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
Chapter one Introduction and Literature survey
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
Chapter one Introduction and Literature survey
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
Chapter one Introduction and Literature survey
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).
Chapter two Theoretical Background
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,
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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:
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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.
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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 .
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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 =
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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]
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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 photo- diodes) 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
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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.
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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]:
Chapter two Theoretical Background
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]
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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)
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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].
Chapter two Theoretical Background
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= ]
Chapter two Theoretical Background
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
Chapter two Theoretical Background
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 +=
Chapter two Theoretical Background
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.
Chapter three Research procedures
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 .
Chapter three Research procedures
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.
Chapter three Research procedures
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
Chapter three Research procedures
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
Chapter three Research procedures
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
Chapter three Research procedures
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).
Chapter three Research procedures
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.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Chapter three Research procedures
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
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Appling error correction technique for three type of polynomial (255,247),(255,239),(255,223)for this case only.
Chapter three Research procedures
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.
Chapter three Research procedures
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).
Chapter four Simulation Results
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
Chapter four Simulation Results
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
Chapter four Simulation Results
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).
Chapter four Simulation Results
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
Chapter four Simulation Results
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
Chapter four Simulation Results
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.
Chapter four Simulation Results
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.
Chapter four Simulation Results
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.
Figure (4-7) illustrates the relationship between the number of
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
Chapter four Simulation Results
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
Chapter four Simulation Results
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).
Chapter four Simulation Results
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.
Chapter four Simulation Results
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.
Figure (4-10) illustrates the relationship between the number of
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.
Chapter four Simulation Results
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)
Chapter four Simulation Results
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)
Chapter four Simulation Results
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,
Chapter four Simulation Results
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
Figure (4-14) The relationship between numbers of
Simultaneous user versus Q factor for the case (w=7, µ=16)
Simultaneous user versus Q factor for the case (w=7, µ=17)
Figure (4-15) The relationship between numbers of
Figure (4-16) The relationship between numbers of
Simultaneous user versus Q factor for the case (w=7, µ=18)
Simultaneous user versus Q factor for the case (w=7, µ=22)
Chapter four Simulation Results
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
factor with (w=5), (µ=17)
Figure (4-19) The relationship between number of simultaneous user versus q
factor with (w=5), (µ=18)
Figure (4-20) The relationship between number of simultaneous user versus q
factor with (w=5), (µ=22)
Chapter four Simulation Results
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).
Chapter four Simulation Results
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.
Chapter four Simulation Results
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.
Chapter four Simulation Results
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 .
Chapter four Simulation Results
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 .
Chapter four Simulation Results
81
Figure (4-25) The relation between the number of simultaneous user versus BER for the
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.
Chapter four Simulation Results
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.
Figure (4-26) The relation between the number of simultaneous user versus BER for the
case (µ=17, w=5
Chapter four Simulation Results
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.
Figure (4-27) The relation between the number of simultaneous user versus BER for the
case (µ=18,w=5)
Figure (4-28) illustrates the relationship between the number of
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
Chapter four Simulation Results
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.
Figure (4-28) The relation between the number of simultaneous user versus BER for the
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
Chapter four Simulation Results
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.
Figure (4-29) The relation between the number of simultaneous user versus BER for the
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
Chapter four Simulation Results
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.
Chapter four Simulation Results
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
Chapter four Simulation Results
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.
Chapter four Simulation Results
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)
Figure (4-35) The relation between the number of user versus BER for the case (w=5 ,µ=18 ,Pres=2µw)
Figure (4-36) The relation between the number of user versus BER for the case (w=5 ,µ=22 ,Pres=2µw)
Chapter four Simulation Results
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
Chapter Fiver Conclusion and Future work
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
Chapter Fiver Conclusion and Future work
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
Chapter Fiver Conclusion and Future work
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)
Figure (4.12) The relationship between number of simultaneous user
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)
Figure (4.15) The relationship between number of simultaneous user
Versus Q factor for the case (w=7, µ=18)
Figure (4.16) The relationship between number of simultaneous user
Versus Q factor for the case (w=7, µ=22)
Figure (4.17) The relationship between number of simultaneous user
Versus q factor with (w=5), (µ=16)
Figure (4.18) The relationship between number of simultaneous user
Versus q factor with (w=5), (µ=17)
Figure (4.19) The relationship between number of simultaneous user
Versus q factor with (w=5), (µ=18)
X
Figure (4.20) The relationship between number of simultaneous user
Versus q factor with (w=5), (µ=22)
Figure (4.21) The relation between the number of simultaneous user
Versus BER (dB) for the case (w=7, µ=16)
Figure (4.22) The relation between the number of simultaneous user
Versus BER for the case (µ=17, w=7)
Figure (4.23) The relation between the number of simultaneous user
Versus BER for the case (µ=18, w=7)
Figure (4.24) The relation between the number of simultaneous user
Versus BER dB for the case (µ=22, w=7)
Figure (4.25) The relation between the number of simultaneous user
Versus BER for the case (µ=16, w=5)
Figure (4.26) The relation between the number of simultaneous user
Versus BER for the case (µ=17, w=5)
Figure (4.27) The relation between the number of simultaneous user
Versus BER for the case (µ=18, w=5)
Figure (4.28) The relation between the number of simultaneous user
Versus BER for the case (µ=22, w=5)
Figure (4.29) The relation between the number of simultaneous user
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)
Figure (4.33) The relation between the number of user versus BER for
the case (w=5 ,µ=16 )]
Figure (4.34) The relation between the number of user versus BER for
the case (w=5 ,µ=17 ,Pres=2µw )
Figure (4.35) The relation between the number of user versus BER for
the case (w=5 ,µ=18 ,Pres=2µw)
Figure (4.36) The relation between the number of user versus BER for
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
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