by gafar mohamed

Republic of Iraq

Ministry of Higher Education and Scientific Research

University of Technology

Laser and Optoelectronics Engineering Department

IMPROVEMENT OF THE

PERFORMANCE OF OPTICAL CDMA

BY USING ERROR CORRECTION

CODE

A Thesis

Submitted to the Laser and Optoelectronics Engineering

Department, University of Technology in Partial Fulfillment

of the Requirements for the Degree of Master of Science in

Optoelectronic Engineering

By

Gafar Mohamed B. Sc. Electrical Eng.

2001

Supervised by

Dr. Hosham Salim

2008

August 2008 A. D. Shaban 1429A. H.

جمھورية العراق مي لوزارة التعليم العالي والبحث الع

معة التكنولوجية الجا قسم ھندسة الليزر والبصريات الالكترونية

ألمتعدد ألبصري تحسين أداء منظومة ألاتصال

تقنية تصحيح ألتشفيري بأستخدام بالتقسيم

ألخطأ ألمشفر

رسالة مقدمة الى قسم ھندسة الليزر والبصريات الالكترونية الجامعة التكنولوجية

ألبصريات نيل درجة الماجستير علوم في ھندسة من متطلبات كجزء ألالكترونية

المھندس تقدم بھا

جعفر محمد ضيف

بإشراف هشام سليم عنيدالدكتور

ھ١٤٢9 رمضان م ٢٠٠8 أب

Abstract

Optical code division multiple access networking is one possible

technique that allowed multiple users in local area networks to access the

same fiber channel. The modern optical CDMA network are endeavoring to

present multi services, like internet service, multimedia, upload, download

etc, in addition to providing high quality of video and audio for users. All

these services need a high data rate. The objection of this thesis is enhance

the data transmit in optical communication systems by applying CDMA

technique based error detection and correction code. This work includes the

study and analysis the difference important variables for optical CDMA

system, this thesis is focused on increasing the system performance by

selecting the optimum values for different variables to reduce the multiple

access interference problems. Also by applying error detection and

correction code with the selecting of the best polynomial. The detected and

corrected code technique is become more active because the selection of

the optimum values from the variables network which helped to decrease

the interference sources and noise to lower value. The selection of optimum

values help on reducing the number of the added correct bits in the transmit

code word consequence enhancement the system performance because

exploited the channel to transmit the information.

The results show enhancement in system performance when selecting

optimum value of received power (2µ Watt), where the enhancement ratios

equal to (23%). Also this research proved the use of error correction

technique became very active with the optimum values of received power

(2 µWatt), so the improvement ratios with applying ECC equal to (22%).

II

Chapter one Introduction and Literature survey

Chapter One

Introduction 1.1 Optical communication system

The optical fiber is a very attractive communication medium since

it offers a large bandwidth and low attenuation and can therefore

facilitate demanding services such as high-quality video transmission[1].

As the reach of optical fiber is being extended to the access network it

is economically attractive to share fibers between different users

without adding active components in the network. The most common

multiple access method for such passive optical networks is time

division multiple access (TDMA), but lately there has been an increased

interest in using wavelength division multiple access (WDMA) and

optical code division multiple access (OCDMA)[2].

The concept of code multiplexing spans the electromagnetic

communication spectrum, but differing device capabilities and constraints

unique to each spectral domain influence the details of implementation

[3].The roots of CDMA are found in Spread Spectrum communication

techniques [4]. OCDMA offers an interesting alternative for LANs because

neither time management nor frequency management of all nodes is

necessary. OCDMA can operate asynchronously, without centralized

control, and does not suffer from packet collisions (in case of well designed

codes with reduced multi-user interference); therefore, very low latencies

can be achieved. Dedicated time or wavelength slots do not have to be

allocated, so statistical multiplexing gains can be high [5].

Also Optical Code Division Multiple-Access: Enabling Future LANs

and is an excellent candidate for future LANs. It may provide concurrent

access by a large number of users without access delay [4].

1

Chapter one Introduction and Literature survey 1.2 Literature survey

In 1995 G.Ramakrishnaiah S.Kar demonstrate an approach for the

performance evaluation of CDMA fiber optic LANs Time domain models

for the optical sources encoders (electrical and optical), single mode fibers,

decoders and APD detectors have been discussed. These models have been

used to evaluate the end to end performance of CDMA LANs and the

simulation results are in good agreement with experimental results, the

effect of laser chirping, fiber dispersion and APD noise on fiber optic

code division multiple access net works is investigated[6].

J.-G Zhang and A. B. Sharma presented MPR codes for OCDMA

applications in (2000). The use of MPR codes can remove the code-size-

dependent power loss of OCDMA encoder and decoder. As a result, the

proposed design method can be used to efficiently reduce both system cost

and band width expansion in an OCDMA network. More over, the code-

design procedure described in this paper can be used to construct variable-

length or/and non constant-weight MPR-codes. This is because optical fiber

networks need to support broadband services and multimedia applications,

with varieties of performance and traffic requirements [7].

K. Kamakura presented in his dissertation optical code division

multiple access (CDMA) techniques the enhancement of capacity and

reliability of fiber optic communication systems in (2002). The main issue

considered in his dissertation is to solve multi-access interference (MAI)

problems for the realization of high-speed and high-quality fiber optic

communications with OCDMA techniques. For this purpose, this

dissertation proposes to three types of optical CDMA techniques: time-

2


D. P. Wei, and R. Slavik (2003) show the results of the BER

measurements with the SFS and the MFL show that the power penalty

associated with the beat noise is approximately 1 dB in the present FFH-

OCDMA system. Furthermore, the measurement of the beat noise power

spectral density, with an incoherent source and an encoder/decoder pair,

was performed and compared to numerical calculations. The present

system imposes several limitations on the BER measurement. First, a

frequency-hopping time-spreading pattern with 5 frequencies, and 100 GHz

adjacent frequency spacing, was chosen according to the frequency spacing

of the MFL source [9].

S. A. Aljunid, and M. K. Abdullah presented a new variation of optical

code structure for amplitude-spectral encoding OCDMA system has been

successfully developed in (2004). The MDW code has been proven to

provide a better performance compared to the systems encoded with

Hadamard and MFH codes. This code possess such a numerous advantages

including the efficient and easy code construction, simple encoder/decoder

design, existence for every natural number n, ideal cross-correlation , and

high SNR[10].

In (2005) F. Xue, Z. Ding, and S. J. Yoo presented a performance

analysis approach for arbitrary OCDMA schemes and discussed its

applications for performance evaluation. Also it is demonstrated the

flexibility of this approach by analyzing a representative OCDMA system.

The proposed approaches have proven effective in characterizing the

network dynamics and in examining the effects of packet corruption and

channel collision on network performance. By adopting the BER functions

3

Chapter one Introduction and Literature survey to account for the physical layer performance, this approach enables a

generic platform to conduct packet-level performance comparisons among

various OCDMA solutions [11].

BER of an optical CDMA system using OOC codes with auto and cross

correlation bounded by 2 in the worst case is obtained for active and

passive correlation receivers with and without hard limiters using

Saddle Point approximation presented by K. Jamshidi , M. Abtahi in

(2005).

A comparison between different codes for the equal transmitted

power shows that the performance of the system using OOC’s with

correlation bounded by 2 is better than that of the system using codes

with correlation bounded by 1 in high power regime. For the equal

received power, performance of the system using OOC’s with correlation

bounded by 2 is always better than that of the system using codes

with correlation bounded by 1, especially for passive correlation with

or without hard limiter receiver structures[12].

In 2006 N. Tarhuni and M. Elmusrati applied centralized power

control to evaluate the optimum optical power for a multirate OCDMA

network. A network with multiple length temporal prime encoding was

considered. This paper presents that nodes with longer fibers and higher

QoS will use the highest power. Based on large number of network

realizations, the spectral radius of the system was modeled as a truncated

Gaussian random variable and then the feasibility of the solution was

written in terms of the model parameters [13].

4


This work presented Spectral phase encoding OCDMA provide an

efficient use of the bandwidth which was accomplish by J. M. Castro and

D. F. Geraghty in (2006). However it requires bulky elements that make it

impractical since each user has to be able to decode more than one code.

Integrated encoders/decoders using the anti-symmetric grating can

significantly reduce the size of the encoders. The encoders using this type

of grating and the asymmetric y-branches impose the phase patterns of the

code and separate incoming from outgoing signals in the simpler and small

structure. Encoders for all the set of code words can fit in a small chip area

using [demonstrated fabrication capability in silica-on-silicon] [14].

In 2006 V. J. Hernandez, and S. J. B. Yoo demonstrated the first

error-free SPECTS O-CDMA network testbed with (32) simultaneous

users, each operating at 10 Gb/s. Successful employment of time and

polarization multiplexing increase the total demonstrated throughput to

320 Gb/s while utilizing just eight encoders. FEC enables error-free

operation of the testbed with aminimal per-user power penalty and no

apparent noise floor in the BER performance. Without FEC the testbed is

still able to achieve BER < 10-9 for 28 users and BER <10-8 for 32

users The excellent BER performance of the testbed results from

outstanding suppression of MAI for an increasing number of simultaneous

users[15].

The analysis of transmission scheduling algorithms for optical

CDMA media access control is accomplish by P. Kamath, and J. D. Touch

in (2006). The analysis quantified the difference between throughput of

systems with and without transmission scheduling and showed that

transmission scheduling achieved 30% throughput while non scheduled

5

Chapter one Introduction and Literature survey systems had close to zero throughput. Simulations showed that the

throughput of transmission scheduling is independent of codeset length.

Also show that an increase in weight can lead to degradation in the

performance of these algorithms, although the degradation is not as bad as

systems without transmission scheduling. This thesis also showed that

transmission scheduling prevents degradation when used with a realistic

traffic model based on traffic obtained from a real network.Limitations of

this work include the fact that it assumes perfect state estimation and

neglects errors due to synchronization and receiver contention[16].

A. A. Garba and J. Bajcsy in (2006) presented that the use of optical

amplifiers in power-limited OCDMA transmission is necessary to achieve

practically desirable spectral efficiencies and to prevent network congestion

in a local or metropolitan area network. First, this thesis is presented the

spectral efficiency limits when M-ary OCDMA modulation and single user

decoding are utilized with and without the use of optical amplifiers.

Second, presented simulation results for coded OCDMA network

architecture based on a concatenation of turbo and Reed- Solomon codes,

which allows achieving high spectral efficiencies even under practical

system parameters [17].

Study and analyze the different spreading code sequences in a fiber

optic CDMA Local Area Network is accomplished by M. CHANILA

(2006). This thesis designed and simulated an OCDMA Local Area

Network using certain spreading code sequences. The code sequence was

considered for this evaluation is m sequences Gold sequences, prime

sequences and modified prime codes. The performance of these codes and

their probabilities or error versus the number of users are evaluated from

6


7

simulation and plotted. This thesis represented the analyzed, both coherent

OCDMA and incoherent OCDMA [18].

1.3 Aims Of The Work Study and implementation of the simulation model for optical code

division multiple accesses passive optical local area network (LAN)

system.

Selection the optimum values from all variables for Optical CDMA

system.

Applying error detection and correction code technique based on

Foreword Error Correction Code.

Evaluation the performance of optical CDMA system based on error

detection and correction code.

1.4 Outline of thesis The remaining parts of this thesis are structured as follows:

Chapter two: Gives the theoretical background also shows the idea of the

optical code division multiple access (LAN) passive optical network

system and important concepts of error detection and correction code

technique.

Chapter three: Presents the system simulation, and the implementation of

procedures.

Chapter four: Contains the results of the implementation system.

Chapter five: Gives the conclusions and future suggestions.

Chapter two Theoretical Background

8

Chapter 2

Theoretical Background 2.1. Passive optical networks

There has been a fast development in the area of data communications

over the last years. On one hand, there has been a convergence in the

sense that many different services can be carried over the same

network. On the other hand ,many different types of physical networks are

used to carry the same services .Therefore, high capacity network

technologies, which can simultaneously offer many services, are

important to develop [3]. Networks can be separated into different

types, such as wide area networks, metro area networks, access

networks and local area networks. (The focus in this thesis is

mainly on solutions for access networks, but many of the principles

can also be used for local area networks (LAN)). The access network is

an important element for the operators to offer new revenue generating

services. One trend in networking is that optical communication is

being used more widely[19]. Optical fibers have two very attractive

properties: the attenuation is very low, hence large distances can be

covered, and the bandwidth is very large. Therefore, optical

transmission has taken over in the backbone networks during the last

decade and is continuously being deployed closer to the edge of the

networks [20]. In the access network there is an increased interest in

fiber to the home (FTTH), fiber to the building (FTTB), fiber to the

curb (FTTC) and fiber to the cabinet (FTTCab).


9

2.2 Access networks and LANs

Local area networks connect computers, printers and other equipment

within a limited area such as a building. Typically a LAN is used by an

organization within an office and the number of connected computers

is relatively low[21]. Much of the communication is internal to the

network, for example between a PC and a server. Therefore, the

technologies used for LANs can be optimized to provide efficient internal

communication. It is common to use a shared medium to connect the

stations, for example in a ring or a star topology [2, 22].

An access network is used to connect stations to a larger network.

Typically, it is owned by an operator and is used to connect either end-

customers or other network equipment, for example base stations for

wireless networks [21]. Only a small fraction of the traffic is between the

computers on the access network .Therefore, there is no benefit of using a

shared medium in the same way as for a LAN. However, a shared medium

is attractive from an economical point of view, especially since the

distances can be larger than for LANs and the cost of installing separate

cables can be significant [22]. A tree topology is the most common

alternative for a shared medium in an access network. The node that

connects the stations to the larger network always has an important role in

an access network. It handles all the traffic in the network whereas a LAN

does not require any special node to handle all the traffic [20]. 2.3 Optical broadcast and select networks

Today high-capacity LANs often use optical fiber and Ethernet

switches, but it would also be possible to build LANs with passive optical

components [20]. For optical LANs a star topology can be built with a

passive star coupler as the central node. The star coupler splits the

incoming signal to all the outgoing fibers. Since the signal is split,


10

the power on each outgoing fiber is merely a fraction of the incoming

power, which limits the size of the network. The receiving stations

then have to select the signal addressed to them [1]. Several protocols

have been suggested as random access protocols for broadcast-and-select

networks. The protocols range from simple Aloha to reservation

protocols with separate signaling channels for the reservations, for

example using separate wavelengths. In practice, broadcast and select

networks have not been deployed since there has not been sufficient

advantages compared to technologies such as Ethernet[22].

2.4 Optical access networks

Passive optical networks (PON) are probably the most attractive

alternative for optical access networks. A PON does not contain any active

components, i.e .components that require power, between the sender and

the receiver [21]. Typically it is built using passive splitters to distribute the

signal to several users, without using excessive amounts of fiber [20].

Therefore, the cost of installation and maintenance is low. The

central node in a PON, which is the gateway to the main network, is

called optical line terminal (OLT). The terminals at the user premises are

called optical network units (ONU). Figure (2.1) shows the topology of a

typical PON [20, 21].


11

ONU

Figure (2.1) The topology of a PON with an optical line terminal (OLT), a passive splitter and several optical networking units (ONU)

2.5 PON standards

There are two main categories of PONs, ATM PONs (APON)

and Ethernet PONs (EPON) [41]. The difference is the higher layer

protocols that are used .APONs usually follow the full service access

network (FSAN) standard of the ITU-T where asynchronous transfer mode

(ATM) is used for the higher layer protocols. ATM is a virtual circuit

switched technique where 53-byte cells are used as transmission units.

Support for several types of services with different quality

requirements is included. The typical capacity of the FSAN standard is

either 155 Mb/s or 622 Mb/s [44]. Several vendors have FSAN compliant

PONs ,and PON line cards are available for some ATM switches.EPONs

are currently being standardized by the IEEE [46]. Since Ethernet is

also being used in metro area networks (MAN), EPON is an

economical way of using Ethernet in the access network to connect

MANs and LANs. PON is a new physical layer for Ethernet with a shared

medium. Instead a centralized access control will be used, where the

Up link OLT

Down Link

10 Km


12

OLT will send grants to the ONUs in order to coordinate the

transmissions[41, 42].

Hence, PONs can be part of different network types, but the

functionality will be similar regardless of the higher layers. The common

characteristics include the duplexing which is usually handled by

wavelength division multiplexing .By using a wavelength of 1.55 µm

for the downstream and 1.3 µm for the upstream they can both be sent

over the same fiber . The ITU standard supports up to 32 ONUs and

distances of up to 10 km [46]. Due to different distances between the

OLT and the different ONUs the power can vary as much as 15 dB between

transmissions from the different ONUs. Therefore, the receivers need a

dynamic range of at least 15 dB. The varying distances also need to be

taken into account by the multiple access protocol; therefore a procedure is

used to estimate the delay between the OLT and each ONU [46, 47]. 2.6 Multiplexing methods for PONs

Wireless telecommunications has dramatically increased in popularity,

resulting in the need for technologies that allow multiple users to share

the same frequency. These are called "multiple access systems." The three

types of multiple access system are:

• Frequency Division Multiple Access (FDMA)

• Time Division Multiple Access (TDMA)

• Code Division Multiple Access (CDMA)

These multiple access systems have very different approaches to the

Bandwidth problem, figure (2-2) shows the difference types of these

accesses:


13

Fig 2.2 Schematic illustration of bandwidth allocation in TDM, WDM and CDMA optical networks.

2.6.1 Time division multiplexing

Most PONs rely on time division multiplexing (TDM) for the

sharing of capacity between different users. The early ITU standards

used static TDM where each user received the same capacity, but

new standards are being developed where the capacity can be

dynamically assigned to different users according to their changing

requirements [47]. The dynamic bandwidth allocation (DBA) scheme

firstly requires signaling between ONUs and the OLT in order to

inform the OLT of the capacity needs for each ONU. Secondly the OLT

needs to inform each ONU about the allocation of capacity [20].

2.6.2 Wavelength division multiplexing

A further improvement of PONs is to add more wavelengths using

wavelength division multiplexing (WDM). These can both be used for

separate services or as a method to offer separate wavelengths to different

ONUs [34]. In cases where broadcast services are offered WDM will

only be needed in the downstream whereas it will also be required for

the upstream if it is used to separate users. If a separate wavelength is

used to offer another service, such as TV broadcasting, the change in the

network can be limited to a new sender at the OLT and receiver at the

ONUs [22]. To use separate WDM channels for different ONUs the

power splitter should preferably be changed to a wavelength router or


14

demultiplexer, which separates the wavelengths and forwards them to

the receivers [34]. By splitting the wavelengths less power is lost

compared to simple power splitting. The wavelength router can be

implemented by passive components, using an arrayed wavelength

grating ( AWG) or fiber gratings . The limited output power of LEDs is a

major problem, which may have to be solved by optical amplification in

order to build large network [22]. Compared to single wavelength PONs,

the WDM PONs need to take into account the interference from other

wavelengths when the power budget is calculated [11]. Since the received

power from each ONU depends on the attenuation of the particular

channel the interference can be a significant problem. One possible

solution would be to equalize the power from the different ONUs.

Since the attenuation is approximately constant over time the power could

be measured in a similar fashion as the ranging procedure and the output

power from each ONU could be adjusted accordingly [41].

2.6.3 Code division multiplexing

Another possible multiplexing method for PONs is code division

multiplexing (CDM). CDM is a spread spectrum technique, which

increases the physical bandwidth of the channel by applying a spreading

code. The spreading can be made either by direct sequencing where the

data bits are multiplied by a code sequence and thereby divided into

shorter pulses known as chips, or by frequency hopping where the

communication is spread between several frequency channels [24].

Several users can share the same channel by using different codes for their

communication as shown in figure (2-2). The codes should have low

correlation with each other, thereby separating the different users with

low interference between them . However, when shot noise and thermal

noise is taken into consideration CDMA is much more sensitive to the


15

signal to noise ratio than WDMA. Therefore, it is not clear that the

comparison will hold when also other noise types are taken into account

[2].

CDMA is frequently used in radio networks, where the wider

spectrum is advantageous because of the properties of the channel. Since

a radio channel typically suffers from fading at different frequencies

the performance can be improved substantially by the frequency

diversity that results from using CDMA[53]. An optical fiber does not

have the same problem with fading .Conversely, a wide spectrum leads

to problems with dispersion. Therefore, the gain of using spread

spectrum methods is less applicable than for radio networks [28, 29].

The main advantage of using CDMA in an optical network is that [50]:

- It allows a flexible multiple access method for asynchronous traffic with a

graceful degradation at high interference. Furthermore,

- Variable requirement son error-rates and bit-rates can be satisfied by

suitable choices of codes.

- Random and simultaneous access protocol. No need for the strict timing

synchronization

- No need for the strict wavelength control

- No need for the centralized network control, Simple protocols (e.g. tell-

and-go protocol),

- Self-routing by code sequence. Effective utilization of bandwidth

- High tolerance to noises. Inherent security, Low-cost devices

2.7 Characteristics of optical systems

This section gives a brief background on the properties of optical

networks and the components they are built from. The purpose is to

describe where the specific problems of optical CDMA access networks lie.


16

2.7.1 Components of optical networks 2.7.1.1 Light sources

There are two main categories of light sources that differ

significantly in their characteristics: thermal light sources such as light

emitting diodes (LED) and non-thermal light sources such as lasers[2].

In thermal sources, photons of different energy are emitted

spontaneously, therefore the light contains a wide spectrum of

frequencies. Since the spontaneous emissions of photons depends on the

temperature, the efficiency and the spectrum of a thermal source is

temperature dependent. The spectral range of the light can be

calculated by considering the physical photon generation process, which

gives the expression[2, 27, 51].

hTKF B3.3

=Δ ………. (2-1)

Where k is Boltzmann’s constant, h is Planck’s constant and T is the

absolute temperature. The bandwidth is usually measured as the full

width at half maximum (FWHM), which is the bandwidth where the

power is less than 3 dB lower than the maximum power. The FWHM can

be in the order of 10 THz at room temperature for a LED .

Lasers are based on stimulated emission of light of a certain

wavelength. The spectrum of the emitted light is very narrow, but

multiple peaks outside the main one can exist. The linewidth is the

bandwidth of one such peak whereas the total bandwidth containing all the

peaks is known as the spectral width. The line width can be approximately

expressed as [52].


17

Ρ+

=Δπβ

4)1( 2Rs

f …………………… (2-2)

where β is the linewidth enhancement factor, Rs is the rate of

spontaneous emission and P is the average power. The linewidth can be in

the order of 1-10 MHz for a typical distributed feedback semiconductor

laser.

2.7.1.2 Optical amplifiers

To improve the reach of optical transmission systems optical

amplifiers have been frequently deployed during the last decade. Before

optical amplifiers were invented the light signal had to be electrically

regenerated at regular intervals [2, 3] with optical amplification, the

number of regenerators can be reduced, and the distance between

regenerators will not be limited by attenuation but by nonlinearities

and dispersion. There are two different types of optical amplifiers,

semiconductor optical amplifiers (SOA) and erbium doped fiber

amplifiers (EDFA). Since EDFAs have more attractive properties than

SOAs ,only EDFAs will be described here. An EDFA is a piece of erbium-

doped fiber, with a pump laser that sends light into the fiber .The light will

excite electrons in the fiber to a higher energy state and when the signal

passes through the fiber it will stimulate electrons to switch to the lower

energy state and thereby release photons that amplify the light signal. Some

of the electrons will also change state without being stimulated by the light

signal ,which causes spontaneous emission of photons [2]. The

spontaneously emitted light will also be amplified, therefore it is

known as amplified spontaneous emission (ASE). An EDFA amplifies

the signal over a wide spectral range,which is an advantage for WDM

systems, where it can simultaneously amplify the signal of all wavelengths .


18

An EDFA can also be used as a broadband light source if no external

signal is added; rather the ASE is the only light produced [3].

2.7.2 Additional components of OCDMA networks

Optical CDMA can be implemented in several different ways. The

most promising implementations are the ones that use optical components

for parts of the processing, even though it can also be performed

electronically [51].

The spreading of bits into chips at the sender and the

autocorrelation at the receiver can be implemented by the same type

of device. One possible implementation of a temporal OCDMA coder

is to use an optical splitter to split the optical signal into the

different chips. Each chip is then sent over a delay line of different lengths,

which gives the temporal encoding of the signal .The autocorrelation

receiver is implemented as a matched filter, essentially a time-reversed

version of the encoder [2] . One type of component that could improve

the performance in OCDMA networks is an optical hard limiter. The

functionality would be to limit the optical power at a certain level.

The implementation could be based on alternating materials with

different nonlinearities [31].

2.7.3 Limitations for optical networks

2.7.3.1 Power budget

The attenuation of optical fibers is very low compared to other

transmission media such as air or copper; this allows optical

transmission to cover large distances in a cost effective way. Figure (2.3)

show the relationship between the wave length in micrometer versus

attenuation in dB [2, 25].


19

Figure (2.3) Attenuation Profile of Single-mode Fiber [25]

For a PON a large portion of the power losses occur in optical splitters

since only a fraction of the original signal reaches each receiver [3, 25].

Therefore, the power budget is an important limitation on the number

of users and fiber length in a PON. For a competitive implementation the

light sources and receivers cannot be allowed to cost too much .A possible

remedy is to add an optical amplifier after the encoding. The cost of the

system will be increased, but it would still not require any active

components to be placed away from the ONU or OLT [41]. 2.7.3.2 Dispersion and nonlinearities

The signal propagation speed in optical fibers depends on the

wavelength of the light; therefore the light pulses will be dispersed.

Dispersion can potentially be a significant problem for OCDMA

because of the large bandwidth of the signal. Fortunately the

propagation distance is not long in an access network, so intersymbol

interference is usually not a problem [2, 25].


20

Nonlinear effects in fibers can also be a problem, but mainly for long-

distance communication. The nonlinearities are dependent on the intensity

of the signals and are not significant at low power [41]. The effects

include stimulated Raman scattering, stimulated Brillouin scattering,

four wave mixing, and self- and cross-phase modulation [2]. For a

passive optical access network these effects will be insignificant because of

the limited distances . 2.7.3.3 Noise

Several different types of noise are present in optical

transmission systems .Like in other communication systems there is a

thermal noise which can be included by writing the current in the form

……………. (2-3) )()()( ' titiItI Ts ++=

Where is a current fluctuation induced by thermal noise. )(tiT

Mathematically, is modeled as a stationary Gaussian random

process. A simple approach accounts for the thermal noise of amplifiers in

terms of a noise figure Fn, as:

)(tiT

………………… (2-4) fFnR

Tk

L

BT Δ=

42σ

where T is the absolute temperature, kB is Boltzmann’s constant, Δƒ

is the electrical bandwidth and RL is the receiver resistance. In an optical

transmission system with a PIN detector the thermal noise is normally the

main limitation .A simple approach accounts for the thermal noise of

amplifiers in terms of a noise figure Fn, Physically, Fn represents the factor

by which thermal noise is enhanced by electrical amplifiers used within the

receiver [1, 2].


21

However, if an APD detector is used, the shot noise usually is a more

severe problem than the thermal noise .Shot noise arises because of the

particle properties of light. The receiver can be considered as a device

that counts the photons of the received signal. The photon arrival

process can be seen as a Poisson process with a rate that is

proportional to the light intensity. The variance of the arrival process is

the power of the shot noise and can be expressed as [2, 3]

esh qIB22 =σ ……………….. (2-5)

Where q is the electron charge and I is the light intensity. To be more

precise the shot noise also has a component proportional to the dark

current that is present at the photodetector even when no light is

incident on it [2]. Usually the noise contribution from the dark current is

small in comparison to the intensity dependent shot noise. Hence, the

power of the shot noise is approximately proportional to the square root of

the power of the output current. Thus it will increase when several signals

are superposed in an optical CDMA system[44]. However, the beat

noise, which arises because of the wave properties of the light,

increases proportional to the square of the light intensity and is therefore a

more severe problem .In optically amplified systems another type of noise

appears, namely amplified spontaneous emission (ASE). The ASE is a

form of beat noise that occurs because of the spontaneous photon emissions

over large bandwidths in optical amplifiers. The ASE noise can be divided

into the signal-noise beating and the noise-noise beating. If the signal is

generated by a spontaneous emission light source, the signal-noise

beating will behave the same way as the noise-noise beating. Therefore,

the properties of ASE noise are similar to incoherent beat noise [32].


22

2.7.4 Optical detectors

Optical detectors are based on photodiodes that can be used in

different configurations, the most common is the PIN photodiode. The

output current is proportional to the input optical power also known as the

light intensity. The efficiency can be measured either by the

responsivity or by the quantum efficiency. The responsivity is the

output current divided by the input power whereas the quantum

efficiency is defined as the number of output electrons divided by the

number of input photons [2].

2.7.4.1 Receivers with a p-i-n Photodiode

The performance of an optical receiver depends on the signal-to-noise

ratio (SNR). The SNR of an electrical signal is defined as

2

2

...

σI

powernoiespowersignalaverageSNR == ……….. (2-6)

For a perfect optical signal, total current noise can be obtained by

adding the contributions of shot and thermal noises. Since and

in Eq (2-3) are independent random processes with approximately

Gaussian statistics, the total variance of current fluctuations,

, can be obtained by simply adding individual variances[2,

3,]. The result is

)(tis )(TiT

Ts iiIII +=−=Δ '

( ) fFRTKfIIqI nLBdTs Δ+Δ+=+=Δ= )/4()(2 '2222 σσσ …… (2-7)

In the case of a p-i-n photodiode, useing (2-6) In Eq. (2-7) together with

. The SNR is related to the incident optical power as ind PRI =


23

fFnRTKfIPinRqPRSNR

LBdd

ind

Δ+Δ+=

)/()(2

22

……………….(2-8)

where od hvqR /η= is the responsivity of the p-i-n photodiode for

photons of energy and η is its quantum efficiency [2, 3, 31] . ohv

In most cases of practical interest, thermal noise dominates over shot noise

( >> ). Neglecting the shot-noise term in Eq. (2-8), the SNR becomes 2Tσ

2sσ

fTFkPRRSNRnB

indL

Δ=

4

22

……………….. (2-9)

The SNR varies as in the thermal-noise limit and can be

improved considerably by increasing the optical power reaching the

receiver. It can also be improved by increasing the load resistance [2].

2inΡ

To minimize the effect of thermal noise, the output current can

be amplified within the detector by a process called avalanche

multiplication. A detector with this property is called an avalanche

photodiode (APD). A large bias voltage is used to give the primary

electrons from the photodetection such high energy that they can

generate secondary electrons, thereby starting an avalanche effect. Both

the output current and the shot noise are amplified in the process, but the

shot noise power is proportional to the square root of the output

signal power. A drawback of APDs is that the bandwidth is lower than for a

PIN since the avalanche process takes time [2, 33].


24

2.7.5 Receiver Sensitivity

Receiver sensitivity is an important parameter for any lightwave

system. Among a group of optical receivers, a receiver is said to be more

sensitive if it achieves the same performance with less optical power

incident on it. The performance criterion for digital receivers is governed

by the BER, defined as the probability of incorrect identification of a bit by

the decision circuit of the receiver. For example, a BER of 2 x 10-9

corresponds to 2 errors per billion bits, on average. Modern high-speed

lightwave system transmits data at a bit rate of 10 Gb/s or more per

channel. Such systems often require the BER to be below l0-12 or even the

receiver sensitivity is defined as the minimum average power (Prec)

required by the receiver to operate reliably below a specific BER [2].

2.7.6 Bit-Error Rate The sampled value I fluctuates from bit to bit around an average

value of or depending on whether the bit corresponds to 1 or 0 in

the bit stream. The decision circuit compares the sampled value with a

threshold value and calls it bit 1 if I > or bit 0 if I < . An

error occurs if I < for bit 1 because of noise. An error also occurs if

I > for bit 0. Both sources of errors can be included by defining the

error probability as [2, 51, 52]

1I 0I

dI dI dI

dI

dI

)0/1()0()1/0()1( ppppBER += …………….. (2-10)

where p(1) and p(0) are the probabilities of receiving bits 1 and 0,

respectively, P(0/1) is the probability of deciding 0 when 1 is

transmitted, and P(1/0) is the probability of deciding 1 when 0 is


25

transmitted. Since 1 and 0 bits are equally likely to occur in any realistic

bit stream, p (1) = p (0) = 1/2, and the BER becomes

[ ])0/1()1/0(21 ppBER +=

i

………………….. (2-11)

Figure 2.4(b) shows how P(0/1) and P(l/0) depend on the

probability density function p(1) of the sampled value I. The functional

form of p(1) depends on the statistics of noise sources responsible for

current fluctuations. Thermal noise in Eq. (2-3) is well described by

Gaussian statistics with zero mean and variance . The statistics of

shot-noise contribution in Eq. (2-3) is also approximately Gaussian for

p-i-n receivers. A common approximation treats as a Gaussian random

variable for both p-i-n. Since the sum of two Gaussian random variables

is also a Gaussian random variable, the sampled value I follows a

Gaussian distribution with variance . It is important to note

that both the average and the variance are different for 1 and 0 bits since 1

in Eq. (2-3) equals or depending on the bit received. If and

are the corresponding variances, the conditional error probabilities are

given by [2, 3, 31].

Ti

2 =

2Tσ

s

si

22Ts σσσ +

1I 0I2

1σ2

0σ

⎟⎟⎠

⎞⎜⎜⎝

⎛ −

21

1

σD

II=⎟

⎟⎠

⎞⎜⎜⎝

⎛ −−= ∫

∞− 21

2)(exp

21)1/0( 2

1

21

1 σπσ

D

erfcdIIIpI

……….. (2-12)

⎟⎟⎠

⎞−

20σo

II D

⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛ −−= ∫

∞

21

2)(

exp2

1)0/1( 20

20

0 σπσD

erfcdIII

pI

……… (2-13)

where erfc(x) stands for the complementary error function defined as [2]


26

( )dxyxerfcx∫∞

−= 2exp2)(π ……………. (2-14)

(a) (b)

Figure 2.4: (a) Fluctuating signal generated at the receiver. (b) Gaussian probability

densities of 1 and 0 bits. The dashed region shows the probability of incorrect

identification.

By substituting Eqs. (2-12) and (2-13) in Eq. (2-11), the BER is given by

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛ −=

2241

0

0

1

1

σσII

erfcIIerfcBER DD …………. (2-15)

Equation (2-15) shows that the BER depends on the decision

threshold . Assuming that = 0 andDI 0I 01 σσ ≈ . In practice, is

optimized to minimize the BER. It is possible easy to find the optimum

value of by taking the derivative of Eq. (2-15) with respect to and

DI

DIDI


27

setting it to zero. The BER becomes minimum when is chosen such

that DI

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=

−

0

12

1

21

20

20 ln

22 σσ

σσDD IIII

……………. (2-16)

The last term in this equation is negligible in most cases of practical

interest, and ID is approximately obtained from

( ) ( ) QIIII DD ≡−=− 1100 // σσ ……….. (2-17)

An explicit expression for is DI

10

0110

σσσσ

++

=II

I D …………………………. (2-18)

When 10 σσ = , ( ) 2/01 III D += , which corresponds to setting the decision

threshold in the middle. This is the situation for most p-i-n receivers whose

noise is dominated by thermal noise ( Tσ >> sσ ,) and is independent

of the average current [2, 3].

The BER with the optimum setting of the decision threshold is

obtained by using Eqs. (2-15) and (2-17) and depends only on the Q factor

as.

( )π2

2/exp22

1 2

QQQerfcBER −

≈⎟⎠

⎞⎜⎝

⎛= ……………. (2-19)

The Q factor is obtained from Eqs. (2-17) and (2-18) and is given by

01

01

σσ +−

=II

Q ………………… (2-20)

The approximate form of BER in Eq. (2-19) is obtained by using

the asymptotic expansion [18] of erfc(Q/ 2 ) and is reasonably accurate

for Q > 3. The BER improves as Q increases and becomes lower than 10-9


28

for Q > 6. The Q factor plays an important role as it is a kind of SNR that

determines the BER uniquely [2, 51, 52].

It is possible to relate Q to the electrical SNR. The relation is

particularly simple when the receiver noise is dominated by thermal noise

(as is the case for p-i-n photodiodes) and is thus the same for all bits [2].

Using Tσσσ =≈ 01 with = 0, yields . The requirement Q =

6 translates into an SNR of 144 or 2 1.6 dB. Since SNR scales as Q2, it is

common to define the Q2 factor on the decibel scale as

0I 24QSNR =

QdBQ 102 log20)( = …….…….. (2-21)

2.7.7 Minimum Average Power Equation (2-19) can be used to calculate the minimum average power

that a receiver needs to operate reliably with a BER below a specified

value. For this purpose the Q factor should be related to the incident

optical power. For simplicity, consider the case in which 0 bits carry no

optical power so that = 0, and hence =0. The power required for 1

bit is related to as [2]

0P 0I 1P

1I

…………….. (2-22) recdd PRPRI 211 ==

Where is the average received power defined asrecP ( 2/21 ppPrec )+= .

The RMS noise currents 1σ and 0σ should include the contributions of

both shot and thermal noises and can be written as

( ) TTs and σσσσσ =+= 0

2/1221

Consider first the case of a p-i-n receiver. Since thermal noise or

generally dominates for such a receiver, Prec is given by the simple

expression


29

( ) dTpinrec RQP /σ≈ …………….. (2-23)

From Eq. (2.4), depends not only on receiver parameters such as

and but also on the bit rate through the receiver bandwidth

2Tσ

LR nF fΔ

(typically fΔ = B/2). Thus, increases as ecPr B in the thermal-noise

limit. As an example, consider a 1.55-µm p-i-n receiver with . If

using

WARd /1=

Tσ = 100 nA as a typical value and Q = 6 corresponding to a BER of

10-9, the receiver sensitivity is given by Prec = 0.6 pW or -32.2 dBm [2, 3].

2.8 Models of OCDMA channels

odel of the distribution of both noise and

inter

mber of active users and the

prop

of length L and weight w the maximum number of users is given by:

.8.1 Temporal codes 2

In this section a m

ference for temporally coded channels is describe. The Temporal

OCDMA signal can be generated by the splitting and combining of very

short optical pulses in a parallel optical delay line encoder [51]. A high-

peak optical pulse is encoded into a low intensity pulse train using a

parallel optical delay line network at the transmitter. The decoding is

performed by intensity correlation at the receiver using a matched network

of optical delay lines. Because of the positive nature of the detection

scheme, the interference is quite high [47].

The interference depends on the nu

erties of the code. The optical orthogonal codes (OOC) have attractive

properties in terms of auto correlation and cross correlation. The auto

correlation peak is equal to the weight of the code, there are no other side

lobe peaks higher than one, and the cross correlation of any two codes is

never higher than one [39]. The price for these attractive properties is that

there are few possible code words, and hence few possible users. For codes


30

)1( −wwLN …………………… (2-24) ≤

There are other code of these

odes is that they have worse correlation properties. The probability that

the c

s that allow more users. The drawback

c

hips from a different user collide with the chips of the user of interest

depends on the spreading code. For OOC the multiple access interference

from n-1 other users can be calculated as [39, 40]

iiNN n ww ⎞⎛⎞⎛⎞⎛

−−− − 2121 1

i iin LL

I ⎟⎟⎠⎝

⎟⎟⎠

⎜⎜⎝−⎟

⎠⎜⎝

==∑ 22

10

…………….. (2-25)

For simplicity it has been assumed that the chips from different users

rrive synchronously. This gives an overestimation of the error probability.

but t

n to Error Correcting Codes

⎜⎜

a

In all simulations we have assumed that there is also signal

independent additive white Gaussian noise, like for example thermal noise,

hat the power of that noise is so small that the errors are mainly caused

by interference.

2.9 Introductio

ade in the Shannon channel coding theorem is

vert a noisy channel

(unre

mission is done by using a coding technique of a random nature.

In th

One of the predictions m

that a rather sophisticated coding technique can con

liable transmission) into an error-free channel (reliable transmission

[34, 35].

Demonstration of the theorem about the possibility of having error-

free trans

is technique, message words are arranged as blocks of k bits, which are

randomly assigned codewords of n bits, n > k, in an assignment that is

basically objective function characterized by the addition of redundancy.


31

This objective assignment allows us to uniquely decode each

message. This coding technique is essentially a block coding method [34].

are b

n Systems

ce

tion as well as data storage systems. In optical communication

syste

There are basically two mechanisms for adding redundancy, in

relation to error-control coding techniques. These two basic mechanisms

lock coding and convolutional coding[34, 35].The encoder for block

codes takes a message block of k information symbols represented by a k-

tuple u=(u1 ,u2 , ,uk ) and transforms each message u independently into an

n-tuple v=(v1 ,v2 , ,vn ) of discrete symbols called a code word, where

(n>k). There are a total of qk different possible messages and accordingly

the encoder generates qk possible code words. This set of qk code words of

length n is called a C (n, k) block code. The encoder for convolutional

codes also accepts k-tuple of information symbols u and generates an n-

tuple code word v; however the generated code word v at the time of

encoding depends not only on the current k symbol message, but also on m

previous message blocks. The fundamental difference between block codes

and convolutional codes is that in block coding a finite length of output

code word is generated for all input message words of finite length whereas

input and output symbol sequences are infinite in Another important aspect

is the introduction of memory element in convolutional codes. [35].

2.9.1 Error Correcting Codes in Optical Communicatio

FEC is widely used in wired and mobile communication, deep spa

ommunicac

ms that operate at very high data rate, the challenge is to find low

overhead codes that are capable of correcting random errors due to noise

and burst errors due to dispersion and inter-channel cross talk with special

emphasis on complexity and cost. It is difficult to implement convolutional

codec that operates at high code rates required for fiber-optic systems [2].


32

Algebraic block codes, such as Bose-Chaudhuri-Hocqueaghem (BCH)

and Reed-Solomon (RS) codes are capable of correcting multiple bit-errors

with the low overhead constraint. As mentioned earlier the introduced

redundancy of (n-k) symbols increases the bandwidth requirement. If T is

the time duration required to transmit k symbols without coding, then T/k is

the time required to transmit one symbol. After encoding the k symbols

into a code word of n symbols, it can be transmit n symbols in time

duration T and hence the symbol period is T/n, which is less than T/k.

Thus, the width of each symbol after encoding is reduced by a factor k/n

and the bandwidth required to transmit them is increased by a factor n/k,

which is called the Bandwidth expansion ratio. The ratio k/n is called the

code rate Rc. In case of fiber-optic communication systems operating at

very high data rate (Rc >0.8), while selecting an error correcting code one

should take into account the practical limitation imposed by the hardware

to make it feasible to introduce an overhead of (n-k) symbols. Thus, low

overhead constraint becomes an important parameter while selecting FEC

for optical communication application.

2.9.2 Forward Error Correction

Communication systems that use the FEC approach are not able to

of coded information. Due to this,

all t

request a repetition of the transmission

he capability of the code is used for error correction. The source

information generates a binary signal representing equally likely symbols at

a rate rb [34]. The encoder takes a group of k message bits, and adds to it n

- k parity check bits. This is the encoding procedure for a linear block code

Cb(n, k) whose code rate is Rc = k/n, with Rc < 1. Figure 2.5 shows a block

diagram of an FEC communication system. The transmission rate r over

the channel has to be higher than the source information rate rb [34]:


33

c

bb R

rr

knr =⎟⎠⎞

⎜⎝⎛= . …………… (2-26)

The code used in the FEC system is characterized by having a

minimum distance dmin =2t + 1. T evaluated of a

comm

2.9.3 Advantages o

he performance is

unication system perturbed by additive white Gaussian noise

(AWGN) in the channel, leading to an error probability p << 1 [34, 35].

f Forward Error Correction

The span of an optical link is determined by the optical power budget

e used which add

to th

implementation reduces the transmitted optical power

ced

t.

R for a specified power budget

[1], to create links with large spans, EDFA or repeaters ar

e noise floor of the system. The span can be increased without the use

of EDFA such that using high quality, high cost optical components,

increases the transmitted power. This increases the overall system cost.

With the use of FEC, following benefits can be achieved for a desired link

span [34]

1) Significant gain in the overall optical power budget is achieved.

2) FEC

requirement, thus the intensity dependent impairments are redu

automatically.

3) Relaxation on the high-end specification of the optical components

reduces the cos

4) Correction of burst errors introduced by inter-channel cross talk in

WDM systems. O

Channel

+ ReceiveEncode Transmit

r=rb/Rc Rc=k/n r=rb Gn(f)=No/2

Decod

Pe=p

er

(2.5) B gram o an FECFigure lock dia f system [34]


34

5) The power gain margin can be used to increase the span of the

optical link, which accounts for less number of repeaters and

s the SNR, which pays in terms of lower BER.

amplifiers.

6) Use of few repeaters and amplifiers reduces the overall noise floor

and improve

7) In systems implementing ARQ, retransmission results in wastage of

bandwidth, which can be avoided by implementing FEC.

2.10 Linear Block Codes

Message information to be encoded is grouped into a k-bit block

onstituting a generic message m = (m0, m1,..., mk-1) that is one of 2k

poss

c

ible messages. The encoder takes this message and generates a

codeword or code vector c = (c0, c1 ,..., cn-1) of n components, where

normally n > k; that is, redundancy is added. This procedure is basically a

bijective assignment between the 2k vectors of the message vector space

and 2k of the 2n possible vectors of the encoded vector space. When k and n

are small numbers, this assignment can be done by means of a table, but

when these numbers are large, there is a need to find a generating

mechanism for the encoding process. Given this need, linearity of the

operations in this mechanism greatly simplifies the encoding procedure [34,

35, 38].

Definition : A block code of length n and 2k message words is said to be a

linear block k code Cb(n, k) if the 2k codewords form a vector subspace, of

e of the 2n vectors of n bits. This is a

dimension k, of the vector space Vn of all the vectors of length n with

components in the field GF(2) .

Encoding basically means to take the 2k binary message words of k bits

each, and assign to n them som

bijective function. Since usually k < n, there are more vectors of n bits than

those of k bits, and so the selection of the vectors of n bits has to be done


35

using the lowest level of redundancy while maximizing the distance among

the codewords. The set of 2k codewords constitute a vector subspace of the

set of words of n bits. As a consequence of its definition, a linear block

code is characterized by the fact that the sum of any of two codewords is

also a codeword[35].

2.10.1 Block Codes in Systematic Form

In Table 2.1 it can be seen that the last four bits of each codeword

essage appears as it is,

insid

able 2.1 Codewords of a linear block code C

are the same as the message bits; that is, the m

e the codeword. In this case, the first three bits are the so-called

parity check or redundancy bits. This particular form of the codeword

is called systematic form. In this form, the codewords consist of the (n

-k) parity check bits followed by the k bits of the message [34]. The

structure of a codeword in systematic form is shown in Figure (2.6)

T b(7, 4)

essage Codewords M

0000 0000000

0001 1010001

0010 1110010

0011 0100011

0100 0110100

0101 1100101

0110 1000110

0111 0010111


36

1000 1101000

1001 0111001

1010 0011010

1011 1001011

1100 1011100

1101 0001101

1110 0101110

1111 1111111

Figure 2.6 Systematic Format of a Codeword of a block code [35].

linear

ystematic block code such that the message part of the code word consists

of th

A linear block code with this structure is referred to as a

s

e unaltered k message symbols and the redundant check symbols are

linear sum of the information symbols. The code word could also have the

systematic format with the k left most symbols as message symbols and n–

k rightmost symbols as check symbols. Throughout the report, the

transmitted code word is in the systematic format as shown in figure (2.6)

unless stated explicitly. A block code of length n and k2 code words is

called a linear C (n, k) code if and only if its 2k code words form a k

dimensional subspace of the vector space of all the n-tuples over the field

GF (2) [34, 35].


37

2.10.1.1 Properties of Block Codes

Definition: The minimum distance of a code is the minimum

ode

a

erence in the required SNR per information bit (Eb/No) for coded and

unco

Hamming distance between any two different code words. Any two distinct

c words of C(n, k) differ in at least dmin locations. The minimum

Hamming distance dmin is a very important parameter when comparing the

theoretical performance of different codes of s me length n and dimension

k.

Definition: The net electrical coding gain (NECG) is defined as the

diff

ded system to achieve a specified bit-error rate when operating over an

ideal AWGN channel. It is expressed in (dB). This is another important

parameter, which is used to compare the performance of different codes

having comparable Rc from power budget point of view [34, 35, 38].

2.10.2 Generator and Parity Check Matrices Each of the 2k code words in C (n, k) can be expressed as a linear

he set of these k

lineak

combination of k linearly independent code words. T

rly independent code words form a basis of order k, which generate

(or span) the 2 code words in C (n, k), which, is a subset (or subspace) of

the vector space of 2n vectors. Since the k linearly independent code words

generate the C (n, k) code, these can be arranged as k rows of a matrix

called the generator matrix G for C (n, k) [7]. Let the k linearly

independent code words be denoted by g1, g2, g3,…., gk. Using the

notations introduced in section 2.9, a k-tuple message u is encoded in an n-

tuple code word v by the dot product between u and G [34].

v=u.G ……………………….. (2-27)

nvvvv +++= .....21

kuuuu +++= .....21


38

[ ],21 ..... kgggG =

The generator matrix G is

………….. (2-28)

Thus, the C (n, k) linear code in the systematic format is completely

specified by the k rows of a generator matrix G of the form G = [P Ik*k ]

where I is an (k*k) identity matrix and P is a (k*n-k) parity matrix. For

any

4*3 4*4 3*3 (4*3)

I ] H(4*15)=[I PT ]

( )

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

n

n

n

kkkk

nk

gggg

gggggg

G

........

..

..

321

321

32

222

111

,

⎢ gg1

2

1

(k*n) matrix G with k linearly independent rows, there exists a

(n-k)*n) matrix H with n–k linearly independent rows such that any row

vector of G is orthogonal to the row vectors of H. In addition, any vector

that is orthogonal to the row vectors of H is in the k rows of G. i.e. G.HT

= 0. Thus, alternatively it can be stated that an n-Tuple v is a code word in

the code C (n, k) generated by G if and only if v .H = 0. The matrix H is

called the parity-check matrix of the code C (n, k) [7]. The 2n-k linear

combinations of the rows of H form a (n, n-k) linear code C that is a dual of

the C (n, k) code. The parity-check matrix H of C (n, k) is the generator

matrix for the dual C (n, n–k) code. Given G in the systematic form

G = [P Ik ] for a C (n, k) code the parity-check matrix takes the form H =

[In-k PT ]. The list of form G and H for the (7, 4) and (15, 11) codes is [35].

C(n,k) code Generator Matrixes Parity check Matrixes

C(7,4) G(4*7)=[ P I ] H(3*7)=[I PT ]

C(15,11) G(11*15)=[ P11*4 11*11 4*4 (11*4)


39

2.10.3 Error Detection and Correction

Given the parity check matrix H, it is possible to check whether the

nsider the AWGN channel

d

rror Pattern (e=e1, e2,….. en)

igure (2-7) Additive White Gaussian Noise Channel

) tuple and is called

e syndrome of r. The decoder declares absence of error event if the

synd

of this type are called undetectable error patterns. One important fact to be

received word r is a valid code word or not. Co

mo el shown below [34].

Channel Detector

r'=v+e

E F

The decoder computes s = r .HT where s is a (n–k

th

rome s =0 and accepts r as a valid transmitted code word v. The only

lazy action the decoder has to take in such a scenario is to extract the

rightmost k symbols of the code word v and deliver it to the sink as

transmitted message u. On the other hand, if s ≠ 0, the decoder declares an

error event and in such a case the decoder needs to stimulate its gray cells

and perform some smart computations to locate the errors and correct them.

There is a possibility that even if s =0, the received word r may not be a

valid transmitted code word v and the decoder is fooled by the error pattern

e. In such a situation the error pattern e is identical to a none zero code

word and due to the inherent linear nature of the code the transmitted code

word v gets converted into another code word w of C (n, k). Error patterns

Transmitteword

d code Received word r

V= v ,v ,…vn 1 2

Error Pattern


40

noted here is that the syndrome s of r completely depends on the error

pattern e and not on the transmitted code word v [37].

2.10.3.1 Error Detection

Assume an error pattern of (l ≤ n) errors will cau

se the received word

to differ from the transmitted code word v in l places i.e. [ d(v,r) = l ]. The

word r and declares an error event if s ≠ 0.

This

r

detector observes the received

process is called error detection. If the minimum distance of the block

code is dmin, then an error pattern of 1min −≤ dl errors will for sure result

in a received word r that is not a code word. Hence, a block code with

minimum distance d is capable of detecting all the error patterns of

d or fewer errors. An error pa errors is undetectable

because there exits at least one pair of code words that differ in d

locations, so it causes the received word r to be another valid code word

other than that was transmitted. The same holds true for error patterns of

more than dmin errors. Thus, a block code with minimum distance dmin

guarantees detecting all the error patterns of dmin–1 or fewer errors and is

capable of detecting a large fraction of error patterns with d or more

errors [37].

There are 2k–1 error patterns, which alters the transmitted code word v

into another code word w. These 2k –1error patterns are undetectable and

the decoder

min

min–1 ttern of dmin

min

min

accepts w as the transmitted code word. The decoder is then

said

to have committed a decoder error. However, there are 2n – 2k

detectable error patterns. For large n, 2k –1 is much smaller and only a

small fraction of error patterns pass through the decoder being undetected

[34].


41

2.10.3.2 Error Correction

With the assumption that all code words are equally likely to be

ansmitted, the best decision rule at the receiver would be always to

ecode a received word r into a transmitted code word v that differs from

est positions (components or bits). This

decis

tr

d

the received word r in the few

ion criterion is called maximum-likelihood (ML) decoding. This is

equivalent to minimizing the Hamming distance between r and v. Decoder

based on this principle is called minimum distance decoder [38]. For a C (n,

k) block code with minimum distance dmin the random error correcting

capability can be determined as follows:

2212 min +≤≤+ tdt ; t is a positive integer ……..(2-29)

It can be shown that the block code C is capable of correcting all the

error patterns of t or fewer errors. Let v a

nd r be the transmitted code word

and received word respectively in C.

The Hamming distance between v , r

and w be any other valid code word

and w satisfy the triangle inequality:

( ) ( ) ( )wvdrwdrvd ,,, ≥+ ……………. (2-30)

( ) '12, ttrwd −+≥ ; Where ( ) ', trvd = and tt ≤'

( )rwd , >

Consider the C (7,4) code with dmin = 3

From (2.29),

t

( ) 12/1min =−= dt since d is odd and let min

[ ][ ]01010001101000

==

wrv

[1110010= ]


42

d (w, r) >1 = 4 . If an error pattern of t or fewer errors

occurs, the received word r is closer to the transmitted code word v than to

any other code word w in C in the Hamming distance sense. For all error

atterns with l errors such that l > t, there exists at least one case where the

(v, r) = 1 and d

p

received word r is closer to an incorrect codeword w than the transmitted

code word v, such that d (v,w) = dmin and the following conditions are

satisfied [34, 35]

♦ wvee +=+ 21

♦ 1e and 2e do not have nonzero components in common places.

Consider the C (7,4) code with dmin = 3

v = [1 1 0 1 0 0 0] = [0 0 1 1 0 0 0] and = [0 0 0 0 0 1 0]

r = v + e1 = [1 1 1 0 0 0 0]

the decoder will select w as the

der error occurs. So it can be

u

f

1e 2e w = [1 1 1 0 0 1 0]

d(v, r) = 2 and d(w,r) = 1. In this case,

transmitted code word instead of v and deco

concluded stating that, a block code with minim m distance dmin

( )⎣ ⎦2/1min −= dt guarantees correcting all the error patterns o or fewer

errors. The parameter t is called the random error correcting capability of

the code. A t–error correcting linear block code C (n, k) is capable of

correcting a total of 2n-k error patterns, including those with t or fewer

errors.

2.10.4 Standard Array Decoding

With the knowledge of occurrence of an error event, the decoder is

entrusted the task of determining the true error pattern e . Using the

istributive property, we can write d


43

r equations of (2.27) have solutions

d the true error pattern e is one of the error patterns. For the channel

with a BSC, the most probable error pattern has the sm ber of

components and is chosen as the true error pattern in order to

mini

≤ i ≤

n

sta

e of the received

word r and determining th ≤ i ≤

additional properties in a code [34].

( ) TTTT HeHvHevrHs ... +=+== …….. (2-31)

The solutions to the n–k linea k2

allest num

i

,

an k2

w

nonzero

mize the probability of a decoding error [34]. The received word r

belongs to the vector space of n2 n-tuples over GF (2). The n2 n-tuples are

partitioned into k2 disjoint subsets kDDD 221 ,.....,, such that vi is contained

in the subset iD for 1 ≤ i ≤ k2 . The standard array is an array of rows

called cosets and columns (sub sets) such that each of the 2k disjoint

subsets contains one and only one code word [35]. If v is a transm tted code

word then the received word r will fall in D k2 if the error

pattern is a coset leader. I such as case r ill be decoded correctly into the

transmitted code word v. However, if the error pattern is not a coset leader,

an erroneous decoding will result. The 2n-k coset leaders including the all

zero word are called correctable error patterns. The major drawback of the

ndard array decoding is that the array grows exponentially with k and

becomes impractical for large k. The 2n entries can be reduced to 2 * kn−2

entries in a look up table using syndrome decoding. The syndromes are a

(n-k) tuple and there are kn−2 distinct syndromes. There exist a direct

mapping between the 2n-k syndromes and the kn− coset leaders and hence

kn−2same syndrome accomplish the decoding. The transmitted code word

ie . For large n–k, the implementation becomes impractical. Other

than the linear structure, practical algebraic decoding schemes require

i for 1

2

culating the syndrom

e coset leader i e for 1

is stored in the look-up table. Cal

having the

rv +=


44

2.10.5 BCH Codes

e nonbinary

cyclic codes with code word symbols from GF (qm) and are the most

ving the capabilit of correcting random as well as

urst errors. Since the BCH codes are cyclic in nature it can be

impl

The BCH codes are binary and form a class of multiple random error

correcting cyclic codes. On the other hand, the RS codes ar

powerful block codes ha y

b

emented using high–speed shift–register based encoders/decoders.

This property of the BCH codes has enabled to find its way in optical

communication systems [34].

2.10.5.1 Description of BCH Codes

Definition: The BCH code is defined below with usual notations [35]

Block Length: n = p − 1 m

umber of parity check bits: n − k ≤ mt, m hi X) has roots

inimum distance: dmin ≥ 2t + 1

The 0 1 n-1 o 1

N

Where m is power of p GF (q = p ) in w ch g(

1−n

M

n-tuple code word v = (v , v … v v ) has symbols v , v ,….,

1−nv from GF (q=pm)

Chapter three Research procedures

45

CHAPTER 3

RESEARCH PROCEDURES

There are three important objectives in this chapter, the first

objective is design and implementation of the simulation realistic

model for optical code division multiple access in local area net work.

The second objective is study and analysis the system behavior

with different variables such as codeword weight, codeword length,

threshold of detector, and transmitted power.

Also this research studies the effect of multiple access

interference problems (MAI) with difference numbers of supported

users (N) based on two case of code word weight (w).Thirdly,

applying error correction code technique for three types of polynomial

in forward error correction technique.

3.1 Design Procedures

To realize the aims of research in clear and organized form there

must be description of all variables and data and what follows from

processing and outcome within system having alternate relationship

between elements. The following step illustrate this procedures which

contains

- Summation and analysis of information.

- Presentation of the outcome of the system.

- Applying error detection and correction code.

- Evaluation of outcome and limiting available modifications.


46

3.2 Simulation Of Convolution Optical CDMA LAN

system Depending on procedures of this thesis, the optimum values of the

system can be calculated according to following:

3.2.1 System Input

1. Choose the receiver type of detector which limited by the following equation:

)( AmperPRPhfq

recdresos ==ηλ ……….(3-1)

( )23............../..

−= wattAmperfh

qRdη

sλ : Arrival rate of incident photon due to chip (1) transmission in the signature sequence. η : is the PIN quantum efficiency of the photo detector.

recP : received power at optical correlater. h : is the plank 's constant . f : is the optical carrier frequency.

q : magnitude of electron charge .

dR : Responsivity of photo detector. : is the photon energy. fh. Note:. By using a wavelength of 1.55 µm for the downstream and

1.3 µm for the upstream they can both be sent over the same fiber .


47

3.2.2 Choose The Type Of Desirable Design Area

LAN has a transmission distances relatively short (≤ 10 Km).

Fiber losses as well as the dispersive and non linear effects

occurring inside fiber are not of much concern for LANs.

3.2.3 Optical Power Budget Or Loss Budget If the signal is too weak when it reaches the far end of the system the

data will be difficult to separate from the background noise.

3.2.4 Limitation On The Received Power The receiver power must be high enough to keep the BER to a low

value, and the received power must be low enough to avoid damage to the

receiver.

3.2.5 Limitation On The Transmitted Power On cost and safety it is good to keep the transmitter power to the

minimum acceptable value.

3.2.6 Calculation The Transmitter Power

The following steps show the calculation at the transmitter power:

To find the minimum power losses for the system which is due to the:

1. Fiber

2. Connector

3. Splices.

4. Agging losses.

5. Repairs.

6. Spare.


48

The values of these items are obtained from the manufacturer by catalog.

The attenuation of the fiber will contribute approximately 0.5 dB

over 1Km or 5dB over 10Km. Other losses in connector and optical

filtering are assumed to be 5 dB.

For a system with 32 users the losses in the optical splitter will be at

least 15 dB. To make up for the losses on optical amplifier can be

added after the spreading at the sender.

The summation of all power losses is equal to (25) dB.

Figure (3-1) illustrated the block diagram of losses in optical CDMA

LAN system for star topology.

3.2.7 Calculation The Minimum Received Power The transmitter must supply enough to overcomes the worst case

losses and still meet minimum power level requirement of the receiver, the

receiver minimum power level is a large negative number decibels. This

means that the power level is very small. The transmitter output must be

greater than this level and therefore the numerical value of decibels must be

less negative.

- It can be determine the minimum received power where receiver

need it to operate reliably with BER below a specified value or (10-

9), which equal (1.61 micro watt) or (-57.13) dB depending on

equation (3-1).

Source (LED)

Attenuation Looses Optical splitter

-5 dB -5 dB -15 dB PIN detector

Figure (3-1) illustration the model of losses in optical communication for star topology


49

3.2.8 Calculation The Minimum Transmitter Power The minimum transmitter power = minimum receiver power +losses

……………………….. (3-3)

Which is equal to (460.25) µ watt or (-33.37) dB.

The light source with the nearest value of output power available is

500 µ watt or (-33 dB).

3.2.9 Calculation Of The Maximum Receiver Power To calculate the maximum receiver power the following equation is

used:

(Transmitter power – minimum losses) or (5.88 micro watt)

= -52.3dB. …………………… (3-4)

The benefit of this value is to known how much power would be

received with out damaging the receiver.

By using the equation (2-25) , we calculated the values of

multiple access interference with the difference values of number

simultaneous users for two case of code word weight i.e ( w=5 ,w=7)

with four values of threshold ( 16, 17, 18, 22) and fixed value of code

word length.

Depending on the equation (3-1) it is possible to generate the

information matrix with dimension (255,247).

Added the values of multiple access interference to each chip

with the effect the thermal noise and shot noise by using equation (2-

4), (2-5) respectively .The new form of equation (3-1) will be


50

⎟⎠⎞⎜

⎝⎛ ++++= 222

Ishthoss I σσσλλ ………………….. (3-5)

Where:

soλ : is the chip transmitter.

I: is the multiple access interference.

th2σ , , is the thermal, shot noise and interference in form of

additive white Gaussian noise.

sh2σ I

2σ

In each case the received power (Prec) is variance in three case i.e. (2, 3,

5) µwatt and calculated the following:

3.2.10 Calculating The Signal To Noise Ratio (SNR)

In this section, the signal to noise ratio is calculated and the effects

of increasing power transmit on the system performance can be seen,

and to determine the optimum power which operate the suggestion

system with the best case, depending on the following equation: 24QSNR = ……………….. (3-6)

Note:

When logic zero received, no MAI appear i.e 0=oσ , and when

logic one received the MAI is appear, and the dignity of equation (2-20)

will be )( 1 Io σσσ ++ , then the Q factor can be calculated by the new

form of equation (2-20)

Io

oIIQ

σσσ +++

=1

1 …………………………. (3-7)

Recompense to the equation (3-6) yields


51

2

1

1 ).(4Io

oIISNR

σσσ +++

= ……………….. (3-8)

Where I1=2Rd Prec ……. (3-8) a , σ1= (σ2s +σ2

T) 1/2 …… (3-8) b

I0= 0 ……. (3-8) c , σ0=σT …… (3-8) d

3.2.11 Calculating The Bit Error Rate (BER) In this section, the bit error rate is calculated, to show how the

performance of optical CDMA networks is enhancement with applying

the all difference states. The value of BER can be calculated depending

on equation (3-9) as follows:

( )π2

2/exp22

1 2

QQQerfcBER −

≈⎟⎠

⎞⎜⎝

⎛= ………………… (3-9)

The procedures of all steps of present work can be shown in block

diagram, figures (3-1) and (3-2).


52

Prec=2µwatt

Figure (3-2) The block diagram of the research procedure (case one)

W=7

Th=16

Th=17

Th=18

Prec=3µwatt

Prec=5µwatt

Prec=2µwatt

Prec=3µwatt

Prec=5µwatt

Prec=2µwatt

Prec=3µwatt

Prec=5µwatt

Th=22Prec=2µwatt

Prec=3µwatt

Prec=5µwatt

Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.





53

Prec=2µwatt

Figure (3-3) The block diagram of the research procedure (case two)

W=5

Th=16

Th=17

Th=18

Prec=3µwatt

Prec=5µwatt

Prec=2µwatt

Prec=3µwatt

Prec=5µwatt

Prec=2µwatt

Prec=3µwatt

Prec=5µwatt

Th=22Prec=2µwatt

Prec=3µwatt

Prec=5µwatt






54

3.3 Appling the Error Correction Code In this section, forward error correction code technique is applied

to see the important of error correction code in optical CDMA system.

3.3.1 Encoding

The applying of forward error correction code technique is

accomplished corresponding three types of polynomials which are a

(255,247), a (255,239), and a (255,223).

By these polynomials the correct bits are generated and added to the

message bits as the following:

The first polynomial (255,247) that is shown in appendix which can

generated the code from it,

The polynomial is generates correct bits equal to (8), where this

polynomial dose not loading on the channel, this mean ability exploit the

channel to transmit high data rate.

The principle of choosing this polynomial is supported at the first

system analysis when we choose the optimum power (2µWatt), in addition

to the other variables which yields low interference value.

Also the system have high data rate which means that the received

data must be received with low error and ability to apply error detected and

corrected technique.

The technique which is applied in this thesis is known forward error

correction (FEC). The codes are generated by program and add it to the

message to form codeword that provide to transmit.

Same steps conducted with the second and third polynomial

(255,239), (255,223) but with correct bits equal to (16) and (32)

respectively.


55

3.3.2 Channel Transmitter After generating code by program and add the message to it, the

channel transmit is also generated by program.

Added the noise and the source of interference to the code transmit in

addition to add the attenuation value which happens in all parts of system.

All noise source and interference that happen during transmitter and

the attenuation showed in details at the section (3.2.6) step (1).

3.3.3 Receiver

After the code word received from the transmit channel, the data is

sent to the detection system.

In this section the error caused by the noise and interference which

lead to change the information is detected and corrected.

In the following steps show the procedure of detecting and correcting

code:

1. compute the syndrome of r, r.HT

2. Locate the coset leader el whose syndrome is equal to r.HT .then el .

is assumed to be the error pattern caused by the channel.

3. decode the received vector r into the codeword v*= r+el

Figure (3-4) shows the flow chart for that all case followed in the presented

work.

Chapter four Simulation Results

58

CHAPTER 4 SIMULATION RESULTS

Introduction

This chapter presents the simulation results of the suggested system.

The objective of these results is divided into two main parts, the first part is

demonstrates enhancement the performance of the optical CDMA system

by selection the optimum values of variables such as transmitted power,

code word weight, code word length, and threshold value of detector, also

the limiting of the system performance is measured by calculating Q factor.

The second part is focusing on the results of the optical CDMA with

error detection and correction code using three types of polynomials with

the measured Bit Error Rate depending also on investigate the following

point: code word weight, received power, and for four values of threshold

detector.

First, the results show the effect of the relationship between number of

users versus BER on the behavior of OCDMA system for three values of

code word weight, and showed the effect of code word length with three

values of code word length. Second, shows the effect of relationship

between the number of users versus SNR(dB) for two cases of code word

weight and for four values of detector threshold with varying the received

power, thirdly, measuring the Q factor with two values of weight (w=5

,w=7).Fourthly, show the relationship between the number of users versus

BER with two values of weight (w=5 ,w=7), fifthly, applying error

detection and correction code technique with three types of polynomials at

optimum received power (2µwatt).


59

4.1 The Effect Of Codeword Weight Figure (4-1) illustrates the relationship between thresholds (µ) versus

Bit Error Rate with different values of code word weight. It is seen that the

increasing in weight leads to the increasing in BER, this is because of

increasing in the number of logic one in code word, which means

increasing the attrition of the transmitted power (logic one appears for long

time) during transmitting one code word, this leads to increase multiple

access interference problem (MAI) during the interval of appearing number

one's in one code word.

Figure (4-1) The relationship between threshold value versus BER for three values of

code word weight and (N=30).

From figure (4-1) It can be seen for example, at threshold (µ=4) there

are three cases as in the following:

Case one, BER equal (0.3) when w=9

Case two, BER equal (0.005) when w=7

Case three, BER equal (10-4) when w=5


60

Also, from figure (4-1) it is seen another value of BER at (µ=8), it

can be seen in the first case when (w=7), BER is equal to (10-4) in the

second case when (w=7), BER is equal to (10-5), and in the third case when

(w=5), the BER is equal to (10-6).

From the above, these limits must be taken in to account by designer

when selecting the value of weight to allow the system operation in the best

value of interference.

Therefore, this figure appears that the choice of weight is an effective

element for decreasing the average interference.

4.2 The Effect of Codeword Length: Figure (4-2) shows the relationship between the threshold versus BER

for three values of code word length and for a fixed value of code word

weight (w=7) and number of user equal (30).

Figure (4-2) The relationship between thresholds versus BER for three value of code

word length (L) and (N=30)

This figure shows the increasing in the code word length leads to the

improvement the performance of the system and this means decreasing the

average error, figure (4-2) proves that the increasing in threshold leads to


61

the improvement of the system performance for all values of (µ), for

example when µ=4, the values of L and BER as shown below:

When L=500 BER=8*10-3

L=1000 BER =2*10-3

L=1500 BER=10-4

And when µ=9 the BER at

L=500 equal (8*10-6),

L=1000 equal (8*10-7),

And L=1500 equal (5*10-8)

This result displays the range of improvement in performance. To

assure of the fixed results, the different values of threshold was depended,

and this displayed that there is a ratio of improvement with increasing the

code word length.

Therefore, It can be shown that increasing in code word length lead to

improve in performance, therefore, the best polynomial must be chosen

which leads to improve the performance.

4.3 The Effect Of Threshold Value: Figure (4-3) illustrates the relationship between number of

simultaneous user versus the BER with fixed value of code word length

and different value of threshold (µ).


62

Figure (4-3) The relationship between the number of simultaneous users versus BER for

different values of threshold detector=7, L=1000

It shows the changing in curves because of the changing in threshold,

this is due to the high received power at the receiver which has a negative

effect on the BER because of the multiple accesses interference result from

the number of simultaneous users as shown, from figure (4-3) for example:

when N=22, the BER equal to (0.004,10-2,10*10-2,10-5) for four values of

threshold (16,17,18,22) respectively. Another example when (BER=10-8)

then the number of support users are (7, 9, 11, 14) for the values of

threshold (16, 17, 18, 22) respectively. Therefore, the threshold of detector

is important factor which effected on the performance of the optical CDMA

system.

Figure (4-4) illustrates the relationship between the number of

simultaneous users versus the value of bit error rate at the same values of

threshold but with the code word weight equal (w=5).

The difference it can be seen of curve for four cases comparesion

with figure (4-3) at (w=7), it is clear that the number of supported users at


63

the same value of BER (10-8) is (16,18,20,22) for the values of threshold

(16,17,18,22) respectively .

Figure (4-4) The relationship between numbers of user versus BER for four value of

threshold (µ), w=5, L=1000

Another example, a comparison between figure (4-4) and figure (4-3)

with N=22, shows that the BER is equal (10-4, 3*10-5, 6*10-6, 10-8) for the

values of threshold (16, 17, 18, 22) respectively.

Finally, it may conclude that the weight of code word is the important

factor in optical CDMA system.

4.4 Optimum Received Power

4.4.1 Optimum Received Power at (w=7) To discuses the effect of received power on the suggested system

performance, the effect of variable threshold on the system must be studied,

for many cases of threshold as shown in the following figures (4-5),(4-6),

(4-7), and (4-8).

Figure (4-5) displays the first case when code word weight equal to

(w=7) at (µ=16). The selection of higher value of code word weight

means increasing the power content in code word, this result in increasing


64

the generated noise which added to the channel and the multiple access

interference value will be increases.

Figure (4-5) The relationship between number of simultaneous user versus SNR (dB)

for case (w=7), (µ=16)

Also the figure shows that the number of simultaneous users for three

values of received power for example:

At SNR equal (15) dB, the number of users are (11, 9, 7) for three

values of received power (Pres=2, 3, 5) µW respectively.

This means that the increasing power dose not solve the problem of

MAI which is a consequent of increasing the number of supported users.

Figure (4-5) proves that choosing of the best transmitted power

(which is not necessarily high) is the optimum solution for increasing the

number of supported users and decreasing MAI, for example at Prec=2µ

watt have greater users compare with received power (3, 5) µwatt, so it can

be considered the received power (2µwatt) is the best to the suggested

system.


65

On the other hand, at N=8, the value of SNR (dB) for three values of

received power (Prec=2, 3, 5,) µw is (16.75, 15.5, 13) respectively.

Figure (4-6) shows the relationship between the number of

simultaneous user (N) versus SNR (dB) at threshold value equal (17) and

the value of code word weight (w=7). This figure illustrates the degradation

of the system performance due to the same reason which discussed in

details previously.

Figure (4-6) The relation between the number of simultaneous user versus SNR (dB) for

case (W=7), (µ=17)

Also figure (4-6) displays the increasing in threshold value

improves the suggested system performance compared with figure (4-5).

It can be seen that the slight increment in SNR (dB) at N=8 compared

with figure (4-5) at the same value (N). For example:

At N=8 the values of SNR (dB) for three cases of received power

(Prec=2, 3, 5) µw is equal to (17.3, 17, 14) respectively.


66

On the other hand at SNR (dB) =15 the number of support users for

three values of received power (2, 3, 5) µw is equal to (13, 10, 8)

respectively.

This proved that the performance of the system is better at the power

which not allows generation interference signal. And this figure proves the

stability of the performance with respect to the chosen the suitable value of

the transmitted power.

Also the threshold value has an effete upon the system performance

of optical CDMA.


simultaneous user (N) versus SNR (dB) for the case (µ=18, w=7) .It

displays the degradation of the signal to noise ratio with rising of number

of simultaneous users, this is due to the increasing of multiple access

interference in the channel transmitter.

Figure (4-7) The relation between the number of simultaneous user (N) versus SNR

(dB) for (w=7, µ=18)

It can be seen that there is a little increment in SNR value compared

with figure (4-5) and figure (4-6), for example at N=8 the value of SNR for


67

three cases of received power (Pres=2 ,3 ,5) µW is equal to (19 ,18.5 ,17 )

respectively .

On the other hand, at SNR(dB) =15 , the number of simultaneous

users for three case of received power (Pres=2, 3 ,5 )µw is equal ( 15, 13,

11 ) respectively . This shows the effect of increasing the value of threshold

on the system performance, in addition to stability the system performance

with respect to the choosing of the transmitted power.

Figure (4-8) illustrates the relationship between number of

simultaneous users versus SNR (dB) for three values of received power

(Pres=2, 3, 5) µW at the case (µ=22).

Figure (4-8) The relation between the number of simultaneous user (N) versus SNR

(dB) for (w=7, µ=22)

Figure (4-8) displays the improvement in system performance if

compared with figures (4-5), (4-6), (4-7) for example: at N=8 the value of

SN equal (22.5, 21, and 19) dB for three values of received power (Pres=2,

3, and 5) µw. On the other hand, when SNR =15dB, the number of

supported users equal to (19, 17, 14) respectively. This shows the effect of


68

the value of threshold on the system performance with respect to the

variation of received power which demonstrates that the increasing of

transmitted power is not effectively.

Figures (4-5), (4-6), (4-7) display the range of improvement which

occurs in the system performance when choosing the suitable value of

transmitted power in addition to threshold, figure (4-5) shows that depending on

the received power 2µwatt as the optimum value, the ability of operation with

the number of supported users equal to (11) at SNR(dB)=15.

Figure (4-6) which depending same value of power but with threshold

value equal to (17), the number of supported users equal to (12) at the same

value of SNR.

Also it can be observed continuously the improvement in performance by

choosing the optimum value of power with µ=18, where this shows in figure (4-

7) as number of supported users equal to (15).

The last figure (4-8) provs this improvement which can be noticed as

number of supported users at the same value of SNR equal to (19).

4.4.2 Optimum Received Power at (w=5): To make sure from the stability of the suggested system performance

and to get the best value which gives the improvement in performance, the

other value of code word weight is chosen and its effect on the best value

of the received power is discussed as shown in the following figures.

Figure (4-9) illustrates the relation between the number of

simultaneous users and signal to noise ratio (SNR) for three values of

received power (Prec=2, 3, 5) µ watt and detector threshold equal to (16).


69

Figure (4-9) The relationship between number of simultaneous user (N) with the signal

to noise ratio (SNR) when and (w=5) the value of threshold (µ=16).

The figure (4-9) displays the improvement in the system performance

with increasing the number of simultaneous users (N) compared with figure

(4-5). The increasing in transmitted power leads to reduce the signal to

noise ratio due to the increasing of multiple access interference value where

each user is considered as source of multiple interference to another user.

It can be seen from this figure when the received power is decreased

to (3) µwatt led to enhance the performance of the system and is better

when received power equal (2µ watt).

That insists the important of using the transmitted power value in level

to maintain transmission with less interference value and with high SNR.

The high range in improvement is displayed at SNR value equal (15)

dB, as observed at Prec=5µwatt the number of simultaneous users equal to

(N=10), and with decreasing the power to (Pres=3µwatt), yields number of

simultaneous users equal to (N=13) at the same value of SNR.


70

However, the big enhancement is got at (Pres=2µwatt) and which

yields the number of simultaneous users arrives to (N=15) with same value

of SNR.

This shows the range of ideal exploit of multiple access technique

by choosing the suitable power to work in this technique ,and this figure

assures that increasing number the simultaneous users by (5) when the

power is varied from (5 to 2)µwatt .

Finally, it can be seen the improvement from economical side when

the power is decreased which led to the improvement in performance of the

system.


simultaneous users versus SNR (dB) for three values of received power.

The performance of the system is the same as in the previous case at

(µ=16), but the difference is only in supported users with the variance value

of threshold or (µ=17). This is because of the same reason which is shown

the figure (4-9) .The difference between this figure and previous figure in

the large number of supported users for example:

At SNR (dB) =15, the number of supported users for each received

power (Prec=2, 3, 5) µw is equal to (20, 18, 15) respectively.

This appears the improvement compared with figure (4-6) at the same

value of SNR with the number of supported users equal to (12, 10, 8) for

three values of received power.

On the other hand at (N=8), the value of SNR for three values of

received power is equal (21.25, 21, 20) dB respectively.


71

Figure (4-10) The relationship between the number of simultaneous user versus SNR

(dB) for the case (w=5), (µ=17) .

Figure (4-11) shows the relationship between the number of

simultaneous users (N) versus signal to noise ratio SNR (dB) for three

values of received power (Pres=2, 3, 5) µw when the value of threshold

equal(µ=18).

Figure (4-11) The relationship between the number of simultaneous user (N) versus

SNR (dB) for the case (w=5), (µ=18)


72

It can be noticed in figure (4-11) as in figures (4-9), (4-10) the

decreasing in the performance of the system with increasing the number of

simultaneous supported users (N) compared with the previous figure for the

same reason which is discussed in detail but with greater number of

supported users compared with the case (w=7, µ=18), for example, at

SNR(dB)=15, the number of supported users for three cases of received

power Pres(2,3,5)µw is (22 ,16 ,12 ) respectively.

On the other hand, at (N=10), the values of SNR is (20.5, 18, 16.75)

dB respectively.

Therefore, this make sure that increasing the threshold value leads to

the increasing SNR carry out enhancement the system performance.

The figure (4-12) illustrates the relationship between the number of

simultaneous users (N) versus the SNR (dB) for three values of received

power (Pres=2, 3, 5) µw when the value of code word weight equal (w=5)

and threshold (µ=22).

Figure (4-12) show the relationship between number of simultaneous user versus SNR

(dB) for (w=5), and (µ=22)


73

It can be seen the increasing in number of users lead to degradation

signal to noise ratio due to the increment in multiple access interference

MAI in the transmit channel which lead to decrease the system

performance .On the other hand, increasing the threshold value of detector

lead to enhance the system work which can be show in the following

example:

At (SNR=15)dB the number of supported users for three values of

received power (Pres=2 ,3 ,5 )µw equal (24, 26 ,30 ) respectively .On the

other hand at (N=8) ,the value of SNR(dB) is (25.5 ,25 ,24 ) for three

values of received power .

Finally, and from these figures, the system of optical CDMA is

affected strongly by threshold value and the designer must be take into

account the suitable value to get the better performance.

4.5 Calculations of Q factor

4.5.1 Q factor with codeword weight (w=7)

From figures (4-13), (4-14),(4-15), and (4-16), it can be observed the

degradation in Q factor with increasing the number of simultaneous users.

These figures show from another side the relationship between the

numbers of simultaneous users versus Q factor for the cases (16, 17, 18,

and 22) of threshold values. It can be seen that the performance of the

system is enhance by increasing increasing the threshold value which can

be notice from the number of supported users, From figures, it can be

noticed that the number of supported users for four cases of threshold

values (16, 17, 18, 22) with the value of Q factor equal to ( 6 ), code word

weight (7) and with the received power ( 5 µw ) is equal to ( 7, 10, 11, 13 )

respectively. Also for (Pres=3µw) the supported users is equal to (9, 10, 13,


74

14) respectively. And for received power equal (2µw) is equal to (11, 13,

15, 16) respectively.

Figure (4-13) The relationship between numbers of


Simultaneous user versus Q factor for the case (w=7, µ=16)







75

4.5.2 Q factor with Codeword weight (w=5): The other case of the relationship between number of simultaneous

users versus Q factor when the code word weight equal to ( 5 ) which can

be observed in figures (4-17),(4-18),(4-19),(4-20) for three values of

received power ( 2, 3, 5 )µw and threshold values (16,17,18,22)

respectively.

Figure (4-17) The relationship between number of simultaneous user versus

factor with (w=5), (µ=16)

Figure (4-18) The relationship between number of simultaneous user versus q







76

From figures (4-17), (4-18), (4-19), (4-20) it can be seen the

difference in behavior of the system performance compared with previous

figure i.e ( w=7) for each threshold value.

Also, it can be seen the enhancement of the system performance by

increasing the number of supported users (N) with the same value of Q

factor for example, at (Pres=5µw) the number of supported users for figure

above with the Q factor equal to (6) are ( 9, 14, 19, 24 ),while at Pres=3µw

the number of support users equal to (11, 16, 22, 25), and for Pres=2µw the

number of support users is ( 13, 18, 22, 25) respectively.

4.6 Calculations of BER

4.6.1 BER with (w=7) Figures (4-21), (4-22), (4-23), and (4-24) show the performance of

the system with the difference cases of received power and for four values

of threshold when the value of code word weight equal (7).

Figure (4-21) The relation between the number of simultaneous user versus BER (dB) for the

case (w=7, µ=16)

Figure (4-21) shows the relation between the number of simultaneous

users versus BER for three values of received power (Pres=2, 3, 5) µW

with threshold value equals to (16) and code word weight (w=7).


77

From figure, it can be noticed the increasing received power has a

negative effect on the system performance, this is because of the high

power in optical channel leads to increase the MAI as a result form raising

the overall noise in the system which increasing the BER value and number

of support users to be reduced.

Also, figure (4-21) shows the improvement in the suggested system

when choosing the power in accuracy; this figure demonstrates the limiting

of selection the transmitted power in accuracy and activity and display the

range of improvement as shown in three curves of the figure, for example:

To obtain the average error of (10-6) the result appears ability of this,

when the power equal (5µw), under this condition, the number of

simultaneous users equal to (2), but when decreasing the received power to

(3µw) it is ability for getting the same value of BER with the number of

users equal (4), and when received power is equal to (2µw) then the

number of users is raising and equal to (6). However, It can be noticed the

big range of improvement of the CDMA system performance where it is

ability to work with the number of addition users about (4) compared with

the case of (Pres=5µw). Also, when the number of users equal to (8) the

BER equal to (10-5, 5*10-4, 5*10-2) for the above three values of received

power respectively.

Finally, the received power which equal (2µw) is considered the ideal

value which can be depending on to obtain the better performance in the

suggested system.


78

Figure (4-22) shows the relationship between the number of users

versus BER for three values of received power with (µ=17, w=7)

Figure (4-22) The relation between the number of simultaneous user versus BER for the

case (µ=17, w=7)

This figure shows the improvement in BER value for this case

compare with figure (4-21). The occurrence of improvement results from

increasing the threshold value which is decreasing the MAI in the system as

a result from getting the better values of BER for example:

When BER =10-2, the number of users equal (11) at (Pres=5 µw).

however, when the system works at received power (Pres=3µw), the

number of users equals to (14), and in the third case at Pres=2µw the

number of users equal to (17). This shows the range of improvement in the

suggestion system, and illustrates the stability in the performance for other

value of BER. On other hand, it can be noticed, when N=8 the BER equals

(5*10-5, 5*10-4, 8*10-3) for three values of received power (2, 3, 5) µW

respectively.


79

Figure (4-23) shows the relation between the number of simultaneous

users versus BER for three values of received power (Pres=2, 3, 5)µw .

Figure (4-23) the relation between the number of simultaneous user versus BER for the

case (µ=18, w=7)

This figure illustrates the improvement in BER value with increasing

the number of users compared with previous figures (4-21), (4-22). This is

due to the same reason which shown in details when the previous figures

(4-21), (4-22) are discussed. By comparing this figure with figure (4-

21), (4,22) it can be notice the difference in support users which display,

for example, at N=8 ,the value of BER equal to (1*10-8 ,2*10-6 ,5*10-5) for

three values of received power (2,3,5)µw. On the other hand, the number

of users at BER (10-7) equal to (10, 8, 6) for three values of received power

(Pres=2, 3, 5) µW respectively.

Figure (4-24) illustrates the relation between the number of

simultaneous users versus BER (dB) for three values of received power

( Prec=2 ,3 ,5)µW for the case µ=22 .


80

Figure (4-24) The relation between the number of simultaneous user versus BER dB for

the case (µ=22, w=7)

This figure displays the improvement in BER compared with figure

(4-23), also for the same reason which shown in detail when the previous

figures are discussed, for example:

When (N=8) the value of BER equal (7*10-9, 5*10-8, 4*10-7) for three

values of received power (Pres=2, 3, 5) µW respectively. On the other

hand, when the system operates at (BER =10-7) the number of users equal

to (13, 11, 9) for three values of received power.

4.6.2 BER with User (w=5): Figures (4-25 ),(4-26) ,(4-27) , and (4-28) show the performance of

the system with the value of code word weight equal (5) and for three

values of received power as shown below and for four values of threshold .


81


case (µ=16, w=5)

Figure (4-25) illustrates other case of the optical CDMA system at

codeword weight (w=5), whenever showing the relation between the

number of simultaneous users versus BER for three cases of received

power (Pres=2, 3, 5) µw. It can be noticed the performance of the system is

improvement compared with the same case at (w=7). The decreasing in

code word weight means decreasing the power contain in the code word as

a result form means decreasing of the MAI which lead to increase the

number of support users.

While comparing the above figure with the previous case (µ=16,

w=7), it is noticed that there is a difference in the value of BER for three

cases, for example when (N=2) the values of BER in this figure is equal to

(10-8 ,5*10-10, 10-11) compared with the figure (4-21) with the values of

BER is equal to (10-6 ,10-7 ,10-9 ) for three cases of received power (prec=2

,3 ,5 ) µw respectively. On the other hand, It can be noticed at BER=10-4

then the number of support users at the above figure is (12, 14, 17) compare

with the case w=7 figure (4-21), where the number of users equal (10, 9, 5)

for three cases of received power (Pres=2, 3, 5) µW.


82

This appears the effect of code word weight and the power transmits

on the optical CDMA system performance.

Figure (4-26) illustrates the relation between the numbers of

simultaneous users versus BER for three cases of received power. From

figure it can be noticed the change in the system performance for three

values of received power. Where it can be observed at (Pres=2) µw the

system display better operation compared with the cases (3 ,5 )µw this is

because of the decrement in the average error in codeword.

Also comparing this figure with the figure (4-22), show the

improvement from of a given period of the number of supported users for

example, at BER=10-5 the number of supported users is equal to (18,21,23)

compared with figure (4-22) with (6 ,7 ,9) for three cases of received power

(2,3,5)µw respectively .

On the other hand it can be notice at (N=4) the value of BER at the

figure above is (4*10-7,10-9,2*10-10 ) compared with the figure (4-22) which

has the value of BER (2*10-8, 10-7 , 10-6) for three values of received power

Pres=(2,3,5 )µw respectively.


case (µ=17, w=5


83

Figure (4-27) illustrates the relation between the numbers of

simultaneous users versus BER for three cases of received power.

This figure shows the improvement from of a given period of the

number of supported users by increasing the threshold value. and appears

the difference of supported users between this figure and previous figure

which can be shown from the following example, at BER =10-5 then the

number of supported users in the figure (4-27) is equal to (18,21,26)

compared with figure (4-23) with N=(14,11,9) for three values of received

power (2,3,5) respectively.

On the other hand, It can be noticed at N=12 then BER in above

figure (3*10-8, 2*10-6, 2*10-5) compared with the figure (4-23) with (10-6 ,

5*10-5 ,5*10-4) for three cases of received power Pres=(2,3,5)µw

respectively.


case (µ=18,w=5)


simultaneous users versus BER for the case (w=5, µ=22). Where this figure

shows the improvement in performance of the system from of a given


84

period of the number of supported users. The number of users reach at the

power received equal (2µw) to (32) users compare with the same relation in

figure (4-24) which comes to (20) users at BER=10-4.


case (µ=22, w=5)

Also it can be noticed at Pres= (3, 5) µWthen the number of supported

users in above figure arrive to (25, 21) compared with the figure (4-24)

which has (19, 17) users respectively.

4.7 Applying error correction code

4.7.1 Applying error correction code at (w=7) The reaching to the optimum applying of the error detection and

correction code in the suggested system must be study all variables of the

system in detail which allowed to choose the optimum values of suggested

system design, where choosing this values is considered an important factor

to applying the error detection and correction code technique successfully,

inturen the optimum exploitation of the channel. The analysis of all system

variables are conducted, where it is able to choose the number of correction

bits that is needed to add with the information in form which allow to


85

transmit large information, also the enhancement in system performance is

done by add the correction bits, consequently the added bits are effectively.

Figure (4-29) illustrated the relation between the number of

simultaneous users versus BER by applying the error correction code for

the case (Prec=2µw, w=7, threshold=16) .This figure corresponding to

three types of polynomials to realize the actively correction code in optical

CDMA system.


case (w=7, µ=16, Pres=2µw)

The result shows enhancement of performance with increasing

correction bits. So it can be noticed the use of error correction technique

based on choosing the optimum values for above variables are more

actively.

Figure (4-29) shows the first code (255,247) that shows the

enhancement in performance with the number of additional bits equal to (8)

bits, which is considered very low compared with the range of

improvement and dose not considered loading on channel capacity, for

example at (N=2) the improvement value is equal to (10-8) compared with


86

the case of incorrect which was equal (10-7). But when (N=10) the value of

the improvement equal to (10-3) compared with the case of incorrect which

was equal to (8*10-2).

From this, notice that the performance is stable which means stability

of the system operation, and the applying error correction code technique in

optical CDMA system based on choosing the optimum values is

successfully. The second polynomial (255,239) yields (16) correction bits

which is considered the suitable number and dose not additional loading in

the channel capacity, this addition bits are considered accepted value with

the large benefit.

From figure, It can be noticed the rang of enhancement by applying

the second polynomial compared with incorrect case for example, when

N=10, the BER= (5*10-3) in the correct case compare with the incorrect

which equal to (8*10-2), but when using the third polynomial (255,223) it

can be noticed increasing the improvement where the average error equal to

(10-9) compared with the incorrect (10-7).

Also, there is a stability of improvement can be shows in this figure at

all values of users for example, at (N=12) the BER equal to (10-2) at the

first polynomial, when using the second polynomial the BER equal to

(6*10-3). And when using the third polynomial the BER equal to (8*10-4).

This gives to the designer the ability of choose the best polynomial to

transmit high data rate and maintain on the transmission process as a result

form optimum exploitation for the channel.

So it is able to use the polynomial which is displays the acceptable

performance and it generates lower corrections bits. Also it is able to

exploit the channel transmission to transmit the additional data. The use of

polynomial that has lower correction bits it gives the ability to transmit

high data rate.


87

However, the figures (4-30) ,(4-31) , and (4-32) show the relationship

between the number of simultaneous users versus BER for the case of

received power Pres=2µw and code word weight equal ( 7 ), but with the

deferent values of thresholds ( 17 ,18 ,22 ) respectively.

Figure (4-30) The relation between the number of user versus BER for the case ( w=7 ,

µ=17 ,Pres=2µw ) for different BCH

Figure (4-31) The relation between number of user versus BER for the case ( w=7

,µ=18 ,Pres=2µw ) for different BCH


88

Figure (4-32) The relation between number of user versus BER for the case ( w=7

,µ=22 ,Pres=2µw ) for different BCH

From these figures, it can be shown the improvement of the optical

CDMA system performance for all number of support users with the same

values of BER if comparing this figures together, for example:

At N= (10), the value of BER in figure (4-29) for the case incorrect is

equal to (10-2) compared with the same case in figures ( 4-30),(4-31),(4-

32) with BER equal to (10-3 ,10-4, 10-5) respectively .

By comparing these three cases when using three types of polynomial,

It can be noticed the difference for each curve in the above figures (4-30),

(4-31), (4-32).

This is proves that there is overall improvement in the system, and its

ability to apply the error correction code with the best performance which

is discussed in detail in figure (4-29)

On the other hand when applying three types of polynomials or BCH

(255,247), a BCH (255,239), and a BCH (255,223), shows there is

improvement or lowest bit error rate for same number of users is achieved

by the code with the highest amount of correct bits.


89

4.7.2 Applying error correction code at (w=5) Figures (4-33),(4-34),(4-35),(4-36) illustrates the another case of

relationship between number of simultaneous users versus BER with code

word weight equal ( 5 ) and received power equal (2µw) for three

difference of threshold values (16 ,17 ,18 ,22 ) respectively .

These figures indicate four cases which are incorrect, and three types

of polynomial a BCH (255,247), a BCH (255,239), and a BCH (255,223)

respectively.

Figure (4-33) The relation between the number of user versus BER for the case (w=5 ,µ=16 ,Pres=2µw)

Figure (4-34) The relation between the

number of user versus BER for the case

(w=5, µ=17, Pres=2µw)




90

It can be noticed in figure (4-33) there is improvement when applying

the error correction code technique by decreasing the values of BER for

example,

At N=2, the value of BER for incorrect case equal to (5*10-11), with

applying error correction code technique, optical CDMA system

performance trend to a way of enhancement and reach to the best case with

BCH(255,223) with BER =( 10-14).

This means that the separation of information with lower length of bits

in one code word is the best from the way separation in longer length.

On the other side, the polynomial BCH (255,223) has error correction

equal (4) bits in 255 bits (length code word).

Otherwise, whenever the redundancy bits are longer, the system

performance is better.

While these figures (4-34), (4-35), (4-36) show the same relation but

with the difference value of thresholds or (17, 18, 22) respectively. It can

be observed the difference values of BER for each figure above, which

appear the improvement during the number of supported users compared

with the same figures (4-29),(4-30),(4-31),(4-32) at code word weight ( 7 ).

If comparing between together, it can be noticed in clear the difference in

the performance of the system and it is proved the effect of code word

weight which is shown in details previously.

Chapter Fiver Conclusion and Future work

91

CHAPTER 5 CONCLUSIONS AND FUTURE SUGGESTIONS

5.1 Conclusions

The results of this thesis show the enhancement in the performance of

the data transmition in the optical communication system by using CDMA

technique. It is noted from using this technique that there is a bad selection

of variables lead to decrease the efficiency of this technique in the optical

communication system, so it is important to solve the problem which lead

to interference and this inturn cause an error in the received information.

This shows the importance of the optical system design independently

(with out applying ECC), also includes selecting the optimum values of

variables for example, transmit power, code word length, code word weight

and threshold value, where the selection of the better values gives a

positive result which leads to the enhancement the system performance, for

this reason the applying of ECC became very effective.

As follows the explanation of the most important conclusion based on

the results,

1- The results showed that the code word weight has an active effect in

the system performance, where the error ratio was equal to (10-3)

when varying the word weight from (9) to (5) for the same number

of users, so this ratio appears the important of choosing the suitable

weight.

2- The optimum selection of code word length has given the best

improvement of the system performance, where it can be noticed that

the ratio of improvement when the length is changed from (500) to

(1500) is equal to (13%) for the same number of users.

3- It is necessary to take into account the quality of optical detector,

where it is appeared the improvement in performance. Also it can be


92

noticed that the ratio of improvement is increasing when the value of

threshold increases, this means that the ability of detector to detect,

the is results appeared when the threshold is increasing from (16) to

(17), the ratio of improvement is equal to (17%), also when the

threshold value is changed from (17) to (18), the ratio of

improvement is equal to (22%), and from (16) to (22) the ratio of

improvement became at the best case and gave the big enhancement

of the performance.

4- The selection of optimum transmitted power is considered very

important, and it is limited MAI problem during transmition process.

So it can be noticed in this result, the optimum power transmit given

the best performance, which leads to apply the ECC with very

effective as an exploit the transmission channel and the ability to

correct, where it can be noticed the rate of improvement of SNR is

equal to (23%) when changing the value of received power from (5)

to (2) µw.

5- The selection of optimum value for Q factor shows that there is an

improvement in performance of optical communication CDMA

system and this can be noticed from the result of the proposed

system where the value of Q factor will be changed by increasing the

number of users consequently increasing the ratio of interference. So

it is necessary to take into account the value of this factor because of

its importance in improving the system performance.

6- The selection of suitable number of users is limited by power

transmit. Where it can be noticed the increasing of the number of

users lead to increase the average error with increasing the

transmitted power. So by decreasing the transmitted power, the

system performance will be improved. From results the improvement

is conducted with decreasing the transmitted power where the ratio


93

of improvement was equal to (23%) when changing the power from

(5) to (2) µw, in addition to enter the weight and threshold value it

can be observed that the system performance is the best.

7- The results showed that there is an improvement in performance

when selection the optimum values for all variables of the system,

where the number of users is increased to (30) users with keeping the

average error at the acceptable value.

8- The selection of optimum variables leads to the ability of applying

the ECC technique in successfully forms. So instead of additional

correcting bits to enhance the performance of the system, where the

improvement is accomplish by the optimum selecting of variable

which inturn leads to optimum exploition of the channel, thus the

additional correcting bits became very effective and proportional

with the average error results from the random interference, Also the

results show that the average value of error at (N=10) for incorrect

case is equal to (2*10-6) compared with the second polynomial which

was equal to (6*10-7). This is appears the successful selection of

system variables with effective applying the error correction code

technique.

9- The results appeared the improvement in the system performance

when using three types of polynomial, the system performance is

enhanced with the increasing of correcting bits generation , it can be

seen when using the polynomial (255,247) compared with (255,

223), where the ratio of improvement value is equal to (22%).

10- The optimum selection for polynomial allowed to transmit high

data rate, this because of exploited the channel capacity to transmit

the information instead of correct bits, where the based of compare is

accomplish on the budget between the range of utilization of

additional correct bits and average of transmit information. This is


94

appeared in the results, where it observed the difference using of

three types of polynomial based on correct bits and this referred on

the systems performance which must be acceptable and the ability to

select the optimum value which allowed transmitting a high data rate

with maintaining on the acceptable correct process.

5.2 Future Suggestions

The future suggestions are

- Studying and analyzing system Network (tree topology) with optical

CDMA.

- Studying and analyzing optical Network based on error correction

code for Long distance.

- Improving the Performance and enhancement of the optical network

by using orthogonal frequency division multiple accesses.

VII

List of Figures

Figure (2.1) The topology of a PON with an optical line terminal

(OLT), a passive splitter and several optical networking units

(ONU)

Figure (2.2) Schematic illustration of bandwidth allocation in TDM,

WDM, and CDMA optical networks

Figure (2.3) Attenuation Profile of Single-mode Fiber Figure (2.4) (a) Fluctuating signal generated at the receiver.

(b) Gaussian probability densities of 1 and 0 bits.

Figure (2.5) Block diagram of an FEC system Figure (2.6) Systematic Format of a Codeword of a block code Figure (2.7) Additive White Gaussian Noise Channel Figure (3.1) The model of losses in optical communication for star

Topology

Figure (3.2) The block diagram of the research procedure (case one) Figure (3.3) The block diagram of the research procedure (case two)

Figure (3-4) shows the flow chart for that all case followed in the

presented work. Figure (4.1) Show the relationship between threshold value versus BER

for three value of code word weight

VIII

Figure (4.2) The relationship between thresholds versus BER for

three value of code word length (L)

Figure (4.3) The relationship between the number of simultaneous user

Versus BER for difference value of threshold detector

Figure (4.4) The relationship between numbers of user versus BER for

four value of threshold (µ)

Figure (4.5) The relationship between numbers of simultaneous user

Versus SNR (dB) for case (w=7), (µ=16)

Figure (4.6) The relation between the numbers of simultaneous user

Versus SNR (dB) for case (W=7), (µ=17)

Figure (4.7) The relation between the number of simultaneous user (N)

Versus SNR (dB) for (w=7, µ=18)

Figure (4.8) The relation between the number of simultaneous user (N)

Versus SNR (dB) for (w=7, µ=22)

Figure (4.9) The relationship between number of simultaneous user

(N) With the signal to noise ratio (SNR) when the value of

Threshold (µ=16), and (w=5).

Figure (4.10) The relationship between the number of simultaneous

User versus SNR (dB) for the case (w=5), (µ=17)

Figure (4.11) The relationship between the number of simultaneous

IX

User (N) versus SNR (dB) for the case (w=5), (µ=18)


Versus SNR (dB) for (w=5), and (µ=22)

Figure (4.13) Show the relationship between numbers of simultaneous

User versus Q factor for the case (w=7, µ=16)

Figure (4.14) Show the relationship between number of simultaneous

User versus Q factor for the case (w=7, µ=17)


Versus Q factor for the case (w=7, µ=18)


Versus Q factor for the case (w=7, µ=22)


Versus q factor with (w=5), (µ=16)





X



Figure (4.21) The relation between the number of simultaneous user

Versus BER (dB) for the case (w=7, µ=16)


Versus BER for the case (µ=17, w=7)




Versus BER dB for the case (µ=22, w=7)










XI

Versus BER for the case (w=7, µ=16, Pres=2µw)

Figure (4.30) The relation between the number of user versus BER for

the case ( w=7 , µ=17 ,Pres=2µw )

Figure (4.31) The relation between number of user versus BER for the

Case (w=7, µ=18, Pres=2µw)

Figure (4.32) The relation between number of user versus BER for the

Case (w=7, µ=22, Pres=2µw)


the case (w=5 ,µ=16 )]


the case (w=5 ,µ=17 ,Pres=2µw )


the case (w=5 ,µ=18 ,Pres=2µw)


the case (w=5 ,µ=22 ,Pres=2µw )

XII

List of Abbreviations

AWGN Additive White Gaussian Noise

ASE Amplified spontaneous emission

ARQ Automatic Repeat Request

ATM Asynchronous Transfer Mode

AWG Arrayed wavelength grating

BCH Bose-Chauduri- Hocqueaghem

BER Bit Error Rate

CDM Code division multiplexing

EPON Ethernet PON

EDFA Erbium doped fiber amplifier

FTTH Fiber To The Home

FEC Foreword Error Correction

FTTB Fiber To The Building

FTTCab Fiber To The Cabinet

FTTC Fiber To The Curb

FSAN Full-service access network

FWHM Full width at half maximum

FFH-OCDMA Fast frequency hopping-OCDMA

GF Galois Fields

IEEE Institute of Electrical and Electronics Engineers, Inc

ITU International Telecommunication union

XIII

LAN Local Area Network

LED Light emitting diode

MAN Metro Area network

MDW Modified-double-weight

ML Maximum-Likelihood

MPR Modified Prime (code)

OLT Optical Line Terminal

ONU Optical Network units

OOC Optical orthogonal code

PON Passive Optical Network

PIN Photodiode with a lightly doped, intrinsic,

Semiconductor region between the P-type regions

Qs S Quality of serves

RS Reed- Solomon

SOA Semiconductor Optical Amplifier

SFS Superflorsent fiber source

SMF Single- mode multiwave length fiber

TDM Time division multiplexing

WDM Wavelength division multiplexing

List of symbols

ΔF Spectral range of the light

KB Boltzmann's constant

h Planck's constant

T Absolute temperature

β Linewidth enhancement factor

Rs rate of spontaneous emission

P Average power

T2σ Thermal noise

Δf Electrical Band width in thermalnoies

R Receiver resistance

Fn Noise Figure

sh2σ Shot noise

q Electron charge

I Light intensity

Be Electrical Band width in shot noise

I2 Average Signal Power

2σ Noise Power

XIV

XV

Rd Responsivity of P-i-n photo diode

hvo Photon energy

η quantum efficiency

Pin Incident Power

SNR Signal to noise Ratio

I1 Intensity of chip one

I0 Intensity of chip zero

ID Threshold decision

N Maximum number of user

W Code word weight

L Code word Length

Iin Multiple access interference

efc(x) error function complementary

K Message symbols (bits)

G generator matrix

95

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APPENDICE Appendix Galois Field m-tuple representation for GF (q = 2m )

for m=8

GF (256) p(X ) = X8 + X4 + X3 + X2 +1 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 2 0 0 1 0 0 0 0 0 3 0 0 0 1 0 0 0 0 4 0 0 0 0 1 0 0 0 5 0 0 0 0 0 1 0 0 6 0 0 0 0 0 0 1 0 7 0 0 0 0 0 0 0 1 8 1 0 1 1 1 0 0 0 9 0 1 0 1 1 1 0 0 10 0 0 1 0 1 1 1 0 11 0 0 0 1 0 1 1 1 12 1 0 1 1 0 0 1 1 13 1 1 1 0 0 0 0 1 14 1 1 0 0 1 0 0 0 15 0 1 1 0 0 1 0 0 16 0 0 1 1 0 0 1 0 17 0 0 0 1 1 0 0 1 18 1 0 1 1 0 1 0 0 19 0 1 0 1 1 0 1 0 20 0 0 1 0 1 1 0 1 21 1 0 1 0 1 1 1 0 22 0 1 0 1 0 1 1 1 23 1 0 0 1 0 0 1 1 24 1 1 1 1 0 0 0 1 25 1 1 0 0 0 0 0 0 26 0 1 1 0 0 0 0 0 27 0 0 1 1 0 0 0 0 28 0 0 0 1 1 0 0 0 29 0 0 0 0 1 1 0 0

30 0 0 0 0 0 1 1 0 31 0 0 0 0 0 0 1 1 32 1 0 1 1 1 0 0 1 33 1 1 1 0 0 1 0 0 34 0 1 1 1 0 0 1 0 35 0 0 1 1 1 0 0 1 36 1 0 1 0 0 1 0 0 37 0 1 0 1 0 0 1 0 38 0 0 1 0 1 0 0 1 39 1 0 1 0 1 1 0 0 40 0 1 0 1 0 1 1 0 41 0 0 1 0 1 0 1 1 42 1 0 1 0 1 1 0 1 43 1 1 1 0 1 1 1 0 44 0 1 1 1 0 1 1 1 45 1 0 0 0 0 0 1 1 46 1 1 1 1 1 0 0 1 47 1 1 0 0 0 1 0 0 48 0 1 1 0 0 0 1 0 49 0 0 1 1 0 0 0 1 50 1 0 1 0 0 0 0 0 51 0 1 0 1 0 0 0 0 52 0 0 1 0 1 0 0 0 53 0 0 0 1 0 1 0 0 54 0 0 0 0 1 0 1 0 55 0 0 0 0 0 1 0 1 56 1 0 1 1 1 0 1 0 57 0 1 0 1 1 1 0 1 58 1 0 0 1 0 1 1 0 59 0 1 0 0 1 0 1 1 60 1 0 0 1 1 1 0 1 61 1 1 1 1 0 1 1 0 62 0 1 1 1 1 0 1 1 63 1 0 0 0 0 1 0 1 64 1 1 1 1 1 0 1 0 65 0 1 1 1 1 1 0 1 66 1 0 0 0 0 1 1 0 67 0 1 0 0 0 0 1 1 68 1 0 0 1 1 0 0 1 69 1 1 1 1 0 1 0 0 70 0 1 1 1 1 0 1 0 71 0 0 1 1 1 1 0 1 72 1 0 1 0 0 1 1 0 73 0 1 0 1 0 0 1 1 74 1 0 0 1 0 0 0 1

75 1 1 1 1 0 0 0 0 76 0 1 1 1 1 0 0 0 77 0 0 1 1 1 1 0 0 78 0 0 0 1 1 1 1 0 79 0 0 0 0 1 1 1 1 80 1 0 1 1 1 1 1 1 81 1 1 1 0 0 1 1 1 82 1 1 0 0 1 0 1 1 83 1 1 0 1 1 1 0 1 84 1 1 0 1 0 1 1 0 85 0 1 1 0 1 0 1 1 86 1 0 0 0 1 1 0 1 87 1 1 1 1 1 1 1 0 88 0 1 1 1 1 1 1 1 89 1 0 0 0 0 1 1 1 90 1 1 1 1 1 0 1 1 91 1 1 0 0 0 1 0 1 92 1 1 0 1 1 0 1 0 93 0 1 1 0 1 1 0 1 94 1 0 0 0 1 1 1 0 95 0 1 0 0 0 1 1 1 96 1 0 0 1 1 0 1 1 97 1 1 1 1 0 1 0 1 98 1 1 0 0 0 0 1 0 99 0 1 1 0 0 0 0 1 100 1 0 0 0 1 0 0 0 101 0 1 0 0 0 1 0 0 102 0 0 1 0 0 0 1 0 103 0 0 0 1 0 0 0 1 104 1 0 1 1 0 0 0 0 105 0 1 0 1 1 0 0 0 106 0 0 1 0 1 1 0 0 107 0 0 0 1 0 1 1 0 108 0 0 0 0 1 0 1 1 109 1 0 1 1 1 1 0 1 110 1 1 1 0 0 1 1 0 111 0 1 1 1 0 0 1 1 112 1 0 0 0 0 0 0 1 113 1 1 1 1 1 0 0 0 114 0 1 1 1 1 1 0 0 115 0 0 1 1 1 1 1 0 116 0 0 0 1 1 1 1 1 117 1 0 1 1 0 1 1 1 118 1 1 1 0 0 0 1 1 119 1 1 0 0 1 0 0 1

120 1 1 0 1 1 1 0 0 121 0 1 1 0 1 1 1 0 122 0 0 1 1 0 1 1 1 123 1 0 1 0 0 0 1 1 124 1 1 1 0 1 0 0 1 125 1 1 0 0 1 1 0 0 126 0 1 1 0 0 1 1 0 127 0 0 1 1 0 0 1 1 128 1 0 1 0 0 0 0 1 129 1 1 1 0 1 0 0 0 130 0 1 1 1 0 1 0 0 131 0 0 1 1 1 0 1 0 132 0 0 0 1 1 1 0 1 133 1 0 1 1 0 1 1 0 134 0 1 0 1 1 0 1 1 135 1 0 0 1 0 1 0 1 136 1 1 1 1 0 0 1 0 137 0 1 1 1 1 0 0 1 138 1 0 0 0 0 1 0 0 139 0 1 0 0 0 0 1 0 140 0 0 1 0 0 0 0 1 141 1 0 1 0 1 0 0 0 142 0 1 0 1 0 1 0 0 143 0 0 1 0 1 0 1 0 144 0 0 0 1 0 1 0 1 145 1 0 1 1 0 0 1 0 146 0 1 0 1 1 0 0 1 147 1 0 0 1 0 1 0 0 148 0 1 0 0 1 0 1 0 149 0 0 1 0 0 1 0 1 150 1 0 1 0 1 0 1 0 151 0 1 0 1 0 1 0 1 152 1 0 0 1 0 0 1 0 153 0 1 0 0 1 0 0 1 154 1 0 0 1 1 1 0 0 155 0 1 0 0 1 1 1 0 156 0 0 1 0 0 1 1 1 157 1 0 1 0 1 0 1 1 158 1 1 1 0 1 1 0 1 159 1 1 0 0 1 1 1 0 160 0 1 1 0 0 1 1 1 161 1 0 0 0 1 0 1 1 162 1 1 1 1 1 1 0 1 163 1 1 0 0 0 1 1 0 164 0 1 1 0 0 0 1 1

165 1 0 0 0 1 0 0 1 166 1 1 1 1 1 1 0 0 167 0 1 1 1 1 1 1 0 168 0 0 1 1 1 1 1 1 169 1 0 1 0 0 1 1 1 170 1 1 1 0 1 0 1 1 171 1 1 0 0 1 1 0 1 172 1 1 0 1 1 1 1 0 173 0 1 1 0 1 1 1 1 174 1 0 0 0 1 1 1 1 175 1 1 1 1 1 1 1 1 176 1 1 0 0 0 1 1 1 177 1 1 0 1 1 0 1 1 178 1 1 0 1 0 1 0 1 189 1 1 0 1 0 0 1 0 180 0 1 1 0 1 0 0 1 181 1 0 0 0 1 1 0 0 182 0 1 0 0 0 1 1 0 183 0 0 1 0 0 0 1 1 184 1 0 1 0 1 0 0 1 185 1 1 1 0 1 1 0 0 186 0 1 1 1 0 1 1 0 187 0 0 1 1 1 0 1 1 188 1 0 1 0 0 1 0 1 189 1 1 1 0 1 0 1 0 190 0 1 1 1 0 1 0 1 191 1 0 0 0 0 0 1 0 192 0 1 0 0 0 0 0 1 193 1 0 0 1 1 0 0 0 194 0 1 0 0 1 1 0 0 195 0 0 1 0 0 1 1 0 196 0 0 0 1 0 0 1 1 197 1 0 1 1 0 0 0 1 198 1 1 1 0 0 0 0 0 199 0 1 1 1 0 0 0 0 200 0 0 1 1 1 0 0 0 201 0 0 0 1 1 1 0 0 202 0 0 0 0 1 1 1 0 203 0 0 0 0 0 1 1 1 204 1 0 1 1 1 0 1 1 205 1 1 1 0 0 1 0 1 206 1 1 0 0 1 0 1 0 207 0 1 1 0 0 1 0 1 208 1 0 0 0 1 0 1 0 209 0 1 0 0 0 1 0 1

210 1 0 0 1 1 0 1 0 211 0 1 0 0 1 1 0 1 212 1 0 0 1 1 1 1 0 213 0 1 0 0 1 1 1 1 214 1 0 0 1 1 1 1 1 215 1 1 1 1 0 1 1 1 216 1 1 0 0 0 0 1 1 217 1 1 0 1 1 0 0 1 218 1 1 0 1 0 1 0 0 219 0 1 1 0 1 0 1 0 220 0 0 1 1 0 1 0 1 221 1 0 1 0 0 0 1 0 222 0 1 0 1 0 0 0 1 223 1 0 0 1 0 0 0 0 224 0 1 0 0 1 0 0 0 225 0 0 1 0 0 1 0 0 226 0 0 0 1 0 0 1 0 227 0 0 0 0 1 0 0 1 228 1 0 1 1 1 1 0 0 229 0 1 0 1 1 1 1 0 230 0 0 1 0 1 1 1 1 231 1 0 1 0 1 1 1 1 232 1 1 1 0 1 1 1 1 233 1 1 0 0 1 1 1 1 234 1 1 0 1 1 1 1 1 235 1 1 0 1 0 1 1 1 236 1 1 0 1 0 0 1 1 237 1 1 0 1 0 0 0 1 238 1 1 0 1 0 0 0 0 239 0 1 1 0 1 0 0 0 240 0 0 1 1 0 1 0 0 241 0 0 0 1 1 0 1 0 242 0 0 0 0 1 1 0 1 243 1 0 1 1 1 1 1 0 244 0 1 0 1 1 1 1 1 245 1 0 0 1 0 1 1 1 246 1 1 1 1 0 0 1 1 247 1 1 0 0 0 0 0 1 248 1 1 0 1 1 0 0 0 249 0 1 1 0 1 1 0 0 250 0 0 1 1 0 1 1 0 251 0 0 0 1 1 0 1 1 252 1 0 1 1 0 1 0 1 253 1 1 1 0 0 0 1 0 254 0 1 1 1 0 0 0 1

by gafar mohamed

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