An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code)

An Overview : Peak to Average
Power Ratio (PAPR) in OFDM
system using some new PAPR
techniques (with matlab code)
Zainab S. H. AL-Hashmi

An Overview : Peak to Average
Power Ratio (PAPR) in OFDM
system using some new PAPR
techniques (with matlab code)
By
Zainab Saad Hadi AL-Hashmi
A graduate of University of
Baghdad, College of Engineering
Electronic & Communications
Engineering Department

i
‫انشدٍى‬ ًٍ‫انشد‬ ‫هللا‬ ‫تغى‬
﴿ِ‫د‬ٍَْ‫ث‬‫ان‬ َ‫م‬ْْ‫أ‬ َ‫ظ‬ْ‫ج‬ِّ‫ش‬‫ان‬ ُ‫ى‬ُ‫ك‬َُْ‫ػ‬ َ‫ة‬ِْْ‫ُز‬ٍِ‫ن‬ ُ‫هللا‬ ُ‫ذ‬ٌ‫ُش‬ٌ ‫ًا‬َّ‫إ‬
‫ٍشا‬ِْٓ‫ط‬َ‫ذ‬ ْ‫ى‬ُ‫ك‬َ‫ش‬َِّٓ‫ط‬ٌُٔ﴾
‫انؼظٍى‬ ً‫انؼه‬ ‫هللا‬ ‫صذق‬
/ ‫{االدضاب‬ٖٖ}

ii
‫االْذاء‬
‫ّحيم‬‫ر‬‫ال‬ ‫ّحمن‬‫ر‬‫ال‬ ‫هللا‬ ‫بسم‬
ٌَ ًِِّ‫ث‬َُّ‫ان‬ ‫ى‬َ‫ه‬َ‫ػ‬ ٌَُّٕ‫ه‬َ‫ُص‬ٌ َُّ‫ر‬َ‫ك‬ِ‫ئ‬ َ‫َل‬َ‫ي‬َٔ َ َّ‫هللا‬ ٌَِّ‫إ‬﴿ٍَِّْ‫ه‬َ‫ػ‬ ‫ٕا‬ُّ‫ه‬َ‫ص‬ ‫ٕا‬َُُ‫ي‬َ‫آ‬ ٌٍَِ‫ز‬َّ‫ن‬‫ا‬ ‫ا‬ٌََُّٓ‫أ‬ ‫ا‬
﴾‫ا‬ًٍِ‫ه‬ْ‫غ‬َ‫ذ‬ ‫ٕا‬ًُِّ‫ه‬َ‫ع‬َٔ‫ذ‬ًََّ‫ذ‬ُ‫ي‬ ِ‫ٔآل‬ ‫ذ‬ًََّ‫ذ‬ُ‫ي‬ ‫ى‬َ‫ه‬َ‫ػ‬ ِّ‫م‬َ‫ص‬ َّ‫ى‬ُٓ‫ـ‬َّ‫ه‬‫ان‬.
‫االيح‬ ‫ٔشفٍغ‬ ‫انشدًح‬ ً‫َث‬ ‫انى‬ ‫أْذٌٓا‬‫عٍذ‬ ‫رَٕتُا‬ ‫ٔشفٍغ‬ ‫لهٕتُا‬ ‫دثٍة‬
‫هللا‬ ‫صم‬ ‫يذًذ‬ ‫انماعى‬ ً‫ات‬ ًٍٍ‫نهؼان‬ ‫سدًح‬ ‫ٔانًثؼٕز‬ ٍٍ‫اجًؼ‬ ‫انخهك‬
ّ‫ٔآن‬ ٍّ‫ػه‬‫هللا‬ ‫سعٕل‬ ‫انؼهى‬ ‫يذٌُح‬ ‫تاب‬ ‫انى‬ ‫ٔأْذٌٓا‬ ‫ٔعهى‬ٍّ‫ػه‬ ‫هللا‬ ‫صم‬
ّ‫ٔآن‬‫هللا‬ ‫سعٕل‬ ‫ػرشخ‬ ‫ٔانى‬ ٍٍُ‫انًؤي‬ ‫ايٍش‬ ٍٍ‫انغثط‬ ٕ‫ات‬ ‫ٔعهى‬
‫انٓذاٌا‬ ٌٔ‫ذشد‬ ‫ال‬ ‫انكشاو‬ ‫أَرى‬ ٔ ّ‫غ‬ ‫آل‬ ‫ٌا‬ ًُ‫ي‬ ‫فرمثهْٕا‬.
‫انًشدٕو‬ ‫ٔجذي‬ ً‫جذذ‬ ‫انى‬ ‫صغٍشا‬ ًَ‫ستٍا‬ ٍ‫ي‬ ‫انى‬ ‫أْذٌٓا‬ ٌ‫أ‬ ‫ٔأدة‬
‫أي‬ ‫ٔانى‬ ٌٍٔ‫ص‬ ‫ػثاط‬ ً‫ػه‬ ٍ‫دغ‬ ‫انغٍذ‬‫انغٍذ‬ ‫تانزكش‬ ‫ٔأخص‬ ً‫ٔأْه‬ ً
ٌٍٔ‫ص‬ ٍ‫دغ‬ ‫فاظم‬ ‫ٔانغٍذ‬ ٌٍٔ‫ص‬ ٍ‫دغ‬ ‫يٍصى‬ ‫ٔانغٍذ‬ ٌٍٔ‫ص‬ ٍ‫دغ‬ ‫لاعى‬
ٌٍٔ‫ص‬ ٍ‫دغ‬ ‫ػادل‬ ‫ٔانغٍذ‬.
ُّ‫ػ‬ ‫يغؤٔل‬ ْٕ ٍ‫ي‬ ٔ‫ا‬ ‫انًششف‬ ًّ‫ظه‬ ‫غانة‬ ‫نكم‬ ‫اْذٌٓا‬ ‫اٌعا‬ ‫ادة‬
‫انذك‬ ‫صادة‬ ‫ٔالٕل‬ ‫يظهٕو‬ ‫نكم‬ ‫اْذٌٓا‬ ‫تاخرصاس‬ ّ‫دم‬ ‫اخز‬ ٔ‫ا‬
‫دمٕلكى‬ ٍ‫ػ‬ ‫فذافؼٕا‬ ٌ‫عهطا‬

iii
Acknowledgments
praise belongs to God who showed favour to us through His
religion, singled us out for His creed, and directed us onto the
roads of His beneficence, in order that through His kindness we
might travel upon them to His good pleasure, a praise which He
will accept from us and through which He will be pleased with
us. !Allah send peace and blessings upon Mohammed and his
progeny (S.A.W.)
Finally I would like to thank my family,
Especially my grandfather Mr. Hassan Ali Zwain,
my mother, Mr. Qasim Hassan Zwain and Mr. Maythem Hassan
Zainab saad hadi
2015

iv
Abstract
The Orthogonal frequency division multiplexing (OFDM) is multicarrier
modulation scheme which has recently become comparatively popular in
both wireless and wired communication systems for transfer the
multimedia data. OFDM could be used at the core of well-known systems
like Asymmetric digital subscriber line (ADSL) internet, digital
television/radio broadcasting, wireless local area network (LANs), and
Long Term Evolution (LTE).
High PAPR is the major drawback of OFDM, which results in lower
power efficiency hence impedes in implementing OFDM. The PAPR
problem is more significant in the uplink because the efficiency of power
amplifier is critical because a mobile terminal has a limited battery
power.
High peak-to-average power ratio (PAPR) occurs due to large envelope
fluctuations in OFDM signal this requires a highly linear high power
amplifier (HPA). Power amplifiers with large linear range are expensive,
bulky 50% of the size of a transmitter lies and difficult to manufacture.
In order to reduce the PAPR, several techniques have been proposed in
this thesis, primarily the repeated frequency domain filtering and clipping
(RFC) has been proposed and compared with the existing method
repeated clipping and frequency domain filtering (RCF). The RFC is
better than RCF in performance especially when I ≥ 2, although they have
the same complexity and cost.
The proposed method is not only improving PAPR but also improving
BER. Best case for the bit error rate (BER) is at I =4 and CR =4, where
Signal to Noise Ratio (SNR) at BER ( ) improved by (5.7601 dB)
and Complementary Cumulative Distribution Function (CCDF) of PAPR
was improved by (4.775 dB) and PAPR was improved by (11.4177 dB).
The best one improvement in PAPR and CCDF of PAPR So as not to
BER deteriorate is at I =4 and CR =1.75. The improvement in PAPR by =
(18.2789 dB), CCDF of PAPR = (8.0187 dB), and the SNR at
BER( ) by = (0.6101 dB).
In addition to (RFC) six new types of companding have been proposed
and compared with the μ-law and A-law compandings. all these proposed
methods have better performance than the μ-law and A-law compandings,
and the best one is Absolute Exponential (AEXP) companding and the

v
best one improvement in PAPR and CCDF of PAPR is at d= 1.1. The
improvement in PAPR by = (17.6492 dB), and CCDF of PAPR = (7.2405
dB), while the SNR at BER( ) deteriorated by = (-3.4186 dB).
Five types of pre-coding are used in this work and then compared them
with each other. The best type of precoding in term of reduced PAPR and
BER is the Discrete Fourier Transform (DFT) pre-coder, while the least is
the Walsh Hadamard Transform (WHT) pre-coding.
Also four new types of hybrids PAPR reduction techniques have been
proposed. These methods are:
1. RCF with precodings (WHT, Discrete Cosine Transform (DCT),
Discrete Sine Transform (DST),and Discrete Hartley Transform (DHT)).
2. RCF with compandings (the all proposed compandings, μ-law and A-
law compandings).
3. RFC with compandings (the all proposed compandings, μ-law and A-
law compandings).
4.and finally precodings (WHT, DCT, DST,and DHT), with compandings
(the all proposed compandings, μ-law and A-law compandings).
The best one improvement is at (RFC with AEXP) because the PAPR,
CCDF of PAPR, and BER. This improvement in PAPR and CCDF of
PAPR is at d = 0.6 and CR =4. The improvement in PAPR by
(21.0509dB), CCDF of PAPR = (8.7178 dB), and the SNR at
BER( ) by (0.0116 dB).
The DHT with tangent Rooting (tanhR) have acceptable results where the
PAPR and CCDF of PAPR were improved while BER was degarded.
The best one improvement for this case is at k=15, y=.8 and DHT. The
improvement in PAPR by = (22.7711 dB), and CCDF of PAPR = (8.9691
dB), while the SNR at BER( ) deteriorated by = (-1.1828 dB).
All methods are simulated using matlab.

vi
Contents
Chapter One: Introduction 1
1.1 Introduction 1
1.2 Literature survey 1
Chapter Two: LTE and OFAM 7
2.1. Introduction 7
2.2. LTE Requirements 7
2.3. LTE Architecture 8
2.4. Air interface in LTE 9
2.5 History of OFDM 10
2.6 OFDM 12
2.6.1 Orthogonality of the subcarriers and OFDM 15
2.6.2 Guard Interval 17
2.6.3 One-tap equalizer 18
2.7 OFDM based Multiple Access 19
2.8 Orthogonal Frequency Division Multiple Access 20
2.9 SC-FDMA 24
Chapter Three: Peak To Average Power Ratio Reduction 27
3.1Definitions of PAPR 27
3.2 PAPR of OFDM signal 28
3.3 Oversampling discrete OFDM symbols to find true (continuous) peaks 29
3.4 Distribution of PAPR 29
3.5 Identification of the Problem 32
3.5.1 Nonlinear HPA and DAC 32
3.5.2 Power Saving 35
3.6 Factors influencing the PAPR 35
3.6.1 The number of sub carriers 35
3.6.2 The order of Modulation 35
3.6.3 Constellation shape 36
3.6.4 Pulse Shaping 36

vii
3.7 The gauge for judgment of the PAPR reduction in OFDM systems 36
3.8 Fitness function-based approach for determining an appropriate Algorithm 37
Chapter Four: PAPR Reduction Techniques 39
4.1There are three different way to divide the PAPR 39
4.1.1The first way is 39
4.1.2 The second way 43
4.1.3The third way 45
4.1.4 And finally there is Hybrid techniques 45
4.2 Clipping and Filtering 46
4.3 Peak Windowing Method 47
4.4 Envelope Scaling 48
4.5 Peak Reduction Carrier 48
4.6 Companding Technique 49
4.6.1 Square-Rooting Companding Technique ( SQRT) for PAPR Reduction in
OFDM Systems
50
4.6.2 Exponential Companding Algorithm 51
4.6.3 Trapezoidal power companding 53
4.6.4 Hyperbolic tangent ( ) companding 53
4.6.5 Error Function ( ) Companding 54
4.6.6 Logarithm Function (log) Companding 54
4.7 Coding techniques 54
4.8 Selective Mapping (SLM) 56
4.9 Partial Transmit Sequence (PTS) 57
4.10 Tone Reservation 59
4.11 Tone Injection 60
4.12 Interleaving 61
4.13 Active Constellation Extension (ACE) 61
4.14 Dummy Sequence Insertion (DSI) 62
Chapter Five: Simulation Results and Analysis 63
5.1 OFDM System model 63
5.2 PAPR techniques used 65

viii
5.2.1 Repeated clipping and frequency domain filtering (RCF) 65
5.2.2 Repeated frequency domain filtering and clipping RFC 72
5.2.3 The OFDM System with discrete time companding 77
5.2.3.1 A companding 77
5.2.3.2 Companding 81
5.2.3.3 Rooting Companding Technique (RCT) 85
5.2.3.4 New error function Companding (NERF) 87
5.2.3.5 Absolute Exponential companding (AEXP) 89
5.2.3.6 Cos companding 91
5.2.3.7 tangent Rooting Companding (tanhR) 95
5.2.3.8 Logarithmic Rooting Companding (logR) 101
5.2.4 OFDM System with pre-coding 104
5.2.4.1 Pulse Shaping or Pre-coding 104
5.2.4.2 Discrete Hartley transform (DHT) 105
5.2.4.3 Walsh-Hadamard Transform (WHT) 105
5.2.4.4 Discrete Cosine Transform (DCT): 106
5.2.4.5 Discrete Sine Transform (DST) Precoding Technique 107
5.2.4.6 The Discrete Fourier Transform (DFT) Precoding 107
5.2.4.7 Simulation results and analysis of OFDM system with pre-coding 108
Chapter six: Simulation Results and Analysis of Hybrid PAPR techniques 110
6.1 Hybrid pre-coding with RCF 110
6.2 Hybrids RCF with companding 119
6.2.1 RCF + A companding 119
6.2.2 RCF + 121
6.2.3 RCF + RCT 123
6.2.4 RCF + AEXP 126
6.2.5 RCF + cos 128
6.2.6 RCF + NERF 130
6.2.7 RCF + tanhR 131
6.2.8 RCF +logR 132
6.3 Hybrid RFC with companding 134
6.3.1 RFC + A companding 134

ix
6.3.2 RFC + companding 137
6.3.3 RFC + RCT 139
6.3.4 RFC + AEXP 141
6.3.5 RFC + cos 143
6.3.6 RFC + NERF 145
6.3.7 RFC + tanhR 146
6.3.8 RFC +logR 147
6.4 Pre-coding + companding 148
6.4.1 Pre-coding + A companding 149
6.4.2 Pre-coding + 152
6.4.3 Pre-coding + RCT 154
6.4.4 Pre-coding + AEXP 156
6.4.5 Pre-coding + cos 159
6.4.6 Pre-coding + tanhR 161
6.4.7 Pre-coding + logR 162
6.4.8 Pre-coding + NERF 163
Chapter seven : Conclusions and future work 165
7.1Conclusions 165
7.2Future work 167
References 168
Appendices
Appendix A : Table of Results A.1
Appendix B : MATLAB Code B.1

Chapter One Introduction
1
Chapter One
Introduction
1.1 Introduction:
During the last two decades, the demand for multimedia wireless communication
services have grown tremendously and this trend are expected to continue in the near
future. Orthogonal frequency division multiplexing (OFDM) is one of such multi-
carrier techniques which have attracted vast research attention from academics,
researchers and industries since last two decades. It has become part of new emerging
standards for broadband wireless access [1].
Energy efficiency, particularly matters in future mobile communications networks. A
key driving factor is the growing energy cost of network operation which can make up
as much as 50% of the total operational cost nowadays [2].
The transmitted signal of OFDM exhibits a high Peak-To-Average Power Ratio
(PAPR). This high PAPR reduces the efficiency of high power amplifier and degrades
the performance of the system [3].
A major source for reducing energy costs is to increase the efficiency of the high
power amplifier (HPA) in the radio frequency (RF) front end of the base stations [4].
However, the efficiency of the HPA is directly related to the PAPR of the input signal.
The problem, especially, becomes serious in OFDM multicarrier transmission, which
is applied in many important wireless standards such as the third Generation
Partnership Project (3GPP) Long Term Evolution Advanced (LTE-A). The PAPR
problem still prevents OFDM from being adopted in the uplink of mobile
communication standards, and, besides from power efficiency, it can also place severe
constraints on output power and therefore coverage in the downlink. In the past, there
have been many efforts to deal with the PAPR problem resulting in numerous papers
and several overview articles, e.g., [5], [6], [7].
PAPR has a deleterious effect on battery lifetime in mobile applications. As handy
devices have a finite battery life, it is significant to find ways of reducing the PAPR
allowing for a smaller, more efficient HPA, which in turn will mean a longer lasting
battery life.
In many low-cost applications, the problem of high PAPR may outweigh all the
potential benefits of multicarrier transmission systems [6]. A number of promising
approaches or techniques have been proposed & implemented to reduce PAPR with
the expense of increase transmit signal Power, bit error rate (BER) & computational
complexity and loss of data rate, etc. So, a system trade-off is required [8].
1.2 Literature survey:
In 1996 Robert [9]. The selected mapping was used for the reduction of PAR. The
selected mapping can be used for arbitrary numbers of carriers and any signal
constellation. The selected mapping provides significant gains at moderate additional
complexity. Actually, it is appropriate for all kinds of multiplex techniques, which
transform data symbols to the transmit signal. Even in single carrier systems where

2
PAR grows as the roll of factor of the pulse shaping filter decreases, selected mapping
can be applied advantageously.
The first nonlinear companding transform (NCT) for PAPR reduction was given by
Wang et.al in 1999 [10]. It was based on the speech processing algorithm µ-law and it
has found better performance than that of clipping technique. The µ-law companding
transform mainly focuses on enlarging small amplitude signals while keeping peak
signals unchanged, and thus it increases the average power of the transmitted signals
and may lead to overcome the saturation region of the HPA to make the performance
of the system worse. In order to overcome the problem of µ-law companding
(increasing average power) and to have an efficient PAPR reduction. [10]
In 2000 Myonghee et.al [11] Hadamard transform is an effective technique to reduce
the PAPR of an OFDM system. The PAPR can be reduced in OFDM system without
any power increase and side information. The increase of system complexity is not
much. As further study, the equalization problem combining with Hadamard
transform, which is induced to reduce PAPR, over multipath fading channel, is
considered.
In 2001 J. Armstrong [12] the clipping and frequency domain filtering PAPR
reduction technique has been described in which an interpolated version of the
baseband signal is clipped and then filtered with a new form of filter. The filter
consists of a forward and an inverse fast Fourier transform (IFFT). It is designed to
remove the out-of-band (OOB) noise without distorting the in-band discrete signal. It
is shown that significant PAPR reduction can be achieved without any increase in
OOB power. Some in-band distortion results, but this will have negligible effect on
the overall BER in most systems.
In 2002 J. Armstrong [13] the repeated clipping and frequency domain filtering of an
OFDM signal can significantly reduce the PAPR of the transmitted signal. This
method causes any increase in OOB power. Considerable PAPR reduction can be
obtained with only moderate levels of clipping noise.
In 2004 Ryu, et al. [14] The Dummy Sequence Insertion (DSI) technique reduces
PAPR through increased the average power of the signal. Herein, after switchting the
input data stream into parallel through the serial to parallel converter a, dummy
sequence is inserted in the input signal. Thus, the average value is raised and the
PAPR is reduced later.
In 2005 Tao Jiang et.al [15] “exponential companding”. It can adjust the amplitudes
of both large and small input signals, while maintaining the average power unchanged
by properly choosing transform parameters, so as to make the output signals have a
uniform distribution (with a specific degree). The exponential companding schemes
can efficiently reduce PAPR for various modulation formats and sub-carrier sizes.

3
The exponential companding schemes make less spectrum side-lobes than µ-law
companding. Simulation results have shown that exponential companding schemes
could provide better system performance in terms of PAPR reduction, power
spectrum, BER, and phase error than the µ -law companding scheme.
In 2007 Wisam et.al [16] square rooting companding (SQRT) companding a simple
method of reducing the PAPR value of OFDM symbol by changing the statistical
characteristics of the output signals . This was achieved by applying a non-linear
square rooting operation of the OFDM signals. The process changed also the
describing parameters of power signals: average and peak power values, and as a
result the PAPR value is reduced. This companding more suitable for OFDM
applications that do not have sophisticated processor, since it allows significant
reduction in PAPR value with very low cost of computational complexity, and only
slight performance degradation.
In 2008 Pisit et.al [17] the simple PAPR reduction method by using the dummy sub-
carriers. The features of proposed method is to decide the frequency data for dummy
subcarriers theoretically by using the certain number of larger amplitude levels
detected in the time domain signal and to achieve the better PAPR performance with
less computational complexity.
In 2008 Carole et.al [18] they present an incipient PAPR reduction technique which
exploits the utilization of used carriers in addition to the phase information of pilot
signals in OFDM systems to limit the PAPR while not degrading channel estimation
or frequency offset. Compared to conventional techniques like clipping and
windowing, this technique introduces significantly lower OOB distortions and
provides a lower BER since there is no interference to the original data signals. There
is additionally no requisite for side information to be transmitted to the receiver.
In 2009 Kazuki and Fumiyuki [19] A tone injection (TI) has been suggested which
exploits the property of a nonlinear modulo function. The TI is identically equivalent
to the one that superimposes a quadrature amplitude modulation (QAM) signal on the
data symbol to reduce the PAPR. Without the transmission of the side information,
the TI dramatically reduces the PAPR level. Albeit the TI-OFDM reduces the 1%
PAPR level by about 3~4.5dB, the BER performance remarkably degrades. However,
the utilization of antenna diversity reception can reduce the BER performance
degradation.
In 2010 Zhongpeng et.al [20] a combined μ companding transform and hadamard
transform technique is suggested to reduce PAPR of OFDM signal .Simulation results
shows that the PAPR reduction performance is improved compared with companding
transform used only. On the other hand, the BER of system using proposed PAPR
reduction scheme is not degraded.

4
In 2010 Imran and Varun [21] the PAPR of discrete hartley transform (DHT)-
Precoded OFDM system for M-ary Quadrature Amplitude Modulation (M-QAM)
(where M=16, 32, 64, 256). The Matlab simulation shows that DHT-Precoded OFDM
System shows better PAPR gain as compared to OFDM-Original system, Walsh
Hadamard transformation (WHT)-Precoder Based OFDM system and selective
mapping (SLM) OFDM (with V=2) system respectively. Thus, it is concluded that
DHT Precoder Based OFDM System shows better PAPR reduction then WHT-
Precoder Based OFDM System, SLM-OFDM System and OFDM-Original system for
MQAM. Additionally, the DHT-Precoded OFDM system does not require any power
increase, complex optimization and side information to be sent for the receiver.
In 2011 Zhongpeng [22] a combined reduction in PAPR of the
OFDM signals based on the combination of the discrete cosine transform (DCT) with
μ companding. While taking both BER performance and PAPR performance into
account, a united DCT and companding scheme to reduce the PAPR of OFDM
signals.
In 2011 Hem [23] a combinational method of pre-coding and clipping is proposed to
reduce the PAPR of an OFDM system. The proposed technique is better than
conventional because it does not require any increase in roll-off factor to reduce
PAPR. Thus, it reduces the overhead in comparison to conventional pre-coding
method. Increasing the roll-off factor degrades the BER as given in [24]. The clipping
after pre-coding reduces PAPR but degrades BER. However, this degradation in not
significant in comparison to degradation obtained by increasing roll off factor.
In 2012 Malhar and Prof.Abhishek [25] tone reservation includes no of set of
reservation of tones. By using this technique reserved tones can be utilized to
minimize the PAPR. This method is used for multicarrier transmission and also
demonstrated the reserving tones to limit the PAPR. Advantage of this tone
reservation is very positive that no process is needed at receiver end. Furthermore
there is no need to transmit the side information combined with the transmitted signal.
In 2012 Eugen [26] The PAPR reduction technique based on combination of a WHT
and a new signal companding function. The numerical results show that the hybrid
scheme realizes an improved PAPR reduction than the component methods. The
computation complexity increases linearly with the number of considered signal
variants because of several signal variants are applied to the precoding block. This
problem can be solved, by using few subcarriers as markers.
In 2012 Chau, and Hsuan [27] presents a combination scheme, which using a
combination of precoding by utilizing least null subcarriers in the frequency domain
and nonlinear companding technique by applying proper -Law characteristic in time
domain, for reducing PAPR. Simulation results indicate that the proposed scheme

5
achieves a advantageous trade-off between OOB power emission in OFDM systems
and the reduction of PAPR.
In 2013 Sroy et.al [28] an Iterative Clipping and Filtering (ICF) Technique for PAPR
Reduction of OFDM Signals: System Using DCT/ inverse discrete cosine transform
(IDCT) Transform. The OFDM symbol enters the ICF block with DCT/IDCT
technique, then clipping and filtering is iteratively performed. Although we
demonstrate that significant PAPR reduction is obtained through Iterative clipping
and filtering using fast Fourier transform (FFT)/IFFT transform, but better results are
observed applying DCT/IDCT in the classical ICF technique.
In 2013 Zihao et.al [29] a trapezoidal power companding method which could
significantly reduce the PAPR for a complex OFDM or Filterbank Based Multicarrier
Transmission (FBMC) system. The proposed approach provides a convenient way for
designing a compander where the trade-offs among several system performances
(such as PAPR, power spectral density (PSD) and BER) can be made.
In 2013 Mohit et.al [30] the performance of tanh and erf companding is
approximately. Log companding is better than the hyperbolic tangent and error
function companding . μ-law and A-law companding give the same performance and
the μ-law and A-law companding is better than the tanh, log and erf companding.
Some more non-linear transform have been suggested in the paper [31, 32, 33, 34, and
35]
In 2013 Jaspreet et.al [36] the performance analyzed in terms of PAPR in Orthogonal
Frequency Division Multiple Access (OFDMA) by utilizing some pre-coding
techniques, called Zadoff-Chu Transform (ZCT) and WHT with the µ-law
companding to limit the PAPR of the OFDM signals .These pre-coding techniques
produced the lower PAPR as compared to the conventional OFDM system.
Furthermore ZCT is better than WHT because it produced the lowest PAPR than
WHT. μ -law companding further reduces PAPR of OFDM signal and as with
increasing the value the PAPR reduces. The obtained results approved that the
proposed method have gotten better results than conventional OFDM.
In 2013 Navneet and Lavish [37] The PAPR reduction method is based on combining
clipping with WHT. Combined technique is simple to implement and has no
limitations on the system parameters such as number of subcarriers modulation order,
and constellation type. This system produces the lowest PAPR and is efficient, signal
independent, distortion less and do not require any complex optimizations
representing better PAPR reduction methods than others existing techniques because
it does not require any power increment, complex optimization and side information
to be sent to the receiver.

6
In 2013 Mohit et.al [38] To reduce the PAPR of OFDM has been proposed Hybrid
Clipping-Companding techniques for PAPR Reduction. the performance of hybrid
PAPR reduction scheme with either tanh or erf as companding function is
approximately same .Hybrid PAPR reduction scheme with log companding function
is better than the last two. Hybrid PAPR reduction scheme with either μ-law or A-law
companding gives the same performance and the Hybrid PAPR reduction scheme
with either μ-law or A-law companding is best.
In 2013 K. muralibabu et.al [39] In the proposed scheme, a combined reduction in
PAPR of the OFDM system by grouping the sub carrier on the basis of the
combination of joining the Discrete Cosine Transform (DCT) with companding
technique. The simulation results indicat that the proposed scheme can yield good
tradeoff between computational complexity and PAPR reduction performance
In 2014 Jijina et.al [40] a comparative study is made on the three typical linear
precoding techniques: Hadamard transform precoding, Discrete Sine Transform
(DST) precoding and Square root raised cosine function precoding used in OFDMA
system. The performance of these different schemes in terms of PAPR reduction is
analyzed with the conventional Random Interleaved OFDMA system. Linear
precoding schemes are efficient, signal independent, distortion less and do not require
complex optimization when compared to the other reduction schemes.

Chapter Two LTE and OFAM
7
Chapter Two
LTE and OFAM
2.1. Introduction:
The growth in data intensive mobile services and applications like Web browsing,
social networking, video streaming and music has become a driving force for
development of the next generation of wireless standards. Thus, new standards are
being developed to provide the data rates and network capacity needful to support
worldwide delivery of these kinds of rich multimedia application. LTE have been
developed to respond to the requirements of this generation and to achieve the aim of
realizing global broadband mobile communications [41].
2.2. LTE Requirements:
The demand for high speed and widespread network access in mobile
communications increases every day as the number of users‟ increases and
applications are constantly developed with greater demand for network resources. As
a result of this trend, mobile communications has experienced significant
developments within the last two decades, which is the result of tremendous research
that has been carried out. [42]
Requirements and objectives for the LTE Discuss the main requirements for the new
LTE system Resulted in a the creation of a formal
„Study Item‟ in 3GPP with the specific aim of „evolving‟ the 3GPP radio access
technology to guarantee competitiveness over a ten-year time-frame. Depending on
the study of this Study Item, the requirements for LTE Release 8 were revised and
crystallized. They can be summed up as follows [41,43, and 44]:
 High peak data rates and diminished delays, in both connection establishment
and transmission latency. These improvements are to be realized through the
simplification of the overall system, the decrease of complexity and the
automated process of system management (i.e. optimization).
 greater flexibility of spectrum usage, in each of the new and pre-existing bands;
 Seamless integration with existing systems (Universal Mobile
Telecommunications System (UMTS), Wireless Fidelity (Wi-Fi), etc.).
Infrastructure-building economy. Although the implementation of every new
system brings construction and building costs, LTE should be realized through
minimal investment and use as much of the existing mobile communication
infrastructure as possible.
 Multi-antenna support.
 Improved system capacity and coverage
 Reasonable power consumption for the mobile terminal. The mobile terminal is
being associated with mobile phones and similar devices which have limited
battery capacities. Therefore a flexible bandwidth system (with lower
frequencies used for uplink transmission) and automated signal power-level
optimization have to be included into LTE [45].
 Seamless mobility, including between different radio-access technologies;
 Simplified network architecture;
 Increased cell-edge bit-rate, for unification of service provision;
 Increased user data rates;
 Reduced cost per bit, implying an enhanced spectral efficiency;

8
 Packet switched domain utilization. To eliminate additional system complexity,
introduced through the support of both the circuit switched and packet switched
domain, the circuit switched domain will not be included into the LTE system.
The traditional voice and text messaging services must be replaced with system-
external subsystems (e.g. Information Management System (IMS)).
 High-level security and mobility. As the mobile communication system is now
similar to a data network (e.g. internet), additional emphasis will be set on new
security measures in combination with IP (Internet Protocol)-security functions.
Mobility efficiency is provided through the use of evolved base stations, i.e.
eNodeBs (E-UTRAN Node-B or Evolved Node-B).
These main targets resulted in the creation of additional requirements and spin-off
functionalities, whose realizations were researched, developed and evolved by 3GPP
and hence introduced in LTE‟s specifications and standardization upgrades.
These improvements were further evolved and enhanced in Release 9, which
contained additional techniques, functionalities and technology approaches to enable a
quick, efficient and low-cost implementation of the LTE system. The following
techniques are included:
 introduction to Self-Organizing Networks (SON),
 improved approach to emergency calls, as they oppose the system‟s security
policy,
 multiple-eNodeB broadcast signal combination (LTE MBMS),
 further improvement of Frequency Division Duplex (LTE-FDD) and Time
Division Duplex (LTE-TDD),
 improvement of SON technologies and mechanisms, and
 Minimization of system drive-tests (MDT).
The LTE system and its standardization are 3GPP‟s most significant milestone
achieved so far, triggering an increase of participation in their further projects and
worldwide acknowledgement of their existing work. Takahiro Nakamura, the 3GPP
RAN Chairman, states: “Operators need to work on issues that have been created in
signaling and the volume of data being carried. Therefore, further improvements to
the 3GPP system are being driven by that data explosion”. A continued evolution of
the system is given in Releases 10, 11 and 12, introducing an improved mobile
communication standard named LTE-Advanced [45].
2.3. LTE Architecture:
The LTE architecture was highly simplified and flattened, as shown in Figure 2.1. The
system contains only two types of nodes named Mobility Management Entity/System
Architecture Evolution Gateway (MME/SAE GW) and evolved Node-B (eNB) [46,
47].
All LTE network interfaces are based on IP protocols and therefore two major
changes were made compared to previous cellular radio architectures. The first
significant modify is that the Radio Network Controller (RNC) is removed from the
data path and its functions are now situated in eNB [46]. The main benefits of this
type of single node access network are the diminished latency and the distribution of
the RNC processing overhead into multiple eNBs. The second major change is that
there are no nodes for Circuit Switched (CS) domain, such as the Mobile Switching

9
Centre (MSC). Therefore speech services are handled as Voice over IP (VoIP) calls in
the LTE network [47, 48].
The eNBs are connected to each other via X2 interface and to Evolved Packet Core
(EPC) through S1 interface, as also shown in Figure 2.1. The S1 interface supports in
addition many-to-many relations between MMEs / SAE Gateways and eNBs [46].
SAE Gateway contains two logical gateway entities named as the Serving Gateway
(SGW) and the Packet Data Network Gateway (P-GW). The S-GW is responsible for
receiving and forwarding IP packets. Therefore, it can be seen as a local mobility
anchor to the eNBs [48]. The P-GW, on the other hand, is responsible for handling the
internet protocol functions, like routing, packet filtering, policy enforcement and
address allocation [47].
The new system architecture was designed so that it will reduce the overhead from
increased traffic. This is achieved because only the MME is responsible for signaling
and therefore the user IP packets do not go over MME. This way the network capacity
stays on a good level as the signaling and the traffic can grow separately [49]. The
main responsibilities of MME are idle-mode User Equipment (UE) reachability
including the control and execution of paging retransmission, different type of
authentication procedures with Non-Access Stratum (NAS) signaling, roaming, P-
GW/S-GW selection, tracking area list management and bearer management
including dedicated bearer establishment [47,48].
2.4. Air interface in LTE:
The air interface and communication environment used in LTE mobile
communication systems is called the LTE Radio Access Network. [45]
The LTE air interface is based on OFDMA for the downlink. OFDMA is an extension
of OFDM for the implementation of a multi-user communication system. For the
uplink, a single-carrier frequency-division multiple access (SC-FDMA) technique has
been selected. Advantages of this method include the relatively low adjacent channel
power, even if the power amplifier is not 100% linear. With SC-FDMA, no exacting
requirements are imposed on the linearity of the power amplifier in the mobile
handset. As a result, power consumption can be kept within limits. [50]
The utilization of OFDM provides considerable advantages over alternative multiple-
access techniques and signals severe departure from the past. Among the benefits are
adaptability for broadband data transmission and high spectral efficiency, impedance
to Inter Symbol Interference (ISI) resulting from the multipath fading, naturally
provide MIMO (Multiple Input Multiple Output) schemes, and provide frequency-
domain techniques like frequency-selective scheduling [51].
The design of the time-frequency representation of OFDM to provide high levels of
flexibility in allocation of each of the time frames for transmission and the spectra.
The spectrum flexibility in LTE supports not only a scalable set of bandwidths, but
also a variety of frequency bands. LTE also supplies a small frame size of 10 ms in
order to reduce latency. By designate short frame sizes, LTE allows better channel
estimation to be carried out the mobile, allowing timely feedbacks needful for link
adaptations to be supplied to the base station.[41]

10
Figure 2.1: System architecture for LTE Rel-8 network [47].
2.5 History of OFDM:
The initial development of multi-carrier communication system was basically done by
military systems in the late 1950s and mid-1960s. KINEPLEX, ANDEFT and
KATHRYN etc. are the few OFDM based systems utilized by US military systems for
high frequency applications [10].
In 1966, the concept of multicarrier communication was first introduced by Chang
[60] .He suggested a multicarrier scheme utilizing the parallel data transmission by
means of 10 frequency division multiplexing (FDM) with overlapping subcarriers. It
was found to be an efficient scheme for bandwidth utilization and to mitigate the
effect of multipath propagation. It also eliminated the requirement of high-speed
equalization technique. He gave the basic concept of OFDM and outlined a theoretical
way to transmit simultaneous data stream trough linear band limited channel without
Inter Symbol Interference (ISI) and Inter Carrier Interference (ICI) [61] [62].

11
These systems are called classical Multicarrier Modulation (MCM) system and
transmitted data on non-overlapped band-limited orthogonal signals. These systems
require analog oscillator and filter of much wider bandwidth and sharp cut-off.
Therefore, the concept of OFDM was not gained so much attention or popularity
because of the difficulty in subcarrier recovery without inter-subcarrier interference
by means of analog filters. Due to this reason only, a number of studies in the 1960s
were dedicated for MCM employing overlapped band-limited orthogonal signals [63,
64, and 65]. In the year 1967, B. R. Saltzberg suggested a MCM system employing
Orthogonal time-staggered Quadrature Amplitude Modulation (O-QAM) on the
carriers [63]. The concept of MCM scheme employing time-limited orthogonal
signals, which is similar to OFDM, was first given by H. F. Marmuth [66] in 1960.
[10]
The KINEPLEX system was developed by Collins Radio Company for data
transmission at high frequency over multipath fading channel, in this system, 20 tones
are modulated by DQPSK without filtering, which resulted in overlapping channels.
Initially the implementation of an OFDM system with large number of subcarriers
was very complex and expensive because it requires the array of sinusoidal generators
and coherent demodulators for parallel operations. In order to avoid the crosstalk
between the subcarriers, the system should be free from frequency and timing offsets
[62].
A major breakthrough in the history of OFDM came in 1971 when Weinstein and
Ebert used Discrete Fourier Transform (DFT) to perform baseband modulation and
demodulation which eliminated the need of bank of subcarrier oscillators thus making
the operation efficient and simpler [1,67].
In 1979, after evolutionary growth and development in signal processing and VLSI
technologies, high speed chips can be built around special-purpose hardware
performing the large size Fast Fourier Transform (FFT) (efficient algorithm for DFT)
at affordable price [68], [69].
All the proposals of OFDM systems used guard spaces in frequency domain and
a raised cosine windowing in time domain to combat ISI and ICI. Another milestone
for OFDM history was when Peled and Ruiz introduced Cyclic Prefix (CP) or cyclic
extension in 1980 [67,70] .This solved the problem of maintaining orthogonal
characteristics of the transmitted signals at severe transmission conditions. The
generic idea that they placed was to use cyclic extension of OFDM symbols instead of
using empty guard spaces in frequency domain. This effectively turns the channel as
performing cyclic convolution, which provides orthogonality over dispersive channels
when CP is longer than the channel impulse response [56,70].
Since 1990s, OFDM has been utilized for many broadband communication systems, it
includes high-bit-rate digital subscriber lines (HDSL) [71], asymmetric digital
subscriber lines (ADSL) [72], very high-speed digital subscriber lines (VHDSL) [72],
high definition television (HDTV) terrestrial broadcasting etc. It has also been utilized
by many wireless standards like Digital Audio Broadcasting (DAB) [73] The DAB
standard was in fact the first OFDM-based standard (project started in 1988 by ETSI
and completed in 1995), Digital Video Broadcasting (DVB) [74].
Many standards have been proposed for wireless local area networks (WLANs)
operating in ISM band, which are based on spread-spectrum technology. A number of
studies regarding the commercial applications of OFDM were made during 1990s like
High Bit rate Digital Subscriber Lines (HDSL; 1.6 Mbps), Asymmetric Digital
Subscriber Lines (ADSL; 6 Mbps), Very High Speed Digital Subscriber Lines

12
(VDSL; 100 Mbps), DAB and High Definition Television (HDTV) terrestrial
broadcasting [75].
In 1997, first OFDM-based WLAN standard, IEEE 802.11, was released. IEEE
802.11 can support a data rate up to 2 Mbps. Later on, in 1999, IEEE approved an
OFDM based standard 802.11a for supporting a data rate up to 54 Mbps. During this
period ETSI has also standardized the HiperLAN/2 standard, which has adopted
OFDM for their PHY standards [1].
In 2001, the FCC came with some new rules for modulations scheme operating in the
2.4 GHz range, which allow IEEE to extend 802.11b to 802.11g standard. Now days,
it has also been used in WiMAX (IEEE 802.16), and mobile broadband wireless
access (MBWA) IEEE 802.10. It is 11 also utilized by 4G wireless communication
systems, such as IMT-A. It is also been considered for 3GPP Long Term Evolution,
which is under deployment [62].
2.6 OFDM:
With the ever growing require of this generation, the necessity for high speed
communication has become a top priority. Different multicarrier modulation
techniques have developed to meet these demands, a few prominent among them
being OFDM and Code Division Multiple Access (CDMA) [52].
The fundamental principle of OFDM is a division of high data rate streams into a
number of lower data rate streams and then transmitted these streams in parallel using
several orthogonal sub-carriers (parallel transmission). Due to this parallel
transmission, the symbol duration increases, thus decrease the prorated amount of
dispersion in time resulting from the multipath delay spread. OFDM can be seen as
either a modulation technique or a multiplexing technique [10].
OFDM communication systems do not depend on increased symbol rates for
achieving higher data rates. That makes the task of managing ISI much easier.
Because data is transmitted in parallel instead of serially, OFDM symbols are
basically much longer than symbols on single carrier systems of equivalent data rate
[53].
The concept of OFDM is very much similar to the well-known and extensively used
technique of Frequency Division Multiplexing (FDM). OFDM uses the principles of
FDM to allow multiple messages to be sent over a single radio channel. It is however
in a much more controlled manner, allowing an improved spectral efficiency [54].
In conventional broadcast, each radio station transmits on a different frequency,
effectively using FDM to maintain a separation between the stations. Due to non-
orthogonal nature of carrier frequencies in FDM, a large band gap is required to avoid
inter-channel interference, which reduces the overall spectral efficiency. The
difference between FDM and OFDM is shown in Figure 2.2 [55].

13
Figure 2.2: Comparison of FDM and OFDM [55]
The sub-carriers are mutually orthogonal (The principle of orthogonality is discussed
in next sub-section.) in the frequency domain which alleviates the effects of ISI as
indicated in the Figure 2.3. All of these sub-carriers experiences „flat fading‟ because
they have a bandwidth less than the Mobile channel coherence bandwidth [56].
Figure 2.4 shows a baseband transceiver structure for OFDM utilizing the Fourier
transform for modulation and demodulation. Here the serial data stream is mapped to
complex data symbols (Phase Shift Keying (PSK), QAM, etc.) with a symbol rate
of . The data is then demultiplexed by a serial to parallel converter resulting in a
block of N complex symbols, .The parallel samples are then passed
through an N point IFFT (in this case no oversampling is assumed) with a rectangular
window of length N.Ts, resulting in complex samples
.Assuming the incoming complex data is random it follows that the IFFT
is a set of independent random complex sinusoids summed together. The
samples, are then converted back into a serial data stream producing a
baseband OFDM transmit symbol of length T=N.Ts [57].
A Cyclic Prefix (CP), which is a copy of the final part of the samples, is appended to
the front of the serial data stream before RF up conversion and transmission. The CP
combats the disrupting effects of the channel which introduce ISI.
In the receiver the whole process is reversed to recover the transmitted data, the CP is
removed prior to the FFT which reverses the effect of the IFFT [58]. The complex
symbols at the output of the FFT, are then decoded and the original bit
steam recovered.
Thus, the IFFT and FFT blocks at the transmitter and at the receiver, respectively, are
important components in an OFDM system. A lot of work has gone into the
optimization of the FFT implementations and the design community has leveraged this
trend to advantage leading to the popularity of OFDM based systems. The time-

14
frequency view of an OFDM signal is shown in Figure 2.5, where the important
parameters like subcarrier spacing and OFDM symbol period are shown [59].
Figure 2.3 OFDM subcarrier spacing [56].
Figure 2.4 a block diagram of a basic OFDM system.
Signal
Mapper
Signal
demapper
Equalizer
And
P/S
DFT
OR
FFT
S/P
D/A
Add
CP
IDFT
OR
IFFT
P/SS/P
Multipath
Fading Ch.
&
noise
A/D
Remove
CP
Input
output

15
Figure 2.5 Time-Frequency view of OFDM signal [59]
2.6.1. Orthogonality of the subcarriers and OFDM:
Two functions or signals are said to be orthogonal if they are mutually independent of
each other. Orthogonality is a feature that lets multiple information signals to be
transmitted skillfully over a common channel with the successful detection [24 and
76].
The subcarrier spacing is chosen so that the waveforms transmitted on different sub
carriers are orthogonal in time, but overlap in frequency. The orthogonality is
achieved by making the peak of each subcarrier signal coincide with the null of the
other subcarrier signals resulting in a perfectly aligned and spaced subcarrier signal
[77].
The principle of orthogonality state that if the time-averaged integral of the product of
any two functions from a set of functions { ( ) ( ) ( ) ( ) }, over a
joint existence time interval [ ] is equal to zero, irrespective of the limit of
existence of the functions, then the functions are told to be orthogonal to each other
within this time-interval [16]. Mathematically, it can be expressed as –
∫ ( ) ( ) (2.1)
The orthogonality property of OFDM signals can be shown with the help of its
spectrum. In the frequency domain every OFDM subcarrier has a ( )
frequency response, as shown in Figure 2.6 [10].
One of the key advantages of OFDM is its efficient use of the frequency band as the
subcarriers are allowed to overlap each other in the frequency domain. The N equally
spaced subcarriers will be orthogonal if the frequency separation between subcarriers
is f = , where N.Ts is symbol duration, and rectangular windowing of the
IFFT is performed. Under these conditions the subcarriers will have a waveform
frequency response [78].
Simple rectangular pulse of the length is used and rectangular shape in time
domain corresponds to a -square shaped spectrum in frequency domain as
illustrated in Figure 2.6. The LTE sub-carrier spacing is set to Δf= 15 KHz [62].

16
Figure 2.6 Per-subcarrier pulse shape and spectrum of basic OFDM transmission [48]
Figure 2.7 shows the frequency response of a 5 carrier system where it is seen that
because of the orthogonal relationship the maximum of a particular sample
corresponds to a null in all other carriers, therefore eliminating the effects of
interference.
Figure 2.7: Frequency spectrum of 5 orthogonal subcarriers of an OFDM transmit
signal [78].
The orthogonality among sub carriers can be viewed in time domain as shown in
Figure 2.8. Each curve represents the time domain view of the wave for a subcarrier.
As seen from Figure 2.3, in a single OFDM symbol duration, there are integer
numbers of cycles of each of the subcarriers [62]

17
Figure 2.8: Time domain representation of the signal waveforms to show
orthogonality among the subcarriers [62]
2.6.2. Guard Interval:
Individual sub channels can be perfectly separated by the FFT at the receiver when
there are no ISI and Inter-channel Interference (ICI) introduced by channel distortion.
Practically these conditions cannot be acquired. Since the spectra of an OFDM signal
is not precisely band limited, linear distortion like multipath fading caused sub
channel to spread energy in the adjacent channels [79, 80].
Figure 2.9 illustrates the CP insertion technicality, the Guard Interval or CP is a
periodic addition of the final part of an OFDM symbol that is added to the front of the
symbol in the transmitter, and at the receiver the CP is removed before demodulation
[81].
It serves as a recurrence of the end of the symbol, so allowing the linear convolution
of a frequency selective multipath channel to be modeled as circular convolution
which in turn might be transformed to the frequency domain utilizing a discrete
Fourier transform (DFT). This process allows for simple frequency domain processing
like channel estimation and equalization [82].
CP insertion, therefore, increases the size of the data symbol from to ,
being the duration of the guard-period containing the CP. The standard length of
the guard-period in LTE is defined to be 4.69 μs, allowing the system to tolerate path
variations up to 1.4 km (considering the standard LTE symbol length of 66.7 μs).
When a cyclic extension longer than a channel impulse response is added, the
negative effect of the previous symbol can be avoided by simply removing that
extension. CP insertion implies the copying of the last part of the OFDM data symbol
and attaching it to the timing at the beginning of the symbol, creating a break between
signals (hence: guarding-period). The receiver can then sample the incoming
waveform at optimum time, as time-dispersion problems (i.e. delays caused by
reflections of the signal) up to the length of the guarding-period are ignored [45].

18
Figure 2.9 the CP insertion mechanism [83]
2.6.3 One-tap equalizer [10]:
The tap-delay line model with path is considered for multipath fading channel.
After Considering the effect of the multipath fading channel, the samples of The
received signal can be expressed as:
( ) ∑ ( ) ( ) ( ) (2.2)
where, ( ) is the impulse response of multipath fading channel with path gains
{ ( ) }, is the path delay of path, and ( ) is a zero-
mean, unit variance complex Gaussian noise.
After discarding first G sample of the received signal and taking Z-point FFT, the
output of FFT block is ( ) given as :
(2.3)
Where, the term is the channel response to the subcarrier frequency and is
the Additive white Gaussian noise (AWGN) term in the frequency domain. To
compensate the fading effect of the channel, one-tap equalizer is used and each
element of the vector is multiplied by an equalized gain factor the output of
equalizer may be written as –
̂ (2.4)
Where, is defined as –
(| | ( ))
. (2.5)

19
2.7 OFDM based Multiple Access:
Various multiple access schemes can be combined with OFDM transmission and they
include orthogonal frequency division multiplexing-time division multiple access
(OFDM-TDMA), OFDMA, and multicarrier code division multiple access (MC-
CDMA). In OFDM-TDMA, time-slots in multiples of OFDM symbols are used to
separate the transmissions of multiple users as shown in figure. 2.10. This means that
all the used subcarriers are allocated to one of the users for a finite number of OFDM
symbol periods.
The only difference from OFDM-TDMA is that the users capture the channel and use
it for certain duration, i.e., the time dimension is used to separate the user signals [84]
Figure 2.10: Time – Frequency view of an OFDM-TDMA Signal
In OFDMA systems, both time and/or frequency resources are used to separate the
multiple user signals. Groups of OFDM symbols and/or groups of subcarriers are the
units used to separate the transmissions to/from multiple users. In figure 2.11, the
time, frequency view of a typical OFDMA signal is shown in a case where there are 3
users. It can be seen from figure 2.11 that users‟ signals are separated either in the
time-domain by using different OFDM symbols and/or in the subcarrier domain.
Thus, both the time and frequency resources are used to support multiuser
transmissions. We shall discuss this technique in more detail in the subsequent
sections and also compare it with OFDM-TDMA [85].

20
Figure 2.11: Time – Frequency view of an OFDMA Signal [85]
2.8 Orthogonal Frequency Division Multiple Access:
The approach used in LTE‟s access techniques consists of using OFDMA for the
downlink (DL) and SC-FDMA for the uplink (UL).
The main reason that justifies different access techniques for the UL and DL is the
fact that SC-FDMA optimizes range and power consumption at the UE, while
OFDMA minimizes receiver complexity and enables frequency domain scheduling
with flexibility in resource allocation. OFDMA is a multi-carrier transmission scheme
in opposition to SC-FDMA. Both allow multiple user access, depending on the
available bandwidth, by dynamically allocating each user to a specific time-frequency
resource, depending on which duplexing is deployed. OFDM requires a large dynamic
range due to PAPR [86 and 87].
The main difference between an OFDM system and an OFDMA one is represented in
Figure 2.12. The different colors represent different users using resources. In OFDM,
users are assigned to resources in the time domain only, while in OFDMA, users can
be assigned also in the frequency domain, optimizing resource usage.
In OFDMA systems, the multiple user signals are separated in the time and/or
frequency domains. OFDMA has been developed with multi-user operation as its
purpose, allowing a flexible assignment of bandwidth to users according to their
needs.
Typically, a burst in an OFDMA system will consists of several OFDM symbols. The
subcarriers and the OFDM symbol period are the finest allocation units in the
frequency and time domain, respectively. Hence, multiple users are allocated different
slots in the time and frequency domain, i.e., different groups of subcarriers and/ or
OFDM symbols are used for transmitting the signals to/from multiple users. For
instance, we illustrate an example in figure 2.13 wherein the subcarriers in an OFDM
symbol are represented by arrows and the lines shown at different times represent the
different OFDM symbols. We have considered 3 users and we have shown how
resources can be allocated by using the different subcarriers and OFDM symbols [88
and 89].

21
Figure 2.12 Difference between OFDM and OFDMA resource by user allocation [86].
Figure 2.13: Example allocation of resources to users in an OFDMA system [85].
Figure 2.14 is a detailed block diagram of OFDMA. The LTE PHY (Physical Layer)
specification has been designed to adapt bandwidths from 1.25 MHz to 20 MHz
OFDM was selected as the main modulation scheme due to its robustness with a
severe multipath fading. Downlink multiplexing is achieved through the OFDMA.
OFDM is the modulation scheme for the DL. The primary subcarrier spacing is 15
kHz, with lower subcarrier spacing of 7.5 kHz available for some MB-SFN
(Multicast-broadcast single-frequency network) scenarios. OFDM modulation
parameters summarizes in Table 2-1 [90]

22
Table 2-1 Downlink OFDM Modulation Parameters [90]
Transmission
BW
1.25 MHz 2.5
MHz
5 MHz 10 MHz 15 MHz 20 MHz
Sub-frame
duration
0.5 ms
Sub-carrier
spacing
15 kHz
Sampling
frequency
192 MHz
(1/2 x 3.84
MHz)
3.84
MHz
7.68
MHz
(2
x 3.84
MHz)
15.36
MHz
(4 x
3.84
MHz)
23.04
MHz (6
x 3.84
MHz)
30.72 MHz
(8 x 3.84
MHz)
FFT size 128 256 512 1024 1536 2048
No. of
occupied
subcarrier
76 151 301 601 901 1201

23
Figure 2.14 Complete block diagram of an OFDMA transmitter and receiver [91]

24
2.9 SC-FDMA:
In cellular systems, the wireless communication service in a certain geographical area
is supplied by multiple base stations. The downlink transmissions in cellular systems
are one-to-many, whilst the uplink transmissions are many-to-one. A one-to-many
service means that a base station transmits concurrent signals to multiple users‟
equipment‟s in its coverage area. This demands that the base station has very high
transmission power ability; as a result of the transmission power is involved for
transmissions to multiple users‟ equipment‟s [92]. On the other hand, in the uplink, a
single user‟s equipment has all its transmission power available for its uplink
transmissions to the base station. In the uplink, the design of an effective multiple
access and multiplexing scheme is more challenging than on the downlink because of
the many-to-one nature of the uplink transmissions. Another consequential requisite
for uplink transmissions is the low signal peakiness by means of the limited
transmission power at the user‟s equipment [92].
One of the main parameters that affect all mobile UE devices is their battery life. It is
therefore necessary to ensure an economic and efficient power use in the transmission
and reception of signals. With the RF power amplifier (i.e enhancer of mixed signals)
and the transmitter being the parts with the highest energy consumption within the
mobile UE; it is essential to establish a transmission model with near constant
operating power level [45].
The downlink physical layer of LTE is depending on OFDMA. Thus, in spite of its
many advantages, OFDMA has specific drawbacks like high sensitivity to frequency
offset (Doppler spread by cause of mobility and Arising from the instability of
electronics) and PAPR. PAPR occurs due to the random constructive addition of sub-
carriers and results in spectral spreading of the signal which leads to adjacent channel
interference. It is a problem that could be insurmountable with high compression point
power amplifiers and amplifier linearization techniques. While these approaches may
be utilized on the base station, they become costly on the UE [93 and 94].
In LTE, a new concept is used for the access technique of the uplink, called SC-
FDMA. Its characteristics combine lower PAPR of single-carrier systems because
there is only a single carrier unlike N carriers. (Which allows maintaining a lower
operating power level than OFDMA) with immunity to multipath interference, as well
as flexible subcarrier frequency allocation (as a crucial part of OFDM) [45]. Figure
2.15 shows the concepts of OFDMA and SC-FDMA.

25
Figure 2.15 frequency domain description of downlink and uplink LTE access
technologies
SC-FDMA differs from OFDMA in one additional transmission step, caused by the
single-path transmission of single-carrier systems. That transmission step, called
resource element mapping (and its counterpart, resource element selection), shifts all
symbols obtained through the FFT to the desired center frequency and passes them on
to the IFFT for further conversion Figure 2.16.
Since the power of the modulation signals used in this process is constant (QPSK
(Quadrature Phase Shift Keying), 16QAM and 64QAM) and the result of the resource
element mapping step is a waveform similar to the original, on another center
frequency; the required result of a constant-power signal is achieved [45].
For practicality, SC-FDMA is implemented in LTE utilizing a Discrete Fourier
Transform Spread OFDM transmission (DFTS-OFDM) which is repeatedly referred
to as a frequency-domain generalization of SC-FDMA. The DFT is used to multiplex
uplink transmissions in definite frequency allocation blocks within the general system
bandwidth in accordance with eNodeB scheduler instructions. The bandwidth of the
single carrier is specified based on the desired data rate by the user. Data remains
serial and not parallelized as done on the downlink with OFDMA (i.e. one
information bit is being transmitted at a time). This results in similar link performance
parameters for the uplink and downlink. Nevertheless, there would be comparatively
high ISI for the uplink because of the single carrier modulation. Thus, the eNodeB
receiver requires a low-complexity equalizer to rectify for the distorting impacts of
the radio channel. SC-FDMA is not as sensitive to Doppler Effect and frequency
instability the as OFDM by cause of its single carrier nature [93].

26
Figure 2.16 Block diagram of an SC-FDMA transmitter and receiver [37]

Chapter Three Peak-to-Average Power Ratio Reduction
27
Chapter Three
Peak-to-Average Power Ratio Reduction:
High PAPR of transmitted signals is one of the major issues of the OFDM system. A
large dynamic range of input data symbols is the main cause of getting high PAPR.
An OFDM signal consists of independent data symbols modulated on N orthogonal
subcarriers, and when these signals are added to the same phase, higher peak
amplitude is observed. The value of this peak may be times of the average
amplitude [10].
3.1 Definitions of PAPR:
For a continuous time baseband OFDM signal, the PAPR of any signal is defined as
the proportion of the maximum instantaneous power of the signal and its average
power. If x (t) is a transmitted baseband OFDM signal, then PAPR is defined as:
, ( )-
, ( ) -
(3.1)
Where, is the average power of x (t) and can be computed in frequency domain
because IFFT is a unitary transformation is useful duration of an OFDM symbol
[95].
For a discrete OFDM signal, the PAPR is computed from time oversampled
OFDM signal as:
, ( )-
[ ( ) ]
[ ( ) ]
(3.2)
The , ( )- at (dB) =
[ ( ) ]
[ ( ) ]
(3.3)
Where, , - denotes the expectation operator and is the total number of sub-
carriers. The PAPR of pass band OFDM signal is approximately twice that of
baseband PAPR [95].
The above power characteristics can also be described in terms of their magnitudes
(not power) by defining the crest factor (CF), which is defined as the ratio between
maximum amplitude of OFDM signal ( ) and root-mean-square (RMS) of the
waveform. The CF is defined as:
| ( )|
,|| ( )| |-
√ (3.4)
In most cases, the peak value of signal ( ) is equals to a maximum value of its
envelope | ( )| However, it can be seen from Figure 3.1 that the appearance of peak
amplitude is very rare, thus it does not make sense to use max | ( )| to represent the

28
peak value in real application. Therefore, the PAPR performance of OFDM signals is
commonly measured by certain characterization constants which relate to probability
[96].
Figure 3.1: High PAPR when sub-carriers are modulated by same symbols [96]
3.2 PAPR of OFDM signal [62]:
The discrete time baseband OFDM signal is defined in (6). The PAPR of the discrete
time OFDM signal determines the complexity of the digital circuitry in terms of the
number of bits necessary to achieve the desired signal to quantization noise ratio
during signal digitization and recovery. To better approximate the PAPR of a
continuous time OFDM signal, the discrete time OFDM signal is to be obtained by L
times oversampling. The oversampled discrete time OFDM signal can be obtained by
performing LN point IFFT on the data block with (L-1) N zero padding as follows:
, ( )-
√
( )
, 0≤ n ≤NL-1 (3.5)
PAPR of the oversampled OFDM signal of becoming
, ( )-
, ( ) -
, ( ) -
(3.6)
where, E[. ] denotes the expectation operator and N is total number of sub-carriers.
The PAPR of passband OFDM signal is approximately twice that of baseband PAPR.
Complementary Cumulative Distribution Function (CCDF) for an OFDM signal can
be written as:
P (PAPR > PAP )= ( ) (3.7)
Where PAP is the clipping level.
This equation can be read as the probability that the PAPR of a symbol block exceeds
some clip level PAP .

29
3.3 Oversampling discrete OFDM symbols to find true (continuous)
peaks:
The PAPR for the discrete-time baseband signal x [n] may not be the same as that of
the continuous-time baseband signal ( ) In fact, the PAPR for , - is lower than
that for ( ), simply because , - may not have all the peaks of ( ) In practice, the
PAPR for the continuous-time baseband signal can be measured only after
implementing the actual hardware, including digital-to-analog convertor (DAC). In
other words, measurement of the PAPR of the continuous-time baseband signal is not
straightforward. Therefore, there must be some means of estimating the PAPR from
the discrete-time signal , -. Fortunately, it is known that , - can show almost the
same PAPR as ( ) if it is L-times interpolated (oversampled) as shown in Figure 3.2
where L ≥ 4 [97 and 98].
Figure 3.2 Block diagram of L time‟s interpolator [83]
3.4 Distribution of PAPR:
To design and develop an effective PAPR reduction technique, it is very important to
accurately identify the distribution of PAPR in OFDM systems. The distribution of
PAPR plays an important role in the design of the whole OFDM system. The
distribution of PAPR can be used in determining the proper output back-off of the
HPA to minimize the total degradation. It can be used directly to calculate the BER
and to estimate the achievable information rates [10].
For the OFDM system, if we assume that the input data stream is statistically
independent and identically distributed (i.e.) then the real and imaginary parts of x[n]
are uncorrelated and orthogonal. From central limit theorem, it follows that, for large
values of N, the real and imaginary parts of x[n] are independent and identically
distributed (i.e.) Gaussian random variables, each with zero mean and variance
,| , - | - . (3.8)
The probability distribution of complex OFDM signals with large N is a complex
Gaussian distribution given by following relation:
* , -+
√
.
, -
/ (3.9)
Where Pr{.} denotes the probability distribution function. Where, is the variance
of , -.The amplitude of OFDM signal has a Rayleigh distribution and its
probability density function (PDF) is given by:
* , -+
| , - |
.
| , - |
/ (3.10)

30
The histogram plots for the real part, imaginary part and the absolute value of a time
domain OFDM signal are shown in Figure 3.3(a), (b) and (c) respectively. The plots
shown in Figures 3.3(a) and (b) are obtained after performing the computer
simulations of an OFDM system having N=256 QPSK modulated subcarriers as
shown in Fig. 2.4. The signal obtained from IFFT block of Figure 2.4 is complex
OFDM signal. After that real, imaginary and absolute values of OFDM signal (x[n])
are calculated and their histograms are plotted [62].
The power of OFDM signal has chi-square distribution. The distribution of PAPR is
often expressed on the one hand Complementary Cumulative Distribution Function
(CCDF). In probability theory and statistics, the CCDF describes the probability that a
real-valued random variable X with a given probability distribution will be found at a
value greater than or equal to x [99 and 10].
The Cumulative Distribution Function (CDF) of the PAPR of the amplitude of a
signal sample is given by
( ) ( ) (3.11)
The CCDF of the PAPR of the data block is desired in our case is to compare outputs
of different reduction techniques. This is given by:
( ) ( ) (3.12)
( ) (3.13)
( ( ) (3.14)
Where, is the given reference level.
Figure 3.3 (a)

31
Figure 3.3 (b)
Figure 3.3 (c)
Figure 3.3: Histogram of (a) Real part of OFDM signal amplitude (b) Imaginary part
of OFDM signal amplitude (c) OFDM signal magnitude [63].

32
3.5 Identification of the Problem:
Multi-carrier phenomena is considered to be one of the major development in wireless
communication and among them OFDM is becoming the important standard.
However, high PAPR is the major drawback of OFDM, which results in lower power
efficiency hence impedes in implementing OFDM. To overcome the low power
efficiency requires not only large back off and large dynamic range DAC but also
highly efficient HPA and linear converters. These demands result in costly hardware
and complex systems. Therefore to lessen the difficulty of complex hardware design it
has become imperative to employ efficient PAPR reduction techniques [100 and 101].
The drawback of a large dynamic range is that it places pressure on the design of
components such as the word length of the IFFT/FFT pair, mixer stages, and most
importantly the HPA, which must be designed to handle irregularly occurring large
peaks, decreases the SQNR (Signal-to-Quantization Noise Ratio) of ADC (Analog-to-
Digital Converter) and DAC, The PAPR problem is more important in the uplink
since the efficiency of power amplifier is critical due to the limited battery power in a
mobile terminal. Failure to design components with a sufficiently large linear range
result in saturation of the HPA [98, 78]. Saturation creates both in band distortion,
increasing the BER and out of band distortion, or spectral splatter, which causes
Adjacent Channel Interference (ACI). One obvious solution is to design the
components to operate within large linear regions, however this is impractical as the
components will be operating inefficiently and the cost becomes prohibitively high.
This is especially apparent in the HPA where much of the cost and ~50% of the size
of a transmitter lies which will be explained in next sections [98, 78].
3.5.1 Nonlinear HPA and DAC:
HPA are used in the transmitter of communication systems for sufficient transmission
power. To achieve maximum output power efficiency they have to be operated at or
near the saturation region. [100]
If the data on the subcarriers add up in a constructive manner at the transmitter, the
resulting signal could exhibit large PAPR. As a result, the composite transmit signal
could be severely clipped by the DAC and power amplifiers for their bounded
dynamic range as described in Figure 3.4. In this case, the reconstructed output ̂( )
can possess a significant amount of distortion. It can be reduce the PAPR of an
OFDM signal by modifying the signal characteristics in time-domain or frequency
domain clipping of the composite OFDM signal causes several undesirable outcomes,
such as signal distortion and spectral regrowth. For instance, clipping causes in band
noise that results in a degradation of the BER performance .Moreover, higher-order
harmonics that spill over into OOB spectrum can also result from signal clipping.
Although filtering after the HPA can be employed to remove this spectral leakage, it
is very power-inefficient, so it is an undesirable solution. Therefore, the dynamic
range of DAC should be large enough to accommodate the largest peaks of signals or
high PAPR values [102].
A high-precision DAC support high PAPR with acceptable amount of quantization
noise, but could be very costly to a certain sampling rate of the system. On the other
hand, a low-precision DAC would be cheaper, but the quantization noise will be
significant, which reduces the signal SNR (Signal to Noise Ratio) when the dynamic
range of DAC is increased to support high PAPR. Otherwise, the DAC will saturate
and clipping will occur [48, and 103].

33
Figure 3.4 An example illustrating effect of clipping.
The dynamic range of the power amplifiers should also be large enough to
accommodate large PAPR values. Otherwise, the power amplifiers may saturate and
clipping might occur. The component cost of the DAC and power amplifiers increase
with the increase in the dynamic range.

34
It is worth mentioning that the clipping of high signal peaks rarely happens, resulting
in a comparatively low incidence clipping noise. In this manner, the impact of
clipping at the transmitter on the error performance of the OFDM system liable to be
subjected frequency selective fading is minimal [102].
If an HPA with limited linear range is utilized for amplification, it may operate near
saturation and can cause OOB radiations and in-band distortion. The OOB
distortion/noise is a major concern, especially in wireless communications, where
large differences in signal strength from a mobile transmitter impose stringent
requirements on ACI [104]
Figure 3.5 demonstrates a classic input-output characteristic of a power amplifier. For
prevent or limit signal distortion input signals must be preserved below the Non-linear
area. The result is that the amplifier is not completely used [105]
IBO = 10 ( ) (3.15)
OBO = 10 ( ) (3.16)
IBO (Input Back-Off) or OBO (Output Back-Off)
High PAPR results in a wide variety of OFDM signal amplitudes which due to
nonlinear characteristics of HPA findings in inter-modulation among the various sub
carriers and leading to an increment in BER. To realize a low BER and minimal
signal distortion, HPA must be a large dynamic range and work in the linear amplifier
region. But, these types of HPA are expensive and smaller power efficient. The power
efficiency in wireless communication is very important for achieving efficient area
coverage and small size terminals. Thus, the power efficient process of non-linear
HPA is so important. Accordingly, it is best to target the reduction of PAPR the
OFDM signals before transmitting the signal into nonlinear DAC and HPA [100].
Figure 3.5 Typical input-output characteristics of a power amplifier showing the
Relation between Output Back-Off (OBO) and Input Back-Off (IBO) [98].

35
3.5.2 Power Saving [100]:
A high dynamic range HPA has low power efficiency. The power could save by
reducing PAPR. This power saving that is implemented in such a way to provide a
direct correlation with the desired average output power.
On the assumption a linear model of HPA, the power efficiency is:
(3.17)
(3.18)
The η= HPA efficiency .
= the average of the output power.
. = A fixed amount of power regardless of their input power.
For example: an OFDM signal with 256 sub carriers that demand an IBO equal to the
PAPR at the probability level lower than 0.01%, i.e. (25.235).This makes
η = 0.5/25.235≈1.98%
The PAPR of OFDM systems has to reduce for avoiding this level of power
inefficiency.
3.6 Factors influencing the PAPR:
3.6.1 The number of sub carriers:
In Multi-Carrier Systems the complex base band signal for one symbol in an OFDM
system can be expressed as follows:
( )
√
∑ (3.19)
Where N is the modulating symbol and is the number of sub carriers. For moderately
large numbers of m-PSK (multiple phase-shift keying) sub carriers the quadrature
components of x (t) each tends towards a Gaussian distribution (giving the sum of
their power amplitude a Rayleigh distribution). Consequently, whilst the peak value
possible is N times the individual sub carrier peak, the probability of any value close
to that peak occurring is very low. For example, with only 24 sub carriers, the
probability of the PAPR exceeding 4dB is and of exceeding 8dB is only
[99].
3.6.2 The order of Modulation:
High data bandwidth efficiency (in terms of b/s/Hz) this can be achieved by utilizing
higher order modulations based, for instance, on QAM. When using a higher-order
modulation such as QAM type, the PAPR of the summed OFDM signal is increased
by the PAPR of the QAM constellation utilized. Nevertheless, the probability of these
higher peaks happening is accordingly less. Furthermore, since among benefits of
OFDM is one that sub carriers could have their modulation independently varied to
adapt to channel conditions, the joined PAPR in any system utilizing this technique
might are hard to predict and control. PAPR for an unfiltered base band signal is listed
in the following Table 3.1. [100].

36
Table 3.1 PAPR for picked modulation formats
3.6.3 Constellation shape:
The last entry in Table 3.1 is for a constellation obtained by modifying 256- QAM to
reduce PAPR. This modified constellation shape is shown in figure 3.6. However,
there is an additional processor load associated with encoding and decoding this
constellation.
Figure 3.6 256-QAM constellations: (a) regular and (b) modified mapping to reduce
PAPR
3.6.4 Pulse Shaping:
In terrestrial communications, it is popular to use pulse shaping to the base band
signal, to decrease the bandwidth of the transmitted spectrum, but this causes
overshoot and can increase the PAPR of the modulating signal by 4-5 dB [100].
3.7 The gauge for judgment of the PAPR reduction in OFDM systems
[106, 107, 108]:
Every method used to reduce the PAPR has some drawbacks and merits. There is
always a trade-off between PAPR reduction and some other factors like bandwidth,
computational complexity, average power etc. An ideal PAPR reduction technique
should have following characteristics:
1) High potential to limit the PAPR: It is a key factor to consider in the selection of
technology to reduce the PAPR with few adverse side effects like in-band distortion
and OOB radiation.
2) Low average power: even though it can reduce PAPR through the average power of
the original signals increase, it needs a bigger linear operation region in HPA and
which led in the deterioration of BER performance.
Modulation PAPR
256-QAM 4.23dB
64-QAM 3.68dB
256-QAM (modified) 2.85dB
16-QAM 2.55dB
m-PSK (reference) 0 dB

37
3) Low implementation complexity: mainly, complexity techniques viewing better
capability of PAPR reduction. Nevertheless, practically, both time and hardware
requisites for the PAPR reduction must be minimal.
4) No bandwidth expansion: The bandwidth is an infrequent resource in systems. The
bandwidth expansion has directly resulted in the data code rate loss because of side
information (like the complementary bits in Complement Block Coding (CBC) and
phase factors in PTS). Furthermore, when the side information is received in error
unless some methods of protection like channel coding employed. For that reason,
when channel coding is utilized, the loss in data rate is incremented further due to side
information. Then, the loss in bandwidth because of side information must be avoided
or at least be preserved minimal.
5) No BER performance degradation: The objective of the PAPR reduction is for the
best system performance, including BER than that of the original OFDM system. For
that reason, all the methods, which have an incrementation in BER at the receiver,
must be paid more attention in practice. Additionally, if the side information is
received in error at the receiver, which may also result in entire wrong data frame and
thus the BER performance is reduced.
6) Without the additional power required: The design of a wireless system must
always take into account the efficiency of power. If an operation of the technique
which reduces the PAPR require more extra power, it deteriorates the BER
performance when the transmitted signals are normalized back to the original power
signal [109].
7) No spectral spillage: Any PAPR reduction techniques cannot devastate OFDM
fascinating technical features like immunity to the multipath fading. Thus, the spectral
spillage must be avoided in the PAPR reduction.
8) Other factors: It must be driven greater concentration on the effect of the nonlinear
devices utilized in signal processing loop in the transmitter like DACs, mixers and
HPAs since the PAPR reduction fundamentally avoid nonlinear distortion as a result
of these memories-less devices introducing into the communication channels. At the
same time, the expense of these nonlinear devices is too the important factor to design
the PAPR reduction scheme.
3.8 Fitness function-based approach for determining an appropriate
Algorithm [110]:
In order to determine an appropriate PAPR reduction algorithm for a given system, it
is desirable to consider all above-listed requirements. The number and nature of these
requirements may vary depending upon the system (or user) under consideration. For
a given scenario and requirements, we propose to use the fitness value or
appropriateness value of the algorithm, which is defined as the weighted sum of the
relative changes in the above-listed factors. The appropriateness value provides a
single metric for determining the appropriateness of a PAPR reduction algorithm.
Suppose X1 be the relative degradation in BER performance at certain SNR level, for
given channel conditions, AWGN or multipath, given by:
X1 = −10 ( ) (3.20)
Let X2 be the relative increase in system complexity given by:
X2 = −10 ( ) (3.21)

38
Let X3 be the relative PAPR reduction given by:
X3 = −10 ( ) (3.22)
Let X4 be the relative cost savings given by:
X4 = −10 ( ) (3.23)
Let X5 be the relative increase in transmit power given by:
X5 = −10 ( ) (3.24)
Let X6 be the relative increase in spectral spillage given by:
X6 = −10 (O ) (3.25)
Let X7 be the relative reduction in goodput5 given by:
X7 = −10 ( ) (3.26)
The aggregate fitness value of the PAPR reduction algorithm can be computed as the
weighted sum of these factors, where the weights correspond to their relative
importance levels. These weights can be determined as per the system or user
requirements. Therefore, the fitness value of the algorithm is given by:
∑ (3.27)
Where
∑ (3.28)
Based on these fitness values, an appropriate algorithm can be chosen in order to
achieve large reduction in PAPR values as well as satisfy other system requirements.

Chapter Four PAPR Reduction Techniques
39
Chapter Four
PAPR Reduction Techniques
4.1There are three different way to divide the PAPR:
4.1.1The first way is [110]:
PAPR reduction techniques can be categorized into deterministic and probabilistic
approaches, as shown in Figure 4.1. Deterministic approaches guarantee that the
PAPR of an OFDM signal does not exceed a predefined threshold, whereas the
probabilistic approaches minimize the probability that the PAPR of an OFDM signal
exceeds a predefined threshold. These categories will be discussed in the following
sections
1) Deterministic Approach
Deterministic PAPR reduction approaches can be classified into techniques that
perform either time-domain based clipping or frequency-domain based coding. The
simplest approach for PAPR reduction is to deliberately clip the amplitude of the
signal to a predefined value before amplification [111]. However, the technique
suffers from various drawbacks, such as signal distortion and spectral regrowth.
Therefore, clipping alone is not a suitable option for PAPR reduction. Modified
clipping techniques exist, which fall under the probabilistic approach explained in the
next section.
Coding techniques are applied to OFDM signals in order to map symbols to codes
with smaller PAPR values [112] .
Each symbol has a choice of two or more codes, where the code yielding the lowest
PAPR is selected. However, this technique works well only when the number of
subcarriers is small. With the increased number of subcarriers, the search space for
finding codes with minimum PAPR increases exponentially and large lookup tables
are needed for encoding and decoding.
2) Probabilistic Approach
Probabilistic approaches attempt to minimize the number of occurrences of OFDM
symbols with PAPR values exceeding a predefined threshold, while simultaneously
minimizing the signal distortion and spectral growth. Probabilistic approaches can be
classified according to whether time domain processing or frequency domain
processing is involved:
 time Domain-Based Processing:
Time domain-based processing approaches focus on manipulating the power of the
signal in the time domain. This approach can be further classified into blind and non-
blind techniques. Blind techniques imply that the receiver is oblivious to the changes
made at the transmitter side, whereas non-blind techniques imply that the receiver
requires a priori knowledge about the modifications made at the transmitter side for
correctly demodulating the received signals. Thus, non-blind techniques require
additional side information in order to operate, whereas blind techniques might
degrade the error performance of the system since the receiver is transparent to the
changes made at the transmitter side.

40
The simplest blind technique for PAPR reduction is to clip the amplitude of the signal
to a predefined value and filter the signal to suppress the out-of-band interference
[113,114, 115 ] . The clipping process might result in spectral regrowth, whereas
filtering the signal might result in some peak regrowth. Therefore, clipping may not
be an effective technique when reducing the PAPR of the OFDM signals as long as
the transmitted OFDM signal is strictly band-limited. Even though numerous
algorithms based on amplitude clipping and filtering have been proposed in the
literature, it has been shown that clipping does not improve the reduction of total
degradation [116]. Instead, an unclipped system outperforms a clipped system
because of the inter-carrier interference (ICI) caused by clipping, and offsets the gain
of the PAPR reduction [116]. Another technique called peak windowing can also
reduce the PAPR, where large signal peaks are multiplied with a certain narrowband
window such as Gaussian, Cosine, Kaiser, and Hamming windows [117].
Among the non-blind techniques, several companding4 techniques for compressing
the large peaks of an OFDM signal in time domain, including μ-law companding , and
exponential companding , have been proposed in literature. By compressing the large
peaks of an OFDM signal by companding, the dynamic range of the D/A converters
are reduced. However, the receiver needs to expand the compressed signal for correct
demodulation.
 Frequency Domain-Based Processing
Frequency domain-based processing approaches focus on minimizing the correlation
of the input signals since it is known that the PAPR of an OFDM signal is high when
the input sequences are highly correlated. It has been shown that by altering the phase
and/or power of the input sequence, it is possible to lower the correlation of the input
sequence, thereby reducing the PAPR of an OFDM signal. However, some
approaches also try to directly manipulate the correlation of the input signals.
Frequency domain-based processing approaches can be further classified into blind
and non-blind techniques. In blind phase adjustment-based techniques, the phase of
the subcarriers are adjusted in order to reduce the coherence between the different
subcarriers such that the PAPR value of the OFDM signal is reduced. The phase
adjustments should be kept relatively small so as to minimize bit-error-rate (BER)
performance degradation. For example, signal set expansion technique maps original
signal set into an expanded signal set with two or more points, such as binary phase
shift keying (BPSK) into quadrature phase shift keying (QPSK), which provides more
freedom for phase selection and yields lower PAPR values for the OFDM signal
[118].
Blind power-based techniques alter the power level of the subcarriers such that the
PAPR of an OFDM signal is reduced. These techniques are suitable only for the
MPSK-based OFDM system since the receiver is unaware of the information about
the transmit power levels. For example, the input sequence envelope scaling technique
adjusts the power of the subcarriers so that the power of the individual subcarriers
becomes unequal yielding a minimized PAPR value [119]. Since the phase
information of the original signal is unchanged, the receiver can decode the received
signal without any side information.
In blind power and phase-based techniques, both the phase and the power of the
subcarriers are altered such that the PAPR of an OFDM signal is reduced. If the total
transmit power needs to be kept constant, these techniques are suitable only for low
order modulation techniques since the error robustness of the higher modulation
techniques degrades rapidly with the blind phase and power alterations at the

41
transmitter. When the order of the modulation techniques in-creases, the complexity
(and limitations) of the algorithm increases as well as transmit power level increases.
For example, the active constellation extension (ACE) [120,121] and dynamic
constellation shaping techniques allow changing the power and phase of some data
symbols without affecting the error probability of the other data symbols.
Non-blind power-based techniques, as well as power and phase-based techniques,
would be suitable for the higher modulation schemes such as MQAM. Non-blind
phase adjustment-based techniques update phases of the input sequence such that the
PAPR of an OFDM signal is reduced. The information about the phase updates is
transmitted to the receiver for correct demodulation. Several modified algorithms are
proposed in literature, which avoid the requirement of explicit side information. For
example, selective mapping (SLM)[9], partial transmit sequences (PTS) [122],
random phase updating [123] techniques add random phase factors to each subcarriers
in order to reduce PAPR with the information about the phase factors transmitted to
the receiver. The blind techniques reduce the PAPR values at the cost of slight
increase in the bit error rate of the system or increased transmit power level since the
adjustments would result into increased noise level at the receiver, whereas the non-
blind techniques reduce the PAPR values at the cost of a reduced information rate
since the information about the adjustments made at the transmitter need to be
transmitted to the receiver for the correct demodulation.
A low autocorrelation coefficient of a signal is a sufficient condition for low PAPR.
However this is not a necessary condition [124][125]. Non-blind autocorrelation
minimization techniques attempt to minimize the autocorrelation of the input
sequence `and the information about the changes is transmitted to the receiver for
correct
demodulation. For example, the selective scrambling [126] and interleaving
techniques [127] attempt to break the long correlation patterns of the input sequences
to reduce the PAPR. However, the techniques perform well only when the OFDM
signal has moderate PAPR values since interleaving alone is not effective to break the
correlation pattern when the input sequence are highly correlated.
Attempts have been made to develop OFDM signals with a constant envelope to yield
unity PAPR values [128] . The constant envelope waveforms have a constant
instantaneous power. Continuous phase modulation (CPM) is a class of signaling that
has very low side lobe power while maintaining the constant envelope property.
However, CPM increases the complexity of the receiver and has a poor performance
over frequency selective channels.

42
Figure 4.1.the first way taxonomy of PAPR Reduction techniques

43
4.1.2 The second way is :
a) Distortion Based Techniques [11]-[8]-[4]
b) Scrambling Techniques [17]-[16]-[8]
As shown in figure 4.2
a. DISTORTION BASED TECHNIQUES
The schemes that introduce spectral re-growth belong to this category. Distortion
based techniques are the most straightforward PAPR reduction methods. Furthermore,
these techniques distort the spectrum, this spectrum distortion or “spectral re-growth”
can be corrected to a certain extent by using filtering operation [62 ,129]. These
methods reduce the PAPR by distorting the OFDM signal non-linearly. The methods
like clipping and filtering, peak windowing, and non-linear companding are the
example of these techniques. These techniques are applied after the generation of
OFDM signal (after the IFFT) [130].
The distortion category attempts to reduce PAPR by manipulation of signal before
amplification. Clipping of signal prior to amplification is a simplest method but it
causes increase in both out-of-band (OOB) as well as in-band interference thus
compromises upon performance of system. Amongst this category better techniques
include companding, peak windowing, peak power suppression, peak cancellation,
weighted multicarrier transmission etc. Any technique which is used to reduce PAPR
should not only have high spectral efficiency but must be compatibility with the
existing modulation schemes and at the same time must not be computational
complex [100].
b. Scrambling techniques :
Signal scrambling techniques are all variations on how to scramble the codes to
decrease the PAPR. Coding techniques can be used for signal scrambling. Golay
complementary sequences, Shapiro-Rudin sequences, M sequences, Barker codes can
be used efficiently to reduce the PAPR. However with the increase in the number of
carriers the overhead associated with exhaustive search of the best code would
increase exponentially. More practical solutions of the signal scrambling techniques
are block coding, Selective Level Mapping (SLM) and Partial Transmit Sequences
(PTS). Signal scrambling techniques with side information reduces the effective
throughput since they introduce redundancy [131] [132].

44
Figure 4.2.the second way taxonomy of PAPR Reduction techniques

45
4.1.3 The third way is [98]:
These methods are basically divided in five categories:
(1) The clipping technique
(2) Coding Methods,
(3) Probabilistic (Scrambling) Techniques
(4) Pre-distortion Methods.
1. The clipping technique employs clipping or nonlinear saturation around the peaks
to reduce the PAPR. It is simple to implement, but it may cause in-band and out-of-
band interferences while destroying the orthogonality among the subcarriers. This
particular approach includes block-scaling technique, clipping and filtering technique,
peak windowing technique, peak cancellation technique, Fourier projection technique,
and decision-aided reconstruction technique [133] [134].
2. The coding technique is to select such code words that minimize or reduce the
PAPR. It causes no distortion and creates no out-of-band radiation, but it suffers from
bandwidth efficiency as the code rate is reduced. It also suffers from complexity to
find the best codes and to store large lookup tables for encoding and decoding,
especially for a large number of subcarriers. Golay complementary sequence, Reed
Muller code, M-sequence, or Hadamard code can be used in this approach [133][134].
3. The probabilistic (scrambling) technique is to scramble an input data block of the
OFDM symbols and transmit one of them with the minimum PAPR so that the
probability of incurring high PAPR can be reduced. While it does not suffer from the
out-of-band power, the spectral efficiency decreases and the complexity increases as
the number of subcarriers increases. Furthermore, it cannot guarantee the PAPR
belowa specified level. This approach includes SLM (Selective Mapping), PTS
(Partial Transmit Sequence).
4. The pre-distortion methods are based on the re-orientation or spreading the energy
of data symbol before taking IFFT. The pre-distortion schemes include DFT
spreading, pulse shaping or precoding and constellation shaping. The methods like
Tone Reservation (TR) and Tone Injection (TI) are the example of constellation
shaping schemes [10].
The DFT-spreading technique is to spread the input signal with DFT, which can be
subsequently taken into IFFT. This can reduce the PAPR of OFDM signal to the level
of
Single-carrier transmission. This technique is particularly useful for mobile terminals
in uplink transmission. It is known as the Single Carrier-FDMA (SC-FDMA), which
is adopted for uplink transmission in the 3GPP LTE standard [135].
4.1.4 And finally there is Hybrid techniques:
Besides these different PAPR reduction techniques, some hybrid methods are also
available in the literature [136 ,137,138 ] . These methods combine two or more than
two techniques for PAPR reduction like clipping with coding, SLM with coding, pre-
coding with clipping, interleaving and companding , Selective Mapping and Binary
Cyclic Codes, combining Hadamard Transform and Hann peak windowing etc. The
hybrid methods are considered as better choice for PAPR reduction because it possess
the advantages of both techniques used in hybridization with slight increases in
complexity.

An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code)

An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code)

Recomendados

Recomendados

Mais conteúdo relacionado

Mais procurados

Mais procurados (20)

Destaque

Destaque (20)

Semelhante a An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code)

Semelhante a An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code) (20)

Último

Último (20)

An Overview : Peak to Average Power Ratio (PAPR) in OFDM system using some new PAPR techniques (with matlab code)