical domain. OPM is not strictly related to quality-of-

service (QoS) measures. Its primary performance moni-

toring application is to certify service level agreements

between the networks operators and their clients [1].

Besides that, OPM may also be used in other applications

such as routing decisions and compensation of signal

degradation, by tuning, for instance, optical amplifiers or

dispersion compensators [1]. While the demand for supe-

rior data rates and bandwidth creates increasingly complex

networks, with much more variables varying through time

[2], the introduction of OPM in the physical layer allows a

‘‘smart’’ operation of the network, capable of managing the

network as parameters vary.

Several impairments exist although we will focus in

three main impairments. Despite their linearity, the inter-

actions between them, demand that a nonlinear modeling

algorithm is used, to distinguish between them, as we will

demonstrate in further sections.

• Chromatic dispersion (CD). Single-mode optical fibers

cause pulse broadening, due to the impact of fre-

quency-dependent group velocities. The shape of the

pulse becomes wider creating intersymbol interfer-

ence. It is measured in picoseconds (ps) for nanometer

(ps/nm) and increases linearly with the length of the

fiber, although environment conditions such as tem-

perature may also cause residual CD increment/

decrement [3].

• Polarization mode dispersion (PMD). PMD is a linear

electromagnetic propagation effect occurring in single-

mode optical fiber due to the random change of

birefringence along the fiber which results in random

coupling between the two modes of polarization. These

two modes of propagation travel at different group

velocities, resulting in a mean differential group delay

(DGD) between the two principal states of polarization

V. Ribeiro (&) � M. Lima � A. Teixeira

Instituto de Telecomunicacoes, Campus Universitario

de Santiago, 3810-193 Aveiro, Portugal

e-mail: vitor.ribeiro@ua.pt

123

Neural Comput & Applic

DOI 10.1007/s00521-013-1405-z

(PSPs). DGD causes pulse broadening and intersymbol

interference reducing the quality of transmission (QoT).

The mean DGD is given in ps and is proportional to the

square root of the length of the fiber [4].

• Optical signal to noise ratio (OSNR). The amplification

of an optical signal in wavelength division multiplexing

(WDM) optical communications system is provided by

an erbium-doped fiber amplifier (EDFA). Amplification

takes place by stimulated emission from an upper

energy level to the ground level of Er3? ions. In the

upper energy level, the Er3? ions can also emit

radiation by the process of spontaneous emission .

The resultant optical radiation is called amplified

spontaneous emission (ASE) noise [5]. ASE noise in

conjunction with attenuation (0.2 dB/km) of the optical

fiber is a serious impairment to the transmission of the

optical signal. OSNR gives a measure of the impact of

this impairment and is given in dB.

We present parametric asynchronous eye diagram

(PAED) [6, 7] with ANNs to monitor several impairments,

such as CD, PMD and OSNR. We demonstrate that a

nonlinear modeling algorithm is required, to accurately

model the linear optical impairments, by using a linear

regression algorithm as a term of comparison. We present

the diagram obtained from PAED technique, to monitor a

signal modulated at 10 Gbit/s NRZ and a QPSK modulated

signal. The results are compared between two pattern

recognition techniques using ANNs, one using 6 subsets of

the diagram and other using 4 subsets (quadrants) of the

diagram.

2 Optical performance monitoring using artificial

neural networks

Artificial neural networks (ANNs) have been applied to OPM

since 2008 [10], from the best of our knowledge. ANN has

the ability to distinguish between different parameters, with

the aid of optical performance diagrams or histograms, which

turns them suitable for multi-impairment OPM.

In Fig. 1, we can see a simplified optical communica-

tions link setup. In the link terminal, three optical moni-

toring techniques are described: PAED, asynchronous

amplitude histograms (AAH) and Delay-Tap Asynchro-

nous Sampling (DTAS). PAED uses a differentiator in

parallel with a connection cable, properly adjusted to

compensate the propagation delay (not represented in the

figure), of the differentiator. Two analog-to-digital con-

verters are used to capture the samples of the differentiated

signal and the signal itself. Ones are plotted against the

others as schematically shown in Fig. 2. AAH samples the

signal asynchronously. The sampler has a clock that it is

not related to the clock of the signal. The signal is repre-

sented in a diagram, from which amplitude histograms are

taken (on the right Fig. 2b). DTAS use a delay in parallel

with a connection cable. The way to represent the infor-

mation is similar to PAED, although instead to plot the

signal against a differentiated signal, it plots against a

delayed copy of the signal (delay line in Fig. 1). The three

techniques have their technical advantages and disadvan-

tages. AAH is the simplest to implement, although DTAS

allows a more comprehensive diagram, from which one can

Fig. 1 Simulation setups of two well-known techniques and para-

metric asynchronous eye diagram (on the top). In the middleasynchronous amplitude histograms (AAH) and below Delay-Tap

Asynchronous Sampling (DTAS). PAED plots the derivative of the

signal against the signal itself. AAH samples the signal asynchro-

nously and plot a diagram with a Gaussian random distribution in the

zero and one level. DTAS uses a delayed copy of the signal to plot it

against the non-delayed copy of the signal. See Fig. 2

Neural Comput & Applic

123

extract visually information about the impairments [11].

Furthermore, the amplitude histograms extracted from

DTAS technique have the potential to be more accurate

than AAH [11]. However, one has to take into account the

delay-bit period relationship used to clearly extract the

information about the impairments. One can see [11] where

several diagrams with different delays are sketched. PAED

simplifies this issue because it provides diagrams that stress

the features of synchronous eye diagram, which ease the

understanding of the diagram, independently of the OOK

modulation format involved and bit rate. Although the

differentiator discriminates noise a little, which results as if

‘additional jitter’ was added to the diagram as we will see

later on, in further sections. However, optical filtering can

improve this ‘additional jitter’.

In Fig. 2, the typical post-processing of the information

for the three techniques is shown. In the case of PAED, the

diagram is split in 6 or 4 subsets of the diagram and the

mean and variances of both the X and Y axis for each subset

are calculated. This information is used as features that are

subsequently inserted as inputs in the ANN [6].

One example of training neural networks with AAH is

shown in [8]. Radial basis functions are used as the non-

linear element of the neural network. The number of counts

and the amplitude levels are used as part of a large input

training dataset, and interesting results are achieved.

Delay-Tap Asynchronous Sampling (DTAS) has been

used often with ANN [9, 12, 13]. The scheme of training in

[9, 13] is similar to the one presented in Fig. 2c. The delay-

tap diagram is split in 4 subsets, but only three are used,

because the fourth is symmetric to Q2. For each quadrant,

the mean and standard deviations are computed and an

additional parameter is calculated, which is similar to the

Q-factor. This is the simplest approach of the three, in

terms of ANN processing, but the requirement for balanced

detection in [13], complicates the setup and increase cost a

bit.

3 Why use neural networks?

Neural networks allow nonlinear modeling, although is

useful to inspect the requirement for a nonlinear approach,

which from the best of our knowledge has not been done

yet, in the literature. We have used linear partial least

squares (PLS) regression as a term of comparison. The

setup used to capture the results is similar to Fig. 1, and the

transmitter sends a NRZ modulated signal at 10 Gbit/s.

(a)

(b)

(c)

(d)

Fig. 2 Signal processing using

three techniques. a Parametric

Asynchronous Eye Diagram

(PAED). b Asynchonous

amplitude histograms (AAH).

c Delay-Tap Asynchronous

Sampling (DTAS). d Figures a,

b and c are post-processed by an

ANN. For a see [6], b see [8],

c see [9]

Neural Comput & Applic

123

In Figs. 3 and 4, we demonstrate the results using PLS and

ANN, respectively, for modeling CD, PMD and OSNR,

splitting PAED in 4 and 6 subsets for pattern recognition,

methodologically similar to Fig. 2a. The mean and stan-

dard deviations for each subset, and for each axis of the

diagram, were calculated and inserted as inputs in the two

models. The inputs are scaled, and the principal compo-

nents are made orthogonal using principal component

analysis. The ANN model uses 40 neurons in the hidden

layer, which yields a relatively large network. Although the

accuracy, through the range of CD, PMD and OSNR,

justify this approach. In [6], we have compared the accu-

racy between 10 and 40 neurons, in the hidden layer and is

clear, that higher accuracy is achieved in the 40 neurons

approach.

Comparing the results of Figs. 3 and 4, we may achieve

to the conclusion that the approach using PLS is less

accurate than the approach using ANN. We stress out that

PLS is almost insensitive to the number of subsets used to

split the diagram, while ANN clearly shows better results

when splitting PAED in 6 subsets. This may indicate that

since PLS cannot learn well the relationships between the

input and the output, it does not matter how much

information is added to the model. So, we may conclude

that a nonlinear approach, such as ANN, is necessary for

multi-impairment modeling in fiber, when using PAED.

4 Simulation results and discussion

The results shown in Fig. 4 are demonstrated for an NRZ

modulated signal at 10 Gbit/s, using a setup equal to Fig. 1.

The results demonstrate that the CD accuracy is lower in

the limits of the monitoring window, i.e, in 0 and 3,200 ps/

nm. The sensitivity of CD in this region is lower. The root

mean square error (RMSE) of PMD is almost steady during

its range, although some peaks appear, which may have

statistical nature. The RMSE of OSNR increases while

increasing the value of OSNR. This is common to DTAS

[9]. Accuracy measures can be calculated, to compare both

techniques, like using cross-correlation between the

derivative and the signal itself, in PAED, or the delayed

copy of the signal and the signal itself, in DTAS. In prin-

ciple, low cross-correlation, between the two signals, may

indicate that better accuracy is achieved, since correlation

between input variables leads to redundancy [14] and

0 500 1000 1500 2000 2500 3000 350050

100

150

200

250

300

350

400

450

500

CD (ps/nm)

RM

SE

CD

(ps/

nm)

4 Quadrants6 Quadrants

(a)

0 10 20 30 40 500

5

10

15

20

25

PMD (ps)

RM

SE

PM

D (

ps)

4 quadrants6 quadrants

(b)

10 15 20 25 302

3

4

5

6

7

8

9

OSNR (dB)

RM

SE

OS

NR

(dB

)

4 Quadrants6 Quadrants

(c)

Fig. 3 Linear PLS regression results using a 10 Gbit/s NRZ signal. PAED is split in 4 and 6 subsets of the diagram. For each subset, the mean

and the variance for the X and Y axis are calculated. Results for a CD, b PMD, c OSNR

(a)

0 10 20 30 40 500

1

2

3

4

5

6

7

PM

D R

MS

E (

ps/n

m)

PMD (ps)

4 quadrants6 quadrants

(b)

10 15 20 25 300.5

1

1.5

2

2.5

3

3.5

OSNR (dB)

OS

NR

RM

SE

(dB

)

4 quadrants6 quadrants

(c)

Fig. 4 ANN results using a 10 Gbit/s NRZ signal. PAED is split in 4 and 6 subsets of the diagram. For each subset, the mean and the variance

for the X and Y axis are calculated. Results for a CD, b PMD, c OSNR

Neural Comput & Applic

123

worsened performance [15] when using neural networks.

The cross-correlation between the two signals may depend

on the pulse shape, which can lead to different conclusions,

when comparing PAED and DTAS.

In Fig. 5, we show some plots using PAED and compare

it with synchronous eye diagrams in Fig. 5a, b and an

oscilloscope visualizer, in Fig. 5c. The diagrams were

taken using a simulation setup equal to Fig. 1, using dif-

ferent modulation formats in the transmitter. In Fig. 5a, d, a

synchronous eye diagram has been compared with PAED,

using a 10 Gbit/s NRZ signal. The signal is impaired with

CD equal to 500 ps/nm, PMD equal to 0 ps and OSNR of

18 dB. A, B, C and D regions are marked in both diagrams.

We can see that we can get similar information from the

diagrams, in the marked regions. The diagram is a little

impaired with the ‘additional jitter’ that we have previously

mentioned in Sect. 2 caused by the fact that the differen-

tiator discriminates noise a little.

In Fig. 5b, e, the signal shown in both diagrams is

impaired with CD equal to 400 ps/nm, 0 ps of PMD, 27 dB

of OSNR. The ‘jitter’ is improved by using an additional

optical filter before the photodetector in the simulation

setup of Fig. 1. This is an RZ modulated signal with 50 %

duty cyle at 10 Gbit/s. Region E shows one distinguishable

feature of PAED. It brings the information to the center of

the diagram.

In Fig. 5c, f, a 40 Gbit/s QPSK modulated signal is

shown, in a time domain oscilloscope visualizer and

PAED, respectively. The signal shown in the diagrams is

impaired with CD equal to 60 ps/nm, PMD equal to 0 ps

and OSNR equal to 30 dB. An optical filter before the

photodetector was also used. We can see that PAED is able

to distinguish the amplitude distortion caused by the phase

shifting of 90� and 180�. This is only possible for CD

below approximately 80 ps/nm in a 40 Gbit/s QPSK signal

and above a few ps/nm. This is a remarkable feature of

PAED, using only single-ended detection. Wu et al. [13]

presented results that demonstrate that DTAS cannot give

comprehensible diagrams when using single-ended detec-

tion (just a photodetector in the receiver as is shown in

(a) (b) (c)

(d) (e) (f)

Fig. 5 Comparison between SED and PAED. a, d 10 Gbit/s NRZ

modulated signal, b, e 10 Gbit/s RZ modulated signal c, f 40 Gbit/s

QPSK modulated signal. a, d CD = 500 ps/nm PMD = 0 ps,

OSNR = 18 dB, b, e CD = 400 ps/nm, PMD = 0 ps, OSNR =

27 dB, c, f CD = 60 ps/nm, PMD = 0 ps, OSNR = 30 dB

Neural Comput & Applic

123

Fig. 1) and a half bit delay tap. This in fact may be the

reason why poor results are reported by Wu et al. [13] with

single-ended detection when using DTAS. The impact of

PMD includes more distortion. When PMD is too high, it is

not possible to see clearly the impact of phase shifting any

more.

In Fig. 6, we demonstrate reasonable accuracy, using

PAED, with single-ended detection. For CD, the errors are

again higher in the limits of the monitoring window while

tend to decrease as we increase the value of CD, becoming

higher in the upper limit of CD monitoring range. For PMD,

the errors remain steady during the whole monitoring win-

dow. In OSNR, the maximum RMSE is about 2 dB in the

upper border of the monitoring window. These results were

achieved using a similar methodology as the results obtained

in Fig. 4. In this case, we have used 6 subsets of the diagram,

to obtain the results. The variances and the means were

calculated, for the differentiated signal and the signal itself,

for each subset and inserted as inputs in the neural network.

The setup is equal to the setup of Fig. 1.

5 Conclusions

Several conclusions have been drawn. Linear PLS regres-

sion has been compared with ANN. We stress that PLS

regression is insensitive to the number of subsets used. This

seems to indicate that since linear PLS regression is not

able to learn the relationships between the input and the

output, it does not matter how much information is added

to the model. We achieved to the conclusion that when

using PAED, a nonlinear model such as ANN is required to

model the impairments.

Results for NRZ 10 Gbit/s modulated signal have been

demonstrated with positive results. Synchronous eye dia-

grams have been compared with PAED, and we achieve to

the conclusion that it is easy to find in PAED the infor-

mation provided by synchronous eye diagrams.

A 40 Gbit/s QPSK signal is also demonstrated with

PAED. We achieved to the conclusion that comprehensible

diagrams can be drawn with PAED, using also a phase

modulated signal such as QPSK. This is in fact a remarkable

feature of PAED that makes it distinguishable from other

techniques overviewed in this paper (AAH and DTAS).

Acknowledgments The grant SFRH/BD/69577/2010 from the

Portuguese Foundation for Science and Technology is acknowledged.

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