Comparative analysis of Wavelet Packet based MC-CDMA with the Conventional MC-CDMA using HHT tool

1. 1
Chapter 1
INTRODUCTION
1.1 Overview of MC-CDMA System
Multi-Carrier Code Division Multiple Access (MC-CDMA) can be referred to as a
multiple access system which is applied in telecommunication systems based on Orthogonal
Frequency Division Multiplexing (OFDM), permitting the system to provide backup to
numerous users simultaneously. Every user symbol is spread by this system in the frequency
domain meaning that every user symbol is transferred over several parallel sub carriers, however
these user symbols are usually phase shifted (normally 0 or 180 degrees) as per value of the
code. The values of the code vary according to each sub carrier as well as according to each user.
Every sub carrier signal is combined by the receiver by assessing these to recompense changing
strengths of the signal and untie the code shift. Since the signals of dissimilar users possess
dissimilar code values, these can be easily separated by the receiver. As every data symbol
inhabits considerably broader bandwidth (in hertz) as compared to the data rate (in bit/s), a SINR
of lesser than 0 dB is possible. In these systems, numerous parallel streams having lower rate are
generate by segregating the higher data rate stream. Every sub stream is then use to modulate a
dissimilar subcarrier which before transmission is spread over the entire bandwidth [1]. Though a
system like this which makes use of great amount of subcarriers is liable to Inter-Carrier
Interference (ICI) issues. Space-time coding method as well as MC-CDMA system is
investigation hot topics owing to their higher frequency spectrum effectiveness as well as higher
data rate transmission. This Work proposes a complex orthogonal wavelet packet based MC-
CDMA system and investigates the system bit error rate performance and different modulation
techniques over AWGN channel.
In a multi carrier CDMA system, the waveform produced from a complete binary wavelet
packet tree also referred to as wavelet packet waveform set, is used as the modulation waveform.
A fresh receiver is considered which uses time domain localization characteristic of the wavelet
packets. Multi path signals inside single chip period are joined in the time domain in this design
of the receiver. This is done to attain time–domain diversity comparable to the design of the

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traditional RAKE receiver. Wavelet packet transform is used in every RAKE receiver with a
goal of demodulating the equivalent path of the multicarrier signal in the time–domain instead of
frequency domain. After this, equivalent spreading codes are used to de-spread the demodulated
signal. OFDM or MC-CDMA use the Wavelet Packet time diversity combining method which
eliminates the requirement of guard intervals in them. When matched with Filtered multi tone
modulation in wireless application, every sub carrier’s spectra as well as WP method are
overlapped, leading to greater effective use of the spectrum. Or one can say that the
orthogonality of the communicated waveforms cannot be accomplished by either CP (cyclic
prefix)or by sub channels (which are non-overlapping), however it can be accomplished by using
the distinctive simultaneous time as well as frequency localization characteristics of the wavelet
packets that cannot be attained by the traditional DFT-OFDM and MC-CDMA. This is
analogous in sprit as compared to the pulse-shaped OFDM. However only single wavelet
Waveform based MC-CDMA System is used in this design as a replacement for using whole set
of wavelet waveforms. This is not similar to the blind technique based on sub-space, in addition
to this, this is furthermore not similar to the optimum frequency combining also. Furthermore,
time diversity combining is in the sub chip level. Very large amount of narrow frequency bands
constitute the complete frequency band that makes duration of the chip very long as equated to
MC-CDMA system. Consequently, recommended method could be considered as a hybrid
amongst MC-CDMA and WP-MC- CDMA, however the sinusoidal waveforms are substituted
by the WP waveforms.
1.2 Literature Survey
A. Ali et al. [1] Discussed the augmented MC-DS-CDMA system’s performance by
making use of STBC methods as well as DWT. The performance assessments of BER for the
traditional MC-DS-CDMA based on FFT, STBC MC-DS-CDMA and DWT based STBC MC-
DS-CDMA in the dissimilar channel prototypes are done. Also, their assessment for greatest
attainable bit error rate is shown. Experimentation outcomes are given to validate that substantial
improvements could be accomplished by familiarizing such combination method having very
less decoding complexity.

3. 3
A. Qasaymehet al. [2] Presented a new SLT-MC-CDMA transmitter and receiver design
based on the SLT-OFDM which is applied as an elementary unit in the design of Multi-Carrier
Code Division Multiple Access transmitter and receiver to preserve the orthogonality to counter
multiple path frequency SFC. Experimentation outcomes are given to validate the substantial
improvement in the performance of the suggested method. The bit error rate of proposed system
is equated with FFT-MC-CDMA as well as verified in AWGN.
A. Kattoush [3] Introduced wireless digital communication networks which are quickly
increasing leading to a greater requirement for consistent in addition to higher spectral
proficiency systems. Furthermore it was established lately that Radom-DWT based OFDM is
proficient of decreasing the ISI as well as the ICI that are initiated when orthogonality among the
carriers gets lost. Radon-DWT-OFDM could likewise support considerably greater spectrum
effectiveness as equated to FFT- OFDM.
A. Kumar et al. [4] Established as well as assessed MC-CDMA system based on wavelet
packets. In the proposed design of the system, a group of wavelet packets are applied as the
modulation waveforms in a Multi-Carrier Code Division Multiple Access system. The
requirement for CP is eradicated in the proposed design because of the decent orthogonality in
addition to time-frequency localization characteristics of the wavelet packets. Wavelet Packets
possess decent characteristics for instance orthogonality and multi rate flexibility, and have led to
a multiple works for its uses.
A. Almeida et al. [5] Introduced an effective acquisition/correlation method for DS-
CDMA systems by making use of a frequency-domain method using TCH - based training block.
The suggested passive matched-filter type frequency domain method has been compared with the
traditional time-domain active acquisition method. Furthermore by making use of the
information that N-point Discrete Fourier Transform (DFT) could be separated in M smaller
DFTs, this paper offers technique for concurrent decoding/ dispreading as well as
synchronization that shift among 16 bit-length and 256 bit-length cyclic codes consequently
delivering variability in the code rate.
F. and S. Kaiser [6] Study the ideologies of elementary methods as well as the multipath
channel which are required for transmission of the signals. MC-CDMA is defined as a frequency

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PN arrangement and MC-DS-CDMA is defined as a straight forward modification of DS-
CDMA. The authors argue that these identical asymmetric methods are appropriate for 4th
Gen
(4G) as the former one is appropriate for the downlink and latter one is appropriate for the uplink
communication in the cellular systems. Though former one outperforms the latter method, it
requires chip synchronization among users which makes is problematic to position in the uplink.
Consequently, it is imperative to know the multi-carrier spread spectrum techniques for this
asymmetric configuration. Hybrid multiple access systems corresponding to Multi-Carrier
FDMA system is used in this paper.
G. Tomas et al. [7] Introduced wavelet packet transform as an alternative to Fourier
transform in multi-carrier communication. Research papers from this arena dedicate frequently
with Haar or Daubeschies mother wavelet. Different kinds of mother wavelet are considered as
well as equated in flat Rayleigh channel in this paper.However this article deals with employing
wavelet packet transform WPT instead of FT because WP possess decent characteristics which
mark them a contender for user signature waveforms in a CDMA communication system.
H. Steen damet al. [8] Investigated a variation of the traditionalMC-CDMAsystem for
downlink communication. In the suggested MC-CDMAsystem, the amount of chips per symbol
(Nchip), the amount of carriers (Ncarrier) as well as the length of FFT (NFFT) is selected
independently such that the accessible resources could be used extra efficiently. The flexible
MC-CDMAsystem’s bandwidth is proportionate to Nchip, whereas the power spectrum’s
spectral density is contrariwise proportionate to N chip: the transmitted power is not dependent
of N chip. Additionally, the power of small band interfered is spread over a larger bandwidth by
the flexible MC-CDMAsystem such that the resistance of the system to small band interferers
surges for growing N chip.
J.Andrewset al. [9] Developed a smaller complex design of MC-CDMA system with SIC
(MC-SIC) IS which is strong against the sources causing deprivation. The issue of latency
however still exists. But the suggested design of the system could diminish the signal processing
obligatory for every iteration by carrying out the carrier demodulation only single time at the
receiver. When the dispersive channel is present and when the amount of users are equivalent to
N chip, the powers of the beneficial constituent, the interference as well as noise are not
dependent of the amount of chips per symbol, though an optimum guard interval could be
accomplished that increases the performance.

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L.Franciset al. [10] Proposed a novel wireless communication system designated as
Multi-Code Multi-Carrier Code Division Multiple Access that is the achieved by combining
Multi-Code CDMA as well as MC-CDMA, is examined in this article. The proposed system
could fulfill multi-rate services by making use of multi-code systems and multicarrier services
which are used for higher rate transmission. The proposed method is assessed by making use of
Traveling Wave Tube Amplifier (TWTA).This kind of amplifiers keep on offering the finest
micro-wave high power amplifiers (HPA) performance in context of power effectiveness, size as
well as cost, however when it comes to linearity they lag behind Solid State Power Amplifiers
(SSPA's). This article offers a method for increasing linearity of TWTA. The application of pre-
distorter (PD) linearization method is defined to deliver TWTA performance equivalent or
greater to traditional SSPA's.
M. Islamet al. [11] Proposed a new design of Radon-DWT-MC-CDMA transmitter and
receiver based on the Radon-DWT-OFDM which is used as an elementary unit for the design of
MC-CDMA transmitter and receiver with an intention of increasing the orthogonality. The
increased orthogonality helps to tackle the multi-path frequency selective fading channels.
Experimental outcomes are given to validate the substantial improvements in performance as
well as easiness owing to the suggested method. The BER of the suggested system was equated
with FFT-MC-CDMA, Radon-MC-CDMA, and DMWT based Code Division Multiple Access.
These were also verified in Flat fading, AWGN and Selective fading channels. The experimental
outcomes exhibit the better performance of the suggested system when compared with the other
systems.
E. Eskandrani et al. [12] Examined the wavelet transform’s performance as well as WP-
MC-CDMA communications in Rayleigh fading channel for dissimilar classes of the wavelet.
The substitution of the Fourier based complex exponential carriers of MC-CDMA with
orthonormal wavelets packets is an effective technique to evade addition of the guard band or CP
when using the discrete wavelet packet transform (DWPT) based Multi-Carrier Code Division
Multiple Access. This technique also increases the system’s performance. The BER of the
wavelet transform and WP-MC-CDMA Communications in Rayleigh fading channel and
AWGN Channels are equated. Furthermore, the outcomes are equated with the FFT-MC-CDMA

6. 6
in Rayleigh fading channel. It was observed that wavelet packet multicarrier modulation
achieves healthy performance.
M. Yeeet al. [13] Presented that with a swelling upsurge in requirement for individual
wireless radio communications inside the previous era, there is a rising necessity for technical
inventions to fulfil these requirements. Upcoming technology should be capable to permit users
to effectively share mutual resources, if it includes the sharing of frequency spectrum, or
computing services, databanks, or storage amenities. When it comes to mobile cellular
telephony, the powerful forces after this demand comprises the mobility as well as flexibility
provided by this technology. In contradiction of wired communications, forthcoming private
communication networks will permit users the association to an assembly of resources although
appreciating the liberty of mobility. A specific region of rising curiosity is indoor wireless
communications.
P.Grant, et al. [14] Has suggested application characteristics of a MC-CDMA receiver
having software configurable power depletion. This receiver permits the power depletion to be
lessened at the expenditure of a surge in processing delay. Such delay might be imperative in real
time response uses for example voice communication show ever it may not be significant for
other uses for example downloading information and consequently the depletion of power could
be optimized to the traffic. Power lessening is accomplished at the expense of bigger receiver
latency. The MC-CDMA receiver’s performance is correspondingly explained at the close of the
article.
R. Charde. [15] Presented a method related to wavelet transform and median filter for
image reconstruction. In the previous two eras, numerous noise lessening methods have been
established for eradicating noise as well as holding edge details in image. The key objective of
noise lessening is to eradicate the noise sans losing considerable details enclosed in it. Wavelet
transforms are particularly applied for compression, de-noising, thresholding error lessening,
reconstruction as well as image synthesis.
S. Baig [16] Introduced multimedia applications in wireless communication systems in
the third and fourth generations, it is crucial that modulation methods used in this situation are
capable to support higher data rates of the order of 20 Mps to 100 Mbps. One option is to

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associate Multicarrier Modulation (MCM) with CDMA, resulting in a hybrid MC-CDMA digital
data modulation technique. MC-CDMA possesses the interference elimination ability of Code
Division Multiple Access, and the capability of alleviating multiple path propagation impacts of
OFDM. Nevertheless, as in Orthogonal Frequency Division Multiplexing, sub channel
decomposition could not be accomplished sans some guard band, which leads to spectral
inefficiency.
S. Hara [17] Review the three kinds of Multicarrier CDMA scheme, and explain their
benefits as well as drawbacks in terms of transceiver Structures, the spectral effectiveness and
the downlink BER Performance. In this paper the performance comparison of traditional
Discrete Fourier Transform (DFT) based MC-CDMA and DWT-MC-CDMA with two of the
finest prevalent wavelets, specifically Haar and Daubechies wavelets has been presented.
S. Salihet al. [18] Suggested prototype based on phase matrix rotation to increase the
performance of MC-CDMA lies in FFT procedure under the AWGN as well as frequency
selective fading channel. This prototype is applied to decrease the impact of multipath fading.
The outcomes obtained by a computer experiment for a solo user are equated with the novel
method for MC-CDMAbased on FFT for both systems. As a consequence, it could be observed
from the suggested method that a higher enhancement in performance was acquired over the
traditional MC-CDMA, in which the bit error rate is extensively decreased under dissimilar
channel features for frequency selective fading as well as the Additive White Gaussian Noise
channel.
S. Sharma et al. [19] Presented the summary and the performance assessment outcomes
of an OFDM system by making use of FFT as well as DWT. The spacing of the sub carriers is
ideally negligible leading to precisely compact consumption of the spectrum. The outcomes
shown in the study are based on computer experiments achieved by making use of MATLAB,
extremely effective software for numerous applications.
U. Deviet al. [20] Demonstrated the process of a WP-MCM system. Multi-stage tree-
structured Para unitary filter banks are used to generate the wavelet packets by selecting the
correct tree structure. This is done with an aim of lessening the bit error amid the anticipated and
obtained signal for a specific channel state. The proposed technique is examined for the Additive

8. 8
White Gaussian Noise channel. Experimental outcomes validate the effectiveness as well as the
flexibility of the suggested method. The BER is revealed to be similar, and at some instances
improved, to traditional Fourier based OFDM. Assessment of dissimilar class of wavelets was
done and Meyer wavelet appears to be the maximum appropriate wavelet packet.
X.Yu, Guangguo [21] Proposed a new MC-CDMA system which is based on complex
wavelet packet and turbo coding. Rayleigh fading channel has also been used to examine the
BER of the system. The proposed system could tackle the reduction of spectrum effectiveness as
well as energy of traditional MC-CDMA because of introducing cyclic prefix (CP). It also makes
complete use of capability of the turbo codes to tackle fading channel to increase the bit error
rate performance additionally. Theoretic examination and experimental outcomes all indicate
that the suggested system outdoes traditional Multi-Carrier Code Division Multiple Access
system, and its performance is greater as compared to that of the traditional Multi-Carrier Code
Division Multiple Access with cyclic prefix.
M.Li at.al [22] Presented on the basis of time-frequency distribution (TFD) of signals
growing uses in numerous regions of science and engineering for recognizing signals which are
non-stationary as well as signals which are non-linear in nature. This article shows their work of
TF examination of wave signal encountered in ship science by making use of the Hilbert–Huang
transform (HHT).The outcome in the study display that the Hilbert–Huang transform based time-
frequency distribution of encountered wave signal has improved resolution as compared to those
caused from the classical techniques, for example STFT, Wavelet transform (WT) time-
frequency distribution, and Choi –William time-frequency distribution.
The common techniques are OFDM and CDMA, STFT, Wavelet transforms time-
frequency distribution, and Choi –William time-frequency distribution methods in MC-CDMA
system and WP-MC-CDMA, System model and designing of transceiver of MC-CDMA and WP
based MC-CDMA system is discussed in literature review.
1.3 Rationale
The OFDM, CDMA methods are anticipated in the previous works. The Traditional
Fourier transform based MC-CDMA given in the literature review. To tackle ISI and ICI, CP is
added among WP MC-CDMA symbols that consume approximately 25 % of bandwidth. This

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motivates us to propose, Hilbert Huang Transform based MC-CDMA system by making use of
dissimilar modulation methods (BPSK, QPSK) and BER and no. of user, In order to further
improve bandwidth efficiency (spectral efficiency) and lessen the level of interference (ISI and
ICI). This work aims at designing the HHT based MC-CDMA system to overcome the
drawbacks and limitations of WP-MC-CDMA system.
1.4 Problem Statement
In the literature survey, although MC-CDMA systems deliver novel abilities as well as
functions for progressive & more efficient communication, still there exist numerous issues
related with these systems. These issues are linked to carriers, the recognition technique and the
basic channel fading issues. In this thesis these issues impersonated by sinusoidal carriers
problem, channel fading problem, and detection problem are solved by wavelet packets based
MC-CDMA System, but this System is used for non-stationary signal. And it can consider only
desirable signal. But there is no estimated error detection. In this dissertation these problem
posed by HHT based MC-CDMA System proposed in this work and performance assessment of
HHT based multi carrier CDMA Communication with dissimilar modulation methods (BPSK,
QPSK) and BER and throughput has been done. Evaluation of these two techniques based on
some performance parameters with the conventional MC-CDMA system is done. The
experimental study is performed on MATLAB to verify the result of analysis.
1.5 Objective
This study targets at design of an effective MC-CDMA system for wireless
communication network as well as executing it. The aim of this study is to deliver advanced
efficient communication network. This work is completed by studying related theoretical work
and conducting simulation using MATLAB tool. It also assesses the performance of HHT-MC-
CDMA system, WP-MC-CDMA System and Conventional MC-CDMA System based on
performance parameters via the simulation outcomes and equates the outcomes of improved
network; this simulation work is done by using MATLAB tool.
The goal of this research to explore the features of HHT-MC- CDMA and WP-MC-
CDMA System by implementing the system on MATLAB for different scenarios.

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The primary goal of this research is to design the HHT-MC-CDMA communication
system by making use of different modulation methods and BER to solve the drawbacks of
Wavelet Packet Based MC-CDMA System.
 To Overcome the Inter-Carrier Interference (ICI) problems.
 To avoid the near far effect problem.
 To Minimize Inter-Sub stream Interference (ISSI) Data service up to the rate of 2
M bps.
 To overcome estimated error detection problem in WP-MC-CDMA System.
 To improve the performance using Different Modulation Methods in WP-MC-
CDMA System.
 To improve the higher data rate transmission.
 To analyze the effect of BPSK, QPSK modulation techniques in MC-CDMA
System and WP-MC-CDMA System.
 To analyze its performance of HHT-MC-CDMA System using different
parameters like BER, number of users.
1.6 Methodology
This research is divided into three phases.
1. The initial phase involves review of various literatures on its basis of given MC-CDMA
and WP based MC-CDMA communication system and its process.
2. The second phase consists of design the conventional MC-CDMA system and WP-MC-
CDMA system and HHT-MC-CDMA system. We have used following steps:
 Simulation of CDMA technology with fading channel.
 Simulation of conventional MC-CDMA system using MATLAB.
 Simulation of WP-MC-CDMA system.
 Simulation for the different modulation methods like (BPSK, QPSK)
modulation technique.
 Simulation of HHT based MC-CDMA system.
 Comparative study of HHT-MC-CDMA system, WP-MC-CDMA system with
the traditional MC-CDMA system using BER and different number of users.

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3. Finally, the proposed method will be analyzed and compared to current methods. The
comparison will involve different parameters like BER and different number of user. The
complete methodology will be described in detail in result section.
1.7 Organization of Thesis
The contents of this thesis are organized in five chapters.
Chapter I, Present the problem statement, the methodology of the work, the research
work and the core role of this thesis. The theories of MC-CDMA technique are introduced.
Carrier problem, sinusoidal carrier problems are also presented. After this the explanation for the
wavelet as well as wavelet packets features, the modulation methods by making use of wavelet
packets and the application of wavelet and wavelet packets in communication systems is
presented. HHT based MC-CDMA system is also explained in these dissertations. Performance
of these three methods is measured in communication systems are presented using different
parameters specifically, BER and different modulation methods and quantity of users.
Chapter II, Design the transmitter and the receiver models of traditional MC-
CDMAsystem, WP-MC-CDMAsystem and HHT-MC-CDMAsystem are described and
analyzed.
Chapter III, a study of the HHT based MC-CDMAsystem’s performance has been
presented. The SNR, BER, different number of user, different modulation techniques
performances of the system are, correspondingly given in Chapter. The impact of some of the
system parameters for example, the BER, different modulation methods, quantity of users,
different wavelet packets families is measured. Furthermore, an assessment of proposed system
performance with HHT-MC-CDMAsystem, WP-MC-CDMA system and conventional MC-
CDMAsystem is presented.
Chapters IV, based on the performance of HHT-MC-CDMAsystem is analysed the BER
and different modulation techniques namely (BPSK and QPSK) performances of HHT based
MC-CDMA.
Chapter V, a HHT-MC-CDMA communications system is analysed. Models for
Transmitter, channel as well as receiver which use combining method are presented. The

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performance on the basis of BER and number of user is also shown. Furthermore, the
performance of the system is associated to that of WP-MC-CDMA systems and conventional
MC-CDMA systems.
Lastly, Chapter V presents the various results in the chapter and provides the conclusion
of this study. In addition to this, it also provides future work which could be derived from it.

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Chapter 2
THEORETICAL BACKGROUND
2.1 Conventional MC-CDMA System
2.1.1 Concepts of CDMA
For diverse streams of data multiplexing may be done by multiplication of the data
stream’s data symbols with a spreading code entirely allocated to the respective stream of data.
This is done before superposition of the other streams of data with the spread data symbols.
Entire streams of data make use of the identical bandwidth at the identical time in CDM.
Dependent on the type of use, the spreading codes must be orthogonal mutually to the extent
with the intention of reducing interfering among diverse streams of data. Numerous access
systems in which the users’ data is divided by CDM are mentioned as CDMA. Such systems are
required, for instance, in mobile radio systems, WCDMA/UMTS. Furthermore they can also be
used in HSPA, IS-95, in addition to CDMA-2000.
CDMA is a method of multiplexing in which many users concurrently as well as non-
synchronously use a channel. They do it by modulation and then spread the irinfo-carrying
signals with already-allocated signature series/sequences. CDMA is assumed to be a contender to
provide backing for audio-visual amenities in mobile radio communications, since it possess its
specific abilities to manage asynchronous behaviour of audio-visual data traffic, to offer
advanced capability as compared to orthodox access methods for example TDMA and FDMA.
Another reason is attributed to its ability to battle the aggressive channel frequency selectivity. In
contrast, the multiple carrier modulation method, frequently named OFDM, is also gaining
importance in the arena of radio communications. This is mostly for the reason of the
requirement to communicate higher data rate in a mobile atmosphere that creates an extremely
aggressive radio channel.
2.1.2 Benefits and Disadvantages of CDMA System
Orthodox CDMA method shave numerous benefits in cellular environments comprising
uncomplicated frequency scheduling, higher resistance to interfering when a higher processing
gain is considered as well as dynamic data rate adjustment. In addition to these benefits, CDMA

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grieves from numerous glitches in multiple-user wireless Communications systems having
inadequate accessible bandwidth [2].
 Multiple Access Interference (MAI). DS-CDMA system’s performance declines
quickly with the surge in amount of instantaneously active users because the capability of
system having modest processing gain is restricted by MAI.
 Complication. Using a matched filter receiver is necessary to make use of entire multi-
path diversity which is estimated by a rake receiver having enough amount of arms. In
such cases, the mandatory quantity of arms is given by D = τmax/Tc+ 1. Furthermore, the
coordination of receiver is also necessary to the channel impulse response which is time-
variant in nature. Therefore, appropriate channel approximation is essential. This causes
additional receiver complexity having adjustable receiver filters as well as a significant
signalling overhead.
 Single/Multi-Tone Interference. The receiver of orthodox CDMA system disseminates
the interfering signal across the entire communication bandwidth when single-tone or
multi-tone interference is considered while the anticipated signal portion is not spread. If
such kind of interference suppression is insufficient, extra processes are required to be
carried out at the receiver, for example notch filtering in the time domain or in the
frequency domain to partially decline the quantity of interfering [14,19]. Henceforth, this
additional processing causes extra receiver difficulties.
2.1.3 Multi Carrier Concept
To transform a higher rate stream of data which is serial in nature, on to numerous
parallel lower rate sub-streams, multi-carrier communication is used. This technique modulates
every piece of sub-stream over extra sub-carrier. This lessen the impacts of delay spread, i.e. ISI,
considerably since the symbol rate on every sub-carrier is lesser as equated to the original serial
data symbol rate. On the other hand, OFDM is a much lesser complex system used for
modulation of several sub-carriers proficiently by making use of digital signal processing.

15. 15
Figure 2.1 Diagram of Multi Carrier Transmissions
A specimen of MCM having four sub-channels Nc = 4 are portrayed in above figure 2.1.
The 3-D time/frequency/power density illustration is considered to demonstrate the standards of
numerous multi-carrier as well as multi-carrier spread spectrum methods. 3Dparametric range of
the signal is specified by the cuboid. Signal’s maximum energy is placed in this but it does not
describe regarding the pulse or spectrum modeling.
Figure 2.2 Diagram of Multi Carrier Modulation Having Nc = 4 Sub-Channel
There is an imperative planning objective for a multi-carrier communication system
relying on OFDM in a mobile radio channel. First one reflects the channel as non-varying in time
frame throughout single OFDM symbol and second one assumes flat fading for each sub-
channel. Consequently, the duration of Orthogonal Frequency Division Multiplexing symbol
must be lesser than channel’s coherence time (t)c; in addition to this the bandwidth of sub-carrier
must be lesser as compared to channel’s coherence bandwidth (f)c. Once these requirements are
satisfied, the recognition of smaller complex receivers is thinkable.
(A)
(E)
(D)
(C)
(B)
1cf f 2cf f 3cf f 4cf f 5cf f
1
T
1
T
Orthogonal
Orthogonal, n=3
Orthogonal, n=2
Orthogonal, n=1
Non Orthogonal

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 Damage to spectral effectiveness owing to the guard interval.
 Extra delicate to Doppler spreads as compared to single-carrier modulated
schemes.
 Phase noise initiated by the faultiness of the transceiver oscillator Influences
the performance of the system.
 Precise frequency as well as time synchronization is compulsory.
2.1.4 Orthogonal Frequency Division Multiplexing (OFDM)
The OFDM can be considered as a multi-carrier modulation technique that is extensively
accepted as well as maximum frequently used now-a-days. In this, the modulation as well as
demodulation is realized effortlessly by Inverse DFT and DFT operators. The input data bits are
essentially trimmed by a quadrilateral window. In addition to this, the spectrum’s envelope is
similar to the sinc(w) that produces relatively higher side lobes. This causes relatively higher
interfering once the channel losses cannot be entirely compensated. Faults related to time
synchronization initiating from bad alignment of symbols at demodulator side is a severe design
concern. This happens for the reason that they lead to ISI as well as ICI that rigorously reduces
the performance of the system. Numerous investigations have been done to alleviate this
difficulty. For digital modulation, Wavelet transformation has lately appeared as a solid
contender. It was initially suggested by Lindsey in 1997 which can be used as a substitute to
OFDM. The essential concepts of both systems possess several resemblances in the context of
how they function and perform nevertheless there are few noteworthy dissimilarities that give
these systems distinguishing features. While the former one uses Fourier bases, the latter one
makes use of wavelet packet bases that are created using a family of finite impulse response
filters named Para unitary filters. The former one’s signals only overlay in the frequency domain
whereas the signals used in the latter technique overlay in time as well as frequency domain.
Owing to time overlapping, WPM systems could not make use of CP or guard interval which is
frequently considered in suchsystems. OFDM exploits cyclic prefix to prevail over the
interfering of the signals instigated by dispersive channels. The utmost inspiration for using
WPM systems is because of the independence they offer to communication systems engineers.
Contrasting to the Fourier bases that are fixed sines/cosines, WPM makes use of wavelets that
provide elasticity as well as adjustment which may be personalized to fulfil a manufacturing
requirement.

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A communication scheme has NC source symbols having complex values Sn, {n = 0, 1,
2, ...., NC– 1}. These symbols are modulated using multi-carrier technique and sent in parallel on
to NCsub-Carriers. The acquisition of these symbols can be done afterwards source and channel
coding, interleaving, and Symbol Mapping. For data symbols which are serial in nature, the
source symbol duration Tdis achieved after Serial-to-parallel transformation in the Orthogonal
Frequency Division Multiplexing symbol duration.
Ts= NC Td.
NC sub-streams are modulated by OFDM on sub-carriers which are having a space of Fs=
1/ Ts with the intention of achieving orthogonality among the signals on the NCsub-carrier,
assuming a rectangular pulse modeling. The NC parallel modulated source symbol Sn, n = {0, 1,
2, ...., NC –1}, are mentioned as an Orthogonal Frequency Division Multiplexing symbol.
The frequencies of NC sub-carrier are positioned at Fn= n/ Ts, n = {0, 1, 2, ...., NC –1}.
The 16 sub-carriers are depicted by a solid curve in figure 1.3 displays a solid curve
against the normalized frequency ftd. It could be seen that the power density spectrum is moved
towards the middle frequency. The symbols are communicated with identical power. The
primary modulated sub-carrier’s power density spectrum is shown by the dotted curve. The
creation of the complete power density spectrum has been specified as the addition of NC
separate power density spectra, every symbol moved by Fs. When NC has larger values, the
power density spectrum turns out to be flat in the normalized frequency having the range − 0.5 ≤
fTd ≤ 0.5 which comprises the NC sub-channels.
Figure 2.3 Diagram of OFDM Technique

18. 18
This Figure 2.3 represents four subcarriers modulated by assigned symbols to it and
hence narrow channels exhibit sinc shape. Subcarriers are also maintaining the orthogonality . It
represents the overall transmission bandwidth. The orthogonality of the subcarriers can be
proved by multiplying the time waveforms of any two subcarriers are also maintaining the
orthogonality over the symbol period. The outcome will be nil. When we multiply the two
orthogonal sinc waves together, it is the similar to mixing these subcarriers. The result is addition
as well as subtraction frequency component, that is permanently the integer subcarrier frequency.
This is because the frequency of the two mixing sub carrier possess an integer of cycles. Because
of linearity of the system, the integral of respective frequency element distinctly and then joining
the outcomes by totaling the two sub-integrals are nil. Consequently the subsequent totaling of
the two comes out to be nil too. Therefore the mutual orthogonal nature of frequency
components is proven.
2.1.5 Time Domain Analysis
Orthogonal Subscriber setting in the frequency domain with 32 point IFFT bin (the IFFT
bin is symmetrical about center with real and imaginary parts) corresponding time domain
interpolations for interval N= 32 samples.
Figure 2.4 Diagram of Time Domain Analysis

19. 19
2.1.6 OFDM Technology:-
Figure2.5.Diagram of OFDM Technology
2.1.7 Why Need Use Guard Period.
Figure 2.6 Diagram of Function of the Guard Period for Shielding Against ISI.
In high data communication, the ISI is a basic found issue. It happens once the
transmission intervenes with own self and the transmission couldn’t be decoded by the receiver
properly, the added guard interval and its effect in reducing ISI. On condition that the multipath
delay echoes keep inside the duration of the guard period, there is stringently no restriction
concerning the echo’s signal level. They might surpass smaller path’s signal level. The energy of

20. 20
the energy from entire routes adds up at the input side to the receiver. As the fast Fourier
transform is energy saver, the complete accessible power is given to the decoder. However when
the spread of delay is lengthier as compared to the guard interval, it starts to create ISI.
In OFDM modulation, the available channel divided into several independent Subcarriers
orthogonal to each other preventing ICI. The received signals are retrieved in the reverse way.
The orthogonal frequency difference is not selected arbitrarily but is selected based on the data
rate or symbol time.
2.1.8 Benefits and Disadvantages of OFDM
This segment reviews the strong points as well as flaws of MCM based on OFDM.
 Benefits:
 Higher spectral effectiveness owing to approximately rectangular frequency
spectrum for higher amount of subcarriers.
 Modest digital realization by means of the fast Fourier transform process.
 Lesser complex receivers owing to the prevention of ISI as well as ICI having an
adequately large Guard interval.
 Dynamic spectrum adjustment could be recognized, for instance, notch filtering.
 Diverse modulation methods could be considered on separate sub-carriers that are
adjusted to the transmission situations on respective sub-carrier, for example,
water filling.
 Weaknesses:
 Multi-carrier signals having higher PAPR need great linear amplifiers. Else,
performance depreciations happen besides it will also lead to enhancement in the
out-of-band power.
2.1.9 Diagram of MC-CDMA Communication.
MC-CDMA broadcasts user’s data symbol concurrently on numerous narrowband sub-
channels. After broadcasting of these data symbols, their multiplication is done using the chips of
user–particular spreading code. This is demonstrated in figure 2.7. MCM is accomplished by
means of the less complex OFDM process. Basic equalization having single complex-valued
multiplication for each sub channel could be achieved because of flat fading on the narrowband

21. 21
sub-channels. MC-CDMA suggests a dynamic design of system permitting adaptable receiver
complexities, as length of the spreading code should not be necessarily selected equivalent to the
amount of sub-carriers.
The basic signal in MC-CDMA is created by a sequential concatenation of traditional
DS-CDMA with Orthogonal Frequency Division Multiplexing. Every chip of the direct sequence
spread data symbol is mapped onto a dissimilar sub-carrier. Consequently, by making use of
MC-CDMA these chips are communicated in parallel on dissimilar sub-carriers, as compared to
a sequential communication in case of DS-CDMA. Suppose Multi-Carrier Code Division
Multiple Access mobile radio system has K amount of concurrently active users.
Figure 2.7 Diagram of MC CDMA System
Above figure displays multi-carrier spectrum spreading which is done for single data
symbol d(k) having complex values is assigned to user k. The symbol rate of serial data is 1/Td.
For briefness, however without losing generalization, the signal creation in MC-CDMA is
defined for one data Symbol for every user. This is done to omit data symbol index. In the
transmitter, multiplication of the symbol d(k) is carried out with the Spreading code of the
respective user
W(k) = (w(k)0, w(k)1 . . . w(k) L−1) T
L = Pr.G,
Where Pr.G describes the processing gain. The chip rate of the serial spreading code
w(k) earlier to serial-to-parallel change.

22. 22
2.1.10 OFDM with Code Division Multiplexing (OFDM-CDM)
OFDM with Code Division Multiplexing is a multiplexing system which is capable to use
diversity in a superior way as compared to traditional Orthogonal Frequency Division
Multiplexing systems. For dissemination of all the data symbols, numerous sub-carriers and/or
numerous OFDM symbols are used. This is how the system exploits extra time and/or frequency
diversity. Self-interfering among data symbols could be reduced by making use of orthogonal
spreading code. However, self-interfering happens in fading channels because orthogonality gets
lost among the spreading codes. To lessen this damage, effective data discovery as well as
decoding method is obligatory. The working of OFDM-CDM is displayed in Figure 2.8.
Figure 2.8 Diagram of OFDM- CDM Transmitters and Receiver
2.1.11 MC-CDMA System
In MC-CDMA systems, stream having higher data rate is divided innumerous parallel
streams having lesser rate. After division, every sub stream modulates a dissimilar sub carrier
which is then spread over the entire B Width prior to broadcast. Nevertheless, system like this
that uses huge amount of Sub carriers is susceptible to ICI issues.
MC-CDMA communicates user’s data symbol concurrently on numerous narrowband
sub-channels. Multiplication of these data symbols is then carried out by the chips of the
spreading code specific to a particular user. MCM is attained by making use of the lesser
complex OFDM process.
• It is Frequency domain spreading method.

23. 23
• The resultant spectrum of every sub carrier could fulfill the orthogonality
requirement having the smallest frequency separation.
• Hadamard Walsh codes can also be used as an optimal orthogonal set in a
(synchronous) down-link mobile radio communication channel.
• It is a possible contender for the 4th wireless communication system.
Figure 2.9 Diagram of MC-CDMA System
2.1.12 MC-CDMA System Parameters
No. Parameter Value characteristics
1 Spreading codes Walsh–Hadamard codes
2 Spreading code length L 8
3 System load Fully loaded
4 Symbol mapping QPSK,8-PSK,16-QAM
5 FEC code rate R and FEC decoder 4/5, 2/3, 1/2, 1/3 with Viterbi decoder
6 FEC codes Convolution codes with memory 6
7 Channel estimation and synchronization Perfect
8 Mobile radio channel Uncorrelated Rayleigh fading channel
Table 2.1 Different performance parameter of MC-CDMA System

24. 24
The MC-CDMA system’s performance shown in this segment is valid to any MC-CDMA
system having a random communication bandwidth B or having a random amount of sub-
systems Q, besides having a random amount of data symbols M communicated for each user in
an OFDM symbol, ensuing in a random amount of sub-carriers. There must be 8 sub-carriers
inside a sub-system, whereas the Amplitudes of the channel fading must be Rayleigh-distributed.
Furthermore, they must not be correlated on the sub-carriers of a sub-system because of suitable
frequency interleaving. The damage in signal to noise ratio because of the guard interval has not
been considered in the outcomes. The purpose is to calculate damage caused to SNR (occurring
because of guar interval) separately for every guard interval. Consequently, the outcomes shown
could be adjusted to any guard interval.
2.1.13 MC-CDMA Transmitter
An OFDM carrier signal results from the addition of multiple orthogonal sub-carriers,
having baseband data on every sub-carrier that is autonomously modulated normally by means of
some sort of QAM or BPSK. This combined baseband signal is normally required for the
modulation of a foremost RF carrier. Let us suppose S(n) represents a sequential stream of binary
numbers which are initially de-multiplexed in N parallel streams by doing inverse multiplexing.
After this, by means of modulation constellation, everyone is mapped onto a (probably complex)
symbol stream. Since the constellations might be dissimilar, therefore some streams might
transmit a greater bit-rate as compared to others.
An IFFT is calculated for every group of symbols, resulting in a group of complex time-
domain values. These values are afterwards quadrature -mixed to pass-band by the normal
technique. DACs are used to change the real and imaginary parts to the analogue domain. After
this, the obtained analog signals are used for the modulation of cos and sin waves at the carrier
frequency fc, correspondingly. Signal to be transmitted, S(t), is then realized by summing up
these signals.

25. 25
Figure 2.10 Diagram of MC CDMA Transmitter
2.1.14 MC-CDMA Receiver
Suppose r(t) represents the signal received by the receiver. This uses cos and sin waves to
quadrature-mix the signal down to baseband at the same carrier frequency. Signals generated
from this process are positioned on 2fc, therefore to reject such signals, low-pass filters are used.
After this sampling and digitization of the baseband signals is carried out by means of ADCs, in
addition to this, to change the signals back to the frequency domain forward fast Fourier
transform is used which yields N parallel streams. In order to change every single stream to a
binary stream, a suitable symbol detector is used. To have a sequential stream s(n), these streams
are recombined such that the obtained sequential stream is an approximation of the initial binary
stream at the transmitter.
Figure 2.11 Diagram of MC-CDMA Receiver
(c) Receiver
1cos(2 )f t
2cos(2 )f t
1
j
q 
2
j
q 
Received
Signal
cos(2 )Nf t
j
Nq 
LPF
LPF
LPF

j
D 
my

26. 26
2.1.15 Advantages of MC-CDMA Communication.
The key advantage of MC communication is its strength in frequency selective fading
channels. In this communication, the equalization is usually done in the frequency domain
leading to another main advantage, i.e. less signal processing complexity. Some other advantages
are as follows:
 MC-CDMA has higher spectral effectiveness as well as the less receiver
complexity that allows it to be chosen as decent contender for the downlink of a
cellular system.
 The less value of PAPR of MC-CDMA having less quantity of subcarriers marks
it as suitable for the uplink of a multiple user system.
 Scalability.
 Interoperability in Network and mobile Environment.
 Easy application with Hada mard Transform and Fast Fourier Transform.
 Less complex receivers
 Great spectral effectiveness.
 Great frequency diversity gain because of spreading in the frequency.
 Minimum Frequency Separation
2.1.16 Drawbacks of MC-CDMA Communication.
Some disadvantages of MC-CDMA communication are as follows:
 Least frequency separation among every sub carrier at the similar time.
 Time diversity.
 Detection problem
 Carrier Problem.
 High PAPR Especially in the uplink.
2.1.17 Applications of MC-CDMA Communication.
 Beyond 3G and 4G High data rates: 100 Mbps for DL 20 Mbps for UL
 Higher spectral efficiency in multi-cell environment.
 Slot/frame acquisition channel estimation: MIMO and UL,UL synchronization.
 Competition with evolution of existing DS-CDMA systems.

27. 27
 Power line communications (PLC)
 Cellular system: resistance to inter-cell interference.
 High data rates (100 Mbps).
 Compliant with authorized spectrum mask.
 Competition with OFDMA.
 Cognitive radio
 Adaptive to unused frequency bands.
 Efficient image transmission.
 Quality evaluation
 After 3G, Signal could be effortlessly communicated as well as received By
means of FFT Device sans increase in complexity.
2.1.18 Walsh–Hada Mard Codes
Orthogonal Walsh-Hada mard codes are easy to produce repeatedly by means of the
subsequent Hada mard matrix generation.
CL = [CL/2 CL/2]
[CL/2−CL/2]
L = 2m, m≥ 1, C1 = 1.(1)
The greatest amount of obtainable orthogonal spreading codes is L that decides the
greatest quantity of active users K. The generation of Hada mard matrix defined in Equation (1)
could similarly be used to accomplish L-ray Walsh–Hada mard modulation that could be used in
the uplink of aMC-CDMA system along with PN spreading [14, 15]
2.1.19 Additive White Gaussian Noise (AWGN) Channel
An AWGN channel is defined as additive white Gaussian noise to the signal that goes
through it. The components of signal incoming through dissimilar propagation routes might add
in a destructive way, leading to phenomena known as signal fading.

28. 28
2.2 Wavelet Packet Based MC-CDMA System
2.2.1 Wavelet Based Communication Systems.
Wavelets can be considered as minor waves having limited energy. Their energy is
restricted in time domain so as to provide an instrument for the examination of temporary, no
stationary or time changing functions. Although a wavelet possesses the oscillating wave-like
features, it furthermore possesses the capability to permit concurrent time as well as frequency
examination having dynamic mathematical features. These are also used to examine signals in
similar method like complex exponential is examined in Fourier analysis of signals. Functions of
the wavelet could be used to examine not only static signals (the random variations in the signal
remain same in context of time, i.e., its mean as well as variance are not dependent of time.
Furthermore, the auto-correlation function depends only on time variance), these can furthermore
be used for decomposition of non stationary as well as time fluctuating signals. The elementary
notion in the application of wavelets in communication systems and other applications is to
characterize the signal or info by making use of wavelets more effective than by using sinusoids.
2.2.2 Wavelet and Wavelet Transform.
Wavelet transform can be defined as a dual-parameter expansion of a signal in context of
specific base functions or wavelets. Let ψ (t) denotes the mother wavelet, scaling as well as
translation of ψ (t)is done to obtain the daughter wavelets as:
Ψa, b (t) =1/√a ψ(t −b/a)
Where a represents the scale or transposed frequency parameter, b represents real value
and known as the shift parameter. The element 1/√a maintains the daughter wavelets’ energy at
constant level. Every scaled as well as transformed wavelet maintains the figure of the basic
wavelet. Furthermore, it possesses the identical amount of fluctuation just like the basic wavelet.
Nevertheless, the scaling as well as transformation should be done in proper order as these
processes are not commutative. The ψa, b (t) transform is termed as Continuous Wavelet
Transform (CWT) since {a, b} are continuous-valued,

29. 29
2.2.3 Detection Method
In DS-CDMA, a different signature code is allocated to every user with the intention of
modulating as well as spreading the information signal. It is then permitted to communicate over
the identical channel along with other users. Obtained signal is compared with the signature code
sequence of very user for demodulating the information signals communicated by every user.
MC-CDMA and WP-MC-CDMA have the identical detection. Since the carrier, code, and
wavelet packets are required to modulate the signal at the transmitter side, these are similarly
required to demodulate as well as compare the signal at the receiver.
2.2.4 Conventional Single User Detection
In order to detect the single user conventionally, received signal is demodulated first and
then correlated with the signature code of the specific user. After this the verdict is made by and
the detector by matching the outputs of the correlator with threshold values suitable for energy
level of every user. As the verdict for signal of every user is merely based on the correlator’s
output which makes use of the signature waveform of the specific user, the detector does not
considers the interferences or evenly simulates the total noise and interfering, as noise. The type
of detector is best whenever Code Division Multiple Access signature codes possess
orthogonality. Nevertheless, in real-world uses the signature code might not show orthogonality
instead they might display some cross-correlation characteristics triggering the existences of
small amount of nosiness. This impacts the receiver and results in meager BER performance.
The near-far issue because of MAI is solved by the putting into practice a very quick plus precise
power control.
2.2.5 Multi User Detection.
Multiple user detection denotes to the finding of signals that are interfering with each
other that happens in numerous MAC systems. The procedure uses the info of every user as well
as interfering users in the systems. The best performance can be obtained by suppressing MAI
which also supports greater quantity of users and releases power control necessities too.
However, computational difficulty of the optimum detector surges exponentially along with the
product of the amount of users in the system and the channel memory. This leads to the

30. 30
exploration for detectors which may lessen the complexity necessities of multiple-user detectors
and can provide almost-optimal performance.
2.2.6 Performance Measures
The objective in communication systems is to plan systems which communicate info to
the receiver having slight deterioration possible though filling design limits of permissible
transmitted energy, permissible signal bandwidth as well as price. In this work, the proposed
system’s performance is computed in terms of SNIR, BER and outage probability.
2.2.7 Wavelet Packet Based MC-CDMA.
 Negligible side lobe energy leakage.
 Reducing nosiness produced by ICI and MAI.
 Orthogonal in nature
 Well-localized in time as well as frequency domains.
 Decreases the necessity of frequency or time guard among dissimilar user signals.
 Retains the orthogonality for overlapped wavelet packets in time as well as
frequency domains.
2.2.8 Characteristics of Wavelet Packet.
 For data compression analysis.
 Effect of non-ideal conditions.
 Frequency selective channel
 The received signal from numerous routes, having the identical info, is presumed
to be uncorrelated.
2.2.9 Wavelet and Wavelet Packets Applications in Communications.
Wavelets are considered as a substitute to the Fourier transform from the time it came
into existence. This is owing to the fact that it is beneficial for the examination as well as
processing of a set of signals for which a sinusoidal demonstration is insufficient. This set of
signals comprises no stationary in addition to a transient signal. With the intention of suppressing
certain kinds of interferences, the wavelet transform is assumed to be more superior to the

31. 31
Fourier transform. Selection of transform to change the interference to a delta function in the
transform domain is the best way for mitigating the interference. At that time, basic exciter could
eliminate the interfering sans eliminating a substantial quantity of the anticipated signal’s energy.
After that anticipated signal which is free from almost any kind of interference can be produced
from an inverse Transform. The lessening of side lobes in the changed domain is the foremost
benefit of using wavelets as contrast to STFT basis functions.
The interference alleviation method based on wavelet transform is used in DS-Spread
Spectrum. This method was compared with Fourier transform interference alleviation methods.
These methods segregate a substantial quantity of fixed narrowband jammer to a moderately
lesser quantity of bins. For lesser quantity of eliminated bins, Short-Time Fourier Transform
based method beats the DWT. Though, with a great quantity of eliminated bins, DWT based
method beats the Short-Time Fourier Transform. For non-stationary interference, the Short-Time
Fourier Transform is not proficient of segregating the pulsed interference energy to a lesser
quantity of bins.
2.3 HHT BASED MC-CDMA SYSTEM
2.3.1 Hilbert–Huang Transforms (HHT)
A signal could be disintegrated into intrinsic mode functions (IMF) by means of Hilbert–
Huang transform (HHT) which can also be used to obtain immediate frequency information. It is
intended to do fine for information that is non-stationary as well as non-linear. This transform is
identical to a procedure (an experimental method) when compared to other basic transforms for
example, the Fourier transform. Furthermore it could be applied to a data set too.
2.3.2 Introduction of HHT
The name of Hilbert–Huang transforms (HHT) was designated by NASA and it was
recommended by Huang et al. (1996, 1998, 1999, 2003, 2012). It is the outcome of the empirical
mode decomposition (EMD) and the Hilbert spectral analysis (HSA). The decomposition of the
signal in IMF is done by using the EMD technique and immediate data related to frequency can
be obtained by the HAS method. The HHT delivers a novel technique of examining no stationary
and non-linear time series data.

32. 32
2.3.3 Introduction to Empirical Mode Decomposition (EMD) and Intrinsic
Mode Functions (IMF)
The empirical mode decomposition (EMD) technique is the most important fragment of
the Hilbert–Huang transforms. By making use of the EMD technique, one can decompose any
kind of complex data set in a predetermined and lesser amount of components. These
components are a group of IMFs that signifies a normally basic oscillatory mode as basic
harmonic function. By meaning, this is identical to the function having the identical amount of
extrema as well as zero crossings. Also it has its envelopes which are symmetric in regards to
zero. The explanation of intrinsic mode function promises a good Hilbert transform of the
function. This technique working in the time domain is adjustable and extremely effective. It
could be used for non-linear as well as no stationary processes because it is dependent on the
local features of time scale of the data.
2.3.4 Introduction to Hilbert Spectral Analysis (HSA)
The Hilbert spectral analysis (HSA) offers a technique for investigating the Intrinsic
Mode Function’s immediate data related to frequency as functions of time which provides sharp
IDs of embedded structures. The final outcome is an energy-frequency-time spread that can be
labeled as the Hilbert spectrum.
2.3.5 Empirical Mode Decomposition (EMD) Techniques.
The EMD method is an essential phase to lessen any particular data in a group of IMFs
and to these groups the Hilbert spectral investigation could be realized. An Intrinsic Mode
Function can be considered like a function which fulfills the subsequent necessities. In the
complete set of data, the amount of extrema as well as the amount of zero-crossings should be
equivalent to one or difference should not be more than one.
 Local maxima define the average value of the envelope at any point and the envelope
defined by the local minima is zero.
Consequently, an Intrinsic Mode Function characterizes a basic oscillatory mode like a
matching part to the basic harmonic function. Nevertheless it is far more common: an Intrinsic
Mode Function can be used as a replacement for uniform amplitude and frequencies in a basic

33. 33
harmonic constituent since it possess flexible amplitude and frequency along the time axis. The
process of taking out an Intrinsic Mode Function is known as sifting which is carried out in the
following way:
1. Categorize entire local extreme in the investigation data.
2. Formulate the upper envelope by joining all the local maxima by a cubic spline line.
3. Generate the lower enveloper by reiterating the process for the local minima.
The data should be covered between the upper as well as lower envelopes. Their average
is m1. Suppose h1 is the initial component which is the difference among the data and m1. In an
ideal condition; h1 must fulfill the description of an Intrinsic Mode Function for constructing h1
defined above must have made it symmetric and possessing entire positive maxima and entire
negative minima. Once the primary round of sifting is completed, local maximum can be found
from a crest. The appropriate modes absent in the original investigation are essentially disclosed
by fresh extrema produced in this manner. In the succeeding sifting procedure, h1 could be
considered like a proto-Intrinsic Mode Function. In the following stage, it is considered like the
data, and after repetitive sifting upto k times, h1 converts into an Intrinsic Mode Function, that is
Then, it is designated as the first IMF component from the data:
The stopping conditions of the sifting procedure
The stopping condition controls the amount of sifting stages to generate an IMF. Two
dissimilar stopping conditions are used conventionally:
 The primary condition is suggested by Huang et al. (1998) which is identical to the
Cauchy convergence test. The sum of difference, SD, is defined as:
At that time the sifting procedure is halted once SD is lesser as compared to an already
assumed value.
 The second condition is based on the quantity known as the S-number. It is referred to the
amount of successive siftings once the quantities of zero-crossings as well as extrema are
equivalent or they are having difference less than one. Precisely, it is already-assumed.
The sifting procedure haltsin the condition when for S successive periods the quantities
of zero-crossings as well as extrema remain identical, and are equivalent to one or having

34. 34
the difference not more than one. After carefully choosing the stopping conditions, the
initial IMF, c1, could be found. Generally, c1 must encompass the shortest period
element of the signal. As lengthier period deviations in the data can be still present in the
residue, r1, therefore it is possible for one to detach c1 from the remaining part of the
data which is considered as the novel data plus it is exposed to the identical sifting
procedure as explained above.
This process could be reiterated to entire succeeding rj’s, and the outcome is the sifting
procedure halts as a final point once the residue, rn, turns out to be a monotonic function from
which Intrinsic Mode Function cannot be extracted anymore. From the equations given above,
one could be convinced that a disintegration of the data in n-empirical modes is accomplished.
The modules of the Empirical Mode Decomposition are commonly expressive. It has also been
shown by Flandrin et al. (2003) and Wu and Huang (2004) that the Empirical Mode
Decomposition is equal to a dyadic filter bank.
2.3.6 Hilbert Spectral Analysis
The instant frequency could be calculated by making use of the Hilbert Transform once
the components of the IMF have been obtained. The primary data could be stated as the real part
after executing the transform on every IMF constituent in the subsequent system.
2.3.7 Present Applications
 Biomedical uses: The pulmonary arterial pressure on awake and unrestricted rats was
analyzed by Huang et al. [1999b].
 Chemistry and chemical engineering: A conformational variation in Brownian dynamics
(BD) as well as molecular dynamics (MD) experimentations was examined by Phillips et
al. [2003] by making use of a relative examination of HHT and wavelet techniques. HHT
was also used by Wiley et al. [2004] to examine the impact of flexible digitally filtered
MD that could improve or subdue particular frequencies of motion. Furthermore Hilbert–
Huang transforms was also applied by Montesinos et al. [2002] on those signals which
are acquired from BWR neuron stability.

35. 35
 Financial uses: HHT was used by Huang et al. [2003b] on non stationary financial time
series and in addition to this, the authors also proved that it can be used on a daily
mortgage rate data.
 Processing of Images: Hariharan et al. [2006] made use of Empirical Mode
Decomposition to image fusion as well as image improvement. On the other hand, a
better version of EMD was used by Chang et al. [2009] for iris recognition that proved to
be 100% quicker in computational speed sans giving up precision as compared to the
novel EMD.
 Climatic and meteoro logical uses: HHT method was applied by making use of Southern
Oscillation Index(SOI) data by Salisbury and Wimbush [2002] in order to decide if the
SOI data are satisfactorily free from any kind of noise such that valuable forecasts could
be prepared and if forthcoming ENSO happenings could be foreseen from the data. In
addition to this, HHT was also used by Pan et al. [2002] to examine satellite scatter meter
wind data over the northwestern Pacific as well as equated the outcomes to VEOF
outcomes.
 Ocean engineering: The use of Hilbert–Huang transforms was presented by Schlurmann
[2002] to illustrate non-linear water waves from two dissimilar viewpoints, by making
use of lab experimentations. Veltcheva [2002] made use of HHT to analyze information
related to waves from Near shore Sea. HHT was also applied by Larsen et al. [2004]to
illustrate the electromagnetic atmosphere in underwater and recognize transient man-
made electromagnetic disturbances.
 Solar Physics: Barnhart and Eichinger [2010] used HHT to excerpt the periodic modules
inside sunspot data, comprising the 11-year Schwabe, 22-year Hale, and ~100-year
Gleissberg cycles. The authors equated their outcomes against basic Fourier
investigation.
 Seismic studies: Hilbert–Huang transforms were used by Huang et al. [2001] to create a
spectral depiction of earthquake information. Hilbert–Huang transforms were used by
Chen et al. [2002a] to define the dispersion arcs of seismic surface waves and equated the
outcomes to Fourier-based time-frequency investigation. Shenet al. [2003] used Hilbert–
Huang transforms to ground motion and equated the Hilbert–Huang transforms outcome
against the Fourier spectrum.

36. 36
 Structural uses: Quek et al. [2003] demonstrate the possibility of the Hilbert–Huang
transforms as a means to process the signals for finding an irregularity which can be like
a crack, de-lamination, or loss of rigidity in beams and plates based on substantially
attained propagating wave signals. By making use of Hilbert–Huang transforms, Li et al.
[2003] examined the outcomes of a pseudo dynamic test of two rectangular reinforced
concrete bridge columns.
 Health nursing: HHT was applied by Pines and Salvino [2002] in structural checking of
health. Hilbert–Huang transforms were used by Yang et al. [2004] for finding damage
and applied EMD to excerpt damage points because of sudden variations in structural
rigidity. Yu et al. [2003] made use of Hilbert–Huang transforms for fault analysis of
roller bearings.
 System identification: The probability of applying Hilbert–Huang transforms was
discovered by Chen and Xu [2002] to recognize the modal damping proportions of a
structure having narrowly spaced modal frequencies and equated their outcomes to fast
Fourier transform. Xu et al. [2003] equated the modal frequencies and damping ratios in
numerous time additions and diverse winds for highest composite constructions in the
sphere.
 Recognition of Speech: Huang and Pan [2006] applied the Hilbert–Huang transforms for
determination of speech pitch.[1]
2.3.8 Limitations
Chen and Feng suggested a method to augment the performance of the HHT process. The
researchers observed that the Empirical Mode Decomposition is imperfect in differentiating
dissimilar constituents in narrow-band signals that might comprise (a) constituents which possess
nearby frequencies (b) constituents which do not possess nearby frequencies. However one of the
constituents has considerable greater energy intensity as compared to the other constituents. The
enhanced method is based on beating-phenomenon waves.
The detailed analysis on the performance and limits of Hilbert–Huang transforms with
specific uses to uneven waves was carried out by Datig and Schlurmann [2004]. The researchers
carried out detailed examination into the spine interpolation. They argued by making use of extra
points, both advancing and recessive, to govern healthier envelopes. The authors likewise

37. 37
executed a parametric analysis on the suggested modification and exhibited substantial
perfection in the global EMD calculations. They observed that HHT is proficient of
distinguishing among time-varying constituents from any assumed data. Their analysis also
presented that HHT was capable of distinguishing among riding as well as carrier waves.

38. 38
Chapter 3
SYSTEM MODEL
3.1 MC-CDMA System Model.
MC-CDMA is a digital modulation method which communicates a solo data character at
multiple narrowband subcarriers. This is then encrypted using a phase offset of 0 and π as a
replacement for spreading code. The BPSK modulated signals are used to generate narrowband
subcarrier, with every signal at dissimilar frequencies. These signals at baseband are at multiples
of a harmonic frequency, 1/𝑇𝑏. Subsequently, the generated subcarriers have the properties such
that at the baseband they are mutually orthogonal, besides this the element at every subcarrier
might be blocked by modulation of the signal received along with the frequency equivalent to the
frequency of the specific subcarrier and summing it through duration of the symbol. The
orthogonality among the subcarrier is retained if the frequencies of the subcarrier are
disseminated separately by the multiples of 𝐹/𝑇𝑡 𝑠, here F is an numeral (e.g F=1,2…). Every
component of the spreading code resembles to the phase of corresponding subcarrier. If we
consider that spreading code has dimension of N, it means that number of subcarriers are also N.
It can also be said that MC-CDMA transmitting antenna spreads the initial signal by making use
of a specified spreading code. Furthermore, a segment of the symbol analogous to spreading
code’s chip is communicated via dissimilar subcarriers. It is indispensable to have frequency
non-discerning diminishing over every subcarrier for the MC-CDMA transmitting antenna.
Consequently, if the initial symbol rate is extraordinary on the higher side just adequate to get
exposed to frequency selective fading, then it is required to be converted from serial-to-parallel
before it can be spread over the frequency domain. The simple transmitter configuration is
analogous to the OFDM, the key dissimilarity is that the Multi-Carrier Code Division Multiple
Access communicates the identical symbol in parallel over a numerous subcarriers, while OFDM
communicates dissimilar symbols.
 System Model:
The length of the codes are supposed to be identical to the amount of subcarrier, N. the
separate components of the codes are denoted as chips. Every code’s chip fits to the set {1,-1}.
The anticipated characteristic of the codes of dissimilar users needs to be orthogonal i.e.,

39. 39
𝐶𝑙 𝑖 𝐶 𝑚 [𝑖] = 𝑁𝛿(𝑙 − 𝑚)
𝑁−1
𝑖=0
A Pseudo random code is single likely set of codes created with the help of shift registers.
Such generate codes are known as pseudo-random since they seem to be arbitrary having a stable
run of -1’s and +1’s. By making use of the shift register having length n, the code length that is
produced is 2 𝑛
-1. Consequently simply codes of odd length could be produced.
Walsh-Hadamard codes are the second likely set of codes. These are produced by the
matrix procedures:
𝐻𝑜 =
1 1
1 −1
OR
𝐻𝑛 =
𝐻𝑛−1 𝐻𝑛−1
𝐻𝑛−1 −𝐻𝑛−1
Size of 𝐻𝑛=2 𝑛
∗ 2 𝑛
Size of 𝐻𝑛−1 = 2 𝑛−1
∗ 2 𝑛−1
with 𝐻𝑜.
Each row of𝐻𝑛, provides the code for single user. It might be confirmed that these codes
are impeccably orthogonal. The interior product among any two dissimilar codes is zero.
3.1.1 MC-CDMA Transmitter Model.
The data symbol at the input side is represented by 𝑏 𝑚 𝑘 , and it is anticipated to be
binary antipoal, here k signifies the 𝑘 𝑡𝑕
interval plus m signifies the 𝑚 𝑡𝑕
user. This considers
values +1 and -1 having equivalent a-priori possibility. The creation of MCCDMA signal could
be defines by a signal data symbol which is imitated in N parallel replicas. To create a PN code,
chip 𝐶 𝑚 𝑖 is multiplied by𝑖 𝑡𝑕
subcarrier of the parallel stream. The communicated signal
comprises of the summation of the outcome of these divisions.

40. 40
𝐶𝑘[0] 𝑐𝑜𝑠2𝜋𝑓𝑐 𝑡
𝑏 𝑘(𝑚) 𝑆 𝑘(𝑡)
𝐶𝑘[1]
cos 2𝜋𝑓𝑐 𝑡 −
2𝜋𝐹𝑡
𝑇𝑏
𝐶𝑘[𝑁 − 1] cos 2𝜋𝑓𝑐 𝑡 −
2𝜋𝐹 𝑁 − 1 𝑡
𝑇𝑏
Figure 3.1 Diagram of MC-CDMA Transmitter
Transmitter signal for user K may be articulated as:
𝑆 𝑘 𝑡 =
2𝑝𝑔𝑓𝑑𝑑
𝑁
∞
𝑚=−∞
𝑏 𝑘 𝑚 𝑘 𝑇 𝑏
𝑡 − 𝑚𝑇𝑏 𝐶𝑘,𝑛
𝑁
𝑛=1
cos 𝜔 𝑛 𝑡 + Ф 𝑘 (1)
P is the power of information bits.
𝑏 𝑘(𝑚)= 𝑚 𝑡𝑕
data bit
𝐶𝑘,𝑛 𝑛=1
𝑁
= Spreading sequence
𝜃 𝑘 = arbitrary carrier phase of user K.
𝑘 𝑇 𝑏
= rectangular pulse having the range in [0,𝑇𝑏]
𝜔 𝑛 = 𝜔𝑐 +
2𝜋𝑛𝐹
𝑇 𝑏
is𝑛 𝑡𝑕
subcarrier, while 𝜔𝑐= radio frequency, F = positive integer.
3.1.2 MC-CDMA Receiver Prototype:
Once there is K active user, the signal received is:
𝑟 𝑡 =
2𝑝
𝑁𝑏
∞
𝑚=−∞
𝑏 𝑘(𝑚)
𝑘
𝑘=1
𝑢 𝑇 𝑏
𝑡 − 𝑚𝑕𝑇𝑏 𝛽𝑘,𝑛 𝐶𝑘,𝑛
𝑁
𝑛=1
cos 𝜔 𝑛 𝑡 + Ф 𝑘,𝑛 + 𝑛 𝑡 (2)
∑

41. 41
Ф 𝑘,𝑛 = 𝜃 𝑘 + 𝜑 𝑘,𝑛where, 𝛽𝑘,𝑛 and 𝜑 𝑘,𝑛 are supposed to be autonomous as well as
uniformly spread (i.i.d) for dissimilar k or n.
n(t)= AWGN having double sided power spectral density
𝑁0
2
.
2
𝑇𝑏
cos⁡(2𝜋𝑓𝑐 𝑡 + 𝜙0,0)𝑐0 0 𝑑0,0
𝑟(𝑡)
2
𝑇𝑏
cos⁡(2𝜋𝑓𝑐 𝑡 +
2𝜋𝐹𝑡
𝑇𝑏
+ 𝜙0,1)𝑐0 1 𝑑0,1
2
𝑇𝑏
cos⁡(2𝜋𝑓𝑐 𝑡 +
2𝜋𝐹(𝑁 − 1)𝑡
𝑇𝑏
+ 𝜙0,𝑁−1)𝑐0 𝑁 − 1 𝑑0,𝑁−1
Figure 3.2 MC-CDMA Receiver Model
Consider that a coherent parallel receiver having maximal ratio combining (MRC). We
assume the zero data bit of user 1 having a decision parameter specified by
∆= 𝛽1,𝑛 𝐶1,𝑛
1
𝑇𝑏
𝑁
𝑛=1
𝑟 𝑡 cos 𝜔 𝑛 𝑡 + Ф1,𝑛 𝑑𝑡 (3)
𝑇 𝑏
0
Its element at the 𝑛 𝑡𝑕
subcarrier could be presented as:
∆ 𝑛= ∆ 𝑛 + 𝛽1,𝑛 𝐶1,𝑛
𝑘
𝑘=2
𝛽𝑘,𝑛 𝐶𝑘,𝑛 cos 𝜔 𝑛 𝑡 + Ф1,𝑛 + 𝜂 𝑛
Where,
∑ Decision

42. 42
∆ 𝑛= 𝛽1,𝑛
2
And 𝜂 𝑛 is Gaussian random variable
𝜎𝜂 𝑛
2
=
𝑁
2 𝐸𝑏 𝑁0
𝛽1,𝑛
2
 BER Calculation :
We first calculate the moment generating function (MGF) of decision variable as:
𝜑∆ 𝑠 = 𝐸 exp −𝑠∆ (4)
MGF of ∆ is two sided Laplace transform. So,
𝜑∆ 𝑠 = 𝜑∆ 𝑠 𝛾1,𝑛 𝑓𝛾1,𝑛
𝛾1,𝑛 𝑑𝛾1,𝑛
∞∁
0
𝑁
𝑛=1
(5)
When 𝛾1,𝑛 = 𝛽1,𝑛
2
which is exponential distributed and written as:
𝑓𝛾1,𝑛
= exp −𝛾1,𝑛 (6)
𝜑∆ 𝑠 𝛾1,𝑛 = 𝜑 𝜃 𝑛
𝑠 𝛽1,𝑛 ∗ 𝜑𝜂 𝑛
𝑠 𝛽1,𝑛 ∗ 𝜑 𝑘,𝑛 𝑠 𝛽1,𝑛
𝑘
𝑘=2 (7)
= exp 𝑗𝜔𝛽1,𝑛
2
exp −
𝛽1,𝑛
2
𝜔2
4 𝐸𝑏 𝑁0
exp −
𝛽1,𝑛
2
𝜔2
4
So, using (6) and (7) into (5) and integrate over 0 to ∞.
∅∆ 𝑠 =
2𝑎 𝑁
𝑏2𝑁 1 −
𝑠−𝑎
𝑏
2
𝑁 (8)
Where,𝑎 =
1
2
𝑁
4𝐸 𝑏 𝑁0
+
𝑘−1
4
𝑏 = 𝑎2 + 2𝑎
So, BER
𝑃𝑒 = 𝑓∆ 𝑥 𝑑𝑥
∞
0
(9)

43. 43
Where,
𝑓∆ 𝑥 = 𝐿−1
{∅∆ 𝑠 }
𝑃𝑒 = 𝐿−1
{∅∆ 𝑠 }𝑑𝑥
∞
0
= 𝐿−1
2𝑎 𝑁
𝑏2𝑁 1 −
𝑠−𝑎
𝑏
2
𝑁 𝑑𝑥
∞
0
As we know,
𝐿−1
1
1 − 𝑠2 𝑁
=
(𝑥/2) 𝑁−
1
2
𝜋 Г𝑁
𝐾 𝑁−
1
2
𝑥 , 𝑁 > 1/2
So,
=
2𝑎 𝑁
𝑏2𝑁−1
𝑒 𝑎𝑥
∞
0
(𝑏𝑥/2) 𝑁−
1
2
𝜋 Г𝑁
𝐾 𝑁−
1
2
𝑏𝑥 (10)
Where,
Г(.) =gamma function
𝑘 𝑣 . = 𝑣 𝑡𝑕
Order modified Bessel’s function.
From (10), we get
𝑃𝑒 =
2𝑎 𝑁
(𝑎 + 𝑏)2𝑁
Г(2𝑁)
Г 𝑁 Г𝑁 + 1
{2𝐹1(2𝑁, 𝑁; 𝑁 + 1,
𝑎 − 𝑏
𝑎 + 𝑏
)}
Where, 2𝐹1(. )= hypergeometric function
3.2 Wavelet Based MC-CDMA
3.2.1 Transmitter of WP MC-CDMA Arrangement.
We have analyzed the model based MC-CDMA system prototype for downlink; the
transmitter and receiver of wavelet based MC-CDMA are displayed in figures. The wavelet

44. 44
packet function 𝑔 𝑚 𝑡 is considered as the signature waveform at the transmitter, besides this the
shifting orthogonality amongst 𝑔 𝑚 𝑡 ,{m=1,…..M} can be specified as < 𝑔𝑖 𝑡 𝑔𝑗
∗
𝑡 − 𝑛𝑇𝑠 >=
𝛿 𝑖 − 𝑗 , where 𝛿 is the kronecker function, and <. > signifies the internal product and * denotes
complex conjugate.
𝐶𝑘(1)
𝑆 𝑘(𝑡)
𝑏 𝑘(𝑖)
𝐶𝑘(2)
𝑒 𝑗 𝑤 𝑐 𝑡
𝐶𝑘(𝑀
The transmitter baseband signal of the 𝑘 𝑡𝑕
user is written as:
𝑆 𝑘(𝑡) =
2𝑃
𝑀
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 𝑔 𝑚 𝑡 − 𝑖𝑇𝑠 (1)
∞
𝑖=0
𝑀
𝑚=1
Where, P is the power of data bits.
Where, k= 1…k, k is the active user number.
𝑏 𝑘 𝑖 = BPSK 𝑖 𝑡𝑕
data symbol at the 𝑘 𝑡𝑕
user, and anticipated to be autonomous as
well as uniformly dispersed arbitrary variable taking the value of {0,1} with equal
apriori probability.
𝑇𝑠 =Symbol period
𝐶𝑘 ={𝐶𝑘 𝑚 , 𝑚 = 1, … … . 𝑀}is the walsh hadamard code, which represent the 𝑘 𝑡𝑕
user
spreading code. And the code length = number of subcarrier (M).
∑
g1(t)
g2(t)
gM(t)
Figure 3.3 Diagram of Transmitter of WP MC-CDMA System

45. 45
3.2.2 Receiver Model of WP MC-CDMA System.
𝐶𝑘(𝑀)
𝑟(𝑡) 𝑑 𝑀
𝐶𝑘(2)
𝑒−𝑗 𝑤 𝑐 𝑡
𝑑2
𝐶𝑘(1)
𝑑1
𝑏 𝑘
^
(𝑛)
Figure 3.4 Diagram of WP MC-CDMA Receiver Model
In this study, we have assumed a frequency selective Rayleigh fading channel, supposing
every modulated subcarrier practices autonomous as well as uniform fading, therefore the low
pass impulse reaction of the 𝑚 𝑡𝑕
subcarrier channel for the 𝑘 𝑡𝑕
user might be written as:
𝑕 𝑘,𝑚 𝑡 = 𝛼 𝑘,𝑚 𝑡 𝑒 𝑗𝜑 𝑘,𝑚 𝑡
(2)
Where,
𝑕 𝑘,𝑚 = complex Gaussian arbitrary variable having zero mean and variance𝜎2
.
LPF
𝑔1
∗
(−𝑡)
𝑔 𝑀
∗
(−𝑡)
𝑔2
∗
(−𝑡)
Sampler
Sampler
Sampler
∑

46. 46
The amplitude 𝛼 𝑘,𝑚 = autonomous as well as uniformly disseminated Rayleigh variables
having variance𝜎2
.
Ф 𝑘,𝑚 = autonomous as well as uniformly spread unvarying variables in range [0,2𝜋].
Considering the downlink communication, every the user signal passes via the identical
channel, the random m, 𝛼 𝑘,𝑚 𝑡 = 𝛼 𝑚 (𝑡), Ф 𝑘,𝑚 𝑡 = Ф 𝑚 𝑡 . Consequently, after the down
transforming to baseband at the receiver, the signal may be stated as:
𝑟 𝑡 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 𝑔 𝑚 𝑡 − 𝑖𝑇𝑠 ∝ 𝑚 𝑡 𝑒 𝑗∅ 𝑚 𝑡
+ 𝑛 𝑡 (3)
𝑀
𝑚=1
𝐾
𝑘=1
n(t)= AWGN (0,𝑁0/2)
Once the signal has passed via a low pass filter (LPF) as well as wavelet packet based
matched filter is sub channel l, the resulting signal at the 𝑢𝑇𝑠 sampling period is:
𝑦𝑙 𝑢 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 ∝ 𝑚 𝑒 𝑗∅ 𝑚 𝑡
𝑅 𝑔
𝑚𝑙
𝑖 − 𝑢 𝑇𝑠 + 𝑛𝑙 𝑢 (4)
𝑀
𝑚=1
𝐾
𝑘=1
Where,
𝑅 𝑔
𝑚𝑙
𝑡 = 𝑔 𝑚 𝑡 − 𝜏 𝑔𝑙
∗
(𝑡)𝑑𝑡
= 𝐸 𝑔 𝑚 𝑡 − 𝑖𝑇𝑠 𝑔 𝑚
∗
𝑡 − 𝑖𝑇𝑠
𝑛𝑙 𝑢 = 𝑛(𝑡)𝑔𝑙
∗
(𝑡 − 𝑢𝑇𝑠)𝑑𝑡
So, (4) can be further be written as:
𝑦𝑙 𝑢 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 ∝ 𝑚 𝑒 𝑗∅ 𝑚 𝑡
𝑅 𝑔
𝑚𝑙
(𝑖𝑇𝑠) + 𝑛𝑙 𝑢 (5)
𝑀
𝑚=1
𝐾
𝑘=1
For simplicity, assume user 1 is the chosen user, so the decision variable for the 𝑢 𝑡𝑕
data symbol of the is:

47. 47
𝑑1(𝑢) = 𝐶1(𝑙)𝐴𝑙 𝑦𝑙(𝑢)
𝑀
𝑙=1
=
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 + 𝑢 𝐶𝑘 𝑚 ∝ 𝑚 𝑒 𝑗∅ 𝑚 𝑡
𝑅 𝑔
𝑚𝑙
𝑖𝑇𝑠 𝐶1 𝑙 𝐴𝑙 +
𝑀
𝑚=1
𝐶1 𝑙 𝐴𝑙
𝑀
𝑙=1
𝑛(𝑡)𝑔𝑙
∗
(𝑡 − 𝑢𝑇𝑠)𝑑𝑡 (6)
𝑀
𝑙=1
𝐾
𝑘=1
Where,𝐴𝑙 = channel equalization gain for the𝑙 𝑡𝑕
subcarrier.
So, 𝐴𝑙 = 𝑒−𝑗∅𝑙
Thus, (6) can be representing after some simplification as:
𝑑1 𝑢
=
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 + 𝑢 𝐶𝑘 𝑚 𝑅 𝑔
𝑚𝑙
𝑖𝑇𝑠 𝐶1 𝑙
𝑀
𝑙=1
∝ 𝑚 𝑒 𝑗∅ 𝑚 𝐴𝑙
𝑀
𝑚=1
𝐾
𝑘=2
+
2 𝑃
𝑀
∞
𝑖=0
𝑏 1 𝑖 + 𝑢 𝐶 1 𝑚 𝑅 𝑔
𝑚𝑙
𝑖 𝑇 𝑠 𝐶 1 𝑙
𝑀
𝑙=1
∝ 𝑚 𝑒 𝑗 ∅ 𝑚 𝐴 𝑙
𝑀
𝑚=1
+
2 𝑃
𝑀
∞
𝑖 =1
𝑏 1 𝑖 + 𝑢 𝑅 𝑔
𝑚𝑙
𝑖 𝑇 𝑠
𝑀
𝑙 =1
∝ 𝑑 +
2 𝑃
𝑀
𝑀
𝑙 =1
𝑑 1 𝑢 𝛼 1
+ 𝐶 1 𝑙 𝐴 𝑙
𝑀
𝑙 =1
𝑛 ( 𝑡 ) 𝑔 𝑙
∗
(− 𝑢 𝑇 𝑠 ) (7)
𝑑 1 𝑢 = 𝐼 1 + 𝐼 2 + 𝐼 3 + 𝐼 4 + 𝐼 5
𝐼 3 =Interference from the same sub-channel l and the identical user k=1.
𝐼 2 =Interference from the other subcarrier and identical user.
𝐼 1 =Interference from the other user 𝑘 ≠ 1.
So,
𝐼 2 = 𝐼 3 = 0 And 𝐼 1 can be presented as:
𝐼1 =
2𝑃
𝑀
𝑏 𝑘 𝑢 𝐶𝑘 𝑙 𝐶1 𝑙 ∝𝑙 (8)
𝑀
𝑙=1
𝐾
𝑘=2
Where,

48. 48
𝑅𝑓
𝑚𝑙
𝑖𝑇𝑠 = 𝛿(𝑚 − 𝑙)𝛿(𝑖)
And ∝𝑙 is Rayleigh distributed N(0,𝜎2
) and using the same steps as used in derivation of
MCCDMA, we get
𝑉𝑎𝑟𝐼3 =
𝑃
𝑀
𝑘 − 1 𝑀 4 − 𝜋 + 𝜋 𝑅 𝑘,1
2
𝐾
𝑘=2
𝜎2
2
(9)
Where,
𝑅 𝑘,1 =Correlation among user k and 1’s spreading code
Assuming
𝑅 𝑘,1 = 0
𝑉𝑎𝑟𝐼3 =
𝑃
𝑀
𝑘 − 1 𝑀 4 − 𝜋
𝜎2
2
(10)
So, the probability of error from (7)
𝑃
𝑒
𝛼1
=
1
2
𝑒𝑟𝑓𝑐
𝐸[𝐼4]2
2[𝑣𝑎𝑟 𝐼1 + 𝑣𝑎𝑟(𝐼5)]
𝑣𝑎𝑟 𝐼5 =
𝑀𝑁0
2
(12)
𝛼 = 𝛼𝑙
𝑀
𝑙=1 thus𝐼4 =
2𝑃
𝑀
𝑑1(4)𝛼
And for large number
𝛼 ≈ 𝑀𝐸[𝛼𝑙]
∝= 𝑀 ∝𝑙 𝑓𝑑 𝑙
(∝𝑙)𝑑 ∝𝑙
∞
0
= 𝑀 ∝𝑙
1
𝜎2
𝑒
−𝛼 𝑙
𝜎2
𝑑 ∝𝑙
∞
0
=
𝑀𝜎 𝜋
2
(13)
Thus BER

49. 49
𝑝 𝑒 =
1
2
𝑒𝑟𝑓𝑐
𝛼2 𝑝
𝑀
[(𝑘 − 1)(4 − 𝜋)𝜎2 𝑝/2 + 𝑀
𝑁0
2
]
∞
0
𝑓(𝛼)𝑑𝛼
=
1
2
𝑒𝑟𝑓𝑐
𝑀𝜎2 𝜋
2
𝑘 − 1 4 − 𝜋 𝜎2 +
𝑀
𝑆𝑁𝑅
(14)
Where,𝑆𝑁𝑅 =
𝑃
𝑁0
3.3 Hilbert Transform Based MC-CDMA System
Hilbert transform of x is considered as the convolution of x(t) with the function 𝑕 𝑡 =
1
𝜋𝑡
. Since h (t) cannot be integrated so the integrals describing the convolution do not meet.
𝑕 𝑡 =
1
𝜋
𝑕(𝑡)
𝜏 − 𝑡
𝑑𝑡
∞
−∞
3.3.1Transmitter By Making Use of the Hilbert Transforms
Sk(t)
𝑒 𝑗 𝑤 𝑐 𝑡
Figure 3.5 Diagram of HHT based MC-CDMA Structure
The communicated baseband signal of the kth
user is presented as:
𝑆 𝑘 𝑡 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 𝑕 𝑚 (𝑡 − 𝑖𝑇𝑠) (1)
𝑀
𝑚=1
Where,𝐶𝑘 𝑚 = 𝐶𝑘,𝑚 𝛿(𝑚 − 𝑛𝑇𝑠)𝑚
𝑏 𝑘(𝑖)
LPF
LPF
LPF
Hilbert
Hilbert
Hilbert ∑
Serial
to
Parallel

50. 50
𝐶𝑘,𝑚 =PN code sequence for 𝑘 𝑡𝑕
user
𝛿 𝑡 = Kroncher data function
𝑕 𝑡 = Hilbert transform of h(t)
Where h(t) is the wave shaping filter impulse response.
𝑚 𝑡𝑕
Subcarrier channel for the 𝑘 𝑡𝑕
user might be presented as:
𝑔 𝑘,𝑚 𝑡 = 𝛼 𝑘,𝑚 (𝑡)𝑒 𝑗∅ 𝑘,𝑚 𝑡
(2)
Considering the same channel irrespective of different user.
𝛼 𝑘,𝑚 𝑡 = 𝛼 𝑚 𝑡
∅ 𝑘,𝑚 𝑡 = ∅ 𝑚 𝑡

51. 51
3.3.2 Receiver of HHT Based MC-CDMA System:
𝐶𝑘(𝑀)
𝑟(𝑡) d M
CK(2)
𝑒−𝑗 𝑤 𝑐 𝑡
𝑑2 d2
CK(1)
𝑑1
𝑏 𝑘
^
(𝑛)
Figure 3.6 Diagram of HHT based MC-CDMA Receiver System
Thus, the received signal r(t) is
𝑟 𝑡 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 𝑕 𝑚 (𝑡 − 𝑖𝑇𝑠) 𝛼 𝑚 (𝑡)𝑒 𝑗∅ 𝑚 𝑡
+ 𝑛(𝑡) (3)
𝑀
𝑚=1
𝐾
𝑘=1
Following the similar steps as used for wavelet based MC-CDMA, we will get the
received signal for the 𝑙 𝑡𝑕
subcarrier at the receiver before passing through the gain
device and decision making process. Thus, we get-
LPF
𝑕1
∗
(−𝑡)
𝑕 𝑀
∗
(−𝑡)
𝑕2
∗
(−𝑡)
sampler
sampler
sampler
∑

52. 52
𝑦𝑙 𝑡 =
2𝑃
𝑀
∞
𝑖=0
𝑏 𝑘 𝑖 𝐶𝑘 𝑚 𝛼 𝑚 𝑒 𝑗∅ 𝑚 𝑡
𝑅𝑓
𝑚𝑙
(𝑖𝑇𝑠) + 𝑛𝑙(𝑢) (4)
𝑀
𝑚=1
𝐾
𝑘=1
Where,
𝑅𝑓
𝑚𝑙
𝜏 = 𝑕 𝑚 (𝑡 − 𝜏)𝑕 𝑚 𝑡 ∗
𝑑𝑡
= 𝐸[𝑕 𝑚 𝑡 − 𝜏 𝑕 𝑚
∗
𝑡 − 𝑖𝑇𝑠 ]
𝑛𝑙 𝑢 = 𝑛(𝑡)𝑕 𝑚
∗
(𝑡 − 𝑘𝑇𝑠)𝑑𝑡
Consequently, ensuing the analogous phase after transmitting the 𝑙 𝑡𝑕
subcarrier signal to
gain blocks in addition to terminating the interfering term similar to the one in wavelet
multicarrier CDMA one may mathematically compute the BER. Since the closed form
explanation is very problematic and is inflexible. Consequently, we might mathematically
compute the Bit Error Rate.

53. 53
Chapter 4
RESUTLS AND DISCUSSIONS
The objective in communication systems is to propose/strategize systems that
communicate info to the user at receiving end with as minute weakening as conceivable even
though sustaining design restrains of permissible communicated energy, permissible bandwidth
of the signal in addition to budget conditions. In this study, the suggested system is assessed as
per different modulation techniques (BPSK, QPSK), BER and throughput.
4.1 Different Parameter.
 Bit error rate (BER).
 Dissimilar Modulation Methods (BPSK, QPSK).
 Number of Users
4.1.1 Bit Error Rate (BER)
This is the quantity of bit errors divided by the entire quantity of transmitted bits through
a considered time period. The BER of Binary Phase Shift Keying in Additive White Gaussian
Noise might be computed as
BER = Error/ total amount of bits
4.1.2 Effect of Number of Users
For these two simulations, For QPSK and BPSK modulations the same parameters are
used except that K = 100, 200, 300 and 400 and it is varied from 0 to 100. It is evident seeing
those two graphs that, since numerous users are communicating signal concurrently, it leads to
decrease in SNIR. Therefore, The greater the amount of users, the greater the multiple user
interfering produced by the undesirable user. Accordingly it leads to poor performance. Once can
either reduce the cost or increase the quality, as greater amount of users may cause rise in
volume with a lesser amount of value of services.
4.1.3 Different Modulation Techniques (BPSK, QPSK)

54. 54
4.2 BER vs SNR for Conventional MC-CDMA for Different Users
Fig.4.1 BER vs SNR for Conventional MC-CDMA for Different Users
Figure4.1.Displays the bit error rate against signal to noise ratio curvatures for diverse
users of traditional MC-CDMA system. It is perceived from the graph that the surge in amount
of users leads to considerable lessening of the BER for wide range of SNR. For instance, BER
was found to be less than 10−3
for K=1when the value of SNR was 20 dB, however when the
value of K was 2, at the same value of SNR, the BER is equivalent to 10−3
.

55. 55
4.3 BER vs SNR for Wavelet Packet Based MC-CDMA for Dissimilar Users
Figure 4.2 BER vs SNR for Wavelet Packet Based MC-CDMA For Dissimilar Users
Figure 4.2.Displays the BER against SNR for dissimilar users of Wavelet packet based
MC-CDMA system. It is observed from the graph that the surge in the quantity of users
diminishes the BER in the entire range of SNR. Even though, when the values for SNR are low
in some area (SNR=0dB ~10dB) the BER is virtually identical with surge in the amount of users.
This is for the reason that in the lesser SNR area this system cannot deliver considerable
enhancement in the spectral effectiveness, and therefore demonstrates the analogous values.
Conversely, in higher SNR area the BER surges considerably for dissimilar quantity of users. For
instance, as soon as the SNR =25 dB, the BER is equivalent to10−4
under K=1, however at the
identical SNR =25 dB, the BER is larger than 10−5
for K=2.

56. 56
4.4 BER vs SNR for Hilbert–Huang Transform Based Multi-Carrier Code
Division Multiple Access for Dissimilar Users
Figure 4.3 BER vs SNR for Hilbert–Huang Transform Based Multi-Carrier Code Division
Multiple Access for Dissimilar Users
Figure 4.3 displays the BER against SNR for dissimilar users of Hilbert–Huang transform
based MC-CDMA system. It was observed that with the surge in amount of users the BER
declines in the entire range of SNR. When the values of SNR are less in the area ranging from
0dB ~10dB, the BER is significantly enhanced as the amount of users surges as equated to
wavelet packet based system. For instance, in the lesser signal to noise ratio area having the
values equal to 10 dB, the BER is better than 10−2
when the value of K is 1, however at the
identical value of SNR, the BER is bigger than 10−3
when value of K is 2. This is for the reason
that HHT based MC-CDMA system in the lesser SNR area delivers considerable enhancement in
the spectral effectiveness, therefore overtakes the wavelet packet based system. In the great SNR

57. 57
area the BER rises considerably for diverse amount of users. For instance, in the great SNR
system having value of SNR at 25 dB, the BER is better than 10−5
for K=1, however at the
identical value of SNR, the BER is better than 10−7
for K=2.
4.5 BER vs SNR Assessment of Three Systems for k=1
Figure 4.4 BERvs SNR Assessment of Three Systems For k=1
Figure 4.4 displays the BER vs. SNR arcs assessment for three systems when the value of
K=1. It is eminent from the graph that when the value of K is 1, HHT based system beats
traditional system as well as wavelet packet based system. In the regions with very less SNR
having the values in the range of 0dB ~5dB, the BER of HHT based system is marginally lesser
equated to other two system. This is owing to the point that former system is marginally having
lesser spectral effectiveness equated to other two systems in less SNR. However, with the surge
in the values of SNR, the BER of proposed system surges considerably and beats other systems.
For instance, in the higher SNR region having the value of SNR at 25 dB, the BER of traditional

58. 58
system is superior than 10−3
, besides BER of wavelet packet based system is equivalent to 10−4
,
while, the bit error rate of proposed system is more than 10−5
. Consequently, it is decided that
proposed HHT based system is greater to both traditional as well as wavelet packet based
system.
4.6 BER vs SNR Comparisons of Three System When k=2
Figure 4.5 BER vs SNR Comparisons of Three Systems When k=2
Figure 4.5 displays the BER vs SINRarcs assessment for all three systems when K=2. It
is eminent from the graph that when the value of K is 2, HHT based system beats traditional
system as well as wavelet packet based system. In the region with lesser values of SNR ranging
from 0dB ~5dB, the BER of HHT based system is improved associated to other systems as
amount of user rises. This is due to the fact that the spectral efficiency of proposed system
equated to other systems surges as the quantity of user rises. It can be noted that as the SNR
raises the BER of HHT based system rises considerably as well as beats other systems. For

59. 59
instance, in the when the value of SNR is 25 dB, the BER of traditional system is equivalent to
10−4
and that of wavelet packet based system is equivalent to 10−5
, while, the BER of HHT
based system is more than 10−7
.
4.7 Performance Analysis of BER Using BPSK Method in MC-CDMA
In this segment, we have shown several BER versus SNR graphs. Performance of the
traditional system and Wavelet Packet Based system as presented in fig4.6 and fig4.7 separately
for AWGN Channel. Experimental outcomes in fig4.6 and 4.7 display that the advantage of
BPSK modulation method for the traditional system and wavelet packet based system Binary
Phase Shift Keying modulation in is fairly acceptable as associated to other modulation methods
in Additive White Gaussian Noise channel.
Figure 4.6 Performance Analysis of BER using BPSK Method in MC-CDMA

60. 60
4.8 Performance Analysis of BER Using QPSK Technique in MC-CDMA
Figure 4.7 Performance Analysis of BER Using QPSK Technique in MC-CDMA
Performance of WP MC-CDMA for two users in AWGN channel is presented in Fig4.8 and performance
of MC-CDMA for 2 users in AWGN channel is displayed in Fig 4.9.

61. 61
4.9 Performance Analysis of BER Using QAM8 Method in MC-CDMA
Figure 4.8 Performance Analysis of BER using QAM8 Method in MC-CDMA
4.10 Comparison Analysis of MC-CDMA using BPSK, QAM8 Modulation
Techniques
Figure 4.9 Comparison Analysis of MC-CDMA Using BPSK, QAM8 Modulation Technique
-20 -15 -10 -5 0 5 10 15 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
SNR
BER
Performance of one user MC-CDMA for AWGN
BPSK
QPSK

62. 62
4.11 Comparative Study of WP MC - CDMA Scheme Using BPSK, QPSK
Techniques
Figure 4.10 Comparative Study of WP MC - CDMA Scheme using BPSK, QPSK Techniques
Comparative study of traditional scheme with wavelet packet based scheme by making
use of diverse modulation methods is displayed. The analysis is carried out for one user as well
as two users. The results presented show the performance of diverse modulation methods.
Wavelet packet based scheme BPSK modulation is fairly acceptable as associated to other
modulation methods in Additive White Gaussian Noise channel.

63. 63
Chapter 5
CONCLUSION AND FUTURE WORK
In this thesis, we examined how traditional MC-CDMA scheme, this scheme with
orthogonal wavelet packet system, and HHT based Multi-Carrier Code Division Multiple Access
system performs. In precise, we considered the performance of second scheme by scheming a
group of wavelet packets which was applied as the modulation waveforms in a multiple carrier
CDMA structure. Furthermore, we examined the performance of third system that uses HHT.
Arithmetical plus experimental outcomes demonstrate that system using HHT beats both wavelet
packet based system as well as traditional system in context of BER. It aids to lessen the impact
of nosiness and channel diminishing.
5.1 Conclusion
In this thesis, the traditional MC-CDMA scheme WP-MC-CDMA as well as MC-CDMA
system based on HHT has been analyzed. In precise, we investigated how orthogonal WP based
scheme performs by scheming a group of wavelet packets. These wavelet packets were assumed
as the modulation waveforms in a MC-CDMA system. Furthermore, we examined HHT based
system. Arithmetical as well as experimental consequences demonstrate that the HHT based
System, outperforms other two in context of BER, and supports to alleviate the impact of
nosiness and channel diminishing. The upgraded performance of wavelet based system by
making use of HHT based MC-CDMA system is examined. The evaluations of BER
performance for the traditional system based on FFT, wavelet based system and HHT based
system in the diverse channel prototypes along with their evaluation for greatest realizable bit
error rate have been shown.
Experimental outcomes were given to validate that substantial throughput, BER and
different modulation techniques like BPSK, QPSK and M Ray QAM might be realized by
presenting such grouping method having very less decoding difficulty. Consequently, the WT
based system is a practical method to reach the succeeding advancements in wireless
transmission sintended for great information rates as well as uses. In this thesis, HHT Based MC-
CDMASystem is also evaluated. In this Paper, the diverse models of the grouping of multiple-

64. 64
carrier communication with spread spectrum, specifically MC-CDMA and system based on
wavelets, as well as HHT based MC-CDMA system are comprehensively evaluated and
investigated, numerous solo-user as well as multiple-user recognition approaches and their
performance in context of bit error rate and spectral effectiveness are observed.
5.2 Future Work
In this dissertation, proposed the first technology MC-CDMA system based on HHT,
second technology MC-CDMA System based on wavelet packet and traditional MC-CDMA
system. The quantity of handlers/users surges, the BER drops considerably for extensive range of
SNR but when it comes to low SNR area this system has not delivered ample enhancement in the
spectral effectiveness. The limitation of first system beats the traditional MC-CDMA as well as
second system. When the area has very less SNR having less than 5dB, the BER performance of
proposed scheme is somewhat lesser equated to two systems HHT based MC-CDMA system
overcome the limitation of second system hence it can be extended or proposed in nearby future.
This is owing to the point that proposed system is marginally less spectral competent associated
to two systems in less SNR. However, when the SNR surges the BER of proposed system surges
considerably as well as it beats two systems.