Impact of Multi-Rate and Multi-Format Crosstalk Signals on the

Performance of 40 Gbit/s DQPSK Optical Receivers

João L. Rebola

1,2

, Luís G. C. Cancela

1,2

and João J. O. Pires

1,3

Instituto de Telecomunicações, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal

Department of Information Science and Technology, Instituto Universitário de Lisboa (ISCTE-IUL),

Av. das Forças Armadas, Edifício II, 1649-026 Lisboa, Portugal

Department of Electrical and Computer Engineering, Instituto Superior Técnico, Lisboa, Portugal

Keywords: Differential Quadrature Phase-Shift Keying, In-band Crosstalk, Monte Carlo Simulation, Optical Receivers.

Abstract: The coexistence of signals with different modulation formats and different bit rates in metropolitan optical

networks is, nowadays, a reality. In-band crosstalk can be very detrimental to the performance of those

networks. In this work, the impact of in-band crosstalk due to multi-format and multi-rate signals on the

performance of 40 Gbit/s DQPSK optical receivers is evaluated. It is shown that the worst interferer is the

10 Gbit/s OOK signal, which is the most common modulation format in today’s optical networks.

1 INTRODUCTION

Optical transport networks are, currently,

characterized by their ability to transport signals

with multiple modulation formats and a multitude of

bit rates and the actual trend is to further increase the

number of different formats and bit rates that coexist

in the network (Nag, 2010). The main reason for this

increase is the widespread use of coherent

technology and the flexibilisation of the 50 GHz

optical grid – the so called flexgrid (Sambo, 2012).

Nevertheless, this technology, that allows the use of

advanced modulation formats with greater spectral

efficiency and increased signal bit rate, is mostly

used in long-haul networks (Winzer, 2012). On the

other hand, optical metropolitan area networks

(MANs) are still based in intensity modulation direct

detection systems, because of their simplicity and

low power consumption characteristics. The typical

signals coexisting in these metro networks are the

10 Gbit/s OOK (On-Off Keying) and DPSK

(Differential Phase-Shift Keying) signals, and the

40 Gbit/s DPSK and DQPSK (Differential

Quadrature Phase-Shift Keying) signals.

The physical constraints of optical MANs are an

important issue in network planning and

performance evaluation. In particular, in-band

crosstalk is considered an important physical

limitation (Monroy, 2002). The impact of this

phenomenon has been intensively studied in direct

detection systems. In the majority of these studies, it

is assumed that the crosstalk signals have the same

bit rate and modulation format than the selected

signal. Examples of these studies for OOK, DPSK

and DQPSK signals are, respectively, given in

(Attard, 2005), (Pires, 2010) and (Cancela, 2012).

There are also a few studies which consider that the

selected signal has a different bit rate and

modulation format than the crosstalk signals

(Cancela, 2013), (Filer, 2010). In (Cancela, 2013),

an analytical formalism is used to evaluate the

impact of a single OOK interferer in a DPSK

system, and in (Filer, 2010) the impact of a single

OOK/DPSK/DQPSK interferer in a DPSK system is

evaluated in an experimental and simulation setup.

In this work, we extend these studies and

evaluate the impact of in-band crosstalk due to

10/40 Gbit/s OOK/DPSK/DQPSK multiple

interferers on the performance of 40 Gbit/s DQPSK

optical receivers. The crosstalk impact is evaluated

by Monte Carlo (MC) simulation, and an analytical

formalism based on the moment generating function

(Cancela, 2012) is used to validate the MC

simulation for the single interferer scenario. The

impact of the extinction ratio of OOK signals and

the impact of the crosstalk signal duty cycle on the

receiver performance are also assessed.

This paper is structured as follows. Section 2

describes the simulation model to assess the impact

of multi-format interferers in a DQPSK receiver.

L. Rebola J., G. C. Cancela L. and J. O. Pires J..

Impact of Multi-Rate and Multi-Format Crosstalk Signals on the Performance of 40 Gbit/s DQPSK Optical Receivers.

DOI: 10.5220/0004700900560062

In Proceedings of 2nd International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS-2014), pages 56-62

ISBN: 978-989-758-008-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

)(tE





)(tE





()



()



()







()



ASE

Figure 1: Block diagram of the DQPSK optical receiver.

Numerical results are discussed in Section 3 and

conclusions are presented in Section 4.

2 SYSTEM DESCRIPTION

In this section, the model used to characterise the

DQPSK optical receiver is described. The

implementation of the MC simulator used to assess

the performance of the optical receiver when

impaired by in-band crosstalk is also presented.

2.1 Optical DQPSK Receiver

The structure of a typical differential direct detection

DQPSK receiver is depicted in Figure 1 (Ho, 2005).

It consists of an optical pre-amplifier with a constant

power gain

over the amplifier bandwidth; an

optical filter with –3 dB bandwidth

;

B and a 3 dB

coupler to split the signal between the two branches

of the optical receiver. Each branch of the optical

receiver consists of a delay line interferometer with a

differential delay equal to the symbol period T

; a

balanced photodetector; and a post-detection

electrical filter with –3 dB bandwidth

In the

lower branch (Q), the arms of the interferometer have

a phase difference of 

/4, while in the upper branch

(I), the interferometers arms phase difference is

/4

(Ho, 2005). Throughout this work, the possible

imperfections of the optical DQPSK receiver are

neglected.

The electrical field at the optical filter output,

(),Et



can be expressed as (Cancela, 2012)



() () () ()

sciASEo

tGEtGEtEtht



  









 

(1)

where



stands for convolution and

()

is the

impulse response of the optical filter. The first term

of Eq. (1),

(),



corresponds to the electrical field of

the incoming DQPSK signal, named selected signal

and is described as





() exp () ,







sss

Et P j t e

where P

is the average signal power at the optical

pre-amplifier input;

()



is the signal phase that

carries the DQPSK symbol information, with

possible values





4,43,43,4





; and



the signal polarization unit vector.

The second term of Eq. (1),

(),







corresponds to the electrical field of the in-band

crosstalk, with M possible interferers. The complex

envelope of the i-th crosstalk signal field can be

represented as







,,,,

,,,

()

exp ( )

ci ci ci ci

ci ci ci c

Et PAt







 





 







(2)

where P

c,i

is the crosstalk power. The crosstalk level

of the i-th interferer is defined as the ratio between

the crosstalk power, P

c,i

, and the signal power, P

The total crosstalk level is the sum of the crosstalk

levels of the M interferers. In Eq.







,,,,

,,,

()

exp ( )

ci ci ci ci

ci ci ci c

Et PAt







 





 







(2)

,ci





is a random time shift within one symbol

period, which is modelled considering a uniform

distribution over that period (Winzer, 2005);

,ci





a random phase difference with respect to the

selected signal, which is modelled considering a

ImpactofMulti-RateandMulti-FormatCrosstalkSignalsonthePerformanceof40Gbit/sDQPSKOpticalReceivers

uniform distribution over the interval [0, 2[

(Winzer, 2005);



is the crosstalk signal polarisation

unit vector, which as a worst-case assumption is

assumed co-polarised with the selected signal,





;

()

and

()



are, respectively, the envelope

and the phase of the crosstalk signal, which define

the modulation format of the i-th interferer. The

modulation formats and bit rates of the crosstalk

signal considered in this work are 10 Gbit/s OOK, 10

Gbit/s DPSK, 40 Gbit/s OOK, 40 Gbit/s DPSK and

40 Gbit/s DQPSK. The extinction ratio of the OOK

crosstalk signals is defined as

rPP

, with

defining the average power of the bits ’1’ and

the

average power of the bits ‘0’. The duty-cycle of RZ

(Return-to-Zero) pulses, D, is defined as the fraction

of time that a rectangular pulse lasts within a symbol

period, before it returns to zero.

The third term of Eq. (1),

(),

ASE



corresponds to

the complex envelope of the electrical field of the

amplified spontaneous emission (ASE) noise

originated at the optical pre-amplifier. The ASE

noise is assumed as a zero mean white stationary

Gaussian noise with single-sided power spectral

density in each polarisation described by

/2,

NhvGF

where

is the photon energy at

the signal wavelength, and

is the pre-amplifier

noise figure.

The 3 dB couplers and delay interferometers are

modelled as in (Seimetz, 2009). For the I branch, the

electrical fields

()Et





and

()Et





are described by



() ( ) exp 4

()

() ( ) exp 4

()

jE t jE t T j

Et Et T j











 















(3)

Using the same model described in (Seimetz, 2009),

the electrical fields after the delay line interferometer

of the Q-branch of the optical receiver can be readily

calculated. The photodetectors are modelled as ideal

square-law detectors.

2.2 Monte Carlo Simulation

In the MC simulation, a sequence of bits of length

corresponding to the information carried by the

DQPSK selected signal is generated using deBruijn

sequences (Jeruchim, 2000). The differential

encoding and conversion to quaternary symbols with

Gray coding follows (Ho, 2005) and (Costa, 2010).

Then, the sequence of symbols is discretized in N

samples per symbol, which allows considering the

signal waveform within a symbol period [for

example, non-RZ (NRZ) or RZ pulses]. Hence, the

effect of intersymbol interference on the

performance of the DQPSK optical receiver can be

rigorously evaluated on the MC simulation.

In the simulator, the ASE noise is generated

using a random number generator, which follows a

Gaussian distribution with zero mean and variance

of N

B

sim

, where B

sim

is the bandwidth used in the

MC simulation. In each iteration of the simulation, a

sample function of the ASE noise is generated

(Jeruchim, 2000).

At that same iteration, a sample function of the

crosstalk signal is also constructed. Each i-th

crosstalk signal is generated considering a random

sequence of bits, which are, then modulated. The

same modulation format is considered for all i-th

crosstalk signals.

After the generation of selected signal, crosstalk

signal and ASE noise sample functions, the

electrical field given in Eq. (1) is obtained and is

propagated through the DQPSK optical receiver

depicted in Figure 1. The current at the output of the

I branch and Q branch is, then, determined and

sampled at the time instants corresponding to the

maximum eye-opening obtained without noise and

crosstalk. After sampling, each received bit in its

respective branch, which is corrupted by noise and

crosstalk, is compared to the corresponding

transmitted bit to find out if an error has occurred.

The bit error probability (BEP) is, then, calculated

from (Costa, 2010)

BEP BEP

BEP





(4)

where

BEP

and

BEP

are the bit error

probabilities, respectively, of the I and Q branches,

which are estimated through direct error counting

using

it b

BEP





(5)

it b

BEP





(6)

where N

is the number of iterations of the MC

simulation, which is equivalent to the number of

simulated sample functions and N

E,I

and N

E,Q

are the

number of counted errors, respectively, in the I and Q

branches of the receiver. A specific number of

counted errors is set as a stopping criterion of the MC

simulation.

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

3 NUMERICAL RESULTS

In this section, the impact of multi-format and multi-

rate crosstalk signals on the performance of 40 Gbit/s

DQPSK pre-amplified optical receivers is evaluated

using MC simulation. The duty-cycle variation of the

crosstalk signals, the extinction ratio variation of

OOK crosstalk signals and single and multiple

interference are considered in these studies.

Throughout this section, the amplifier noise

figure, F, is 5 dB, the pre-amplifier gain, G, is 30 dB,

and both ASE noise polarisations are considered. The

optical filter is a Gaussian filter with normalized

3 dB bandwidth given by

5

. The electrical

filter is a Gaussian filter with normalized 3 dB

bandwidth given by

0.7

. The optical signal-

to-noise ratio (OSNR) is measured in the reference

bandwidth of 0.1 nm at



1550 nm. The total

crosstalk level considered for the interferers is

13 dB, for all data rates and modulation formats.

This means that the power corresponding to the sum

of powers of each individual interferer is 13 dB

below the original DQPSK signal power. We also

assume that the power is equally distributed by the

interferers. The modulation formats of the crosstalk

signal considered are 10 Gbit/s OOK, 10 Gbit/s

DPSK, 40 Gbit/s OOK, 40 Gbit/s DPSK and

40 Gbit/s DQPSK. The bit rate of the selected

DQPSK signal is 40 Gbit/s. The number of simulated

bits is N

, N

128 samples per symbol and

sim

5.1 THz are used. The BEP is estimated using

MC simulation considering at least N

E,I

= 1000 or

E,Q

= 1000 counted errors.

3.1 Single and Multiple Interference in

Multi-rate and Multi-format

Scenarios

In this subsection, the impact of multi-rate and multi-

format crosstalk signals on the selected DQPSK

signal is evaluated. The pulse shape of all modulation

formats is NRZ and the extinction ratio of the OOK

interferers is ideal,

r

. The influence of the

random time shift

,ci





is neglected, since it has been

verified that its influence on the receiver performance

is minor, when considering NRZ pulse shapes.

Figure 2 shows the BEP as a function of the

OSNR, for a single interferer, M = 1, with different

modulation formats and bit rates on the crosstalk

signal. The BEP obtained without crosstalk is also

depicted in Figure 2 for comparison purposes. To

check the MC simulation results, the BEP is also

computed using the analytical formalism (A)

proposed in (Cancela, 2012), considering the absence

of crosstalk and a 40 Gbit/s DQPSK crosstalk signal.

This analytical formalism uses an eigenfunction

expansion technique to decompose signal, crosstalk,

and ASE noise, at the optical filter input, in a series

of orthogonal functions and relies on the moment

generating function to describe the decision variable

statistics. From Figure 2, a good agreement between

simulation and analytical results is observed.

Figure 2 shows that the 10 Gbit/s OOK crosstalk

signal leads to the most severe interference on the

40 Gbit/s DQPSK optical receiver. For very high

OSNR, the BEP is reaching a floor. The 40 Gbit/s

OOK interferer leads to the second worst BEP

degradation, especially for OSNRs above 17 dB,

where the signal-crosstalk beating power is becoming

significant. The 40 Gbit/s DQPSK and 10 Gbit/s

DPSK crosstalk signals provide similar

performances, while the less harmful interferer is the

40 Gbit/s DPSK. As a main conclusion, the

interference of amplitude modulated signals leads to

higher BEP degradation than phase-modulated

signals interference. This conclusion is in agreement

with the results presented in (Filer, 2010) for a single

interferer and considering a 40 Gbit/s DPSK signal as

the selected signal. This conclusion is similar to the

one found in the presence of cross-phase modulation

(XPM) (Sambo, 2012). Amplitude modulated signals

at 10 Gbit/s induce a higher XPM on coexisting

phase modulated signals at higher bit rates, and as a

result, lead to higher performance degradation.

Figure 2: BEP as a function of the OSNR for a single

interferer, M = 1 and different modulation formats and bit

rates on the crosstalk signal.

It is still an open issue if this scenario is kept for

M > 1. Figures 3 and 4 depict the BEP as a function

of the OSNR for, respectively, M = 4 and M = 8

interferers, considering different modulation formats

and bit rates on the crosstalk signals. It should be

pointed out that, we have considered that, all M

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

40 Gbit/s OOK

40 Gbit/s DPSK

10 Gbit/s OOK

10 Gbit/s DPSK

40 Gbit/s DQPSK

Without crosstalk (A)

40 Gbit/s DQPSK (A)

ImpactofMulti-RateandMulti-FormatCrosstalkSignalsonthePerformanceof40Gbit/sDQPSKOpticalReceivers

interferers have the same modulation format and bit

rate.

Figure 3 shows that, for M = 4, the BEP reaches

a floor for high OSNRs for all crosstalk signals,

except for the 40 Gbit/s DPSK interferer case. For

such high OSNRs, the beating between signal and

crosstalk is dominating the optical receiver

performance, and the power increase of the selected

signal gives no longer any performance

improvement. The higher BEP degradation occurs

also for the 10 Gbit/s interferer. However, in

comparison with M = 1, the 10 Gbit/s DPSK

interferer leads to a higher BEP degradation than

40 Gbit/s OOK and DQPSK signals, which exhibit a

similar performance.

Figure 3: BEP as a function of the OSNR for M = 4

interferers and different modulation formats and bit

rates on the crosstalk signal.

Figure 4: BEP as a function of the OSNR for M = 8

interferers and different modulation formats and bit

rates on the crosstalk signal.

Figure 4 shows the enhancement of the

behaviours observed in Figure 3, with the increase of

the interferers number. The 40 Gbit/s OOK and

40 Gbit/s DQPSK crosstalk signals lead practically

to the same receiver performance. The BEP with the

10 Gbit/s DPSK crosstalk signal is becoming similar

with the 10 Gbit/s OOK crosstalk signal. Notice that

between Figures 3 and 4, the increase on the number

of interferers had no particular influence on the BEP,

when considering the 10 Gbit/s OOK signal. This

means that the superposition of the symbol patterns

of the interferers is not contributing for further

degradations of the receiver performance. For the

40 Gbit/s DPSK crosstalk signal, the increase of the

number of interferers practically does not influence

the BEP.

As a main conclusion, we have seen that with the

increase on the number of interferers, the slower bit

rate signals, 10 Gbit/s, are the ones that lead to a

higher BEP degradation. As the bit rate is smaller,

when there is a combination of symbols on the

crosstalk signals that impairs significantly the

receiver performance, it affects at least four times

the same number of symbols on the selected

40 Gbit/s DQPSK signal.

3.2 Duty-cycle and Extinction Ratio

Variation

In this subsection, the influence of the duty-cycle of

the crosstalk signals on the receiver performance is

investigated. All results are obtained considering a

40 Gbit/s DQPSK NRZ signal and M = 4 interferers.

In these studies, the influence of a random time shift

,ci





inside the symbol period is taken into account

in the BEP estimation. Although the main qualitative

conclusions are not changed, the values of the BEP

may differ noticeably, when neglecting this random

time shift for interferers with RZ pulse shape.

Some final results discussing the influence of the

extinction ratio of OOK interferers on the receiver

performance are also presented.

Figures 5, 6 and 7 show the BEP as a function of

the OSNR for, respectively, 10 Gbit/s OOK,

10 Gbit/s DPSK and 40 Gbit/s DQPSK crosstalk

signals, for several duty-cycles. The extinction ratio

of the OOK interferers is assumed ideal,

r

Figures 5-7 show that the reduction of the duty-

cycle of the interferers reduces the crosstalk impact

on the receiver performance. For very low duty-

cycles (below 20%), the BEP estimated in the

presence of crosstalk becomes very close to the BEP

estimated in its absence. With the duty-cycle

reduction, the fraction of time of the pulse that is

interfering with one pulse of the selected signal is

becoming smaller, and the crosstalk impact on the

receiver performance is decreased, although the total

crosstalk power is the same.

Similar conclusions to those taken from Figures

5-7 have been drawn when considering 40 Gbit/s

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

40 Gbit/s OOK

40 Gbit/s DPSK

10 Gbit/s OOK

10 Gbit/s DPSK

40 Gbit/s DQPSK

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

40 Gbit/s OOK

40 Gbit/s DPSK

10 Gbit/s OOK

10 Gbit/s DPSK

40 Gbit/s DQPSK

PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology

Figure 5: BEP as a function of the OSNR for

10 Gbit/s OOK crosstalk signal with M = 4 and

different duty-cycles.

OOK and 40 Gbit/s DPSK crosstalk signals.

Figure 8 depicts the BEP as a function of the

OSNR for 10 Gbit/s OOK NRZ crosstalk signals,

with the extinction ratio as a parameter. Figure

shows that the 40 Gbit/s DQPSK optical receiver

performance is practically independent of the

extinction ratio of the interferer. The same

conclusion has been drawn for the 40 Gbit/s OOK

interferer and is in agreement with the results

presented in (Cancela, 2013) for DPSK optical

receivers.

Figure 6: BEP as a function of the OSNR for

10 Gbit/s DPSK crosstalk signal with M = 4 and

different duty-cycles.

4 CONCLUSIONS

In this work, the impact of in-band crosstalk due to

multi-rate and multi-format interferers on the

performance of 40 Gbit/s DQPSK optical receivers

has been assessed using MC simulation.

It has been shown that the 10 Gbit/s OOK

interferer, which is the traditional modulation format

of optical communication systems, is the one that

leads to the highest performance degradation of

Figure 7: BEP as a function of the OSNR for

40 Gbit/s DQPSK crosstalk signal with M = 4 and

different duty-cycles.

Figure 8: BEP as a function of the OSNR for

10 Gbit/s OOK NRZ crosstalk signal with M = 4 and

different extinction ratios.

the 40 Gbit/s DQPSK receiver. For a high number of

interferers, slower bit rates, i. e., 10 Gbit/s, on the

crosstalk signals are the most detrimental to the

receiver performance. The crosstalk induced by

40 Gbit/s DPSK signals is the less harmful and is

practically independent of the number of interferers.

It has been shown that the reduction of the duty-

cycle of the interferers decreases the crosstalk

impact on the receiver performance and that the

influence of the OOK interferer extinction ratio on

the DQPSK receiver performance is practically

negligible.

ACKNOWLEDGEMENTS

This work was supported by Instituto de

Telecomunicações of Portugal within the project

IXOS3D – PEst-OE/EEI/LA0008/2011.

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

D = 80%

D = 67%

D = 50%

D = 33%

D = 20%

D = 10%

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

NRZ

D = 80%

D = 50%

D = 33%

D = 20%

D = 10%

12 14 16 18 20 22 24 26 28 30 32

−4

−3

−2

−1

OSNR [dB]

Bit error probability

Without crosstalk

NRZ

D = 67%

D = 50%

D = 33%

D = 20%

D = 10%

12 14 16 18 20 22 24 26 28 30 32

−3

−2

−1

OSNR [dB]

Bit error probability

r = ∞

r = 30

r = 20

r = 10

ImpactofMulti-RateandMulti-FormatCrosstalkSignalsonthePerformanceof40Gbit/sDQPSKOpticalReceivers

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PHOTOPTICS2014-InternationalConferenceonPhotonics,OpticsandLaserTechnology