CLIPPING DISTORTION IN OPTICAL WIRELESS COMMUNICATION SYSTEMS:
MODEL, SIMULATIONS AND STATISTICS
Omar Falou and Xavier N. Fernando (ofalou, fernando@ee.ryerson.ca)
Dept. of Electrical and Computer Engineering, Ryerson University, Toronto, Canada
ABSTRACT
Clipping distortion has been a subject of interest in
many recent studies on frequency-division subcarrier
multiplexing (SCM) used in cable television applications
and wireless communication systems. Clipping occurs
when the modulating signal current, which drives the laser
diode, occasionally drops below the laser threshold
current, turning the laser off. A model was built to
investigate this phenomenon. A Rayleigh fading channel
was used to simulate the wireless channel. It was found
that, for channels with four fading paths, an increase in the
number of these paths for the same fading channel will not
increase the clipping percentage by as much as it was
expect. Furthermore, an increase in the threshold current
of the laser diode can significantly minimize the signal
distortion.
1. INTRODUCTION
Communications through optical fiber have become a
major information-transmission system due to many
advantages it provides. Networks based on optical fiber
technology provides, fast, efficient and reliable means of
transmitting
information
compared
to
other
communication systems such as wireline and wireless
systems [1].
A fiber optic transmission system consists of three
basic elements: the optical transmitter, the fiber optic
cable and the optical receiver. The optical transmitter
converts electrical signal into an optical signal. The source
of the optical signal can be either a Light Emitting Diode
(LED) or a Laser Diode (LD). LDs have some advantages
over LEDs since they can be focused to a very narrow
range, allowing control over the angle of incidence. They
also preserve the character of the signal over long
distances, which make them ideal for long transmission
distances [2].However, one of the disadvantages of LDs, is
that signal distortion can occur, mainly the clipping
distortion.
Fig. 1. Relationship between optical output power and
laser diode drive current [1]
Clipping distortion has been a subject of interest in
many recent studies on frequency-division subcarrier
multiplexing (SCM) used in cable television (CATV)
applications [3]-[5]. Clipping occurs when the modulating
signal current, which drives the laser diode, occasionally
drops below the laser threshold current, turning the laser
off [3],[6].
In this project, we build a Simulink model to simulate
an optical transmission system having a LD as its optical
transmitter. Then, we use this model to investigate the
effect of various Rayleigh fading channels on clipping
distortion.
2. OVERVIEW OF CLIPPING DISTORTION
For laser diodes, the relationship between optical output
power and diode drive current is shown in Fig. 1. At lower
drive currents, only spontaneous radiation is emitted,
therefore, no increase in the power output is observed
(Region 1). As the drive current reaches the lasing
threshold, a sharply increase in optical power output
occurs (Region 2). This region is called stimulated
emission region or linear region. At high power outputs,
the slope of this curve decreases due to junction heating
and saturation is reached (Region 3) [1].
As depicted in Fig. 1, the laser exhibits a threshold
current, Ith, and the drive current is biased to a DC
Fig. 3. Small-scale fading manifestations and degradations
Fig. 2. Fiber optic transmission system used to study
clipping distortion
operating point, IB [7]. Clipping occurs at the zero power
level when the drive current falls below the threshold
current Ith.
In order to study clipping distortion, let us consider
the following optical transmission system shown in Fig. 2.
Initially, the signal s(t) is modulated using Quadrature
Phase Shift Keying (QPSK). Then, the resulted analog
signal is passed through a Rayleigh fading channel in
order to simulate a wireless communication channel. After
that, the modulated signal is transformed into optical
signal or power using the Laser Diode. The optical signal
is transmitted in the optical fiber where it’s detected by the
photo detector, converted into current, then demodulated
to regenerate the original signal s(t).
The clipping distortion happens while the signal x(t)
is being converted into optical power P(t). It occurs when
the intensity of the injected current x(t) is less than the
threshold Ith as mentioned above. A key component of the
fiber optic transmission system is the Rayleigh fading
channel, which gives rise to amplitude fluctuations which
are the main cause of clipping. This channel will be
studied in details in the next section.
2. RAYLEIGH FADING CHANNEL
In a wireless communication system, a signal can
travel from a transmitter to a receiver over multiple
reflective paths. This phenomenon is called multipath
propagation. This can cause fluctuations in the amplitude,
phase or angle of arrival, of the transmitted signal at the
receiver’s end, which gives rise to what we call multipath
fading [8]. Fading can also be caused by channel variation
due to motion between transmitter and receiver, physical
changes in the medium and shadowing effect of large
obstructions [8]. The variations of amplitude, phase or
angle of arrival, in the transmitted signal can be
characterized by two main manifestations [8], large-scale
and small-scale fading.
Large-scale fading represents the path loss due to
motion over large areas such as hills, forests, etc… [8].
The path loss can be computed as a function of distance
between the transmitter and the receivers by statistical
method, which is described in terms of mean-path loss and
a log-normally distributed variation about the mean [8].
Small-scale fading is also called Rayleigh fading since
multiple paths exists between the sender and the receiver
and there’s no line-of-sight signal component, so the
envelope of the received signal can be described by a
Rayleigh pdf expressed as:
 r

 r2 
for
r
≥
0
 2 exp −


2
p ( r ) = σ

 2σ 


otherwise 
0
(1)
where r is the envelope of the received signal, 2 2 is the
prediction mean power of the multipath signal [8]. The
Rayleigh faded component or non-specular component is
also called scatter, random or diffuse component. When
there is a predominant line-of-sight (specular) component,
the envelope amplitude of the received signal can be
statistically described by a Rician pdf [9].
Based on [8], small-scale fading manifest itself in two
mechanisms: signal dispersion caused by time spreading of
digital pulses within the signal, and, time variance of the
channel due to the relative motion between the sender and
the receiver. Furthermore, these manifestations can be
categorized in various degradations types as Fig. 3
illustrates.
From a time domain point of view, a channel exhibits
frequency-selective fading when the maximum excess
delay time is greater than the symbol time. In other words,
when the maximum spread in time of a symbol is greater
σ
than the duration of the symbol. This is also known as
channel-induced ISI since it yields to inter-symbol
interference distortion [8]. From a frequency domain point
of view, frequency-selective fading occurs when some
spectral components of a signal, are affected in a different
way than the rest of components. When the above
conditions are not met, a channel is said to exhibit flat
fading.
Similarly, from a time domain point of view, a
channel is considered to be a fast fading channel when the
time duration in which the channel’s response is invariant,
or coherence time is greater than the time duration of a
transmission symbol. This may cause distortion of the
shape of the baseband pulse. A fast fading channel, from a
frequency point of view, can be described as a channel in
which the symbol rate (inverse of spread time of a symbol)
is less than the fading rate (inverse of the coherence time).
On the other hand, a slow fading channel is a channel in
which the aforementioned conditions are unmet.
3. SIMULATIONS AND RESULTS
Fig. 4 shows the Simulink model used to investigate the
effect of wireless channel on clipping distortion. The
model is composed of several bocks. A sampled read from
workspace block is used to create a data vector of size
10000, by executing the RANDINT Matlab function,
which generates in our case, 10000 random integers
between 0 and 3. The data output sample time was set to
10-4 sec. In other words, 10000 random integers were
generated over 1 sec time duration. The data vector was
used as an input for the QPSK modulator block, which
outputs a baseband representation of the modulated signal.
The phase offset and the samples per symbol were set to 0,
1 respectively.
After the signal is modulated, it passes through the
Rayleigh fading channel to simulate a wireless channel
with no line-of-sight signal component. Table 1 presents
the parameters that define this channel.
Parameter
Doppler
Frequency
Value
40Hz
Sample
Time
-1
Delay
Vectors
[0] s
Gain
Vectors
Initial
Seed
[0] dB
1234
Description
The maximum Doppler shift,
apparent change in frequency due
to the relative motion of the sender
and the receiver
The period of each element of the
input signal. Inherited from
previous block (10-4 s)
Specifies the propagation delay for
the path. In this case, we assume
that there’s only one path whose
delay is zero
Specifies the gain for the path. We
assume that it’s zero
The scalar seed for the Gaussian
noise generator.
Table 1. Simulation parameters defining the Rayleigh
fading channel
A bias current (we assume, the bias current has a zero
intensity throughout the computer simulations) is then
added to faded signal, and the magnitude of the resulting
signal is plotted versus the time as shown in Fig. 5.
We assume that our threshold value is 2.0V, therefore
the signal will be clipped if it goes above 2.0V. Fig. 6.
shows a histogram of the number of samples for different
voltage levels. It can be concluded that for this fading
channel, 159 samples out of 10000, or 1.59% of samples
will be cut off or clipped.
2.5
3.5
2.0V
2.1V
2.2V
2.3V
2.4V
2.5V
3
threshold
2
Clipping Percentage
Signal Magnitude (V)
2.5
1.5
1
2
1.5
1
0.5
0.5
0
0
0.1
0.2
0.3
0.4
0.5
Time (s)
0.6
0.7
0.8
0.9
1
Fig. 5. Magnitude of faded signal as a function of time (1
path with 2.0V as threshold voltage)
1000
1
2
3
4
Number of Fading Paths in the Channel
5
Fig. 7. Clipping percentage versus the number of paths in
the fading channel for various current thresholds.
Furthermore, we observed that by increasing the
threshold voltages by 0.5V in laser diode, the clipping
percentage may be reduced by as much as 1.75%.
However, this has a drawback since an increase in the
threshold voltage, can reduce the stimulated emission
region’s range, which will eventually affect the efficiency
of current-to-optical power conversion in the laser diode.
900
800
700
Number of Samples
0
600
500
10. REFERENCES
400
300
[1] Keiser, G., Optical Fiber Communications, McGraw-Hill
Higher Education, 3rd Edition, USA, 2000.
200
100
0
−0.5
0
0.5
1
1.5
2
2.5
Signal Magnitude (V)
Fig. 6. Histogram of samples for different voltage levels (1
path with 2.0V as threshold voltage)
Similar experiments were conducted for fading
channels with 2, 3, 4, 5 paths, whose time delays are 1x103
, 2x10-3, 3x10-3, 4x10-3 s and gains are -1, -2, -3, -4 dBs
respectively. The above steps were repeated for various
threshold voltages. The results are shown in Fig. 7.
4. DISCUSSIONS AND SUMMARY
Based on the results shown in Fig. 7., we can conclude
that, for channels with four or less fading paths, a major
clipping percentage variation is observed, whereas a minor
variation is noted for channels with 4 or more paths.
[2] Forouzan, B.A., Data Communications and Networking,
McGraw-Hill Higher Education, 2nd Edition, New York, USA,
2001.
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Analysis of Clipping-Induced Noise in AM-VSB Subcarrier
Multiplexed Lightwave Systems,” Journal of Lightwave
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Saltzberg, “A New Approach for Evaluating Clipping Distortion
in Multicarrier Systems,” IEEE Journal on Selected Areas in
Communications, vol. 20, no. 5, pp. 1037-1046, Jun. 2002.
[5] A. J. Rainal, “Limiting Distortion of CATV Lasers,” Journal
of Lightwave Technology, vol. 14, no. 3, pp. 474-479, Mar.
1996.
[6] K., -P. Ho, and J. M. Kahn, “Optimal Predistortion of
Gaussian Inputs for Clipping Channels,” IEEE Transactions on
Communications, vol. 44, no. 11, pp. 1505-1513, Nov. 1996.
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Index for Reverse Path Lasers in Hybrid Fiber/Coax Networks,”
IEEE Photonics Technology Letters, vol. 8, no. 11, pp. 15551557, Nov. 1996.
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