Abstract—This paper describes the use of a low cost eye

diagram reconstruction method, based on digital signal

processing techniques, for optical communication network

performance monitoring by means of bit error rate (BER)

estimation through Gaussian fitting Q-Factor calculation.

A morphological analysis of the reconstructed eye diagram is

also proposed, which allows for the qualitative investigation of

impairments such as amplitude and phase noise as well as

signal distortion due to linear and non-linear effects.

A complete Eye Diagram Analyzer equipment prototype

transparent to signal bit rate was developed and constructed to

validate the proposal.

Index Terms—Eye Diagram, Digital Signal Processing,

Optical Communications, Network Performance Monitoring.

I. INTRODUCTION

PTICAL performance monitoring has been an issue of

great interest, stimulated by the ever growing capacity

demands that led to the use of dense wavelength division

multiplexing (DWDM) with large channel counts and by

new network architectures such as the ones using optical

packet and/or burst switching for metropolitan applications

[1]. The evolution of these optical networks towards higher

transparency brings requirements on low cost solutions for

distributed optical performance monitoring. In order to

detect fiber transmission degradations or equipment failure

and to maintain the quality of service, it is necessary to

monitor real time signal bit error rate (BER) and distortion

(morphological analysis) in the networks.

Recently, a solution for transparent BER estimation has

been proposed [2, 3], based on the analysis of a signal

amplitude histogram built using commercial high speed

digital sampling oscilloscopes.

In this paper we describe the use of a digital signal

processing technique [4, 5] to reconstruct an eye diagram of

Manuscript received April 15, 2006. This work was supported by

FUNTTEL and FINEP.

Eduardo Mobilon and Miriam R. X. de Barros are with CPqD

Telecom & IT Solutions, Rod. Campinas Mogi Mirim, km 118.5,

13.086-902, Campinas, SP, Brazil (e-mail: mobilon@cpqd.com.br,

mbarros@cpqd.com.br).

Amauri Lopes is with School of Electrical and Computer Engineering

in the State University of Campinas - UNICAMP, Campinas, SP, Brazil

(e-mail: amauri@decom.fee.unicamp.br).

a high speed optical communication signal using a low cost

asynchronous (no clock recovery) undersampling strategy.

A complete low cost Eye Diagram Analyzer (EDA)

equipment based on this method was developed and a

working prototype is now available. Its accurate BER

estimation as well as morphological analysis potential was

verified for different optical signal to noise ratio (OSNR)

values. This EDA will be used for network performance

monitoring in an experimental high speed network testbed,

the Brazilian GIGA Project [6].

Section II briefly describes the eye diagram reconstruction

technique. Hardware development is presented in section III.

The experimental validation of the algorithms and the EDA

equipment prototype is shown in section IV. Conclusions are

presented in Section V.

II. EYE DIAGRAM RECONSTRUCTION TECHNIQUE

In order to estimate the bit error rate and to analyze signal

distortion, an eye diagram must be obtained from the high

speed optical communication signal. In our low cost

approach, it is recovered (reconstructed) by the use of a

special digital signal processing technique applied to a

dataset obtained from asynchronous undersampling.

Samples of the high speed optical communication signal

are acquired using a very low sampling frequency, which is

totally uncorrelated with the signal bit rate. The resulting

dataset, plotted in Fig. 1, does not seem to provide any

useful information but indeed it contains spectral frequency

information that can be used to synchronize and correct the

phase of each point, what leads to the reconstruction of a

complete eye diagram period, as shown in Fig. 2.

Asynchronous undersampling is a very low cost solution,

when compared to a commercially available high speed

digital sampling oscilloscope, and also allows for

transparency to the signal bit rate, since clock recovery is no

longer needed. In this way, it is possible to monitor the

performance of an optical network with no previous

knowledge of either the protocol or the line bit rate.

The frequency component used for phase correction is

obtained by the calculation of a periodogram, which is

essentially a method of power spectrum estimation applied

to the asynchronous dataset.

Low Cost Eye Diagram Reconstruction and

Morphological Analysis for Optical Network

Performance Monitoring Using

Digital Signal Processing Techniques

Eduardo Mobilon, Miriam R. X. de Barros, and Amauri Lopes

O

85-89748-04-9/06/$25.00 © 2006 IEEE ITS2006643

Fig. 1. Asynchronous undersampled dataset of a high speed

optical communication signal.

Fig. 2. Corresponding reconstructed eye diagram of an asynchronous

undersampled dataset of a high speed optical communication signal.

Before performing the periodogram calculation, the

original sampled dataset needs to be modified in such a way

that a strong Fourier component manifests itself in the

spectrum, which will then be chosen as the synchronization

frequency for the eye diagram reconstruction algorithm.

Basically, DC component extraction and the application of a

non-linear function were the modifications used for this

purpose.

The periodogram, which is essentially an average of the

squared modulus of the discrete Fourier transform (DFT),

is then calculated using the following expressions

12

1

1( ) ( )

M

k

k

P YM

ω ω

−

=

= ∑ and (1)

1

0

( ) [ ]L

j m

k

m

Y y kL m eω

ω

−

−

=

= + ⋅∑ , (2)

where y[n] represents the modified sampled sequence.

Since just frequency information is necessary,

normalization factors were not applied in the power

spectrum estimation provided by the periodogram,

calculated for each of the M blocks of L samples of a

sequence.

The periodogram of y[n] is shown in Fig. 3. After the

modification of the original sampled dataset, frequency

components can be clearly seen and the strongest one is

selected to be used for synchronization and eye diagram

reconstruction.

Fig. 3. Periodogram of the modified sequence y[n] with clearly visible

spectral frequency components.

To reconstruct the eye diagram, a correction of the

position of each sample in the sequence x[n] must be

performed. This can be done by means of a synchronization

process with respect to the frequency information obtained

by the periodogram calculation.

The idea [4] is based on the fact that for any period T and

any time instant t,

2

arg( )

2

j tTt e

T

π

π

= . (3)

Phase shifts accumulate with time but considering that

they are locally small, one period of the eye diagram can be

reconstructed from the following sequence, calculated using

a sufficiently small window of 2K+1:

( ) [ ]bjkK

k K

Yn y n k e

ω

ω

−

=−

= + ⋅∑ , (4)

where ωb represents the aliased bit frequency found by the

periodogram method.

Now, from (3) and (4) the samples of x[n] can have their

time positions corrected according to the following pairs:

{ [ ], [ ]}t n x n with arg( [ ])

[ ]2

Ynt n

ω

π

= . (5)

In our implementation, an efficient quicksort algorithm

was used to organize the t[n] sequence in an ascending

order. Each sample position exchange in t[n] had a

counterpart in x[n], leading to the reconstruction of one

period of the eye diagram.

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III. HARDWARE DEVELOPMENT AND PROTOTYPE

The EDA equipment, based on the described eye diagram

reconstruction technique, was developed to be used for

optical network performance monitoring. Dedicated

algorithms for morphological analysis and BER estimation

generate parameters for the network performance

qualification. Fig. 4 shows a block diagram of the EDA.

Fig. 4. Block diagram of the Eye Diagram Analyzer.

The first block performs an opto-electronic conversion

with high bandwidth and is the optical signal input of the

equipment. It features an avalanche photo diode (APD) and

a 10 GHz variable gain amplifier (VGA) to provide a

constant output voltage within the dynamic range of the

receiver.

The second block is the sampling module, responsible for

acquiring samples of the high speed digital signal with a low

and asynchronous sampling frequency. This is the most

critical block of the EDA. Regular analog-to-digital

converters (ADCs) have a “sampling window” much larger

than the high speed transitions (rise and fall time) of the

input signal. A microwave sampler was used in our design to

capture samples of RF high speed signals, outputting a

FWHM impulse-like waveform that must be digitized

exactly 7.2 ns after the strobe (sample) pulse by a fast ADC

with an aperture of 500 ps or less, to ensure low sampling

amplitude error. In our design a time base circuit was

developed using an adjustable delay line IC that generates a

strobe pulse for the microwave sampler and a capture pulse

for the ADC.

To digitize the microwave sampler output signal a 12-bit

105 MSPS ADC based on a multibit pipeline with switched

capacitor architecture was used. The ADC is assembled in

the Acquisition Board, which also features a FIFO memory

that can store more than 200.000 samples.

The third main block of the EDA, the DSP Board, is the

one that reconstructs the eye diagram, analyzes its

morphology and estimates the BER, running special

algorithms in a high performance digital signal processor,

a Texas Instruments TMS320F2812 device.

Finally, the last block connects the equipment to the

network management system by means of a regular Ethernet

interface. It comprises an 8051 microcontroller together with

a hardwired TCP/IP stack protocol processor to provide an

Ethernet IP connection to the EDA.

Fig. 5 shows a picture of the main blocks of the EDA,

as well as the microwave sampler module already soldered

on the Strobe and Acquisition Boards.

The DSP Board is mounted over the Acquisition Board.

It generates the sampling frequency, which can be set

between 1 and 10 MHz to strobe the microwave sampler and

clock the ADC, and processes samples stored in memory for

eye diagram reconstruction, BER estimation and

morphological analysis.

Fig. 5. Picture of the main EDA modules.

IV. EXPERIMENTAL VALIDATION OF THE ALGORITHMS AND

THE EYE DIAGRAM ANALYZER PROTOTYPE

In order to validate the algorithms and to verify the

performance of the EDA prototype an experimental setup

was arranged as shown in Fig. 6.

An SDH analyzer generating a 2.488 Gbit/s optical PRBS

signal was used as a BER meter. A first optical amplifier

compensates for insertion losses of the passive components,

while a second one was used to generate amplified

spontaneous emission (ASE) noise. By controlling the

OSNR it was possible to generate both clean and noisy eye

diagrams.

Optical attenuators 1 and 2 were used to ensure constant

optical powers at the input of the BER meter and the EDA.

The sampling frequency was empirically determined to be

around 2 MHz, although even lower values such as around

20 kHz could be used [7].

Fig. 6. Experimental setup used to validate the algorithms and the

Eye Diagram Analyzer prototype.

The collected dataset was preliminarily processed by a

personal computer. Later, all the Matlab algorithms were

rewritten in ANSI-C language and were also verified

running on the digital signal processor of the DSP Board.

DSPNetwork

Management

Interface

Network

Management

InterfaceSamplingSampling

BERMeter

1 30%

-15 dBm

OSA

2 70%

10%

90%

A1A1A1

A2A2A2

50%

50%

-5 dBm

Eye Diagram

Analyzer

EDA

645

A. Quantitative Analysis (BER)

Bit error rate is estimated from Gaussian fitting Q-factor

calculation over the recovered (reconstructed) eye diagram.

Fig. 7 shows the values of the estimated BER for the

reconstructed eye diagrams and directly measured BER as a

function of the OSNR. A corresponding curve of a

synchronous sampled eye diagram dataset, obtained with a

high speed digital sampling oscilloscope, was also included

for comparison.

Fig. 7. Estimated and measured BER for different eye diagrams,

as a function of the OSNR.

The results show a good agreement for BER estimation

using the reconstructed eye diagrams, when compared to the

synchronous ones. The uppermost curve shift, corresponding

to the measured BER, can be explained by the fact that a

fixed decision threshold based on the signal mean amplitude

value is used by the BER meter, while Q-Factor calculation

based on Gaussian fitting performed by the EDA algorithms

(and also by the high speed digital sampling oscilloscope)

ensures more realistic BER measures.

Additionally, the further use of the Expected

Maximization algorithm to fit a mixture of Gaussians could

improve BER estimation, as recently reported [4, 5].

A measurement strategy could be implemented in the

EDA management system in order to provide a means of

detecting, for instance, polarization mode dispersion (PMD)

impairments, by means of the comparison of consecutive

BER values in a defined time interval.

B. Qualitative Analysis (Morphology)

An ongoing work now attempts to perform a

morphological analysis of the recovered eye diagram, with

the objective of inferring possible causes for network

performance degradation. A first approach is based on the

treatment of the eye diagram as an image which is then

compared with stored patterns corresponding to distorted

eye diagrams with known origins.

In this way, the EDA equipment will be able to detect,

for instance, distortions generated by some linear or

non-linear effects, ASE noise accumulated due to several

optical amplifications, time jitter and other waveform

(morphology) related impairments. This is possible because

the recovered eye diagram maintains the pulse shape of the

sampled signal.

Fig. 8 shows eye diagrams obtained synchronously (with a

high speed digital sampling oscilloscope) on the left side and

reconstructed by the EDA, on the right side, corresponding

to BER values of 10-5

and 10-12

. It can be observed that

the reconstructed eye diagrams maintain the same

morphological aspects as the synchronous ones.

Fig.8. Synchronous (left) and corresponding reconstructed (right) eye

diagrams with BER values of 10-5 (top) and 10-12 (bottom).

V. CONCLUSION

In this paper we presented the development of an Eye

Diagram Analyzer equipment based on an eye diagram

reconstruction technique and also discussed its application

as an optical communication network performance

monitoring device, qualifying the network through BER

estimation and morphological analysis. We verified its

performance comparing the estimated BER of the

reconstructed eye diagrams with the measured BER for

different OSNR values.

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PD2.2.

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“Experimental Verification of an Eye Diagram Reconstruction

Technique Based on Asynchronous Undersampling”, Proc. of the

International Microwave and Optoelectronics Conference - IMOC,

2005.

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BE

R)

OSNR (dB)

Measured BER

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