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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

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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.

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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

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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

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

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

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

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

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

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

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

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

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

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

Figure 2.5- Output from the linear MZ modulator in frequency domain

Non-Linear Modulator

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

Figure 2.7- Suppressed single sideband in frequency domain

38

Figure 2.8- Suppressed single sideband in time domain

The receiver Model

Figure 2.9- Optical OFDM receiver

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

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

Figure 3.1- Demodulation without filtering of subbands

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

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

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

Task\Timeline:

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

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;

Task\Individual 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

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

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

[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

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

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

%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

%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

%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

%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

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

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--');