1. REDUCTION OF PEAR TO AVERAGE POWER RATIO IN OFDM
SYSTEMS BY USING NONLINEAR COMPANDING TECHNIQUES
A project Report
Submitted by
REVURU GOPIKRISHNA (R091479)
In complete fulfillment of the requirements for the award of degree of
BACHELOR OF TECHNOLGOY
In
ELECTRONICS AND COMMUNICATIONS ENGINEERING
Under the Guidance of
Mr. B.V. SUDHAKAR REDDY
Lecturer
Electronics and Communications Engineering
Rajiv Gandhi University of Knowledge Technologies (RGUKT)
RK Valley, Y.S.R (Dist.), Andhra Pradesh,
May 2015.

2. Rajiv Gandhi University of Knowledge Technologies
(A.P. Government Act 18 of 2008)
Rajiv Knowledge Valley, Vempalli (M), Kadapa(Dist),
Andhra Pradesh - 516330.
CERTIFICATE
This is to certify that the project titled “REDUCTION OF PEAK TO AVERAGE
POWER RATIO IN OFDM SYSTEMS BY USING NONLINEAR
COMPANDING TECHNIQUES” is a bonafide record of the work done by
REVURU GOPIKRISHNA (R091479) in complete fulfillment of the
requirement for the award of the degree of Bachelor of Technology in Electronics
and Communications Engineering of the Rajiv Gandhi University of Knowledge
Technologies, RK Valley during the year 2014-2015.
Mr. B.V Sudhakar Reddy Mr. Shyam
Project guide Lecturer
Lecturer Head of the Department
Electronics and Communications Electronics and Communications
Engineering Engineering
RGUKT, RK Valley. RGUKT, RK Valley.
Internal Examiner External Examiner

3. iii | P a g e
ACKNOWLEDGEMENT
I owe many thanks to all people who helped and supported me for the
completion of this project effectively in time.
First, I express my deepest thanks to Mr. B.V. Sudhakar Reddy, Lecturer
in the Department of Electronics and Communications Engineering, RGUKT for
giving me an opportunity to carry out this project under his supervision. He
has been very kind and patient while suggesting me the outlines of this project
and has clarified all my doubts whenever I approached him. I thank him for his
overall support.
I sincerely express my humble thanks to Prof. S Satyanarayan, Vice
Chancellor, RGUKT, for his blessings and encouragement throughout my course
of study.
I express my sincere gratitude and thanks to Prof. K Venugopal
Reddy, Director, RGUKT, for his encouragement throughout my course of
study.
I am thankful to Mr. Shyam, Head of the department, Electronics and
Communications Engineering, Rajiv Gandhi University of Knowledge
Technologies.
Finally I wish to express my thanks to all the faculty members and my
friends who were involved in this project work directly and indirectly.

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ABSTRACT
OFDM (Orthogonal Frequency Division Multiplexing) is a special case of
multi-carrier transmission, where all sub channels are orthogonal to each other. It
is a very promising technique in a high data rate transmission, especially in a
radio channel environment with mobility. There are several reasons that make
OFDM so attractive: First, OFDM has a very high bandwidth efficiency. Second,
every sub channel exhibits frequency flat fading, if the channel is time-invariant
for the duration of a single OFDM symbol. Along with these advantages, OFDM
has several disadvantages, which deteriorate its performance considerably. One
of the most severe problems in OFDM is a high Peak-to-Average Power Ratio.
There are lots of methods and techniques intended to reduce PAPR either in a
frequency domain or in a time domain.
This Project proposes the use of nonlinear companding techniques (A-law
and μ-law techniques) to reduce the PAPR of OFDM systems. In companding the
OFDM signal is compressed at the transmitter and expanded at the receiver.
Nonlinear companding transforms transform the amplitude or power of the
original signals into uniform distribution, which can effectively reduce the PAPR
for different modulation formats and subcarrier sizes without any complexity
increase and bandwidth expansion. Nonlinear companding technique adjust
both large and small signals and can keep the average power at the same level.

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CONTENTS Page No
Title Page …………………………………………………………………… i
Certificate ……………………………………………………........................ ii
Acknowledgement …………………………………………………………… iii
Abstract ………………………………………………………………………. iv
Contents ……………………………………………………………………… v
List of Figures ……………………………………………………………….. vi
List of Abbreviations ………………………………………………………… 22
CHAPTER 1 INTRODUCTION 1-3
1.1 Introduction ……………………………………………………… 1
1.2 Motivation ……………………………………………………….. 2
1.3 Contribution …………………………………………………….. 3
CHAPTER 2 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING 4-14
2.1 Evolution of OFDM …………………………………………….. 4
2.2 OFDM System…………………………………………………… 5
2.3 Characteristics of OFDM ………………………………………… 9
2.4 Applications of OFDM …………………………………………… 10
2.4.1 Examples of applications ……………………………… 10
2.5 Peak to Average Power Ratio in OFDM………………………… 11
2.6 PAPR reduction Techniques …………………………………… 13
2.6.1 Frequency Domain Processing …………………….... 13
2.6.2 Time Domain Processing ……………………………… 14
CHAPTER 3 COMPANDING SCHEME ………………………………… 15-18
3.1 System Description…………………………………………… 15
3.2 Advantages of Companding Technique ……………………... 18
3.3 Application of Companding ………………………………….. 18

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CHAPTER 4 SIMULATION RESULTS ………………………………… 19-20
4.1 PAPR Performance in OFDM System ……………………… 19
4.1.1 PAPR without Companding and with Companding….. 19
4.2 BIT Error Rate Performance in OFDM System ……………... 20
4.1.1 BER without Companding and with Companding … 20
CHAPTER 5 CONCLUSION …………………………………………… 21
REFERNCES …………………………………………………………… 23
LIST OF FIGURES
Figure 2.1 Frequency Division Multiple Access (FDM)……………………. 4
Figure 2.2 Bandwidth Utilization in Single and Multi Carrier Transmission... 6
Figure 2.3 Block Diagram for Generating OFDM Signal……………………. 7
Figure 2.4 Sub channels layout in Conventional FDM and in OFDM System… 9
Figure 2.5 Power of OFDM signal……………………………………………. 11
Figure 2.6 Probability Distribution Function of OFDM signal Amplitude…… 12
Figure 3.1 Block Diagram for Companding Scheme ……………………………… 16
Figure 3.2 Characteristics of the Companding Scheme……………………………. 17
Figure 4.1 Performance of PAPR in OFDM Systems………………………………. 19
Figure 4.2 Performance of BER in OFDM Systems……………………………….. 20

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Chapter 1
INTRODUCTION
1.1 INTRODUCTION
In a basic communication system, the data are modulated onto a single carrier frequency. The
available bandwidth is then totally occupied by each symbol. This kind of system can lead to inter-
symbol-interference (ISI) in case of frequency selective channel. The basic idea of OFDM is to
divide the available spectrum into several orthogonal sub channels so that each narrowband sub
channel experiences almost flat fading. OFDM can provide large data rates with sufficient
robustness to radio channel impairments. In an OFDM scheme, a large number of orthogonal,
overlapping, narrow band sub-carriers are transmitted in parallel. These carriers divide the
available transmission bandwidth. The separation of the sub-carriers is such that there is a very
compact spectral utilization. With OFDM, it is possible to have overlapping sub channels in the
frequency domain, thus increasing the transmission rate. The attraction of OFDM is mainly
because of its way of handling the multipath interference at the receiver. Multipath phenomenon
generates two effects: (a) Frequency selective fading [1] and (b) Intersymbol interference (ISI).
The "flatness" perceived by a narrowband channel overcomes the frequency selective fading. On
the other hand, modulating symbols at a very low rate makes the symbols much longer than
channel impulse response and hence reduces the ISI. Use of suitable error correcting codes
provides more robustness against frequency selective fading. The insertion of an extra guard
interval between consecutive OFDM symbols can reduce the effects of ISI even more. The use of
FFT technique to implement modulation and demodulation functions makes it computationally
more efficient. OFDM systems have gained an increased interest during the last years. It is used
in the European digital broadcast radio system, as well as in wired environment such as
asymmetric digital subscriber lines (ADSL). This technique is used in digital subscriber lines
(DSL) to provide high bit rate over a twisted-pair of wires.

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1.2 MOTIVATION
OFDM is very attractive multicarrier modulation (MCM) technique for 4th Generation
(4G) wireless communication. This technique is for high-speed data transmission used in mobile
communication, Digital terrestrial mobile communication, Digital Audio Broadcasting (DAB),
Digital Video Broadcasting terrestrial(DVB-T), wireless asynchronous transfer mode (WATM),
Modem/ADSL. OFDM has many advantages such as robustness in frequency selective fading
channels, High spectral efficiency, immunity to inter-symbol interference and capability of
handling very strong multipath fading.
Multimedia is effectively an infrastructure technology with widely different origins in
computing, telecommunications, entertainment and publishing. New applications are emerging,
not just in the wired environment, but also in the mobile one. At present, only low bit-rate data
services are available to the mobile users. The radio environment is harsh, due to the many
reflected waves and other effects. Using adaptive equalization techniques at the receiver could be
the solution, but there are practical difficulties in operating this equalization in real-time at several
Mb/s with compact, low-cost hardware. A promising candidate that eliminates a need for the
complex equalizers is the Orthogonal Frequency Division Multiplexing (OFDM), a multiple
carrier modulation technique. OFDM is robust in adverse channel conditions and allows a high
level of spectral efficiency. It effectively mitigates performance degradations due to multipath and
is capable of combating deep fades in part of the spectrum. The OFDM waveform can be easily
modified to adjust to the delay spread of the channel. OFDM can handle large delay spreads easier
to do the independence of the carriers and the flexibility of varying the cyclic prefix length. OFDM
allows efficient operation in both FDD and TDD mode as very short or no pre-ambles are needed.
Multiple access techniques which are quite developed for the single carrier modulations
(e.g. TDMA, FDMA) had made possible of sharing one communication medium by multiple
number of users. Multiple techniques schemes are used to allow many mobile users to share
simultaneously a finite amount of radio spectrum. The sharing is required to achieve high capacity
by simultaneously allocating the available bandwidth (or the available amount of channels) to
multiple users. For the quality communications, this must be done without severe degradation in
the performance of the system. FDMA, TDMA and CDMA are the well-known multiplexing
techniques used in wireless communication systems. While working with the wireless systems
using these techniques various problems encountered are (1) multi-path fading (2) time dispersion
which lead to intersymbol interference (ISI) (3) lower bit rate capacity (4)requirement of larger
transmit power for high bit rate and (5) less spectral efficiency. Disadvantage of FDMA technique
is its Bad Spectrum Usage. Disadvantages of TDMA technique is Multipath Delay spread problem.

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In a typical terrestrial broadcasting, the transmitted signal arrives at the receiver using various
paths of different lengths. Since multiple versions of the signal interfere with each other, it
becomes difficult to extract the original information. The use of orthogonal frequency division
multiplexing (OFDM) technique provides better solution for the above mentioned problems.
1.3 CONTRIBUTION
Using MATLAB, simulation of OFDM was done with different modulation techniques using
different transform techniques. The digital modulation schemes such as BPSK and QPSK were
selected to assess the performance of the designed OFDM system by finding their Bit Error rate
for different values of SNR. Different transform techniques such as Discrete Fourier transform
(DFT) and its inverse (IDFT), discrete Hartley transform (DHT) and its inverse (IDHT), Discrete
Cosine Transform and its inverse (IDCT) are used to perform the modulation and demodulation
operations in the implementation of OFDM and compared their performance by finding their Bit
Error rate for different values of SNR.

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Chapter 2
ORTHOGONAL FREQUENCY DIVISION
MULTIPLEXING
2.1. EVOLUTION OF OFDM
Frequency Division Multiplexing (FDM) has been used for a long time to carry more than
one signal over a telephone line. FDM divides the channel bandwidth into sub channels and
transmits multiple relatively low rate signals by carrying each signal on a separate carrier
frequency. To ensure that the signal of one sub channel did not overlap with the signal from an
adjacent one, some guard-band was left between the different sub channels. Obviously, this guard-
band led to inefficiencies.
Figure 2.1: Frequency division multiple access (FDM).
Orthogonal Frequency Division Multiplexing (OFDM) [2] In order to solve the bandwidth
efficiency problem, orthogonal frequency division multiplexing was proposed, where the different
carriers are orthogonal to each other. With OFDM, it is possible to have overlapping sub channels
in the frequency domain, thus increasing the transmission rate. This carrier spacing provides
optimal spectral efficiency. Today, OFDM has grown to be the most popular communication
system in high-speed communications. OFDM can provide large data rates with sufficient
robustness to radio channel impairments.

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2.2 OFDM SYSTEM
In the radio channel a transmitted signal undergoes multiple reflections from different obstacles
(cars, buildings) on its way to the receiver. Each of these reflections reaches the receiver with a
different delay, phase and amplitude. The received signal is constructed as superposition of these
attenuated and delayed signals. This is called a multipath propagation. Signals from the multipath
propagation, depending on a phase, might interfere constructively or destructively. This leads to
frequency selectivity that is the transfer function will vary depending on a frequency. Frequency
selectivity, in turn, will result in intersvmbol interference (ISI) of modulation symbols. Number
of symbols affected by ISI is calculated as follows [3]:
= (2.1)
Where Tmax is the path delay and Ts is the symbol duration.
As we can see from (2.1) if the maximum path delay Tmax will be much larger than symbol
duration Ts many adjacent symbols will be corrupted by 1ST. To compensate this effect of the
radio channel, equalization should be used. The complexity of an equalizer depends on how many
symbols are affected by 1SI. To reduce ISI and thus to avoid complex equalization, we need
symbol duration lo be much larger than the maximum path delay. This leads us to the definition
of narrowband channel and coherence bandwidth. In a narrowband channel symbol duration Ts
is much larger than the maximum path delay Tmax- This makes the channel transfer function to
be constant over the signal bandwidth. Such bandwidth, i.e. within which the channel transfer
function can be considered as not changing is called coherence bandwidth Bc:
Bc ≈ (2.2)
Increase of the maximum path delay will result in small coherence bandwidth and consequently in
increase of frequency selectivity.
If we want to have a high data rate we have to choose symbol duration as small as possible. This
will give us high bandwidth. But on the other hand, we will have an issue with ISI due to high
frequency selectivity as was described above. This is the main disadvantage of a single- carrier
transmission technique. The multi-carrier transmission overcomes this disadvantage by using total
bandwidth to transmit many subcarriers in parallel, instead of transmitting them in a serial way
like it is done in the single-carrier technique. Both transmission techniques are depicted in figure
(2.2).

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In the multi carrier transmission each sub-carrier uses certain part of whole bandwidth,
which we will denote as
∆ = 1 Ts⁄ (2.3)
∆ is much smaller than signal’s total bandwidth, thus we will have large symbol duration. This
means that ISI will be reduced considerably. In the same time we will not lose the data rate because
we transmit many channels simultaneously. Underlining what was said above, multi-carrier
techniques give us the ISI free transmission with no loss in the data rate.
(a)Single-carrier transmission (b) Multi-carrier transmission
Figure 2.2: Bandwidth utilization in single carrier and multi carrier transmission
The full OFDM transmission chain is depicted in figure 2.3. The bit sequence coming from
some source is coded with a certain coding technique, which depends on the channel property.
This is done to be able to detect errors, occurring during the transmission and correct them at the
receiver. For example to combat burst errors Reed-Solomon codes could be used. Then to
maximally avoid burst errors an interleaver is used. It changes the order of bits so that burst errors,
occurring during the transmission, will be transformed to a single bit error after deinterleaving.
After that, the baseband signal is mapped to the complex modulation symbols S using one of
modulation methods, e.g. M-PSK, M-QAM (where M shows the number of modulation symbols
in a constellation diagram). Then pilot symbols arc placed between modulation symbols with a
certain pattern. Pilot symbols are already known at the receiver, and used for channel estimation.

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Random Data
Figure 2.3: Block diagram for generating OFDM signal
Now let introduce some notations. Let denote the number of subcarriers in parallel transmission
as N, , denote the complex modulation symbol of the kth
subcarrier at the ith
block. Then Inverse
Fast Fourier Transformation of Sk will give us discrete time samples of OFDM symbol [4]:
, =
√
∑ , , (2.4)
Where √
is used for normalization.
As can be seen from (2.4) the OFDM symbol is calculated as superposition of the complex
modulation symbols, which are assumed to be independent and identically distributed (i.i.d)
random variables. After arranging the OFDM symbols in a serial way (P/S), a cyclic prefix is
added to each symbol. The cyclic prefix is a periodic extension of the OFDM symbol that helps
to avoid ISI completely. In order to do that, duration of the cyclic prefix should be equal to the
maximum path delay, TG = Tmax. There is no meaning to make it larger than Tmax because the data
rate will be reduced in this case. Thus symbol duration will be increased to:
= + (2.5)
S/P Modulation IFFT Add Cyclic Prefix
Demodulation FFT Remove Cyclic Prefix S/P
P/S
AWGN
Channel
P/SOFDM signal

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After digital-to-analog conversion the OFDM signal is modulated to a carrier frequency, amplified
and transmitted through the radio channel. At the radio channel signal undergoes multipath fading
and AWGN is added. At the receiver site reverse operations are performed. First, the analog signal
is mixed down to the baseband and converted to the digital signal, then windowing extract each
OFDM symbol. Note that no ISI occurs due to the cyclic prefix. After serial-to-parallel conversion
(S/P), the sampled time signal is transformed to a frequency domain by the Fast Fourier
Transformation Algorithm (FFT) [5].Meanwhile the channel transfer function is estimated
estimated based on pilot symbols. Estimated channel transfer function , is used to equalize an
effect of the channel by performing coherent demodulation.
, = , . , + , , (2.6)
Where Ri,k is the received complex signal on the subcarrier k, , is the channel transfer
function and , , is noise. If a good channel estimation was done, we can get the transmitted
signal dividing the received signal by the estimated channel transfer function:
, ≈ , ,⁄ (2.7)
Obtained complex information symbols mapped back to the bit stream, after what it enters the
deinterleaver, which transforms burst errors into the single bit error. Finally, errors are analyzed
and error correction schemes are applied.
Another significant advantage of the system, along with the flat fading channel for each
subcarrier, is orthogonality. In the OFDM system subcarriers are located very dense to each other,
such that their spectrum overlap. But nevertheless they do not interfere with each other because
they are orthogonal. This property allows to use bandwidth much more efficiently than it is done
in the conventional FDM multi-carrier technique. This could be seen from figure 2.4. [6]
(a) FDM multi-carrier modulation

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(b) OFDM multi-carrier modulation
Figure 2.4: Sub channels layout in conventional FDM and in OFDM system
2.3 CHARACTERISTICS OF OFDM
 Can easily adapt to severe channel conditions without complex time-domain equalization.
 Robust against narrow-band co-channel interference [7].
 Robust against intersymbol interference (ISI) and fading caused by multipath propagation.
 High spectral efficiency as compared to conventional modulation schemes, spread
spectrum, etc.
 Efficient implementation using Fast Fourier Transform (FFT).
 Low sensitivity to time synchronization errors.
 Tuned sub-channel receiver filters are not required (unlike conventional FDM).
 Facilitates single frequency networks (SFNs); i.e., transmitter macro diversity.
 Sensitive to Doppler shift.
 Sensitive to frequency synchronization problems.
 High peak-to-average-power ratio (PAPR), requiring linear transmitter circuitry, which
suffers from poor efficiency.
 Loss of efficiency caused by cyclic prefix/guard interval.

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2.4: APPLICATIONS OF OFDM
OFDM is digital transmission technique developed into a popular scheme for wideband
digital communication systems. It is well suited for wideband, high data rate transmissions. The
main advantage is that less equalization is necessary. The OFDM use has increased greatly in the
last 10 years. Nowadays, OFDM is mainly used for one to many (broadcast) communications like
radio or television broadcasting. Examples are digital broadcasting systems such as DAB and
DVB.
It is now proposed for Digital audio broadcasting such as in Eureka 147 standard and
Digital Radio Mondiale (DRM). Digital Audio Broadcasting (DAB) is an international,
standardized digital broadcasting system developed by the European EUREKA-147 Project.
OFDM is used for modem/ADSL application where it coexists with phone line. For ADSL use,
the channel, the phone line, is filtered to provide a high SNR. OFDM here is called Discrete Multi-
Tone (DMT.) HDSL: High bit rate Digital Subscriber Line is another implementation for
symmetric speeds (uplink rate = downlink rate).
HiperLAN2 is the all new high performance radio technology, specifically suited for
operating in LAN environments. HiperLAN2 is a technology being developed within the European
Telecommunications Standardization Institute (ETSI). OFDM is the modulation used in the
physical layer of HiperLAN2.
OFDM is also in use in wireless internet modem and this usage is called 802.1la.
2.4.1: Examples of applications are
 ADSL and VDSL broadband access via telephone network copper wires.
 IEEE 802.11a and 802.11g Wireless LANs.
 Terrestrial digital TV systems DVB-T, DVB-H, T-DMB and ISDB-T.
 IEEE 802.16 or Wi-Max Wireless MAN.
 IEEE 802.20 or Mobile Broadband Wireless Access (MBWA).
 Flash-OFDM cellular system.
 Some Ultra wideband (UWB) systems.
 Power line communication (PLC).
 Digital audio, video broadcasting.

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 Wireless ATM transmission system.
 Proposed scheme for UMTS air interface for bit rates higher than 384 kbps
2.5 Peak to Average Power Ratio in OFDM
Along with all its nice properties OFDM has several disadvantages that deteriorate
performance of the system considerably. One of the main advantages of OFDM, orthogonality,
can be affected by a frequency offset. Due to loss of orthogonality, adjacent carriers strongly
interfere with each other, i.e. inter-channel interference occurs. As a counter measure exact
frequency synchronization is needed. Also some subcarriers of the OFDM signal can be strongly
attenuated because of frequency selective channel. This will cause slow BER degradation with
increasing SNR.
Another, and probably one of the most significant problems in OFDM is the high peak-to- average
power ratio (PAPR). OFDM signals exhibit large power variations with high infrequent peaks
comparing to the average power (figure 2.5).
These high peaks result from constructive superposition of modulation symbols within OFDM
block. Let recapitulate that the OFDM symbol is constructed from superposition of many
modulation symbols which are assumed to be independent and identically distributed random
variables.
Figure 2.5: Power of OFDM Signal

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Rewriting equation 2.4 in polar coordinates will give:
= { } + { } = ∅
(2.8)
Where | | { } { }
is the amplitude of time sample of the OFDM signal
and ∅ =
{ }
{ }
ℎ ℎ .
When the number of sub channels N is large enough, the real Re { } and the imaginary Im{ }
parts of are approach Gaussian distribution with zero mean and variance =
(| | )
, ac-
cording to the central limit thermo. Thereby the amplitude will have Rayleigh distribution with
probability density function as :
p ( )
e ( ) for (ρ ) ≥ 0
0 other wise
(2.9)
This gives a theoretical explanation of why do high peaks occur. The tail of Rayleigh distribution
shows the probability of occurrence of high peaks (figure 2.5). Although Rayleigh distribution has
infinite tail, high peaks in OFDM are limited by the number of parallel subcarriers.
PAPR is calculated as ratio of maximum power of a signal to its average power:
PAPR =
{| | |}
{| | |}
(2.10)
Figure 2.6: Probability Distribution Function of OFDM signal amplitude

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In which way do these high peaks affect our system? First, the OFDM signal becomes
very sensitive to nonlinear components of the system such as power amplifiers. Power amplifiers
have some output saturation power, which is the maximum total power available from the
amplifier. The drive power at which output saturation occurs is called the input saturation power.
Because of power jumping in OFDM [8], high peaks could often exceed the input saturation
power. This will cause clipping of high peaks at the amplifier output. Resulting nonlinear
distortions will increase BER, and cause spectral widening leading to inter channel interference.
To avoid this large output back off should be used. Output back off is the ratio of the output
saturation power to the actual output power. Increasing output back off will shift the signal toward
linear part of the amplifier. This, however, will reduce the signal amplification. From the hardware
point of view, power consumption of an amplifier mostly depend on high amplitudes of a signal
than on the average, thus handling occasional high peaks will lower power efficiency.
Another problem caused by high peaks is waste of quantization resolution. AD and DA
converters have limited levels of quantization that is why it is very important to use them
efficiently. When the OFDM signal amplitudes are mapped to quantization levels, high peaks
occupy many of these levels. This will prevent the main signal to use whole quantization range.
Thus quantization resolution will be wasted for infrequent high peaks reducing precision of the
rest signal. Taking into account reasons mentioned above, it becomes obvious that we need some
means to fight with high peaks in the OFDM signal.
2.6 PAPR reduction techniques
Since OFDM is a very successful technique in high data rates transmission, and high PAPR
significantly affect the system, many PAPR reduction methods were purposed in literature. All
these methods could be divided into two groups: frequency domain processing and time domain
processing. In the frequency domain processing PAPR reduction is made before IFFT, by
manipulating complex data inputs. In the time domain processing, reduction is made after IFFT
where we deal with discrete time OFDM signal. Let us have a look into these methods separately.
2.6.1 Frequency domain processing:
The frequency domain processing approaches the problem by investigating its origin. As
we remember from the section 2.3, high peaks occur from the superposition of sub channels that
mostly have the same phase. The idea of frequency domain processing, is that it tries to interfere
the complex input data to IFFT in a way to reduce occurrence of high peaks. One of the methods
of this type tries to change the phase of the complex data, while the others try to change the power.

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For example, signal set expansion technique converts the original signal into new signal with a
higher modulation scheme, e.g. the binary phase shift keying (BPSK) into the quadrature phase
shift keying (QPSK). That gives more freedom to select the phase, and eventually reduce the
PAPR. But in order to keep BER under a certain threshold, phase adjustments must be relatively
small [9] paragraph V. In input, sequence envelope scaling to reduce the PAPR, power of some
subcarriers is adjusted. These were examples of the blind processing techniques that means the
receiver is unaware of changes made in the transmitter. Conversely, in non-blind processing the
transmitter sends additional information about modifications, so that receiver could demodulate
signal more accurate. Selective mapping, partial transmit, sequences and random phase, updating
are the examples for non-blind technique. These techniques change the phase of the subcarriers
by adding some random phase factors to each modulation symbol. Then information about added
phase factors is sent to the receiver for correct demodulation.
2.6.2 Time domain processing:
In the time domain processing PAPR is reduced after frequency-to-time (IFFT)
transformation. This approach is trying to reduce high peaks that have already occurred, while the
frequency domain processing attempts to prevent occurrence of high peaks itself. The time domain
processing could be subdivided to blind and non-blind techniques as well. Clipping is the simplest
blind technique where high peaks are intentionally cut before the amplifier. But this will produce
clipping noise in form of in band and out of band radiation as well as spectrum widening. To
reduce the outbound radiation filters are used, but they however result in peak regrowth. Thus
clipping are not efficient technique in a PAPR reduction.
As the non-blind technique several companding schemes are purposed. Companding comes from
combination of two words: compressing and expanding. The principle of companding is to bring
the signal with large amplitude variations into the uniformly distributed signal by compressing
high peaks or by increasing the level of law signals. Companding is reversible process, i.e. com-
pressed original signal can be perfectly reconstructed at the receiver by performing expanding. In
this work two companding schemes, A-Law [10] companding and -law companding, will be
considered. Schemes will be described in details in the next chapter, and their performances will
be compared with uncompanded scheme in the last chapter.
Reduction of PAPR alone without paying attention on its effect to the other design criteria, such
as computational complexity, throughput, increasing power in the transmitted signal and the bit
error rate, wouldn’t be the right approach. System requirements should be considered for choosing
appropriate PAPR reduction scheme. For example blind techniques reduce PAPR at the cost of
increasing BER, whereas non-blind technique pay with reduction of the data rate because of
redundant information sent to the receiver.

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Chapter 3
COMPANDING SCHEME
3.1. SYSTEM DESCRIPTION
One of the major problems for Orthogonal Frequency Division Multiplexing (OFDM)
system is its high Peak-to-Average Power Ratio (PAPR). More importantly high PAPR due to
coherent combining of subcarriers results in the saturation of high power amplifier (HPA). In High
Throughput WLAN environment, the OFDM signal exhibits high PAPR in multiple ant-enna
configurations, which results in undesirable spectral emissions into adjacent channels and in BER
degrading.
Companding techniques are used to decrease dynamic range of the signal in order to
prevent it from distortions caused by channel with limited range. Wang proposes a simple and
effective companding technique to reduce the PAPR of OFDM signal. The OFDM signal can be
assumed Gaussian distributed, and the large OFDM signal occurs infrequently. So the companding
technique can be used to improve OFDM transmission performance. The bottleneck of the OFDM
system in terms of high PAPR is power amplifiers and AD/DA converters. As was already
mentioned in the previous chapter, power amplifiers have nonlinear characteristic with some
saturation level. High peaks of the OFDM signal usually exceed this maximum amplification level,
which result in clipping of high peaks by the amplifier. Clipping distorts the signal by increasing
the BER and widen its spectrum. The second bottleneck comes from the limited number of
quantization levels in AD/DA converters. High rare peaks will waste quantization resolution by
reducing the range of mapping for the main signal. Thus the quantization error will be increased.
This becomes especially critical when we have a system with small quantization resolution.
The companding technique compresses the signal, making its distribution quasi-uniform,
such that signal’s maximum amplitude does not exceed system’s limitations. Thereby, no
distortions will occur at the bottlenecks. At the receiver site the original signal is obtained by
reverse operation of expanding. The companding scheme is claimed to have better performance
than clipping method, due to absence of clipping noise.

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Figure 3.1 Block diagram for companding scheme
A-LAW COMPANDER
In this work two companding schemes, namely A-law companding and μ -law
companding, will be investigated. Mathematical formulation of A-law compressor is:
y =
| |
( ) ≤ | | ≤
(
| |
)
( ) < | | ≤
(3.1)
Where A is the A-law parameter of the compressor, V is maximum magnitude of the
signal , sgn(.) is the signum function. Which defines as:
Sgn(x) =
=
/| | ≠
(3.2)
At the receiver A-law expander performs the reverse operation:
x =
( )
≤ | | ≤
(
| |( )
) ( ) < | | ≤
(3.3)

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μ-LAW COMPANDER
In the μ -law companding, compressor squeezes the signal at the transmitter site according to the
following formula:
y =
(
| |
)
( )
( ) (3.4)
Where μ is the μ-law compression parameter. And at the receiver μ-law expander restores
original signal by:
x = | | ( )/
− 1 ( ) (3.5)
A-law and -law coefficients are responsible for the compression ratio. Compression increases
with increasing value of the coefficients. Originally A-law and -law companders were used for
voice compression, where -law companding is the conversion standard of North America and
japan, and A-law companding is the ITU-T standard which is used in Europe. Standard values of
the coefficients is 255, and the value of parameter A is 87.6. The profiles of A-law and -law
companding schemes are depicted in figure 3.2.
(a) A-law compander (b) -law compander
Figure 3.2. Characteristics of the companding schemes

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3.2 ADVANTAGES OF COMPANDING TECHNIQUE
1. Very effective for PAPR reduction.
2. No side information required.
3. No loss in data rate.
3.3 APPLICATIONS OF COMPANDING
Companding is used in digital telephony systems, compressing before input to an analog-
to-digital converter, and then expanding after a digital-to-analog converter. This is equivalent to
using a non-linear ADC as in a T-carrier telephone system that implements A-law or μ-law
companding. This method is also used in digital file formats for better signal-to-noise ratio (SNR)
at lower bit rates. For example, a linearly encoded 16-bit PCM signal can be converted to an 8-bit
WAV or AU file while maintaining a decent SNR by compressing before the transition to 8-bit
and expanding after a conversion back to 16-bit. This is effectively a form of lossy audio data
compression. Professional wireless microphones do this since the dynamic range of the
microphone audio signal itself is larger than the dynamic range provided by radio transmission.
Companding also reduces the noise and crosstalk levels at the receiver.

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Chapter 4
SIMULATION RESULTS
4.1 PAPR PERFORMANCE IN OFDM SYSTEM
4.1.1 PAPR WITHOUT COMPANDING AND WITH COMPANDING
(a)PAPR without companding (b) PAPR with companding
Figure 4.1 Performance of PAPR in OFDM systems
The Figure (4.1) shows the Peak to average power ratio of the OFDM system. We can
clearly observe from above figures that peak power had reduced when we use companding
technique compare with the OFDM system without companding.

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4.2. BIT ERROR RATE PERFORMANCE (BER) IN OFDM SYSTEM
4.2.1 BER WITHOUT COMPANDING & WITH COMPANDING
(c) BER vs SNR without companding (d) BER vs SNR with companding
Figure 4.2 BER performance in OFDM system
Simulation results shows that the BER is decreasing as SNR increses.This increment is
more in companded system when we compare with the system without companding
technique.From the above figures we can say that as “A” value increases BER is decreasing
accordingly. We can conclude from the above results that the system performance has
improved i.e. improvement in the performance of OFDM system after the companding
including Bit Error Rate (BER), SNR and Peak to Average Power Ratio reduction.
Simulations, which were conducted, have confirmed our theoretical considerations, and showed
that companded scheme perform better than uncompanded.

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Chapter 5
CONCLUSION
In this project work we considered the PAPR reduction problem in the OFDM system.
We have introduced the companding scheme as an efficient technique for reduction the high
Peak-to-Average Power Ratio in the OFDM system. The PAPR reduction technique was based
upon the companding method. Then performance of the OFDM system is simulated by using A-
law Companding, It is observed that as the value of “A” increases there is a significant reduction
in the PAPR value.
Simulations, which were conducted, have confirmed our theoretical considerations, and showed
that companded scheme perform better than uncompanded.

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List of Abbreviations
AWGN Additive White Gaussian Noise
BER Bit Error Rate
CDMA Code Division Multiple Access
FDMA Frequency Division Multiple Access
FFT Fast Fourier Transform
ICI Inter-Carrier Interference
IFFT Inverse Fast Fourier Transform
ISI Inter-Symbol Interference
MIMO Multiple Input Multiple Output
OFDM Orthogonal Frequency Division Multiplexing
PAPR Peak to Average Power Ration
SNR Signal to Noise Ratio
TDMA Time Division Multiple Access

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REFERENCES
[1] Wikipedia: http://en.wikipedia.org/wiki/Fading
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set expansion”, in Proc. IEEE Int. Conf. Commun.,vol. 2, pp. 867-971, 2004.
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reduction” International Journal of Advanced Research in Computer Science and Software
Engineering, Volume 2, Issue 5, May 2012.
[5] John G Proakis, Dimitris G. Manolakis, “Digital Signal Processing principles, algorithms, and
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[9] Andreas F. Molisch, “Wireless communications, second edition”.
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