Numerical suppression of linear effects in a optical cdma transmission

International Journal of Electronics and Communication Engineering & TechnologyAND
INTERNATIONAL JOURNAL OF ELECTRONICS (IJECET), ISSN
0976COMMUNICATION ENGINEERING &3, October- December (2012), © IAEME
– 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue TECHNOLOGY (IJECET)

ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 3, Issue 3, October- December (2012), pp. 112-121
IJECET
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2012): 3.5930 (Calculated by GISI) ©IAEME
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NUMERICAL SUPPRESSION OF LINEAR EFFECTS
IN AN OPTICAL CDMA TRANSMISSION

Faîçal Baklouti1, Rabah Attia2
(UR-CSE, Polytechnic school of Tunis, EPT, BP 743-2078, La Marsa, Tunis Tunisia. Email:
1
baklouti.isimm@gmail.com, 2rabah.attia@enit.rnu.tn)

ABSTRACT

Fiber characteristics play a critical role in the propagation of short optical pulses. To
implement a temporal Optical Code-Division-Multiple-Access (OCDMA) solution, it is
necessary to take into account the linear and nonlinear effects resulting from the propagation
inside the fiber. In this paper, we study the importance of these phenomena along with the
performance of the network. This study is intended to improve the OCDMA technique by
numerically suppressing the linear effects in a Single-Mode Fiber (SMF). For this goal,
Fractional Step Method (FSM) is adapted to predict the deformation of Gaussian signals
introduced by the support and to reconstitute them after propagation inside the SMF. To
evaluate our study, these phenomena are analyzed starting from the case of a single Gaussian
pulse, going through the case of perfectly-synchronized Gaussian signals for OCDMA
transmission and ending with the case of asynchronous Gaussian signals.

Keywords: FSM, Linear Effects, OCDMA, SMF

I. INTRODUCTION
OCDMA is an optical multiple access technique that allows communication resources
(time and bandwidth) to be shared efficiently in order to improve the capacity of
communication networks [1]. While the vast bandwidth of the optical fiber medium provides
high-speed point-to-point data transmission, the CDMA scheme facilitates random access to
the channel in a bursty traffic environment [2]. It allows multiple users to share a common
optical channel simultaneously and asynchronously [3]. OCDMA is one class of system that
has the advantages of being able to provide a graceful degradation in performance as the
number of users increases, besides its great system capacity and high communication security
[4].
In the context of OCDMA implementation on access networks, assuming the channel
is ideal, the transmission chain is divided into two parts: transmission and reception. Fig. 1
shows a basic OCDMA network architecture. In a direct OCDMA transmission, user's data

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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 3, Issue 3, October- December (2012), © IAEME

are promptly multiplied by the assigned code [5]. The time bit of the data to be transmitted is
divided into a number of intervals called time chips Tc, or chip intervals. The code is defined
by its length F, which is the number of time chips, and its weight W, which is the number of
chips, or pulses in the sequence. The distribution of these pulses in the chip intervals is
related to the code family used [6]. Thus, the coded signal is transmitted through a channel
assumed to be ideal (i.e., the optical fiber). In OCDMA access network implementations, two
possible reception techniques can be employed [7], one with a Conventional Correlation
Receiver (CCR) and the other with a Multi User Detection (MUD) [8].
In the last decade, most researches are interested in the amelioration of the reception
technique using a signal distorted by the support effect. In this work we present an novel
approach in order to eliminate this effect before detection.
This paper is organized as follow: In section II, we study the impact of chromatic
dispersion in CDMA transmission, next we describe our proposed model. In section III, we
present our simulation result starting from the dispersion phenomenon in a Gaussian pulse,
dealing with the case of perfectly synchronized Gaussian signal for OCDMA transmission
and ending with the asynchronous case.

Fig. 1: OCDMA network architecture

II. PROPOSED MODEL
Chromatic dispersion in a SMF is the most important linear phenomenon [9]. This
phenomenon is due to material dispersion and waveguide dispersion. Material dispersion
reflects the fact that the fiber is mainly composed of silica, which has an optical index (i.e.,
refractive index) that vary according to the wavelength. As a result, the pulse emitted in this
fiber spreads out. Waveguide dispersion is caused by the fact that waves propagate in a
waveguide and not in an unlimited environment, thus leading to a dependence in the effective
index based on the wavelength. The effect of chromatic dispersion is that, as the power of
chips decrease when detecting an OCDMA transmission chain, some chips will be detected
as 1, when they are in fact nil [10]. This linear effect of the fiber causes the temporal signal to
spread.
Research has made it possible to model optical signal transmission and to estimate
what may happen to this signal after propagation through the fiber [11]. Thus, we primarily
focus on the reception of signals distorted by dispersion or by other effects (i.e. length of the
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fiber, wavelength) in an attempt to estimate the desired user signal. The idea is to eliminate
the linear effects introduced by the estimated spread in the fiber before data detection takes
place. Fig. 2 shows the proposed model. For this goal, we introduce a class of optical fiber
simulation methods, called Fractional Step Methods (FSM). These methods allow us to take
into account the behaviour of the unsteady flow field and record certain phenomena that
occur within the fiber, such as chromatic dispersion and non-linear effects, which have a
significant impact on the performance of optical communication systems.

Fig. 2: proposed model

When a medium's refractive index depends on the frequency ω of the wave passing
through it, this medium is called a dispersive medium. The relationship between wavelength
λ and refractive index n of a medium is given by the following formula [12]:

B1λ2 B λ2 B λ2
n 2 (λ ) = 1 + + 22 2 + 23 2 (1)
λ2 − C12 λ − C 2 λ − C 3

B1,2,3 and C1,2,3 are the experimentally-determined Sellmeier coefficients. When a wave
propagates in a dispersive medium, the different wave frequency components propagate at
different speeds, creating a temporal spread of the wave. For a given wave, we define the
phase speed at which each wave frequency spreads as:

ω c
vp = = (2)
k n

This is different from the group velocity, which is the speed at which the wave envelope
spreads. The group velocity is also the speed at which energy or information is carried
through the wave and is defined as:

1 c c
vg = = = (3)
dk / dω dn ng
n−λ
dλ

The refractive index of the group νg is defined as follows:

dn
ng = n − λ (4)
dλ

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Thus, it is clear that the group velocity is a function of the wavelength. Therefore, a light
signal travelling in a dispersive medium over a distance L in time t can be expressed as:

L L Ln g
t= = = (5)
vg c c
ng

Since laser sources typically used are not strictly monochromatic but have a wide spectrum
∆λ centered around a central wavelength λ0, the delay ∆t between two wavelengths separated
by ∆λ is:

L  dn g  L  d 2n  (6)
∆t = ∆λ   = ∆λ  − λ 2 
 = LD∆λ
c 
 dλ

 λ = λ0 c  dλ  λ = λ0


1 dng λ d 2n
The parameter D = =− is known as the dispersion parameter. If D is negative,
c dλ c dλ2
the environment has a positive or normal dispersion; thus the signal is transmitted in a normal
dispersion pattern and the high frequency components move slower than the low frequency
components. If D is positive, the environment has an anomalous dispersion and the higher
frequency components move faster over time. Finally, if D is equal to zero, the medium is
non-dispersive and all frequency components of the signal move at the same speed through
the fiber.
In reality, we can approximate a pulse generated by a distributed feedback laser with
a Gaussian signal. The incident pulse at z = 0 inside the fiber has the form:

T2
U (0, T ) = exp(− ) (7)
2T02

where T stands for the time measured from a frame of reference that moves with the pulse of
the group velocity and T0 is the time width at the intensity 1/e. β i is the ith order derivative of
d nβ 
the propagation constant ( β n =  n  ). The amplitude envelope, A(z,T), of the field
 d ω  ω =ω 0
during light propagation in a dispersive optical fiber without loss is governed by
Schrödinger's non-linear equation, simplified as follows :

∂A 1 ∂2 A
i = β2 2 2 (8)
∂z 2 ∂ T

The Fractional Step Method very useful in such kind of study because it allows us to
take into account the behaviour of the unsteady flow field and record certain phenomena that

115


occur within the fiber, such as the linear effects. Our developed programs are based on this
method. We will describe here one part of our detection algorithm which is very interesting to
understand our approach. Starting from the propagation equation :

∂A( z , T ) ^
= D A( z , T ) (9)
∂z

with,
^ i ∂2 α
D = − β2 − (10)
2 ∂T 2 2

when α is the parameter of absorption. We have :

A( z , t ) = U n = A(ndz , t ) (11)

with A (0 , t ) = U 0 = [ f (t 0 ), f (t1 ),..., f (t M −1 )] is the initial distribution of the field at z = 0.
T

Each step of the algorithm requires an iterative procedure to determine Un+1 from Un. Also for
 q +1  ^ 
each n, we calculate U n0 )1 = U n and until convergence is reached  i.e.,U n +1 = exp dz D U n  .
(
+
   
In what follows, we summarize the steps of the previous algorithm to determine a final signal
after its propagation inside a SMF:

1) U 0 ← A(0, T ) = { f (t m )}m =0 (initialization of the field discretized in time)
M −1

2) U fft ← fft (U 0 ) (when fft is the fast fourier transform).
3) For n=0,.., N-1 (number of steps on the longitudinal axis z)
a) U n +1 ← U n
^
b) U fft ← exp(dz D). * fft (U n+1 )
c) U n +1 ← ifft (U fft ) (when ifft is the inverse fast fourier transform).
So, to deduce the initial signal from a resulting signal spreading in a single mode fiber and
distorted by the linear effects, we will repeat the same steps of the previews algorithm but
ˆ ˆ
with replacing the operator ( D ) by (- D ).

III. SIMULATION RESULTS
In this section, we present our simulation results. As will be shown from the following
results, our detection programs prove to be very fast, powerful and efficient. We started our
simulation by modulating a Gaussian pulse with width T0 = 1.8 ps and power P0 = 1 W. In
these results we examine the effect of second-order dispersion on the propagation of a
Gaussian signal in a SMF, ignoring the high-order dispersion parameter and assuming the
non-linearity to be zero. To examine the effect of the wavelength on the signal transmission,

116


we superimposed the simulated pulse response for the case of a wavelength in which the
attenuation in the fiber is minimal (λ = 1.55 µm) and the dispersion parameter D is equal to
3.5 ps/nm.km (case 1), with the case of a wavelength λ = 1.3 µm and D = 19 ps/nm.km (case
2). The light was spread over a distance z = 100 km. Fig. 3 shows the power profiles of the
corresponding signals. As shown from these results, the initial pulse clearly spreads with the
increase of the wavelength (i.e., as the dispersion parameter increases). Next, we examine the
effect of the 2nd-order dispersion for different fiber lengths (z = 20 km and 100 km) for a
transmission wavelength λ = 1.3 µm and a dispersion parameter D = 3.5 ps/nm.km. As Fig. 4
shows, pulse spreading becomes more significant as the fiber length increases.

Fig. 3: 2nd-order dispersion phenomenon for the different wavelengths transmitted

Fig. 4: 2nd-order dispersion phenomenon for different

In addition to the dispersion phenomena, the absorption phenomenon can change the
shape of the transmitted pulse by reducing its intensity. Fig. 5 (case 1) shows the effect of the
2nd-order dispersion without any absorption phenomenon, whereas the results in the same
Figure (case 2) shows the effect of an absorption parameter α = 0.005. Although the
contribution of the 2nd-order dispersion term is dominant in most optical communication
systems, it is sometimes necessary to include higher-order terms proportional to β3. For

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example, when the pulse propagates around the wavelength of zero dispersion, or for the case
when the pulse is very short (T0 < 0.1 ps), the contribution of β3 becomes important. Fig. 6
shows the power profile of a Gaussian pulse emitted at λ = 1.55 µm (D = 19 ps/nm.km) in a
fiber of length z = 100 km, under the influence of 2nd- and 3rd-order dispersion phenomenon
(β3 = 0.1) without any absorption phenomenon. As shown from the previous results, for all
the phenomena illustrated above, it was possible to recover the original Gaussian pulse
without any error. Thus, starting from the pulse distorted by the linear effects, we were able
to estimate the transmitted pulse as a function of the fiber parameters.

Fig. 5: 2nd-order dispersion phenomenon with effect of absorption phenomenon

Fig. 6: 2nd- and 3rd-order dispersion phenomenon without any absorption phenomenon

For the case of a perfectly-synchronized Gaussian signal, we assume that all users transmit a
digital signal (0 or 1) synchronously (i.e., without any delay). These signals are encoded and
the multiplexed signal is sent through the fiber. Using a code equal to "2 2 0 0 3 0 2 1" and Tc
= 10 ps, the transmitted signal will have the form shown in Fig. 7. This signal is then sent
over a single-mode fiber (z = 200 km, λ = 1550 nm, D = 20 ps/nm.km, β3 = 0.1, α = 0.005).
At the end of the fiber, the received signal is shown in Fig. 8.

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We now focus on the signal recovered after propagation in the fiber where we
estimate the transmitted signal. Several simulations were necessary in order to retrieve the
original signal. We found that by choosing a step equal to 100 * Tc, the Bit Error Rate (BER)
was constantly in the order of 10-4 times the power of the wave. Hence, it is possible to
correct for the error and recover the input signal.

Fig. 7: Gaussian CDMA signal before propagation in the fiber (synchronous case)

Fig. 8: Gaussian CDMA signal after propagation in the fiber (synchronous case)

For the case of an asynchronous Gaussian signal, we assume that all users transmit digital
signals (0 or 1) asynchronously (i.e., at different times). We consider the case of three users:
the first with a coded signal "1 0 0 0 1 0 1 0" with a zero delay, the second with a coded
signal "1 1 0 0 1 0 0 1" with a delay of 0.5 * Tc (a more difficult case since the delay is about
n * Tc where n is integer), and the third with a coded signal "0 1 0 0 1 0 1 0" with a delay of
0.3 * Tc. The overall transmitted signal is shown in Fig. 9. This signal is sent over the same
fiber type as in the perfectly-synchronized case where the received signal is shown in Fig. 10.
We applied our simulation method in the same manner and with the same parameters and the
resulting signal matches exactly the original transmitted signal.

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IV. CONCLUSION
In this paper, we have investigated the different effects of optical fiber
communications in CDMA based transmission. In addition, our results are very interesting
for improving the implementation of an optical CDMA transmission chain. So, these
programs can be integrated into an FPGA or a digital calculator, which would eliminate the
linear effects of the propagation of a coded signal in a fiber prior to completing the decoding.
Another advantage of our proposition is the cost reductions caused by cancelling such
physical effects as the compensation fibers for chromatic dispersion. So, further research
should be done to integrate other non-linear effects into our method, as well as applying our
method to Multi-Mode Fibers (MMF) and other types of non-Gaussian signals.

Fig. 9: Gaussian CDMA signal before propagation in the fiber (asynchronous case)

Fig. 10: Gaussian CDMA signal after propagation in the fiber (asynchronous case)

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Numerical suppression of linear effects in a optical cdma transmission

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