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A Master of Science Project Report:
ADVANCED METHODS FOR MULTIPLEXING FOR
FUTURE TERABIT OPTICAL COMMUNICATIONS:
Comparison and Tolerance Analysis
………………………………………………………………………………………………
Student Name: Adekile Olufisayo Adekile
Student I.D No.: 107045822
Exam Number: Y8164832
Date: Wednesday 29th
August, 2012.
Supervisors: Dr. Eugene (Evgeny) Avrutin and
Dr. Ruwan Naminda Gajaweera
The Optical Communications Project Group 2011/12
Department of Electronics,
University of York,
Heslington,
York.
YO10 5DD

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Abstract
The evolutions of communication systems and networks in recent years have been
explosive.
In this work, the performance of an optical OFDM transmission system is investigated.
Its tolerance to the effects of dispersion and non-linearity are also analyzed. Simulation is
performed using matlab.

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Table of Content
1. Introduction
1.1 Project aim
1.2 Project specifications
1.3 Report structure
2. Historical Background
2.1 Modulation and Multiplexing
2.1.1 Modulation
2.1.2 Multiplexing
3. Advanced methods of multiplexing
3.1 OFDM
3.1.1 Setbacks of OFDM
3.1.2 Optical OFDM
3.1.3 Linear effects of the Optical Fiber
4. Optical OFDM System simulation
5. Project Management
6. Conclusion

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1. Introduction
The information technology revolution has significantly shaped the present age with its
innovative forms of communication which has radically transformed the nature of
personal and interpersonal communication in various aspects of human relations (social,
economic and political) in a globalised world. In this regard, globalization points to the
tremendous power of communication revolution in shaping human history.
Communications is described as the transmission of information from one point to
another and has been an important source in the rapid development of the world today.
Information is often transmitted from one destination to another by means of a
communication system and medium irrespective of the distance between these
destinations. In ancient times, information was conveyed through the use of signals such
as smoke signals, flag signals, signal flares or torch signals. However, the advancement
of technology ushered in a revolution in the way information was being sent over
distance in a communication system. Such advancements include information being sent
as electrical signals propagating on wire transmission lines and electromagnetic waves
propagating in space whose frequency range from a few megahertz to hundreds of
terahertz. The frequencies considerably below visible light in this frequency range are
referred to as radio waves and communication systems which use radio waves are called
microwave systems. The radical growth of the communication industry has dramatically
captured the attention of both the public and the media. Consequently, this has caused a
growth in data transmissions and as a result, the need for an increase in capacity and
speed of transmissions as consumers envision multimedia information to be available at
all places and at all times. With bandwidth limited at radio frequency, research was done
into a source that could provide the required bandwidth for the expansion of
communications and a promising approach, the use of light was discovered in the early
twentieth century. Accordingly, communication systems which use higher frequencies in
the range of visible light to near infrared region of the electromagnetic spectrum are
referred to as optical communication systems.

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It against this background of advanced technology in communication, in particular, the
change in transmission capacity that this project is undertaken as an attempt to describe
the optical communication systems in a comprehensive manner with major emphasis on
advanced multiplexing methods.
1.1 Project Aim and Objectives
The overall aim of this project is to investigate chosen advanced methods of multiplexing
for long-haul optical communications links. In this respect, the advanced multiplexing
method considered is the optical OFDM multiplexing method. This method is analyzed
and its tolerance to imperfections such as dispersion and fiber non-linearity are noted.
The objective of the project is to gain a thorough understanding of the different advanced
multiplexing techniques and the processes involved include:
Provide a general overview of optical communications, multiplexing and
advancement in the techniques of multiplexing in optical communications over
the years.
Investigate the effect of non-linearity and dispersion of OFDM systems.
Simulate and optical OFDM communication system using matlab.
Provide a detailed report on OFDM multiplexing scheme.
1.2 Project Specifications
The group was split into two with one team (which I was part of) working on OFDM and
the other working on CoWDM. For the completion of this project, simulations are to be
created using matlab.
The specifications for the project were divided into two in order of importance; core (C)
and desirable (D). The specifications are;
To investigate multiplexing methods for the next generation of optical
communications long haul links. (C)
A special emphasis was placed on Orthogonal Frequency Multiplexing (OFDM).
(C)

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Compare OFDM to CoWDM and investigate their system tolerances to
imperfections that may rise in real working systems like incomplete dispersion
compensation, fibre non-linearity, local oscillator frequency excursion in detector
and other non-ideal components. (C)
Determine the effects on the bit rate and modulation techniques employed on the
required tolerance of the system. (C)
Investigate the effects of nonlinearity in fibres and Semiconductor Optical
Amplifiers in long-haul links and its dependency on modulation and bit rates. (D)
Develop simulations for an optical OFDM system (C).
Suggest the better multiplexing method of the two and its benefits as well as its
shortcomings considering capacity, sensitivity and complexity of implementation.
(C)
That all results of the research will be made available on the 29th
August, 2012.
(C)
1.3 Report Structure
The report is intended to provide a progressive description of the project background,
including the work done, accompanied by the results and conclusion in the end.
This report has been structured into a chapter by chapter basis and is given as follows;
 Chapter Two introduces communications as well as the historical background of
optical communications. A brief introduction to modulation and various
multiplexing techniques are also covered in this chapter.
 Chapter Three focuses on an in-depth literature review on the chosen advanced
multiplexing schemes CoWDM and OFDM, with more emphasis on the OFDM
multiplexing technique. It also investigates the effect of dispersion and non linear
effects on an optical channel.
 Chapter Four. This chapter focuses on the optical OFDM system and its
simulation with matlab. The results from the simulations are also discussed.
 Chapter Five reviews project management
 Chapter Six is the conclusion and future lines

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2. Historical Background
Since time immemorial, communication has been a constant and intimate part of human
experience, assuming many diverse forms in different communities. The use of talking
drums or smoke signals for example served as a means of communications in these times.
However, the early forms of communication encountered various problems, one of which
includes limited amount of information transfer as only a small amount of information
could be sent at a particular time. Furthermore, the high probability of making and
receiving errors in early forms of communication proved to be another impediment to
effective and accurate communication, especially as the transmission distance increased.
Thus research into higher capacity and more efficient communication systems began
which subsequently made way for the era of electrical communications with the invention
of the telegraph and the telephone in the 1830s. Towards this end, the invention of the
telephone in 1830 was seen as a great breakthrough in communication and a vast
improvement as it brought about an increase in system capacity (information transfer)
resulting from the use of coaxial cables [1]. In his book ‘Fiber-Optic Communication
Systems’ Agrawal(what was the year of publishing) posits the claim that the first coaxial
cable put into use, a 3MHz system, was capable of transmitting 300 voice channels with

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its only deficiency being the frequency-dependency losses of the cabal for frequencies
higher than 10MHz. [2]
Subsequent advancement in this field yielded more efficient coaxial cables capable of
performing at bit rates of higher than 270Mb/s. However, in spite of the increase in
transmission capacity brought about by the use of coaxial cables, the surge in the cost of
operation and maintenance of the coaxial cables undermined this development in
communication transmission as a result of their small repeater spacing, which was less
than 1km [2].
This setback in terms of financial cost consequently incited the advancement to
microwave communication systems. Microwave systems are communication systems that
use radio wave frequencies for their operations. Using microwave communication
systems, signals were sent using electromagnetic wave carriers with frequencies ranging
from 1-10GHz and appropriate modulation techniques. Microwave communication
system encouraged larger repeater spacing compared to coaxial cables. However, as the
demand for high speed data transmissions increased, microwave communication systems
encountered the problem of limited bit rates as a result of their relatively low carrier
frequencies. This predicament spurred research into using higher frequencies in the
electromagnetic spectrum into using higher frequencies in the electromagnetic spectrum
(visible light to near infrared regions) to provide the required bandwidth to meet the
increasing demands. It was observed that using modulated light as a carrier offered the
advantage of having unlimited bandwidth and also cheap transmitters and receivers.
Nonetheless progress could not be made, as there was no suitable transmission medium
or optical sourcing available at this time.
The invention of the laser in the 1960s produced a narrow band source of optic radiation
suitable for use as a carrier of information, thus a radical breakthrough in the area of
Optical communication begun [3]. The use of optical fibers to guide light in transmission
soon followed although high losses of the available fibers during this period were a
concern. The optical fiber produced losses in excess of 1000dB per kilometer [2]. These
were the first generation of optical communication systems and they operated at a bit rate
of 45Mb/s, a wavelength of about 0.8µm and offered repeater spacing of up to 10km. As

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a result of larger repeater spacing associated with optical communication systems, the
cost for installation and maintenance of these systems decreased as fewer repeaters were
used [2] [3]. This reduction in cost motivated system designers to research deeper into
this technology and they discovered fiber loss could be reduced to below 1dB per km if
the optical communication systems operated in a region of wavelength near 1.3µm. This
resulted in a huge reduction in repeater spacing, further reducing the cost of
implementation and maintenance of these repeaters. Despite the progression of optical
communication systems at this point, the problem of non-linearity and dispersion in the
optical fiber in this wavelength region was a problem that needed to be solved as it
limited the amount of data that could be transmitted on a single fiber.
Dispersion is a phenomenon where the pulses of the transmitted signal spreads in
the optical fiber and causes degradation of the signal as a result. The problem of
dispersion restricted the bit rate to below 100Mb/s. The use of single mode fibers
resolved this problem and increased the bit rate up to 1.7 Gb/s with a repeater spacing of
approximately 50km [2].
Third generation optical communication systems operated at a wavelength in the region
of 1.55µm with dispersion being a problem. It was postulated that by limiting the laser
spectrum to a single longitudinal mode, the problem of dispersion could be solved. After
much research and works, optical communication systems capable of operating at bit
rates of approximately 4 Gb/s were obtained. Another defect of the third generation
systems was that repeaters were not spaced widely enough however this problem was
solved by improving the receiver sensitivity by use of heterodyne detection scheme in
addition repeater spacing were increased [2].
Non-linearity in the fiber is considered the fundamental limiting mechanism to the
amount of data that can be transmitted on a single optical fiber. They emerge as a result
of increase in optical fiber data rates, transmission lengths, number of wavelength and
optical power levels. The effects of non-linearity in the optical fiber vary widely with the
chromatic dispersion of the fiber and in effect the wavelength, chirps, polarization of the
propagating light waves are also affected giving rise to an affluence of new effects [4].
Also, the core size of the fiber as well as the length of the fiber can strongly enhance
optical non-linearity. [5]. The two major causes of non-linear effects in optical fibers are

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the dependence of the refractive index of glass on the optical power going through the
material and the scattering phenomena which produces stimulated brillouin scattering
(SBS) and stimulated raman scattering (SRS). These effects of non linearity as well as
other effects such as pulse distortion and cross talk between channels can have adverse
effect on optical communication systems such as degradation of receiver sensitivity,
BER. However, they can be used for variety of applications ranging from fiber laser and
amplifiers to demultiplexers and optical switches [4]. Dispersion and non-linearity as
well as their effects are discussed further into this report.
2.1 Modulation and Multiplexing
2.1.1 Modulation
Modulation involves of altering the properties of a high-frequency periodic carrier signal,
with a modulating signal which typically contains information to be transmitted.
Modulation in optical communications cannot be overlooked as it has the potential to
improve the bit error rate (BER) of input data as well as increase spectral efficiency
especially in WDM systems [6]. In optical communications, an optical modulator
modulates a beam of light as it propagates through the optical channel. Modulation in
optical communications can be classified into two main forms: the direct modulation and
the external modulation. Direct modulation is the easiest form of optical modulation as it
involves modulating the intensity of the light generated by a light source. It is
advantageous as there is a possibility of direct current modulation of light emitter diodes
(LEDs) and laser diodes (LDs) [7]. On-off Keying (OOK) is the simplest modulation
technique currently used by fiber optic communication systems and is based on intensity
modulation with direct detection. In this modulation technique, a zero is represented by
zero intensity and a one is represented by a positive intensity [8]. Higher power
efficiencies can be achieved using other modulation schemes. Quaternary modulation
(QAM) has the potential to double spectral efficiency and achieve higher tolerance for to
impairments such as dispersions in the fiber.
However, a set back with using direct modulation technique is the problem of chirp
which is a frequency shift during the optical pulse. Direct modulation introduces chirp,
resulting in modulated linewidths many times greater than the theoretical and this in turn

11. 11
increases the adverse effect of dispersion in a system. The problem of chirp is more
frequent in optical sources with small spectral width. The use of continuous wave lasers
and external modulation has been proven to subdue the effect of chirping. [2][7]. Two
main types of external modulation are the Electro-absorption modulation which
introduces chirp less the 1 compared to the laser with chirp between 3-8, and the Electro-
optic modulator. The electro-optic modulator makes use of a Mach Zehnder
interferometer and reduces chirp to an almost ideal state (0). [7]. The Mach Zehnder
modulator is discussed in detail later in this report.
2.1.2 Multiplexing
A significant and extremely important change in communication advancement in regards
to system capacity and cost has been the phenomenon of multiplexing. According to
Hamad (2011, pg 243), “Multiplexing is the sending of a number of separate signals
together, over the same cable, channel, link, or bearer, simultaneously and without
interference.”[9] What this implies in essence is that multiple signals at a common point
are combined into one signal and transmitted over a common transmission channel. The
total capacity (bandwidth) of the communication channel is divided into several sub-
channels, one for each message signal to be transmitted thus giving each signal a portion
of the total channel. Network cost, as a result of multiplexing is reduced since fewer
communication links are needed between any two points. Figure 1.1 illustrates the
multiplexing of n channels into one link. The reverse process demultiplexing occurs at
the receiver end and can extract the original channels.
Figure 1.1- Basic Representation of Multiplexing

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Multiplexing encompasses a wide range of techniques such as: space-division
multiplexing (SDM), time-division multiplexing (TDM), frequency-division multiplexing
(FDM), and wavelength division multiplexing (WDM). All of which have various
significant alterations [10];
Space Division Multiplexing: In SDM, channel separation is achieved by
physically separating the transmission media either by space or insulation. It
involves different point-to-point wires going through a cable but separated by
space within the cable for different channels [10]. Within each physically distinct
channel, multiple channels can be derived through frequency, time, or wavelength
division multiplexing.
Time Division Multiplexing: Time is the key parameter. Multiple transmissions
occur by dividing the link into sub-channels and interleaving them. It involves
interleaving bits associated with different channels to form a composite bit
stream. Time segments from different signals are interleaved onto a single
transmission path. Users take turns in using time slots in this form of multiplexing
[10]. A problem with time-division multiplexing is that there is a tendency to
waste bandwidth when vacant slots occur because of idle stations.
Frequency Division Multiplexing involves the transmission of signals
simultaneously over a given bandwidth of a transmission medium by sharing the
available frequency among multiple users. The transmitted signals are modulated
on distinct frequency ranges in the transmission channel. To prevent overlap and
allow for ease of recovery at the receiver end, a guard band separates the
modulated signals, which is an unused area of the available frequency [10]. With
FDM however, there is waste of limited frequency spectrum in guards spaces
between the sub-channel and a large complexity of separate modulations for
different sub-carriers. This led to an advanced form of FDM being developed
known as orthogonal frequency division multiplexing (OFDM). According to
Winzer 2009, ‘two signals are orthogonal if messages sent in these two
dimensions can be uniquely separated from one another at the receiver without
impacting each other’s detection performance.’ [11] OFDM solves the issue of

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waste of limited spectrum by allowing sub-channel signals with non-interfering
frequency spectral to overlap and in the process achieves a high bit rate [12].
Nonetheless, the transmitters of OFDM systems experience low power efficiency
due to non-linearity, inter-symbol Interference (ISI), inter-channel interference
(ICI) and chromatic dispersion, which cause losses within the system [11][13].
Wavelength division multiplexing has been the most prominent of the other forms
of multiplexing techniques because it has the ability to push the capacity of a
single fiber link to the order of 10Tera bits per second. The WDM technique
transmits several channels corresponding to different wavelength in the same
optical fiber. A multiplexer launches the different channels into a single fiber and
is separated by a demultiplexer after transmission through an amplified link [14].
Figure 1.2 shows WDM in an optical fiber.
Figure 1.2- Basic representation of a WDM transmission link
Reference: Biswanath Mukherjee. WDM Optical Communication Networks: Progress
and Challenges. IEEE 2000, vol. 18.
Future generation optical communication systems will be able to operate at bit
rates of up to 10Tb/s as a result of the wavelength division multiplexing (WDM)
technology. The introduction of this technology greatly improved the bit rate of optical
communication systems. The change in the slope of fig 1.3 below shows the impact
WDM technology has on the capacity of optical communication systems.

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Figure 1.3- Progress in capacity of fiber-optic communication systems. Red: WDM
aggregate capacities on a single fiber, Yellow: spectral efficiency
Reference: Peter, Winzer: Modulation and Multiplexing in optical communication
systems. IEEE. February 2009.
WDM increases capacity by allowing bidirectional communication over one
strand of fiber by multiplexing different optical carriers onto a single fiber using different
wavelengths. A revolution began at the advancement of the WDM technology where
capacity increases every six months and as at 2001, optical communication systems were
able to operate at a bit rate of 10Tb/s. Optical amplification was used to increase repeater
spacing [9]. However, the receiver structure for this type of multiplexing technique is
complex, as each signal transmitted through the fiber requires its own modulation scheme
and guard spacing. Also, its expensive cost is another setback.
Coherent wavelength division multiplexing (CoWDM) is a modified multiplexing
technique. It is a faster version as it eliminates the process of electrical to optical
conversion, which reduces speed and bandwidth by ensuring that modulation,
multiplexing, and demultiplexing are all done in the optical domain [11]. Power

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efficiency is also enhanced [13]. The increasing growth and demand for higher speed of
transmissions systems will need a befitting system that is bandwidth efficient as well as
fast. Optical CoWDM and OFDM are a promising approach and are discussed in more
detail in the next chapter.

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3. Advanced Methods of Multiplexing
The sensitivity and capacity of a communication system are very important
characteristics to be considered for its implementation. The sensitivity in this regard
measures the minimum power or the minimum signal-to-noise ratio (SNR) required by
the receiver to close a digital communication link. It also includes the effect of linear and
non-linear signal distortions due to the transmission channel [11]. The capacity measures
the amount of data that can be transmitted over the communication medium [11].
In an effort to efficiently utilize available bandwidth as well as combat the problems of
error in the optical channel and also meet the requirements on sensitivity and capacity
under the respective implementation costs, the best suited multiplexing methods have to
be chosen. Advanced multiplexing methods such as OFDM and CoWDM have been
proposed and are believed to be able to do this and improve the quality of transmission in
effect [11] [92]. Section 2.1 discusses OFDM as well as the effect of chromatic
dispersion and non-linearity on the optical channel. It also illustrates the use of OFDM as
a solution to ISI, thereby reducing dispersion. In addition, structures that have been put in
place to remedy these effects are described in this section.
3.1 Orthogonal Frequency Division Multiplexing (OFDM)
The progressively increasingly manner at which data rates currently increases has seen
conventional serial modulation schemes such as quadrature amplitude modulation
(QAM) and non-return to zero (NRZ) unable to compete [2]. In conventional serial
modulation schemes, the symbols are transmitted sequentially and the received signal is
dependent on the multiple transmitted symbols and in essence, the complexity of
equalization accelerates excessively.
However, current researches have proven OFDM to be a capable fix to these
problems as well as the problem of inter symbol interference (ISI) caused by a dispersive

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channel. Its capacity to achieve higher bit rates as well as spectral efficiency has made it
a major player in the communication industry and this technique has now been adopted
by most emerging telecommunication systems. [11] [15]
OFDM multiplexing allows a single data stream to be transmitted over a number
of lower-rate subcarriers. It is a special type of multi-carrier transmission system which
employs the use of parallel data transmissions and also orthogonality between the
individual subcarriers [15]. The signal is divided among individual subcarriers hence
lowering the bit-rate per carrier and transmitted simultaneously through parallel data
transmissions. The use of parallel data transmissions with overlapping sub-channels
significantly reduces the effect of ISI. Also, equalization is made simpler since each sub-
channel covers only a small fraction of the original bandwidth. [12]
The earlier form of frequency division multiplexing involved the use of guard bands to
prevent overlap and allow for ease of recovery however, this was considered a waste of
the limited available bandwidth. [16] Orthogonality provides the possibility of arranging
these carriers such that the sidebands of the individual carriers overlap and the signals
being received without adjacent carrier interference. These narrowband overlapping
signals are in turn transmitted in parallel inside one wideband. Parallel transmissions
avoid the use of high-speed equalization and also combats the problem of ISI and well as
allows for efficient use of the available spectrum. Figure 1.4 illustrates the difference
between non-overlapping multicarrier technique and the overlapping multicarrier
technique and shows the spectral efficiency of OFDM. [17]

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Figure 1.4- Comparison of bandwidth utilization by FDM and OFDM [17]
The different subcarriers can then be modulated using modulations schemes such as
BPSK, QPSK or QAM. However, modern digital signal processing techniques such as
discrete fourier transform (DFT) are used at both the transmitter and receiver ends to
prevent the use of multiple modulators and filters. At the transmitter end, IFFT is used to
generate the signal and FFT is used at the receiver end. These are the main functions that
distinguish OFDM form single carrier systems. Figure 1.5 below shows the system
architecture of a wireless OFDM system.

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Figure 1.5- System architecture of a wireless OFDM system[15]
The IFFT and FFT blocks form the main components in the transmitter and receiver
respectively. The signal is defined in the frequency domain at the input to the transmitter.
The serial to parallel converter is designed such that the discrete fourier spectrum exists
only at discrete frequencies and each OFDM sub-carrier corresponds to one element of
this discrete Fourier spectrum. Hence (X) represents the data to be carried on its
corresponding sub-carrier. The outputs of the IFFT (x) are complex vectors in the time
domain. The output signals of the IFFT are created such that they are orthogonal to each
other thereby producing little to no interference to one another. CP is introduced to
nullify the problems of ISI and ICI. The outputs from the IFFT with CP introduced are
converted back to serial form for transmission over the channel. At the receiver, CP is
removed and the FFT performs a forward transform on the received sample data for each
symbol. The output(Y) is in the frequency domain. [15] [12]

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3.1.1 Set Backs of OFDM
Despite its various advantages, OFDM multiplexing exhibits a few drawbacks, the most
common being the high peak-to-average-power ratio (PAPR) of the transmit signal which
renders implementation of this multiplexing method very costly and inefficient as it
causes high power consumption which is undesirable. PAPR can be defined to be the
ratio between the maximum instantaneous power and its average power. [18]
PAPR [x(t)] =
Where Pav = average power of x(t)
After IFFT, the constructive addition of the signals on the different carrier frequencies
result in spurious high amplitude peaks in the composite time signal and when compared
to the average signal power, the instantaneous power of these peaks are found to be
relatively high. This has an effect on the PAPR which in turn becomes large and the
average power has to be reduced which in turn reduces the range of multicarrier
transmission. [19]
Due to the resultant high PAPR of the transmitting signals, the OFDM receiver’s
detection efficiency becomes very sensitive to non-linear devices such as high power
amplifiers (HPA) and digital-to-analogue (DAC) converters used in its signal processing.
This could critically affect the systems performance causing signal distortion such as in-
band distortion and out-of-band radiation due to the non-linearity of the high power
amplifier (HPA). The non-linearity of the power amplifier could destroy the
orthogonality between the carriers. However, to prevent spectral growth and
intermodulation among sub carriers, the transmit power amplifier has to be operated in its
linear. [18]
This increase in PAPR has resulted in the complexity of the transmitter and the receiver
and has led to intense research in order to decrease high power consumption and also
achieve low complexity required for practical implementation. Techniques such as
amplitude clipping and filtering have been proposed for the reduction of PAPR. This is
the simplest researched technique and it involves limiting the peak envelops of the input
signal to a deliberated value. However, amplitude clipping introduces noise to the system
which results in error performance degradation and also reduces spectral efficiency.

21. 21
Filtering this noise out maybe become difficult and cause peak growth but repeated
clipping and filtering may be done to get to a desired amplitude level. This form of PAPR
reduction can be used with other reduction techniques to significantly reduce PAPR.
Other techniques proposed for the reduction of PAPR include coding which involves the
use of codewords to reduce PAPR for transmission, selected mapping, interleaving, the
active constellation extension technique and the partial transmit sequence technique.
Factors to be considered before choosing any specific PAPR reduction technique includes
careful analysis of performance of the system, cost analysis for realistic environments,
transmit signal power increase, bit-error-rate (BER) increase, data loss. [18] [19]
Other drawbacks experienced by OFDM systems include sensitivity to frequency
offset and phase noise and I/Q imbalance. Differences in the frequency and phase of the
receiver local oscillator and the carrier of the received signal can result in the degradation
of the system performance [15]. I/Q imbalance in OFDM systems also results in ICI.
3.1.2 Optical OFDM
Due to its ability to offer improved transmission performances, OFDM has recently been
adopted for high-speed long-haul optical fiber communication systems. The main
differences between OFDM and optical OFDM can be summarized on figure 1.6
below.
Figure 1.6- Typical OFDM systems vs Typical optical system [2]
The information in a typical OFDM system is carried on the electrical field as compared
to the intensity of the optical signal in an optical OFDM system. At the receiver end for
an optical OFDM system, the receiver uses direct detection and there is no local oscillator
at the receiver which is in contrast to the typical OFDM system where coherent detection

22. 22
is used and the availability of a local oscillator at the receiver end. Figure 1.7 shows the
schematic diagram for an optical OFDM system.
Figure 1.7- Optical OFDM system[21]
As can be seen from figure 1.7, another main difference between a typical OFDM system
and an optical OFDM system is the presence of an optical modulator in the transmitter.
Zero padding at the input of the IFFT provides an interpolated waveform with a well-
controlled spectrum [21]. This optical modulator is responsible for the conversion of data
from the electrical domain to the optical domain. This can be done directly or externally
using the electro-optic modulator. It is assumed to be linearized to provide an optical
output power proportional to the electrical drive voltage. In optical OFDM applications
after modulation, it is important to remove the lower sideband using an optical filter. This
is because the presence of the lower sideband could lead to fading in the presence of
chromatic dispersion and also a reduction in spectral efficiency. The modulated optical
signal is then transmitted through a single mode optical fiber using compensating fibers
which consists of optical amplifiers to upgrade signal power. At the receiver, the optical
signal is detected using typical PIN photodiode or avalanche photodiode with gain
equalization and chromatic compensation and converted back to frequency domain by the
FFT. The signal is decoded and equalization on each channel at the receiver is performed
to compensate for phase and amplitude distortions resulting from the optical and
electrical paths. Thus after equalization, each modulated channel is demodulated to

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produce data channel which are converted to a single data channel using a parallel to
serial interface. [21] [15]
Linearity is a key factor for the successful operation of an optical OFDM system.
The system must be primarily linear between the IFFT at the transmitter and the FFT at
the receiver. However, optical OFDM systems face linear problems in its propagation
through the optical fiber such as attenuation and dispersion and also problems of non-
linearity. All these mentioned characteristic of the optical fiber are functions of the
transmitted wavelength and limit the transmission distance of the signals. The properties
of the fiber as a waveguide affect all of these but most importantly the effects of
dispersion. [School notes]
3.1.3 Linear characteristics of the optical fiber
The two principal factors that limit the performance of optical fiber communication
systems are attenuation and dispersion.
Dispersion
Dispersion is an undesirable but unavoidable characteristic of the optical fiber which can
be defined as the difference in propagation times of the modes with the slowest and
fastest velocities and it places a limit on the information capacity of the communication
system. The effect of dispersion in a multimode fiber is the broadening of optical pulses
as a result of different path lengths as they propagate through the optical fiber. This
phenomenon is referred to as intermodal dispersion. However, the use of single mode
fibers completely nullifies the effect of intermodal dispersion because the number of
modes propagating is reduced to one and energy of the injected pulse is transported by
this single mode. Nonetheless, broadening of the pulses is not completely eliminated as
the group velocity of the single mode is dependent on the frequency which in effect
causes different spectral components of the pulse to travel at different group velocities
and arrive at different times at the fiber output. This is known as chromatic dispersion
and is a resultant of two different dispersions in the fiber: material dispersion and
waveguide dispersion. [23]

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Material Dispersion occurs as a result of the frequency dependent nature of the
dielectric constant of a material and cannot be changed for any given material. For single
mode fibers, the material used for fiber manufacture is silica and it is dependent on
frequency. Waveguide dispersion is dependent on fiber parameters such as the core,
cladding and refractive index difference and results from power distribution with in the
core and cladding of the fiber. It is a function of the geometry of the fiber and can be
tailored such that the total dispersion is relatively small over a wide range of frequencies.
Figure 1.8 shows the total chromatic dispersion in an optical fiber.
Figure 1.8- Chromatic in a standard single mode fiber
Another form of dispersion present in the optical fiber is the polarization-mode dispersion
(PMD). PMD causes broadening of the input pulse at the fiber output resulting in the
appearance of two selected directions known as optical axes 1 and 2 [7] [2].
It brings about birefringence (light modes polarized along these axes have different
propagation constants) due to divergence from the perfect circular symmetry. The
direction of the axis does not coincide with that of the actual light polarization in the
propagating mode and is random. The light is dissolved into the two polarization modes,

25. 25
leading to PMD. The birefringence and hence PMD are weak, but may become a
limitation in long-haul systems. [2]
Dispersion in the optical fiber could lead to the deterioration of an optical
transmission system. The effects includes scattering of the propagation energy in the fiber
as a result of deviation from the ideal circular symmetry, limitation of the bandwidth of
the fiber, introduction of ISI, all of which reduce the ability for effective data recovery.
The dispersion of the fiber, the length of the link and the linewidth of the transmitted
optical signal all contributes to the degree of degradation.
Schemes have been proposed to resist the effects of dispersion on the optical fiber and
extend propagation beyond dispersion limits. Some of these include the use of 3R
regenerators, dispensation compensation schemes such as specially designed single mode
optical fibers. Also, the use of large number of sub-carriers has proven effective in
eliminating fiber chromatic dispersion.
Attenuation
The optical receiver requires a necessary minimum useful power input to be able to
recover the signal. Attenuation contributes to fiber loss in that it reduces the average
power reaching the receiver as light travels through the fiber. The resulting fiber loss
inherently limits the transmission length of the optical fiber. Scattering is a common
cause of attenuation in the optical fiber [2]. The effect is that it scatters light in all
directions in the optical fiber resulting in loss of optical energy (power). It occurs as a
result of the structure of the fiber and impurities found in the fiber. Also, the impurities
found in the optical fiber could lead to absorption of the optical power of the signal [23].
Figure 1.9 shows

26. 26
Figure 1.9- Attenuation in an optical fiber
Fiber loss is dependent on the wavelength of the transmitted light. Figure 1.9 shows the
attenuation of a single mode fiber at wavelengths ranging from 0.8 µm to 1.8µm. The
attenuation for the shorter wavelengths is determined by scattering while for the higher
wavelengths, attenuation is determined by absorption. It can be observed from the graph
that the lowest loss (~0.2dB/Km) exhibited by the fiber is in the wavelength region near
1.55µm. Also, low loss occurs in the region of about 1.3 µm. due to the low levels of
fiber losses in these regions, these wavelengths are deemed attractive for optical
communication systems.
However, for shorter wavelengths, it can be concluded from the figure 2.31 that the loss
significantly increases. Thus, shorter wavelengths are considered unsuitable for long
distance optical fiber communication systems. [2] [23]
Non-linear effects
The effects of non-linearity are very important in the design of optical communication
systems as they either could be unfavorable in which case should be minimized or useful.

27. 27
Recent research has proven that non-linear effects could be exploited to be used for
dispersion compensation for the enhancement of the transmissions properties of the fiber.
As was mentioned earlier, the two prominent causes of non-linear effects in optical fibers
are the Kerr effect (dependence of the refractive index of glass on the optical power
going through the material) which results in phase modulation or generation of new
frequencies by mixing of waves and the scattering phenomena which produces stimulated
brillouin scattering (SBS) and stimulated raman scattering (SRS). [4] Examples of non-
linearity that occurs as a result of the kerr effect include self-phase modulation (SPM),
cross-phase modulation (XPM), four-wave mixing (FWM). Damaging effects of non-
linearity for optical communication especially in WDM systems includes backscattering
Stimulated Brillouin Scattering (SBS) &SRS, pulse distortion (XPM, SPM, Modulation
Instability MI) and crosstalk between channels (XPM, FWM). [5] [4]
Soliton formation is one of the favorable results of combining non-linear effects together.
Solitons are pulses that propagate in the fiber keeping their shape, with nonlinearities and
dispersion compensating each other. [7] [2]
Non-linear effects will be particularly important in the next generation of optical
networks which relays on all optical function for higher speed and greater capacity. This
will allow partial elimination of the optical-electrical-optical conversion in an optical
network making them more transparent ad reconfigurable. The main challenge will be in
controlling this non-linearities and their interplay and will certainly need new types of
fibers which in this case, photonic crystal fibers, hold great promise [4]. Common non-
linearity includes
SBS: is a fiber non-linearity that imposes an upper limit on the amount of optical power
that can be usefully launched into an optical fiber. When the SBS threshold is exceeded
(which is quite low) a significant fraction of the transmitted light is redirected back
towards the transmitter. This results in a saturation of the optical power that reaches the
receiver as well as introduces signal noise into the system, resulting in degraded BER
performance [4]. On the positive side, SBS can be exploited in ultra-narrow linewidth
lasers and for remote sensing

28. 28
SRS: is much less of a problem that SBS. It limits the launch power in a multiple channel
communication system. Due to SRS, a channel at shorter wavelength loses its power to
the longer wavelength channels and the longer wavelength gains power from the shorter
wavelength channels. This is called stoke channel. A channel acts like a pump for all the
longer wavelength as it lose power those channels and acts like a stoke channel for all
shorter wavelength channels and receives power from them [4].
FWM: Here, energy is exchanged between signals of different wavelength. When two
channels have sufficient optical intensities, signals can be generated on the wavelengths
of other channels. The effect is worst in low dispersion fibers.
SPM: is also a phenomenon that is due to the power dependency of the RI of the fiber
core. It interacts with CD and increases the rate at which the pulse broadens. When
increasing the fiber dispersion, the FWM reduces and increase the impact on the SPM
[4][5].
XPM: It is the modulation of the phase of one signal by another as they propagate along
the same optical fiber. Cross Phase Modulation similar to SPM. XPM introduces jitter to
WDM soliton systems.
4. Optical OFDM system simulation.
The previous chapters has discussed and given a literature review of optical OFDM in
detail taking into account the duties of the different blocks at the transmitter and receiver

29. 29
respectively. This chapter however, constitutes the simulation of an optical OFDM
system using matlab codes. Matlab is used to generate random input signal as well as for
the design of the different blocks used in both the transmitter and receiver. Figure 2.0
below shows the system used.
Figure 2.0- Optical OFDM system block diagram[21]
For the purpose of this design, the optical OFDM system can be broken down into three
components subsystems.
The electrical OFDM transmitter which comprises of the modulator, IFFT,
parallel to serial converter and the DAC.
The optical modulator and filter.
The receiver model.

30. 30
4.1 The electrical OFDM Transmitter
Figure 2.1- Optical OFDM Transmitter[21]
As can be seen from the figure above, the high data rate data stream coming in from the
source of the signal is split up and converted into a set of low data rate parallel data
transmissions mapped onto corresponding information symbols for the sub-carriers.
For this simulation, random data is generated for transmission through this system and
has a high data rate of 10Gb/s [21]. It is presented to 512 blocks that go through the
modulator. This is broken down with each modulated sub-carrier having a reduced data
rate of 20MB/s. The incoming bits are mapped to a symbol using the modulation schemes
4-QAM. This encodes two successive bits in a data sequence grouped together to create a
4 symbol complex-valued QAM symbols.
The output of the modulator serves as 512 inputs to the IFFT. Also, a further 512 zero
inputs is fed into the IFFT block. This is termed zero padding and thus the input to the
IFFT is a total of 1024-bit streams comprising of 512 modulated input signals and 512
zero padded.
Zero padding the inputs to the IFFT provides a controlled spectrum and prevents aliasing
of the OFDM signal by creating gaps between the OFDM signal and the DC component.
Aliasing results after sampling. It occurs when different signals to become
indistinguishable after being sampled. It is the distortion that results when the signal
reconstructed from samples is different from the original continuous signal. The resultant
outputs from the IFFT block has to go through the DAC block where it is sampled.

31. 31
Sampling of these outputs brings about the effect of aliasing. The aliases produced
become difficult to separate from the main OFDM signal because it would be right next
to the main it. Zero padding however, corrects the positions of the IFFT input sequence
with zeros can help to shift the aliases away from the OFDM signal and is generally used
to avoid unwanted mixing products. [21]
As was mentioned earlier, the input to the IFFT block is a 1024-bit stream comprising of
512 modulated signals and 512 zero padded frequency signals. The IFFT block modulate
sub-carriers in the digital domain and performs superposition of all the modulated
subcarriers each carrying 20Mb/s with the input channels spaced equivalently to generate
a waveform. The operation of orthogonality is performed by the IFFT and the output of
the IFFT is in the time domain. The outputs of the IFFT block are complex numbers.
Each value of the 1024 complex output is repeated eight times to give a total of 8192
complex numbers. This increases the sub-carriers from 1024 to 8192. These are separated
into its real and imaginary components and passed through two digital to analogue
converters. The signal is then unconverted to a carrier frequency of 7.5GHz. It is
achieved by multiplying the real part of the IFFT by a cosine signal and multiplying its
imaginary part by a sine signal and adding them together at a mixer.
Where Suc(t) = signal after RF mixer
S(t) = complex baseband OFDM signal from the output of the IFFT block
R[s(t)] = Real part of s(t)
I[s(t)] = Imaginary part of s(t)
The process of up conversion displaces the OFDM sidebands and the resulting signal is
the electrical input to the optical modulator. Figure 2.2 shows the input signal to the
optical modulator.

32. 32
Figure 2.2- Input signal to the optical modulator
4.2 Optical Modulator and Filter
The input to the optical modulator is an electric signal which must be converted to an
optical signal if will be transmitted through the optical fiber. As was previously
mentioned, optical modulation can either be performed directly or externally. Direct
modulation is the easiest form of optical modulation as it involves modulating the
intensity of the light generated by a light source. However the problem of chirp is a
fundamental problem. The use of external modulators completely solves this problem.
For this simulation, the external modulator chosen is the linear Mach-Zehnder modulator.

33. 33
Mach-Zehnder Modulator
Figure 2.3- MZ Modulator
The mach-zehnder modulator is used for intensity modulation and functions by splitting
the laser light into two waveguides using a ‘Y’ junction or a three guide coupler.
Materials used in MZM modulator such as lithium niobate exhibits electro-optic
properties thus can be altered by the application of an external voltage [2] [23]. However,
the two arms of the MZM will experience identical phase shifts and interfere
constructively in the inexistence of external voltage thus generating amplitude
modulation. By varying the bias of the MZM, Phase shift is introduced in one of the arms
and the resultant addition of the two arms could destroy the constructive nature of the
interference leading to destructive interference and also reduce the transmit intensity.
Where S(t) = signal after Rf mixer
V = half wave voltage = 2.5 * 10^9

34. 34
Vb = bias voltage = -0.25* V
By setting the bias of the MZM to the null point, the Optical Field Modulation mode can
be achieved. Here, the drive voltage determines the type of modulation performed by the
MZM.
Figure 2.4- Transfer function of the optical field and optical intensity
The output signal produced by MZM is a double side banded. The lower optical sideband
generated by the MZM entails needs to be removed using an optical filter. However, for ease
of implementation of the optical filter, we find the modulus of the FFT of the output of the
linear MZM. This converts it to frequency domain and as such the sidebands can easily be
removed.

35. 35
Figure 2.5- Output from the linear MZ modulator in frequency domain
Non-Linear Modulator

36. 36
Figure 2.6- Output from the non-linear MZ modulator in frequency domain
Filter
Filtering is important for the removal of the lower optical sideband and also to improve the
sensitivity of the receiver. It does this by suppressing the optical carrier which leads to an
increase in the received electrical power for any optical power. [21]
The input to the filter is the output from the MZ modulator. The filter was designed by first
converting the output of the MZ modulator into frequency domain by finding the FFT. The
sidebands are removed by modulating onto a 7.5GHz RF subcarrier band to give an RF
sideband from 5-10GHz. Side band suppression was implemented in the simulation by
assigning zeros to the length of the output of the MZ modulator in the frequency domain thus
suppressing all of it. However, the side band 5-10GHz aligns with the firs 1-750 points when
compared on the graph. This part of the signal is called back while the rest of it remains
suppressed. The output of the filter is plotted in frequency domain. The IFFT is taken to get
the corresponding signal in time domain. [21]

37. 37
Figure 2.7- Suppressed single sideband in frequency domain

38. 38
Figure 2.8- Suppressed single sideband in time domain
The receiver Model
Figure 2.9- Optical OFDM receiver

39. 39
An optical receiver receives the transmitted optical signal, converts it back into electrical
form and tries to recover the original transmitted signal through the system.
The photodiode at the receiver produces a time-domain waveform proportional to the
optical power.
Pout │Eout│2
The input to the photodiode is the suppressed single sideband in time domain. The photo
current which is the output of the photodiode is absolute value squared of this input.
Figure 3.0- Output of Photodetector
The real of the received photocurrent is multiplied by a cosine wave to down convert it.
Also, the real values of the imaginary part is multiplied by a –sine waveform and
converted to a imaginary numbers by multiplying it by ‘i’.

40. 40
The total points for both the real and imaginary are reduced from 8192 to 1024 by
averaging them over 8. The result is 1024 real points and 1024 imaginary points. These
are added together and form the input to the FFT. The FFT transforms the signal into the
frequency domain and the zero padding is removed. Equalization is not carried out as
there was little time to introduce dispersion in the channel.
However, it is observed that if the higher subbands are not filtered out, the IFFT into time
domain will be a lot closer to the original signal. The constellation becomes more like
points.

41. 41
Figure 3.1- Demodulation without filtering of subbands

42. 42
5. Project Management
This chapter gives details of steps and methods under taken to ensure a successful and
qualitative research process and results.
The project group comprises of six key members, two supervisors (Dr. Eugene
Avrutin and Dr. Ruwan Gajaweera), and four students (Olufisayo Adekile, Olufemi
Olorode, Bashir Aloiye Garuba and Dongbo Liu). For ease of completion, the project was
broken down into groups of two students working on the two advanced multiplexing
schemes. I and Olufemi Olorode were assigned optical OFDM and Bashir Garuba and
Dongbo Liu were assigned the task of working on the CoWDM multiplexing scheme.
Prior to this project, none of us had any experience with optical communications. While
working on the OFDM Olufemi and I decided to break it down for better understanding. I
choose working on the optical filter and the optical receiver while Olufemi worked on the
transmitter and the MZ modulator. Both groups simulated their projects using matlab.
Meeting Arrangement
Group and supervisor meeting started as early as January and continued into August.
Project progress was reported to the supervisor Dr. Eugene Avrutin during supervisor
meetings. In this meeting issues such as project progress, difficulties encountered, ways
of resolving them, and interim results are discussed. The supervisor gives suggestions and
advises where necessary. The supervisor was always readily available to offer help
whenever we needed.
The project group meetings are held among project group members. Here individual
progress is discussed as well as difficulties encountered.
Weekly emails are sent to the Supervisors and group members to keep them
updated with new developments.
Project Planning
This section discusses how we planned to achieve the desired goals of our project. The
project group sub-divided into two based on two different areas:
CoWDM Sub-group- Dongbo Liu and Bashir Aloiye Garuba. They worked on
the CoWDM technique.

43. 43
OFDM Sub-group- Olufemi Olorode and Olufisayo Abayomi Adekile.
The schematic diagram below shows how we planned to gain understanding of the
project and also implement all we had to do to achieve our aims.
Block diagram of Project Planning and Execution Sequence.
Background studies is where we focus on understanding optical communications,
multiplexing, its types and special emphases on coherent frequency division multiplexing
schemes, modulation techniques among others.
The literature review stage is where we spend time studying past journals and write ups
on Coherent Wavelength Division Multiplexing (CoWDM) and Orthogonal Frequency
Multiplexing (OFDM) and getting a better understanding of these topics in general and as
it relates to optical communications. We would also look into studying and developing
way of resolving the systems tolerance to non-ideal components effects.
The numerical model stage is where we develop a model from the output of our research
in the literature review. It would be a mathematical model or formulae that we can
translate into a code eventually.
Coding, Simulation, Testing stage simply involves the development of algorithms,
flow charts, program codes, conduct tests (i.e. unit and overall tests) and simulate the
outcome of our research results on either Matlab or any of the programming languages.
Documentation is the final stage which involves compiling all results gotten, making
references to all journals and documents used during the research process. We would also
make reviews of all results obtained are accurate, objectively obtained and as well as the
computer program developed. We would draw up areas of further work and any
suggestions if any.
Background
Studies
Literature
Review
Numerical
Model
Coding,
Simulation,
Testing
Documentation
and Reviews
Project
Research
Results

44. 44
Project Scheduling
This section contains details of our action time plan showing all tasks and major
milestones of to be achieved over the allocated project time. The table below gives an
insight into a summary of the project schedule;
Serial
No. Milestones Timeline
1 Background Studies January/February
2
Literature Review
Numerical Models for both CoWDM and OFDM System. March/April/May
3 Coding Simulation and Testing of Research Results June/July
4 Documentation and Reviews August
January February March April May June July August
TaskTimeline:
Study of Optical Communications.
Study of Multiplexing Schemes.
Tender Document Preparation: Draft
Version.
Tender Document Preparation: Final
Version.
Research on all Literature relating to
OFDM.
Develop a Numerical Model of OFDM.
Exam period
Develop Algorithms, Flowcharts and
Coding of CoWDM Numerical Model.
Testing of Computer Programs of the
OFDM Numerical Model.
Testing of Computer Programs of the
CoWDM Numerical Model.

45. 45
Task Allocation
This section gives an outline of who will be doing what during the course of the project.
The table below shows who will be responsible for what in this research project;
TaskIndividual Handling Task:
Bashir
A.
Garuba
Dongbo
Liu
Olufemi
Olorode
Olufisayo
A.
Adekile
Study of Optical Communications.        
Study of Multiplexing Schemes.        
Tender Document Preparation: Draft Version.        
Tender Document Preparation: Final Version.        
Research on all Literature relating to OFDM.    
Research on all Literature relating to CoWDM.    
Develop a Numerical Model of OFDM.    
Develop a Numerical Model of CoWDM.    
Develop Algorithms, Flowcharts and Coding of OFDM
Numerical Model.    
Develop Algorithms, Flowcharts and Coding of CoWDM
Numerical Model.    
Testing of Computer Programs of the OFDM Numerical
Model.    
Testing of Computer Programs of the CoWDM Numerical
Model.    
Simulation of OFDM Numerical Model.    
Simulation of CoWDM Numerical Model.    
Documentation of All Results.        
Review of the Entire Process, Results Obtained, Difficulties
Encountered, and Further Work.        
Simulation of OFDM Numerical Model.
Simulation of CoWDM Numerical Model.
Documentation of All Results.
Review of the Entire Process, Results
Obtained,
Difficulties Encountered, and Further
Work.

46. 46
6 Conclusion
This report was on the advanced method of multiplexing for long haul systems. OFDM
was considered and an optical OFDM system was simulated using matlab. The report
visited transmission through an optical OFDM system and also considered the tolerance
of OFDM transmissions to effects of dispersion and non-linearity.

47. 47
References
[1] Gowar, J. 2nd
edition. “Optical Communication Systems”. Prentice Hall International
(UK) Ltd 2001.
[2] Agrawal, G. 3rd
edition. “Fiber-Optic Communication Systems”. New York: John
Wiley & Sons, 2002.
[3] Palais, J. 2nd
edition. “Fiber Optic Communications”. New Jersey: Prentice Hall
1988.
[4] J. Toulouse: “Optical Nonlinearities in Fibers: Review, Recent examples and Systems
Applications”. IEEE November 2005.
[5] David R. Goff; ‘The effects of Fiber Nonlinearities’, Olson Technology, February
2007
[6] Joseph Khan: “Modulation and Detection Techniques for Optical Communication
systems”
[7] Dr Eugene Avrutin: “Optical Communications Systems Lecture Handouts”.
[8] Ghassemlooy Z. and Hayes A., Seed N., and Kaluarachchi E.: Digital Pulse Interval
Modulation for Optical Communications. IEEE Communications Magazine. December
1998.

48. 48
[9] Hamad, O. 1st
edition. “Analogue, digital and multimedia telecommunications: Basic
and
Classic Principles”. 2011
[10] Glover, I. and Grant, P. 3rd
edition. “Digital Communications”. Europe: Prentice
Hall. 2010.
[11] Peter, Winzer: “Modulation and Multiplexing in optical communication systems”.
IEEE. February 2009.
[12] Mohamed Khedr, “Optical Orthogonal Frequency Division Multiplexing For High
Speed Wireless Optical Communication”’ IEEE 2008.
[13] S. Ibrahim, A. Ellis, F. Guning, J.Zhoa, P. Frascella, F. Peters. “Practical
Implementation of Coherent WDM”. IEEE 2009.
[14] Biswanath Mukherjee. “WDM Optical Communication Networks: Progress and
Challenges”. IEEE 2000, vol. 18.
[15] Jean Armstrong; ‘OFDM for Optical Communications’ IEEE 2009
[16] Itsuro Morita; “Optical OFDM for High-Speed Transmission”
[17] Ramjee Prasad: “OFDM for Wireless Communication systems” Artech house 2004
[18] Seung H. Jae H. L. “An overview of peak-to-average power ration reduction
techniques for multicarrier transmissions.” IEEE 2005
[19] Laia Nadal, M.S Morelo, J.M Fabrega, G. Junyent; ‘Comparison of peak power
reduction techniques in optical OFDM systems based on FFT and FHT’, Centre Tecnol.
de Telecomunicacions de Catalunya, Barcelona, Spain 2011
[20] Irena Orovic, N. Zaric, Srdjan Stankovic, I. Radusinovic and Z. Veljoric; ‘Analysis
of
[21] Arthur James Lowery, Liang Bangyuan Du and Jean Armstrong; ‘Performance of
Optical OFDM in Ultralong-Haul WDM Lighwave Systems’; IEEE January, 2007
[22] M.A. Jarajreh, Z. Ghassemlooy; “Improving the chromatic dispersion telorance in
long-haul fiber links using the coherent optical orthogonal frequency division
multiplexing”. IEEE 2009.
[23] William B. Jones; “Introduction to optical fiber communication systems”

49. 49
APPENDIX A
% Optical OFDM System
% symbol rate = 20MHz;
% number of sample per symbol= 2*symbol rate;
% Modulation: 4-QAM
% txdatasymbol=1024;
%datasymbolperframetoifft = 256;
datasymbolperframetoifft = 512;
%lengthsymbolforifft=512; %data symbol per frame to ifft *
(number of sample per symbol/symbol rate)=512

50. 50
lengthsymbolforifft=1024; %data symbol per frame to ifft *
(number of sample per symbol/symbol rate)=512
% Total no. of Frames= 1024/256= 4;
% Total Bitrate = 10GHz;
% Generate random bits
bits_per_symbol=2;
numbits=bits_per_symbol*datasymbolperframetoifft;
%usedbits=rand(1,1024)>0.5;
usedbits=rand(1,2048)>0.5;
% 4-QAM modulation
% Angle [pi/4 3*pi/4 -3*pi/4 -pi/4] corresponds to 4-QAM
% Gray code vector [00 10 11 01], respectively
table=exp(j*[-3/4*pi 3/4*pi 1/4*pi -1/4*pi]); % generates 4-QAM
symbols
table=table([0 1 3 2]+1); % Gray code mapping pattern for 4-QAM
symbols
full_len = length(usedbits);
inp=reshape(usedbits,2,full_len/2); %returns the m-by-n matrix
'inp' whose elements are taken column-wise from used_bits
mod_symbols=table([2 1]*inp+1); % maps transmitted bits into 4-
QAM symbols
%scatterplot(mod_symbols);
%To add guard interval to the modulated signals
%NumAddPrefix = 1 + Guardinterval;
%SymCP = zeros(NumAddPrefix,lengthsymbolforifft);
%RowPrefix = (1-Guardinterval+5):lengthsymbolforifft;
%SymCP = [ifft_sig(RowPrefix,:);ifft_sig];
% IFFT
%padding=zeros(1,512);%generating the remaining 512 zeros
padding=zeros(1,1024);%generating the remaining 512 zeros
%inpz=reshape(padding,2,full_len/2);
ifftinp=[mod_symbols,padding];
%ifftinp=[mod_symbols(1:256),padding,mod_symbols(257:512)];
%adding the 512zeros to the 512 modulated subcarriers as input to
d ifft
%ifft_sig = ifft(ifftinp); %inverse fast fourier of the 1024
modulated subcarriers
%ifft_sig = ifft(ifftinp,1024); %inverse fast fourier of the 1024
modulated subcarriers
ifft_sig = ifft(ifftinp,2048); %inverse fast fourier of the 1024
modulated subcarriers
%ifftsiglength=length(ifft_sig);
%for i=1:length(ifft_sig)
%improvedifft_sig(8*(i-1)+1:8*i)=ifft_sig(i);
%end; %good method of for loop

51. 51
%m=expand(ifft_sig,8)
%m=reshape(repmat(ifft_sig',1,8)',length(ifft_sig(:,1)),8*length(
ifft_sig(1
%,:)));% not tested the expand / reshape method
%improvedifft_sig=kron(ifft_sig,ones(1,8));
improvedifft_sig=kron(ifft_sig,ones(1,16));
grid on
figure (1)
plot (improvedifft_sig, 'r --');
title('plot of improved signal after ifft and doubling');
%plot (ifft_sig, 'r --');
%Trying to make the superposition of all modulated sub-carriers
each of 20Mb/s
%ifft_sigmd=interp(mod_symbols,(10*(10^9))); % modulating the
sub-carriers with 20Mb/s
%figure (3)
%plot (real(ifft_sigmd),imag(ifft_sigmd), 'r*');
%Separating the in-phase and quadrature
%tRsig=real(ifft_sig); %extracting the real part of ifft i.e in-
phase %%%
tRsignw=real(improvedifft_sig); %extracting the real part of ifft
i.e in-phase %%%
%tRsignw=ones(1,8192);
%T_Sc = 1/(7.5*10^9);
T_Sc = 1/(12.5*10^9);
%time=zeros(1,length(tRsignw));
%for i = 1: length(tRsignw)
% time(i*((100*10^-9)/(8*1024))) = tRsignw(i);
%end
%time=((1:length(tRsignw))*((100*10^-9)/(8*1024)));
time=((1:length(tRsignw))*((100*10^-9)/(8*2048)));
Cos_of_Real_sig=tRsignw.*cos(2*pi*time/T_Sc);
wdthoffft=abs(fft(tRsignw));
%Cos_of_Real_sig=tRsignw*cos(length(tRsignw)*((100*7.5)/(8*1024))
);
%tIsig=imag(ifft_sig); %extracting the imaginary part of ifft i.e
quadrature %%%
tIsignw=imag(improvedifft_sig); %extracting the imaginary part of
ifft i.e quadrature %%%
%tIsignw=ones(1,8192);
%Sine_of_Imag_sig=tIsignw*sin(length(tRsignw)*((100*7.5)/(8*1024)
));
Sine_of_Imag_sig=tIsignw.*sin(2*pi*time/T_Sc);
%%Insert guard interval
%I2=[tRsig];
%Q2=[tIsig];
%I3=[I2(full_len-Guardinterval+1:full_len,:);I2];
%Q3=[Q2(full_len-Guardinterval+1:full_len,:);Q2];

52. 52
%To multiply the real and imaginary part by cos and sine
%fin_sig_opt=tRsig+tIsig; %summing the two signals together (real
and imaginary)
fin_sig_opt_new=Cos_of_Real_sig+Sine_of_Imag_sig; %summing the
two signals together (real and imaginary)
%fin_sig_opt=I3+Q3; %summing the two signals together (real and
imaginary)
figure (2)
plot (fin_sig_opt_new, 'r --');
title('plot of input signal to the modulator');
%getfreqrespofsig=fft(fin_sig_opt_new);
%absfreqresp=abs(getfreqrespofsig.^2);
%plot (absfreqresp, 'r --');
%plot (fin_sig_opt, 'r --');
%Generate the noise vector
%noise=randn(1,1024)*0.07;
noise=randn(1,2048)*0.07;
figure(3)
hist(noise,50);
title('noise');
%%adding awgn to the ifft signal
%resultant = sign(fin_sig_opt+noise); % returns an array
'resultant' the same size as (fin_sig+noise), where each element
of resultant is:
% 1 if the corresponding element of X is greater than zero
% 0 if the corresponding element of X equals zero
% -1 if the corresponding element of X is less than zero
%figure (5)
%plot (resultant, 'r --');
%Sending the signal through an optical modulator to suppress the
optical carrier and side-band as well as increase the electrical
received power so as to improve the receiver sensitivity.
Ao=1; %maximum voltage
%t=100*10^-9;
V_pi=2.5*10^9; %half wave voltage
Vb=-0.25*V_pi; %bias voltage
theta_b=(Vb*pi)/V_pi;
%time=100ns
%theta_b_new=(a/V_pi);
%Vo=
Emz=Ao/2*(2*cos(theta_b)-
fin_sig_opt_new*sin(theta_b));%.*(exp(j*7.5*10^9*time)+exp(-
j*7.5*10^9*time))));
%Emz=Ao/2*(2*cos(theta_b)-
((fin_sig_opt_new*sin(theta_b))*(exp(j*5*10^9*t)+exp(-
j*10*10^9*t))));

53. 53
%Emz_new=Ao*cos(theta_b)-
((fin_sig_opt*sin(theta_b))*(exp(j*7.5*10^9*t)+exp(-
j*7.5*10^9*t))));
figure (4)
plot(Emz);
title('plot of output of modulator');
Y=fft(Emz);
%gh=real(Y);
%gg=imag(Y);
%abc = ifft(Y);
modEmz=abs(Y);
figure (5)
semilogy (modEmz, 'r--')
%title('plot of modulator in log scale')
%io=zeros(1,length(Y));
%for i=1:length(Y)
%if i>0
%io(i)=Y(i);
%else
% io(length(Y)+i)=Y(i);
%end
%end
%new_i=io;
%modEmznew=abs(new_i.^2);
%for i=1:length(ifft_sig)
%improvedifft_sig(8*(i-1)+1:8*i)=ifft_sig(i);
%end; %good method of for loop
%F=Y*(7.5*10^9);
%IF=ifft(F);
%figure (6)
%plot (IF, 'r--');
%F=zeros(length(Y),1);
%F(1:4100)=Y(1:4100);
%IF=ifft(F);
%figure (6)
%plot(real(IF));
%pw=fft(IF); %confirm the plot to suppress sideband
%pemz=abs(pw); %Confirm plot
%figure (7)
%semilogy(pemz);
%title('plot of to supress sideband');
%D=zeros(length(IF(4100:end)),1);
%D(4100:4883)=IF(4100:4883);
%FinalIF=ifft(D);

54. 54
%plot(real(D));
%pd=fft(D); %confirm the plot
%demz=abs(pd); %Confirm plot
F=zeros(length(Y),1);
%F(1:750)=Y(1:750);
%F(1:1500)=Y(1:1500);
F(1:3000)=Y(1:3000);
IF=ifft(F);
figure (8)
plot(real(IF));
pw=fft(IF); %confirm the plot
pemz=abs(pw); %Confirm plot
figure(9)
semilogy(pemz);
%PH = abs (IF);
%Output of the Photodiode.2nd and 3rd idea
PH_Current = abs(IF.^2);
%PH_Current = abs(abc.^2);
subplot(2,1,1); semilogy(PH_Current);
%subplot(2,1,2); semilogy(abc);
figure(10)
plot(PH_Current)
%q=PH_Current(1:512);
%Cos_PH_Current=PH_Current*cos(length(PH_Current)*((100*7.5)/(8*1
024)));
Cos_PH_Current=(PH_Current)'.*cos(2*pi*time/T_Sc);
%Sine_PH_Current=PH_Current*(-
sin(length(PH_Current)*((100*7.5)/(8*1024))));
Sine_PH_Current=(PH_Current)'.*(-sin(2*pi*time/T_Sc));
Sine_PH_Current_j = Sine_PH_Current*j; % converting reeceived
signal to imaginary
Real_Rxsig_ADC=real(Cos_PH_Current);
Imag_Rxsig_ADC=imag(Sine_PH_Current_j)*j;
for n = 1:2048
%Real_Rxsig_ADC_Reduced(n) = mean(Real_Rxsig_ADC((n*8-
7):n*8));
Real_Rxsig_ADC_Reduced(n) = mean(Real_Rxsig_ADC((n*16-
15):n*16));
end

55. 55
for z = 1:2048
%Imag_Rxsig_ADC_Reduced(z) = mean(Imag_Rxsig_ADC((z*8-
7):z*8));
Imag_Rxsig_ADC_Reduced(z) = mean(Imag_Rxsig_ADC((z*16-
15):z*16));
end
RX_realnimagforfft=Real_Rxsig_ADC_Reduced+Imag_Rxsig_ADC_Reduced;
figure (11)
plot(RX_realnimagforfft)
%Real_Rxsig_ADC_Reduced = (Real_Rxsig_ADC(1:8:end));
%Real_Rxsig_ADC_Reduced=[(sum(Real_Rxsig_ADC(1:8))/8):8:(sum(Real
_Rxsig_ADC(8185:end))/8)];
%Real_Rxsig_ADC_Reduced=
(sum(Real_Rxsig_ADC(1:8))/8):8:(sum(Real_Rxsig_ADC(8185:end))/8);
%Real_Rxsig_ADC_Reduced=Real_Rxsig_ADC(((sum(1:8))/8):8:((sum(818
5:8192)/8)));
%Real_Rxsig_ADC_Reduced=Real_Rxsig_ADC((sum(1:8)/8):8:(sum(8185:e
nd)/8));
%FFT_FINAL_Real=fft(Real_Rxsig_ADC_Reduced);
%Imag_Rxsig_ADC_Reduced = (Imag_Rxsig_ADC(1:8:end));
%FFT_FINAL_Img=fft(Imag_Rxsig_ADC_Reduced);
%RX_realnimagforfft=Real_Rxsig_ADC+Imag_Rxsig_ADC;
%RX_realnimagforfft_reduced = (RX_realnimagforfft(1:8:end));
%FFT_FINAL=fft(RX_realnimagforfft_reduced);
FFT_FINAL=fft(RX_realnimagforfft);
%RxRsig=real(q);
%g=PH_Current(513:1024);
%RxIsig=imag(PH_Current);
%RxIsig=imag(g);
%FFTtotal=fft(RxRsig,512);
%k=[RxRsig,RxIsig];
%k=[RxRsig,RxIsig];
%ReFFT=fft(k);
%ReFFT=real(FFTtotal);
%FFT_FINAL_512=FFT_FINAL([1:572,1026:2048]);
FFT_FINAL_512=FFT_FINAL([1:120,1026:2048]);
%FFT_FINAL_512=FFT_FINAL(513:end);
FFT_FINAL_512_re = real(FFT_FINAL_512);
FFT_FINAL_512_img = imag(FFT_FINAL_512);
scatterplot(FFT_FINAL_512)

56. 56
ipHat(find(FFT_FINAL_512_re < 0 & FFT_FINAL_512_img < 0)) = -
0.7071 + -0.7071*j;
ipHat(find(FFT_FINAL_512_re >= 0 & FFT_FINAL_512_img > 0)) =
0.7071 + 0.7071*j;
ipHat(find(FFT_FINAL_512_re < 0 & FFT_FINAL_512_img >= 0)) = -
0.7071 + 0.7071*j;
ipHat(find(FFT_FINAL_512_re >= 0 & FFT_FINAL_512_img < 0)) =
0.7071 - 0.7071*j;
scatterplot(ipHat);
%=====1st idea
%Real_PH_Current = PH_Current * cos (2*pi*7.5*10^9*100*10^-9);
%Imaginary_PH_Current = PH_Current * (-sin
(2*pi*7.5*10^9*100*10^-9));
%Total=Real_PH_Current+Imaginary_PH_Current;
%FFTtotal=fft(Total);
%figure (10)
%plot (FFTtotal, 'r--')
%plot (ReFFT, 'r--');