1. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
108
SIGNAL QUALITY OF DISPERSION MANAGED QUASI-LINEAR
HIGH BIT RATE OPTICAL TRANSMISSION SYSTEM
Mir Zayed Shames1
, Md. Surat-E-Mostafa2
, Imtiaz Ahmed3
1
(Electrical and Electronic Engineering, Ahsanullah University of Science and Technology,
141-142 Love Road, Tejgaon Industrial Area Dhaka-1208, Bangladesh,)
2
(Electrical and Electronic Engineering, Ahsanullah University of Science and Technology,
141-142 Love Road, Tejgaon Industrial Area Dhaka-1208, Bangladesh,)
3
(Electrical and Electronic Engineering, Ahsanullah University of Science and Technology,
141-142 Love Road, Tejgaon Industrial Area Dhaka-1208, Bangladesh,)
ABSTRACT
This paper investigates the performance of a quasi-linear optical fiber periodic
transmission system by numerical simulation based on Split Step Fourier (SSF)
transformation method. Comparisons of Quality Factor over the Transmission Length,
Transmission Power, Bit Rate and Residual Dispersion between two models (DCF-SMF and
SMF-DCF) are obtained. The simulation results demonstrate that by rearranging the
dispersion management system significant performance improvement can be achieved.
Keywords: Bit Rate, DCF-SMF, High Bit Rate, Quality Factor, Quasi-Linear, Residual
Dispersion, SMF-DCF, Transmission length, Transmission power
1. INTRODUCTION
Optical fiber communication systems are evolving from 40 Gb/s to 160 Gb/s per
channel. At 40 Gb/s, since the signals have wider bandwidth and higher signal power, the
dispersion compensation must be carefully optimized to control the interaction between the
dispersion and nonlinearity. In our work, we have considered the optical transmission of 1000
km to observe the changes in Q for different parameters. We focus here on the effect on Q
with the changes in different parameters of the fiber. These observations can be applied to
improve the signal quality when transmitting through next generation ultra-high capacity
INTERNATIONAL JOURNAL OF ELECTRONICS AND
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ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 3, May – June, 2013, pp. 108-114
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2. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
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communication network that corresponds to the bit rate ranges from 40 Gb/s to 160 Gb/s.
These investigations will in turn help to improve the dispersion compensation and other
factors of the fiber that results in signal weakness. As a result, high signaling rate and robust
signal could be desired through the fiber and at the output.
This research work is intended to address the effects on the signal quality factor Q
with the change in fiber length, bit rate, power and residual dispersion in a high capacity
dispersion managed (DM) quasi-linear system. Before that, we would like to mention some
previous works which have been reported in the literature regarding the quasi-linear system
and high bit rate system. Analytical description of the propagation of quasi-linear optical
pulses in SDM systems is presented by M. J. Ablowitz [1]. Similar study has been done by A.
Biswas [2]. A. Mecozzi [3] has analyzed the intrachannel nonlinear effects in highly
dispersed optical pulse transmission. For high capacity systems, J. Berthold [4] has studied
the evolution of optical networking. Higher bit rates for quasi-linear optical data
transmission systems via constrained coding have studied by V. Pechenkin [5]. M. Oukil [6]
has studied the optimization of high bit rate optical fiber transmission. For Q factor, S. Ohteru
[7] has studied optical signal quality monitoring scheme that is independent of the signal
format.
2. THEORY
2.1 General NLS Equation
The Nonlinear Schrödinger (NLS) equation with damping and periodic amplification,
in the dimensionless form is:
iq୸ ൅
ୈሺ୸ሻ
ଶ
q୲ ୲ ൅ |q|ଶ
q ൌ െiΓq ൅ iሾeΓ୸౗ െ 1ሿ ∑ δሺz െ nzୟሻq୒
୬ୀଵ (1)
Here, Γ is the normalized loss coefficient, za is the normalized characteristic amplifier
spacing, and z and t represent the normalized propagation distance and the normalized time,
respectively, expressed in the usual non dimensional units.
Also, D (z) is used to model strong dispersion management. The fiber dispersion D (z)
is decomposed into two components namely a path-averaged constant value δa and a term
representing the large rapid variation due to large local values of the dispersion [2].
2.2 DMNLS Equation
In this section, dispersion managed nonlinear Schrödinger (DMNLS) equation is
considered. We begin the analysis with the perturbed NLS equation in the presence of
dispersion variation, loss, and lumped amplification [2]. Optical pulse propagating in a fiber
with periodic dispersion management and amplification can be expressed by dimensionless
nonlinear Schrödinger (NLS) equation as:
i
δ୙
δ୞
െ
ୠሺ୸ሻ
ଶ
δమ
୙
δ୘మ ൅ sሺZሻ|U|ଶ
U ൌ iGሺZሻU (2)
Where, U (Z, T), T and Z are the normalized complex envelope of electric field,
retarded time, and transmission distance, respectively. B (Z) represents fiber dispersion, s (Z)

3. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
110
represents the effective fiber nonlinearity and G (Z) represents gain by optical amplifier for G
> 0 or fiber loss for G < 0 in normalized units, respectively [8].
3. MODELS
• Dispersion Compensating Fiber – Single Model Fiber (DCF-SMF)
• Single Mode Fiber - Dispersion Compensating Fiber (SMF-DCF)
3.1 Dispersion Compensating Fiber - Single Mode Fiber (DCF-SMF)
Figure 1 shows the pictorial representation of Dispersion Compensating Fiber - Single
Mode Fiber (DCF-SMF). It is evident from the pictorial representation that DCF-SMF is
formed by combining together a dispersion compensating fiber and a single mode fiber. N
represents the number of configurations of this model in the transmission network. Each span
of this model consists of DCF, SMF and an amplifier. In our case, the value of N is 40 which
mean that the span is repeated 40 times throughout the transmission network.
Figure 1: Pictorial representation of DCF-SMF Model
3.2 Single Mode Fiber - Dispersion Compensating Fiber (SMF-DCF)
Figure 2 shows the pictorial representation of Single Mode Fiber – Dispersion
Compensating Fiber (SMF-DCF). It is evident from the pictorial representation that SMF-
DCF is formed by combining together a single mode fiber and a dispersion compensating
fiber with an amplifier. Each span of this model consists of SMF, DCF and amplifier. This
span is periodically repeated for N times. Here also, the value of N is 40 which mean that the
span is repeated 40 times throughout the transmission network.

4. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
111
Figure 2: Pictorial representation of SMF-DCF Model
4. RESULTS AND DISCUSSION
Simulation results are presented by using the g++ compiler and GNU plot. Following
the analytical approach presented in section 2, Comparison of Quality Factor against the
Length and Transmission Power between DCF-SMF and SMF-DCF are evaluated. The
standard value of Quality Factor, Q is 6. So, it is desired to keep the value of Q over 6.
Plot of Quality Factor vs. Transmission Length (For DCF-SMF and SMF-DCF
models) is shown in fig. 3. From the fig, it is evident that for DCF-SMF model the signal can
travel up to 1300 km keeping the quality factor above the standard line, whereas for SMF-
DCF model the signal can travel up to 1425 km which is 125 more than DCF-SMF model.
Figure 3: Comparison of Quality Factor over Transmission Length between DCF-SMF and
SMF-DCF models

5. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
112
Figure 4: Comparison of Quality Factor over Transmission Power between DCF-SMF and
SMF-DCF models
Plot of Quality Factor vs. Transmission Power (For DCF-SMF and SMF-DCF
models) is shown in fig. 4. From the fig, it is evident that SMF-DCF model transmit signals
with low power more efficiently than DCF-SMF model which is a requirement of good quasi-
linear system.
Plot of Quality Factor vs. Bit Rate (For DCF-SMF and SMF-DCF models) is shown
in fig. 5. From the fig, it is evident that DCF-SMF model can transmit data up to 60 Gb/s
efficiently where as SMF-DCF model can transmit data at a higher bit rate which is up to 80
Gb/s. So we can transmit data much faster.
Figure 5: Comparison of Quality Factor over Bit Rate between DCF-SMF and SMF-DCF
models

6. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
113
Figure 6: Comparison of Quality Factor over Residual Dispersion between DCF-SMF and
SMF-DCF models
Plot of Quality Factor vs. Residual Dispersion (For DCF-SMF and SMF-DCF
models) is shown in fig. 6. From the fig, it is evident that, at 0 RD the signal quality of DCF-
SMF model stays just above 6 whereas for SMF-DCF model the signal quality remains near 8
which is more efficient than DCF-SMF model.
The Assumption parameters for both models for different simulations are as shown in
Table 1.
Table 1: Assumption Parameters
Parameters
Value while
simulating
Transmission
Length
Value
while
simulating
Power
Value while
simulating Bit
Rate
Value while
simulating
Residual
Dispersion
Unit
Span Length (L) 50 50 50 50 km
Length of SMF (L1) 42.5 42.5 42.5 42.5 km
Length of DCF (L2) 7.5 7.5 7.5 - km
Dispersion of L1 17 17 17 17 ps/nm/km
Dispersion of L2 -96.33 -96.33 -96.33 -96.33 ps/nm/km
Bit Rate 40 40 20 to 160 40 Gb/s
Duty Cycle (N) 40 40 40 40 -
Wavelength ( ) 1.55 1.55 1.55 1.55 µm
Peak power (Po) 2 1 to 10 2 2 mW
Residual dispersion
(RD)
0 0 0 +15 to -15 -

7. International Journal of Electronics and Communication Engineering & Technology (IJECET),
ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME
114
5. CONCLUSION
We have observed the change in Quality Factor with the change in Transmission
length, Transmission Power, Bit Rate and Residual Dispersion. These observations are
important in making the optical fiber transmission system more efficient and effective.
Moreover, the comparison will help to determine the superiority among the two models
discussed. Overall SMF-DCF model can transmit low power signal at a much higher bit rate,
to a longer distance maintaining a higher quality of the signal than DCF-SMF model.
6. ACRONYMS
DCF-SMF - Dispersion Compensating Fiber – Single Model Fiber
DM - Dispersion Managed
DMNLS - Dispersion Managed Nonlinear Schrödinger
NLS - Nonlinear Schrödinger
SMF-DCF - Single Mode Fiber - Dispersion Compensating Fiber
SSF - Split Step Fourier
REFERENCES
[1] Mark J. Ablowitz, Toshihiko Hirooka, Managing nonlinearity in strongly dispersion
managed optical pulse transmission, Journal of the Optical Society of America B, vol.
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[2] Biswas, A., Theory of quasi-linear pulses in optical fibers, Optical Fiber Technol., vol.
10, pp. 232-259, 2004
[3] A. Mecozzi, C. B. Clausen and M. Shtaif, Analysis of intrachannel nonlinear effects in
highly dispersed optical pulse transmission, IEEE Photonics Tech. Letters, vol. 12, pp.
392-394, 2000
[4] Joseph Berthold, Adel A. M. Saleh, Loudon Blair, Jane M. Simmons, Optical
Networking: Past, Present, and Future, J. Lightwave Technol., vol. 26, no. 9, May 2008
[5] Pechenkin, V., Kschischang, F. R., High Bit Rates for Quasi-Linear Optical Data
Transmission Systems via Constrained Coading, Optical Fiber communiation
Conference, March 2006
[6] Oukli, M., Kandouci, M., Bouzid, M., and Bendaoud, A., Study and Optimization of
High-Bit Rate Optical Fiber Transmission, Serbian Journal of Electrical Engineering,
vol. 5, no. 2, pp. 361-370, Nov. 2008
[7] Ohteru, S., Takachio, N., Optical Signal Quality Monitor Using Direct Q-Factor
Measurement, IEEE Photonics Techonol. Letters, vol. 11, no. 10, Oct. 1999
[8] Marc Hanna, David Boivin, and Pierre-Ambroise Lacourt, Calculation of optical phase
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[9] S.K Mohapatra, R. Bhojray And S.K Mandal, “Analog And Digital Modulation Formats
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