GUJARAT TECHNOLOGICAL UNIVERSITY AHMEDABAD June 2017 D THESIS_SHATRUGHNA... · 2020. 9. 11. · The...

Investigations on Nonlinearity Effects in Communication

Systems and their Compensation Techniques

A Thesis submitted to Gujarat Technological University

For the Award of

Doctor of Philosophy

in

Electronics and Communication Engineering

By

Shatrughna Prasad Yadav

Enrollment No: 129990911010

Under the Supervision of

Dr. Subhash Chandra Bera

GUJARAT TECHNOLOGICAL UNIVERSITY

AHMEDABAD

June 2017

ii

Investigations on Nonlinearity Effects in Communication

Systems and their Compensation Techniques

A Thesis submitted to Gujarat Technological University

For the Award of

Doctor of Philosophy

in

Electronics and Communication Engineering

By

Shatrughna Prasad Yadav

Enrollment No: 129990911010

Under the Supervision of


GUJARAT TECHNOLOGICAL UNIVERSITY

AHMEDABAD

June 2017

iii

© Shatrughna Prasad Yadav

iv

Declaration

I declare that the thesis entitled “Investigations on Nonlinearity Effects in

Communication Systems and their Compensation Techniques” submitted by me for the

degree of Doctor of Philosophy is the record of research work carried out by me during the

period from November 2012 to December 2016 under the supervision of Dr. Subhash

Chandra Bera, head Satcom & Navigation Systems Engineering Division, Space

Applications Centre, Indian Space Research Organization, Ahmedabad and this has

not formed the basis for the award of any degree, diploma, associateship, fellowship, titles

in this or any other University or other institution of higher learning.

I further declare that the material obtained from other sources has been duly acknowledged

in the thesis. I shall be solely responsible for any plagiarism or other irregularities if noticed

in the thesis.

Signature of Research Scholar Date: 03rd June, 2017

Name of Research Scholar: Shatrughna Prasad Yadav

v

Certificate

I certify that the work incorporated in the thesis “Investigations on Nonlinearity Effects in

Communication Systems and their Compensation Techniques” submitted by Shri

Shatrughna Prasad Yadav was carried out by the candidate under my guidance. To the

best of my knowledge: (i) the candidate has not submitted the same research work to any

other institution for any degree, diploma, Associateship, Fellowship or other similar titles,

(ii) the thesis submitted is a record of original research work done by Research Scholar

during the period of study under my supervision, and (iii) the thesis represents independent

research work on the part of the Research Scholar.

Signature of Supervisor Date: 03rd June, 2017

Name of Supervisor: Dr. Subhash Chandra Bera

Head Satcom & Navigation Systems Engineering Division,

Space Applications Centre, Indian Space Research Organization, Ahmedabad

Place: Ahmedabad

vi

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The viva-voce of the Ph.D. Thesis submitted by Shri Shatrughan Prasad Yadav,

(Enrollment No. 129990911010) entitled “Investigations on Nonlinearity Effects in

Communication Systems and their Compensation Techniques” was conducted on 03rd

June, 2017, at Gujarat Technological University.

(Please Tick any one of the following option)

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xi

Abstract

Nonlinearity effect is one of the most undesirable phenomena in the modern communication

systems which appear in the form of harmonic distortion, gain compression, intermodulation

distortion, phase distortion, adjacent channel interference, etc. Modern communication

systems use multicarrier orthogonal frequency division multiplexing (OFDM) which has

high data rate transmission capability in addition to robustness to channel impairments. One

of its major disadvantages is having high peak-to-average power ratio (PAPR). High PAPR

drives power amplifier into saturation region and causes it to operate in the nonlinear region.

In the present research work mathematical modeling and Matlab simulations have been

carried out on the transceiver of multicarrier OFDM communication systems. Its PAPR have

been calculated using QPSK and QAM baseband modulated signal with different number of

subcarriers. It has been observed that 4 QAM modulated signal has approximately 1.0 dB

higher PAPR than that of QPSK modulation format. Linearization of the class B solid state

power amplifier using feedback, feedforward, and predistortion techniques have been

investigated. Among power amplifier linearization techniques digital predistortion

outperforms when compared with other linearization techniques with 0 dBm reduction in

amplitude and 20 dB reduction in ACPR at 10 MHz of bandwidth. In order to reduce PAPR

of OFDM systems different PAPR reduction techniques such as clipping and filtering,

selective mapping method (SLM), partial transmit sequence (PTS) and single carrier

frequency division multiple access (SCFDMA) have been analyzed. There has been a

considerable reduction in PAPR of 12.2, 4.4, 4.3 and 1.9 dB with interleaved frequency

division multiple access (IFDMA), SLM, PTS and clipping and filtering techniques

respectively. It is to be emphasized that IFDMA gives the lowest PAPR of 0.4 dB obtained

so far in the literature at the cost of marginal implementation complexity. On the other hand

clipping and filtering method is one of the simplest PAPR reduction technique from an

implementation point of view but results in spectral regrowth and degradation in BER

performance. Selective mapping method has better performance than partial transmit

sequence at the cost of marginal computational complexity. The effect of raised cosine pulse

shaping filter has also been investigated in order to reduce the out-of-band signal energy of

SCFDMA systems. From the result obtained it has been observed that effect of pulse shaping

is more on IFDMA than that on localized frequency division multiple access (LFDMA)

technique.

xii

Acknowledgement

I take this opportunity to express a deep sense of gratitude to my honorable guide Dr.

Subhash Chandra Bera, Head, Satcom & Navigation Systems Engineering Division, Space

Applications Centre, Indian Space Research Organization, Ahmedabad, for his enthusiastic

and motivating attitude and kind as well as keen interest he invoked for the present study. I

would like to extend my sincere thanks to Dr. Shashi Bhushan Sharma, Vice President, Indus

University, Ahmedabad for extending his valuable guidance for this study and mentoring he

has provided to me during my present research in order to give right direction.

I am very much thankful and grateful to my doctoral progress committee members Dr.

Dhaval Pujara, Professor, EC department, Institute of Technology, Nirma University,

Ahmedabad and Dr. Sanjeev Gupta, Professor, Dhirubhai Ambani institute of information

and communication technology, Gandhinagar for mentoring me and providing me valuable

guidance as and when required.

My sincere & deepest gratitude stretches its way to the managing trustee, executive

president, registrar of Indus University, director and all staff members of Indus institute of

technology and engineering, Ahmedabad for providing me a conducive environment for the

research work.

I am thankful to the Vice-chancellor, Gujarat Technological University for providing me a

platform for my research work. Also, I am very much grateful to all staff members of GTU

for helping me as and when required with great enthusiasm. I would like to express my

sincerest appreciation to my father late Shri Hulash Prasad Yadav, mother Smt. Lalita Devi,

wife Manju Yadav, son Sudhanshu, Alok and daughter Seema for providing lots of moral

support without which it would have been impossible for me to complete this work.

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Table of Content

Chapter 1 Introduction ....................................................................................................... 1

1.1 Background ............................................................................................................. 1

1.2 Multicarrier OFDM Communication Systems ........................................................ 2

1.3 Power Amplifier Linearization Techniques ............................................................ 2

1.3.1 Feedback Technique ........................................................................................ 3

1.3.2 Feedforward Technique ................................................................................... 3

1.3.3 Predistortion Technique ................................................................................... 3

1.4 PAPR Reduction Techniques .................................................................................. 4

1.4.1 Clipping and Filtering ...................................................................................... 4

1.4.2 Selective Mapping Method .............................................................................. 5

1.4.3 Partial Transmit Sequence ............................................................................... 6

1.4.4 Single Carrier Frequency Division Multiple Access Technique ..................... 7

1.4.5 Comparative Performance of all the four PAPR Reduction Techniques ........ 8

1.4.6 Pulse Shaping Filter Technique ....................................................................... 9

1.5 Definition of the Problem ....................................................................................... 9

1.6 Objectives and Scope of the Study ......................................................................... 9

1.7 Motivation for the Present Work........................................................................... 10

1.8 Research Methodology used for the Research Work ............................................ 10

1.9 Achievements with Respect to Objectives ............................................................ 11

1.10 Organization of the Remainder of Thesis ............................................................. 12

Chapter 2 Literature Review ............................................................................................ 13

2.1 Introduction ........................................................................................................... 13

2.2 Multicarrier OFDM Communication Systems ...................................................... 13

2.3 Linearization of Power Amplifier ......................................................................... 14

2.4 PAPR Reduction Techniques ................................................................................ 17

2.4.1 Clipping and Filtering .................................................................................... 18

2.4.2 Selective Mapping Method ............................................................................ 20

2.4.3 Partial Transmit Sequence ............................................................................. 22

xiv

2.4.4 Single Carrier Frequency Division Multiple Access ..................................... 24

2.4.5 Pulse Shaping Filter Technique ..................................................................... 27

2.5 Research Gap ........................................................................................................ 30

2.6 Conclusion ............................................................................................................ 30

Chapter 3 Multicarrier OFDM Communication Systems and Linearization of Power

Amplifier ............................................................................................................................. 32

3.1 Introduction ........................................................................................................... 32

3.2 OFDM Transceiver Model .................................................................................... 32

3.2.1 OFDM Transmitter Simulation with Matlab ................................................. 37

3.2.2 OFDM Receiver Simulation with Matlab ...................................................... 40

3.3 Peak to Average Power Ratio of Multicarrier OFDM Signal ............................... 44

3.4 Linearization of Power Amplifier ......................................................................... 46

3.5 Power Amplifier Linearization Techniques .......................................................... 47

3.5.1 Feedback Technique ...................................................................................... 47

3.5.2 Feedforward Technique ................................................................................. 50

3.5.3 Digital Predistortion Technique ..................................................................... 55

3.5.4 Comparative Performance of Power Amplifier Linearization Techniques ... 61

3.6 Results and Discussion .......................................................................................... 61

Chapter 4 PAPR Reduction of Multicarrier OFDM Communication Systems........... 63

4.1 Introduction ........................................................................................................... 63

4.2 Clipping and Filtering Method .............................................................................. 64

4.2.1 PAPR of Clipped and Filtered Signal with Matlab ....................................... 65

4.2.2 Bit Error Rate Performance of Clipped and Filtered Signal with Matlab ..... 67

4.2.3 PAPR of Clipped and Filtered Signal with AWR Software .......................... 69

4.2.4 BER Performance of Clipped and Filtered Signal with AWR Software ........ 70

4.2.5 PAPR of Clipped and Filtered Signal with FPGA ......................................... 71

4.2.6 PAPR of Pre-Clipped and Post-Filtered Signal with FPGA .......................... 71

4.2.7 PAPR of Pre-Filtered and Post-Clipped Signal with FPGA .......................... 77

4.2.8 Comparative Value of PAPR of Clipped and Filtered Signal ....................... 79

4.3 Selective Mapping Method ................................................................................... 80

4.3.1 PAPR of Selective Mapping Method with Matlab Simulation...................... 81

4.3.2 PAPR of Selective Mapping Method with FPGA ......................................... 82

4.3.3 Comparative Value of PAPR of SLM with Different Techniques ................ 84

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4.4 Partial Transmit Sequence..................................................................................... 85

4.4.1 PAPR of Partial Transmit Sequence using Matlab ........................................ 88

4.4.2 Comparative Value of PAPR of Partial Transmit Sequence using Matlab ... 89

4.5 Single Carrier Frequency Division Multiple Access Technique........................... 89

4.5.1 SCFDMA Transceiver Systems ..................................................................... 89

4.5.2 PAPR of 4 QAM SCFDMA Signal ............................................................... 93

4.5.3 PAPR of 16 QAM SCFDMA Signal ............................................................. 94

4.5.4 PAPR of 64 QAM SCFDMA Signal ............................................................. 94

4.5.5 Comparative Value of PAPR for SCFDMA Signal....................................... 95

4.6 Comparative Performance of all PAPR Reduction Techniques ........................... 95

4.7 Pulse Shaping Filter Technique ............................................................................ 96

4.7.1 PAPR of SCFDMA Signal using Raised Cosine Pulse Shaping Filter ....... 100

4.7.2 Effect of Roll-off Factor on PAPR Performance ......................................... 102

4.8 Results and Discussion ........................................................................................ 103

Chapter 5 Conclusion ...................................................................................................... 105

5.1 Conclusion .......................................................................................................... 105

5.2 Scope of Future Work ......................................................................................... 108

References ......................................................................................................................... 109

List of Publications .......................................................................................................... 120

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List of Abbreviations

3GPP 3rd generation partnership project

ACPR Adjacent channel power ratio

ADC Analog-to-digital converter

ADSL Asymmetric digital subscriber lines

AM Amplitude modulation

BER Bit error rate

C&F Clipping and filtering

CCDF Complementary cumulative distribution function

CCI Co-channel interference

CDF Cumulative distribution function

CDMA Code division multiple access

CF Crest factor

CP Cyclic Prefix

CR Clipping ratio

DAB Digital audio broadcasting

DFDMA Distributed frequency division multiple accessing

DFT Discrete Fourier transform

DPD Digital predistortion

DSP Digital signal processing

DVB Digital video broadcasting

EI-PTS Estimator iterative PTS scheme

FDMA Frequency division multiple accessing

FFT Fast Fourier transform

FIR Finite impulse response

FPGA Field programmable gate array

HDSL High-bit-rate digital subscriber lines

HDTV High-definition television

ICI Intercarrier interference

IDFT Inverse discrete Fourier transform

IECNC Iteratively estimating and canceling the clipped noise

IFDMA Interleaved frequency division multiple accessing

xvii

IFFT Inverse fast Fourier transform

IMD Intermodulation distortions

IMTA International mobile telecommunications advanced

IPBO Input power back-off

ISI Intersymbol interference

LFDMA Localized frequency division multiple accessing

LTE Long term evolution

LTE-A Long term evolution advanced

MIMO Multiple inputs multiple outputs

MMSE Minimum mean square error

OFDM Orthogonal frequency division multiplexing

OFDMA Orthogonal frequency division multiple accessing

OICF Optimized iterative clipping and filtering

OPBO Output power back-off

PAM Pulse amplitude modulation

PAPR Peak to average power ratio

PM Phase modulation

PTS Partial transmit sequence

QAM Quadrature amplitude modulation

QPSK Quadrature phase shift keying

RC Raised cosine

RF Radio frequency

RMS Root mean square

SCFDMA Single carrier frequency division multiple access

SC-QOSFBC Single carrier quasi-orthogonal space-frequency block code

SC-SFBC Single carrier space-frequency block code

SINR Signal-to-interference-plus-noise ratio

SLM Selective mapping method

SPW Sub-block phase weighting

SSPA Solid state power amplifier

STBC Space-time block code

TI Tone injection

TR Tone reservation

xviii

TWTA Traveling wave tube amplifier

VDSL Very-high-speed digital subscriber line

WLAN Wireless local area network

xix

List of Symbols

Symbol Description

A Clipping Level

B Signal Bandwidth

G Overall Amplifier Gain

L Length of DFT/IDFT (FFT/IFFT)

M Number of Subblock

N Number of Subcarriers

Tg Cyclic Prefix (Guard) Duration

Ts Symbol Period

Tu Symbol Duration

V Number of Phase Factor

W Number of Weighting Factor

X Bandwidth Spreading factor

Δω Subcarrier Spacing

α Roll-off Factor

β Feedback Factor

δ(t) Impulse Function

Δα DPD Error Coefficient

σ RMS Value of OFDM Signal

hn(t) Impulse Response Function

ωc Carrier Frequency

dB Decibel

Pi ,sat Input Saturation Power

Po, sat Output Saturation Power

Pi Input Average Power

Po Output Average Power

xx

List of Figures

FIGURE 1.1 Subcarrier assignments to multiple users in SCFDMA .................................. 7

FIGURE 1.2 DFT spreading for IFDMA, DFDMA, and LFDMA ...................................... 8

FIGURE 3.1 Block diagram of OFDM transceiver ............................................................ 33

FIGURE 3.2 Subdivision of bandwidth in OFDM modulation .......................................... 33

FIGURE 3.3 OFDM subcarrier arrangement ..................................................................... 34

FIGURE 3.4 Addition of cyclic prefix ............................................................................... 35

FIGURE 3.5 OFDM signal generation at transmitter ......................................................... 38

FIGURE 3.6 Frequency response of signal ........................................................................ 38

FIGURE 3.7 Impulse response of the D/A reconstruction filter ........................................ 38

FIGURE 3.8 Frequency response of filter .......................................................................... 39

FIGURE 3.9 Frequency response of D/A reconstruction filter .......................................... 39

FIGURE 3.10 Time response of passband signal ............................................................... 40

FIGURE 3.11 Frequency response of passband signal....................................................... 40

FIGURE 3.12 Receiver model of OFDM systems ............................................................. 41

FIGURE 3.13 Frequency response of bandpass signal....................................................... 42

FIGURE 3.14 Frequency response of low pass filter ......................................................... 42

FIGURE 3.15 Frequency response of sampler ................................................................... 43

FIGURE 3.16 Scatterplot of 4 QAM signal constellation .................................................. 44

FIGURE 3.17 PAPR of the original OFDM system with QPSK modulation .................... 45

FIGURE 3.18 PAPR of the original OFDM system with 4 QAM modulation .................. 46

FIGURE 3.19 Block diagram of Cartesian loop feedback ................................................. 47

FIGURE 3.20 Simulation of feedback loop using AWR software ..................................... 48

FIGURE 3.21 Simulation result of feedback loop .............................................................. 49

FIGURE 3.22 Block diagram of feedforward loop ............................................................ 50

FIGURE 3.23 Simulation of feedforward loop using AWR software ................................ 52

FIGURE 3.24 Simulation result of feedforward loop......................................................... 53

FIGURE 3.25 Simulation result of error amplifier ............................................................. 54

FIGURE 3.26 Simulation result of AM to AM of the main amplifier ............................... 54

FIGURE 3.27 Simulation result of AM to AM of pre-amplifier ........................................ 55

FIGURE 3.28 Concept of predistortion……………………………………………………… 56

FIGURE 3.29 Block diagram of adaptive digital predistortion .......................................... 57

xxi

FIGURE 3.30 Simulation diagram of digital predistortion using AWR software.............. 58

FIGURE 3.31 Power amplifier AM to AM characteristics ................................................ 59

FIGURE 3.32 Power amplifier AM to PM characteristics ................................................. 60

FIGURE 3.33 Power amplifier power spectra using DPD ................................................. 60

FIGURE 4.1 Clipping and filtering with oversampling factor ........................................... 64

FIGURE 4.2 PAPR of clipped signals ................................................................................ 66

FIGURE 4.3 PAPR of clipped and filtered signal .............................................................. 66

FIGURE 4.4 BER Performance of unclipped signal .......................................................... 67

FIGURE 4.5 BER Performance of clipped signal .............................................................. 68

FIGURE 4.6 BER Performance with clipped and filtered signal ....................................... 68

FIGURE 4.7 Simulation diagram of PAPR reduction using AWR software ..................... 69

FIGURE 4.8 Simulation result of PAPR using AWR software ........................................ 70

FIGURE 4.9 Simulation diagram of BER using AWR software ...................................... 70

FIGURE 4.10 Simulation result of BER using AWR software ......................................... 71

FIGURE 4.11 Pre-clipping and post-filtering in time domain ........................................... 72

FIGURE 4.12 Block diagram of pre-clipping and post-filtering ........................................ 72

FIGURE 4.13 Block diagram of 4 QAM Mapper .............................................................. 73

FIGURE 4.14 Block diagram of IFFT ................................................................................ 73

FIGURE 4.15 Block diagram of clipper circuit .................................................................. 74

FIGURE 4.16 Block diagram of hardware cosimulator ..................................................... 74

FIGURE 4.17 Low pass filter response .............................................................................. 75

FIGURE 4.18 System generator for pre-clipping and post-filtering .................................. 75

FIGURE 4.19 Xilinx Spartan 3 Protoboard XC 3S 400 development board ..................... 76

FIGURE 4.20 Hardware cosimulation on Xilinx Spartan 3 Protoboard ............................ 76

FIGURE 4.21 PAPR value of pre-clipping and post-filtering with FPGA ........................ 77

FIGURE 4.22 Pre-filtering and post-clipping in time domain…………………………. 77

FIGURE 4.23 Block diagram of pre-filtering and post-clipping process ........................... 78

FIGURE 4.24 PAPR of pre-filtering and post-clipping with FPGA .................................. 78

FIGURE 4.25 Comparative value of PAPR with different methods .................................. 79

FIGURE 4.26 Block diagram of Selected Mapping Method.............................................. 80

FIGURE 4.27 PAPR of 4 QAM OFDM signal with SLM technique ................................ 81

FIGURE 4.28 System generator for PAPR reduction using SLM technique .................... 82

FIGURE 4.29 Hardware cosimulator block diagram ......................................................... 83

FIGURE 4.30 System generator of OFDM with SLM technique ...................................... 83

xxii

FIGURE 4.31 Comparative value of PAPR ....................................................................... 84

FIGURE 4.32 Block diagram of PTS for PAPR reduction ................................................ 85

FIGURE 4.33 Interleaved method ...................................................................................... 86

FIGURE 4.34 Adjacent method.......................................................................................... 87

FIGURE 4.35 Pseudo-random method ............................................................................... 87

FIGURE 4.36 PAPR reduction with PTS for 4 QAM signal ............................................. 88

FIGURE 4.37 Block diagram of SCFDMA system ........................................................... 90

FIGURE 4.38 Equivalence of OFDMA systems with SCFDMA ...................................... 90

FIGURE 4.39 Subcarrier assignments to multiple users .................................................... 91

FIGURE 4.40 PAPR of IFDMA, LFDMA, and OFDMA for 4 QAM .............................. 93

FIGURE 4.41 PAPR of IFDMA, LFDMA, and OFDMA for 16 QAM ............................ 94

FIGURE 4.42 PAPR of IFDMA, LFDMA, and OFDMA for 64 QAM ............................ 94

FIGURE 4.43 Comparative value of PAPR with different reduction techniques .............. 96

FIGURE 4.44 Response of rectangular and sinc shaped pulse shaping filter ................... 98

FIGURE 4.45 Raised cosine pulse shaping filter response in time domain ....................... 98

FIGURE 4.46 Raised cosine pulse shaping filter response in frequency domain .............. 99

FIGURE 4.47 Eye diagram with 0.5 roll-off factor ............................................................ 99

FIGURE 4.48 Eye diagram with 1.0 roll-off factor ......................................................... 100

FIGURE 4.49 Effect of pulse shaping filter for 4 QAM signal ........................................ 101

FIGURE 4.50 Effect of pulse shaping filter for 16 QAM signal ...................................... 101

FIGURE 4.51 Effect of pulse shaping filter for 64 QAM signal ...................................... 102

xxiii

List of Tables

TABLE 3.1 Numerical Values for the OFDM Simulation Parameters .............................. 37

TABLE 3.2 Simulation Parameter for Feedback Technique .............................................. 49

TABLE 3.3 Simulation Result of Feedback Technique ..................................................... 50

TABLE 3.4 Simulation Parameter for Feedforward Technique ......................................... 53

TABLE 3.5 Simulation Result of Feedforward Technique ................................................ 55

TABLE 3.6 Simulation Parameter for Digital Predistortion Technique ............................ 59

TABLE 3.7 Simulation Result of Digital Predistortion Technique .................................... 61

TABLE 3.8 Comparative Result of Power Amplifier Linearization Techniques ............... 61

TABLE 4.1 Comparative Value of PAPR of Clipped and Filtered Signal with Matlab .... 67

TABLE 4.2 PAPR of Selective Mapping Method with Matlab ......................................... 82

TABLE 4.3 Value of PAPR of SLM with Different Methods ........................................... 84

TABLE 4.4 PAPR Value with PTS Technique .................................................................. 89

TABLE 4.5 PAPR Value of SCFDMA Signal ................................................................... 95

TABLE 4.6 Parameters used for Simulation .................................................................... 100

TABLE 4.7 Effect of Roll-off Factor on PAPR Performance .......................................... 102

1

CHAPTER -1

Introduction

1.1 Background



distortion, phase distortion, adjacent channel interference, etc. Multicarrier orthogonal

frequency division multiplexing (OFDM) is mostly preferred for high data rate transmission

capability in modern communication systems [1]. It has several advantages associated with

it, such as tolerance to inter-symbol interference, good spectral efficiency, the best

performance of frequency selective fading in a multipath environment, robustness to channel

impairments etc. OFDM systems have many applications and are widely used in high-bit-

rate digital subscriber lines (HDSL), digital audio broadcasting (DAB), digital video

broadcasting (DVB) along with high-definition television (HDTV), terrestrial broadcasting,

wireless local area network (WLAN) standards in their physical layers, HiperLAN in

physical layer, IEEE 802.11a in its physical layer [2]. Third generation partnership project

(3GPP) for long term evolution (LTE) and LTE advanced (LTE-A) uses orthogonal

frequency division multiple accessing (OFDMA) for the downlink and SCFDMA technique

for the uplink transmission [3].

OFDM system has one of the major disadvantages of high peak to average power ratio

(PAPR) apart from being sensitive to timing and frequency synchronization errors. Due to

high PAPR, it causes power amplifiers to operate in the nonlinear region and the nonlinear

behavior of power amplifier causes inband signal distortions and out of band spectral growth

both of which are undesirable as it degrades the system performance. There are two important

challenges before the communication design engineer, first to design a highly linear power

amplifier with effective linearization technique and second to reduce the PAPR of

multicarrier OFDM communication system with highly efficient PAPR reduction techniques

[4].

Introduction

2

1.2 Multicarrier OFDM Communication Systems

Multicarrier OFDM communication systems promise to deliver high data rate apart from

being spectral efficient but suffer from high PAPR and cause power amplifiers to operate in

the nonlinear region. In order to compensate the effect of nonlinearity in multicarrier OFDM

communication systems multilevel approach have been investigated. Mathematical modeling

and Matlab simulations have been carried out on the transceiver of multicarrier OFDM

communication systems [5]. Its PAPR have been calculated using QPSK and 4 QAM

baseband modulated signal with different number of subcarriers. Linearization of the class B

solid state power amplifier using feedback, feedforward, and predistortion techniques have

been investigated. In order to reduce PAPR of OFDM system different reduction techniques

such as clipping and filtering, selective mapping method (SLM), partial transmit sequence

(PTS) and single carrier frequency division multiple access (SCFDMA) have been analyzed.

The effect of raised-cosine pulse shaping filter has also been investigated in order to reduce

the out-of-band signal energy of SCFDMA communication systems [6].

1.3 Power Amplifier Linearization Techniques

Linearization of the power amplifier has been implemented for improving linearity along with

efficiency. Nonlinearity of the power amplifiers can be improved by operating it in the power

back-off mode in which the input signals are attenuated. Either output power back-off

(OPBO) or input power back-off (IPBO) is used to specify the power amplifier operating

point. In order to quantify how much output power the amplifier generates compared with

the maximal available power, OPBO is used [7]. But this causes efficiency degradation and

increase in the size of the power amplifier and is unsuitable for practical applications. There

are three different linearization techniques, such as feedback, feedforward, and predistortion

which are used to improve the linearity of power amplifiers. Feedback technique is simple

to implement but results in lowest efficiency. Feedforward technique is used for wide

bandwidths applications in multicarrier systems where feedback technique is impractical.

This technique also costs more due to the use of couplers, delay lines, error power amplifier,

etc. The predistortion technique does not use these RF components and improves linearity

with higher efficiency [8]. All the above three mentioned techniques have been modeled and

simulated using visual system simulator of National Instrument’s AWR commercial

software at 2 GHz operating frequency.

Power Amplifier Linearization Techniques

3

1.3.1 Feedback Technique

It is the simplest technique from the implementation point of view but mostly suitable for

low-frequency operation and its performance degrades when operated at a higher frequency.

Different feedback linearization techniques are envelope feedback, polar loop feedback, and

Cartesian loop feedback in which a portion of the output signal from the amplifier is fed

back and subtracted from the input signal. Simulation has been performed at 2 GHz operating

frequency which has resulted in 5 dBm reductions in amplitude and 30 dB reductions in

adjacent channel power ratio (ACPR) with 10 MHz bandwidth.

1.3.2 Feedforward Technique

It is the oldest method of linearization which provides good linearization for wide bandwidth

applications. This is a stable technique because of the absence of feedback path and in this

nonlinear distortions are corrected at the output level whereas it was done at input level in

feedback technique. But it requires linear and power efficient power amplifier apart from

precise passive RF components such as a coupler, power divider, delay lines, etc. in order to

maintain accuracy from overloading, time, and temperature. Its efficiency is low due to

losses in the passive RF components. At 2 GHz of operating frequency performance of the

power amplifier using a feedforward loop with operating bandwidth of 1.2 GHz has resulted

in 20 dBm reductions in amplitude with 25 dB reductions in ACPR.

1.3.3 Predistortion Technique

In this technique, a nonlinear element is inserted before the RF power amplifier in such a

way that combined transfer characteristic of nonlinear element and power amplifier is linear.

The predistortion technique can be classified into analog predistortion and digital

predistortion. In analog predistortion, a compressive characteristic, created by the

nonlinearity in the lower path is subtracted from a linear characteristic to generate an

expansive characteristic. Whereas in the digital predistortion technique only the data

symbols are distorted using digital signal processing, not the transmit signal and pulse-

shaping is performed after the predistortion stage. In the present research work, adaptive

digital predistortion technique has been investigated using class B solid state power amplifier

with NI’s AWR software at 2 GHz operating frequency. In this technique, the reduction in

amplitude and ACPR is 0 dBm and 20 dB respectively with 3dB bandwidth of 10 MHz.

Introduction

4

DPD has lowest spectral regrowth with the highest gain compared to feedback and

feedforward correction techniques [9].

1.4 PAPR Reduction Techniques

The main aim of PAPR reduction technique is to reduce the fluctuations in the envelope of

the signal which are to be transmitted by the power amplifier. There are different PAPR

reduction techniques such as clipping technique, coding technique, probabilistic

(scrambling) technique, and SCFDMA or DFT-spread technique [10]. The easiest way to

reduce the PAPR is to clip the signal at the transmitter. But, this clipping of the signal distorts

the original signal and increases out-of-band radiation and the bit error rate. There are many

ways through which the PAPR can be reduced without creating distortion noise, and are

known as a distortionless technique [11]. Different types of clipping techniques are block-

scaling technique, clipping and filtering technique, peak windowing technique, peak

cancellation technique, Fourier projection technique, decision-aided reconstruction

technique and coding technique. In the coding technique, code words are selected in such a

way that reduces the PAPR. It does not cause distortion and does not create out-of-band

radiation, but suffers from bandwidth efficiency as the code rate is reduced. Different types

of coding techniques are Golay complementary sequence, Reed-Muller code, M-sequence,

and Hadamard code. In the probabilistic (scrambling) technique, input data block is

scrambled and one of them with the minimum PAPR is transmitted so that the probability of

incurring high PAPR is reduced. Its spectral efficiency decreases and the complexity

increases with increase in the number of subcarriers. The probabilistic (scrambling) method

includes selective mapping method (SLM), partial transmit sequence (PTS), tone reservation

(TR), tone injection (TI). SCFDMA is also known as DFT-spread technique and is a

modified form of orthogonal frequency division multiple accessing (OFDMA). In the

present work, we have investigated clipping and filtering, selective mapping method (SLM),

partial transmits sequence (PTS) and SCFDMA technique.

1.4.1 Clipping and Filtering

It is the simplest technique where PAPR can be reduced by clipping the amplitude of the

transmitted signal and passing it through a low-pass filter [12]. Low pass filter used after

clipping operation moderately enlarges the PAPR which can be further reduced by iterative

PAPR Reduction Techniques

5

clipping and filtering operation. PAPR also depends upon the clipping ratio (CR) which is

defined as the clipping level normalized by the RMS value σ of OFDM signal [13].

Clipping and Filtering with Matlab Simulation: Clipping and filtering method have

been used for QPSK and 4 QAM baseband OFDM signal. Mathematical modeling and

Matlab simulations have been carried out for 64, 128, 256, 512 and 1024 number of

subcarriers with 0.8, 1.0, 1.2, 1.4 and 1.6 clipping ratios. It has been observed that the PAPR

is low when either number of subcarriers are less or value of clipping ratio is low.

Clipping and Filtering with NI’S AWR Visual System Simulator Software simulation:

The clipping and filtering operation have also been simulated using student evaluation

license of National Instrument’s AWR visual system simulator commercial software. The

observed PAPR at CCDF of 10−5 are 4.2 dB and 10.6 dB for only clipped signal and

clipped and filtered signal with 0.8 clipping ratio.

FPGA Implementation of Clipping and Filtering Technique: Clipping and filtering

technique has been implemented on FPGA and tested on hardware cosimulator using Xilinx

Spartan 3 Protoboard XC 3S 400 development board. The values of PAPR for pre- clipping

and post filtering with FPGA implementation of 4 QAM baseband OFDM signal with 1024

number of subcarriers are 10.9, 11.2, 11.5, 11.8 and 12.1 dB for clipping ratio of 0.8, 1.0,

1.2, 1.4 and 1.6 respectively.

Comparative Values of PAPR with Clipping and Filtering: The PAPR obtained through

simulation with Matlab, NI’s AWR software and FPGA implementations have been

compared. The observed value of PAPR with FPGA implementation of pre-filtering and

post-clipping with 0.8 clipping ratio is 2.2 dB. Whereas PAPR values obtained in the case

of the pre-clipping and post-filtering method with 0.8 clipping ratio are 10.6, 10.7 and 10.9

dB with NI’s AWR software, Matlab and FPGA implementations respectively. Although

pre-filtering and post-clipping gives lowest PAPR but is not used practically because of the

high value of bit error rate (BER).

1.4.2 Selective Mapping Method

SLM is one of the most important methods for reducing PAPR of OFDM signals. It is simple

in implementation, has an absence of distortions in the transmitted signal, and results in a

significant reduction in PAPR [14]. In the SLM method, the original data block is converted

Introduction

6

into several independent signals. Different phase rotations are applied to parallel baseband

modulated signals [15].

Matlab Simulation of SLM Technique: Mathematical modeling and Matlab simulation

have been carried out to obtain the PAPR of 4 QAM OFDM signal with phase vectors, V =

16, 8, 4, 2 and 1 for 64, 128, 256, 512 and 1024 number of subcarriers. It has been observed

that PAPR is low when the number of phase vector is high (V= 16) and increases with either

increase in the number of subcarriers or reduction in the number of phase rotations.

FPGA Implementation of SLM Technique: Complete system design has been

implemented on FPGA and tested on hardware co-simulation using Xilinx Spartan 3

Protoboard XC 3S 400 development board with a different number of subcarriers. The phase

sequence which gives minimum PAPR has been selected for transmission.

Comparative Values of PAPR with SLM: The PAPR of the FPGA implementation for the

case of 4 QAM OFDM signal has been compared with the value obtained with Matlab

simulation. For the case of 1024 number of subcarriers the PAPR with FPGA

implementation is 9.8 dB which is 2.8 dB less from the original OFDM signal obtained

without applying SLM technique but 0.9 dB higher than the Matlab simulated value.

1.4.3 Partial Transmit Sequence

PTS technique, partitions an input data block of N symbols into M disjoint Subblock of equal

size that is consecutively located. In PTS technique scrambling is applied to each subblock,

whereas in the SLM technique scrambling is applied to all subcarriers [16]. Each partitioned

subblock is multiplied by a corresponding complex phase factor bn = ejbn where, n =1, 2,

…N and its IFFT is taken and phase vector is chosen such that the PAPR can be minimized.

Selection of the phase factors {bm}N−1N is limited to a set of elements to reduce the search

complexity [17]. The mathematical modeling and Matlab simulations using the pseudo-

random method of block partitioning has been carried out. 4 QAM OFDM signal

constellation has been taken into consideration with 8000 blocks with 64, 128, 256, 512 and

1024 number of subcarriers and has been observed that the PAPR is low when the number

of sub-blocks is large.


7

1.4.4 Single Carrier Frequency Division Multiple Access Technique

The single carrier frequency division multiple access (SCFDMA) is also known as discrete

Fourier transform (DFT) spread technique has been recommended by third generation

partnership project (3GPP) to be used for long-term evolution (LTE) and LTE advanced

(LTE-A). It uses orthogonal frequency division multiple access (OFDMA) for downlink

and SCFDMA for the uplink transmission [18]. SCFDMA has many advantages over

OFDMA system as it has low BER, high throughput, high spectral efficiency and the lowest

PAPR. Because of the lowest PAPR, its power requirement is considerably low and is

suitable for mobile applications [19]. In SCFDMA system all symbols are present in all

subcarriers hence it allows frequency selectivity of the channel. It has one of the major

disadvantages of noise enhancement because of the fact that when DFT despreading is done

at the receiver noise is spread over the entire subcarriers. Its transmitter consists of a serial

to parallel converter, DFT spreading, IDFT despreading, parallel to serial converter, the

addition of a cyclic prefix, digital to analog converter and RF modulation for converting

baseband signal into passband signal before transmitting it through the channel. In case the

size of DFT is same as that of IDFT, the OFDMA system becomes equivalent to the single

carrier frequency division multiple access (FDMA) systems because the DFT and IDFT

operations virtually cancel each other. Then the transmit signal will have the same PAPR as

in a single-carrier system.

1 1 12 2 23 3 3

FrequencyDistributed Mode

1 1 12 2 23 3 3

FrequencyLocalized Mode

FIGURE 1.1 Subcarrier assignments to multiple users in SCFDMA

Fig. 1.1 illustrates the subcarrier allocation in the DFDMA and LFDMA with a number of

terminals (users), Y =3, the number of available channels over the entire bandwidth, Z = 9,

and bandwidth spreading factor, X = 3, where bandwidth spreading factor, X = Z/Y.

Introduction

8

s[0] s[1] s[2]

S[0] S[1] S[2]

S[0] 0 0 S[1] 0 0 S[2] 0 0

S[0] 0 S[1] 0 S[2] 0 0 0 0

s[0] s[1] s[2] 0 0 0 0 0 0

s(n)

S(i)

S’(K)

IFDMA

S’(K)

DFDMA

S’(K)

LFDMA

Frequency

N = X . M

N > X . M

N = X . M

FIGURE 1.2 DFT spreading for IFDMA, DFDMA, and LFDMA

Fig. 1.2 shows the examples of DFT spreading in DFDMA, LFDMA, and IFDMA with Z =

9, Y = 3, and X = 3. It illustrates a subcarrier mapping relationship between 3-point DFT

and 9-point IDFT for three different types of DFT spreading techniques. Among the different

subcarrier allocation methods, IFDMA results with the lowest PAPR than other techniques.

The comparative values of PAPR for SCFDMA signals for 4 QAM, 16 QAM and 64 QAM

modulation format with the number of subcarriers, N=64, 128, 256, 512 and 1024 at 10−2

of CCDF value have been obtained. It has been observed that PAPR is lowest for IFDMA

and highest for OFDMA. Its value increases with either increase in the number of subcarriers

or in the modulation format from 4 QAM, 16 QAM and 64 QAM baseband signal with

different number of subcarriers.

1.4.5 Comparative Performance of all the four PAPR Reduction Techniques

Comparative performance of all the PAPR reduction techniques discussed above has been

analyzed for 4 QAM modulation format with 1024 number of subcarriers. The observed

PAPR values at 10−2 of CCDF with IFDMA technique is 0.4 dB, clipped only at CR = 0.8

has 4.6 dB, LFDMA has 6.9 dB, SLM with number of phase vector, V = 16 has 8.2 dB, PTS

with No. of sub-blocks, M = 16 has 8.3 dB, OFDMA has 10.5 dB, clipped and filtered with

0.8 clipping ratio has 10.7 dB and unclipped signal has PAPR value of 12.6 dB. Reduction

in PAPR value of 12.2, 4.4, 4.3 and 1.9 dB have been obtained with SCFDMA, SLM, PTS

and CF techniques respectively. It has been observed that IFDMA gives the lowest PAPR of

0.4 dB obtained so far in the literature at the cost of a marginal increase in implementation

complexity.

Definition of the Problem

9

1.4.6 Pulse Shaping Filter Technique

A linear filtering operation known as pulse shaping, which is used to reduce the out-of-band

signal energy, has been performed in the transmitter through convolution between the

modulated subcarriers and the filter's impulse response [20, 21]. Mathematical modeling and

Matlab simulations of the SCFDMA signal have been carried out for 4 QAM, baseband

modulation format with 1024 number of subcarriers and 2048 FFT size. 5000 number of

blocks have been taken for iteration with an oversampling factor of 8 and 0.0, 0.3, 0.6 and

0.9 roll-off factors of the RC filter [22]. The Matlab simulated result on the effect of raised

cosine pulse shaping filter on 4 QAM, 16 QAM, and 64 QAM baseband modulated IFDMA

and LFDMA signal with 0.0, 0.3, 0.6 and 0.9 roll- off factor have been obtained. The

observed PAPR with 4 QAM baseband signal is 2.4 dB for IFDMA and 7.7 dB for LFDMA

with roll- off factor 0.9. It increases to 7.2 and 8.7 dB when the roll- off factor is reduced to

0.0 for the case of IFDMA and LFDMA respectively.

1.5 Definition of the Problem

Mathematical modeling and simulation of the transceiver of multicarrier OFDM

systems.

Calculate its PAPR with QAM baseband signal with different number of subcarriers.

Perform linearization of the class B solid state power amplifier using feedback,

feedforward, and predistortion techniques.

Perform PAPR reduction using clipping and filtering, SLM, PTS and SCFDMA

techniques.

Investigate effect of raised cosine pulse shaping filter on SCFDMA signal.

1.6 Objectives and Scope of the Study

Following are the main objectives of the present research work:

To apply multilevel approach at the transmitter and receiver simultaneously by

mathematical modeling and analyzing the transceiver of multicarrier OFDM

systems.

To calculate its PAPR with different number of subcarriers.

To perform linearization of the class B solid state power amplifier using feedback,

feedforward and predistortion techniques.

Introduction

10

To perform PAPR reduction using clipping and filtering, SLM, PTS and SCFDMA

techniques.

To investigate the effect of raised cosine pulse shaping filter on SCFDMA signal.

1.7 Motivation for the Present Work

Modern communication systems use multicarrier OFDM for high data rate transmission

capability. OFDM is desirable because of several advantages associated with it, such as

tolerance to inter-symbol interference, good spectral efficiency, the best performance of

frequency selective fading in a multipath environment, robustness to channel impairments

etc. OFDM systems have many applications and are widely used in high-bit-rate digital

subscriber lines (HDSL), digital audio broadcasting (DAB), digital video broadcasting

(DVB) along with high-definition television (HDTV), terrestrial broadcasting. Third

generation partnership project (3GPP) for long term evolution (LTE) and LTE advanced

(LTE-A) uses orthogonal frequency division multiple accessing (OFDMA) for the downlink

and SCFDMA technique for the uplink transmission.

Powerful techniques have been developed to mitigate the harmful effects of nonlinearity, but

are not effective when applied alone. There is a need to address this issue at the transmitter

and receiver simultaneously. At the transmitter, there is a need to use the efficient

modulation technique such as multicarrier OFDM system with effective PAPR reduction

techniques and utilization of effective power amplifier linearization techniques. Similarly,

effective pulse shaping filter and demodulation technique are required to be used at the

receiver.

1.8 Research Methodology used for the Research Work

Following research methodology has been adopted for investigation on the nonlinearity

effects in multicarrier OFDM communication systems and their compensation techniques:

Mathematical modeling and Matlab simulation of the transceiver of multicarrier

OFDM communication systems and evaluation of its PAPR.

Linearization of class B solid state power amplifiers using feedback, feedforward and

digital predistortion technique using student evaluation copy of visual system

simulator of National Instrument’s AWR version 12.0 commercial software.

Clipping and filtering technique for PAPR reduction with (a) Matlab software

simulation (b) National Instrument’s AWR software (c) FPGA implementation using

Achievements with Respect to Objectives

11

Xilinx Spartan 3 Protoboard XC 3S 400 board and (d) performance comparison with

the above three mentioned techniques.

Selective mapping method of PAPR reduction using (a) Matlab software simulation

(b) FPGA implementation using Xilinx Spartan 3 Protoboard XC 3S 400 board and

(c) Performance comparison with Matlab and FPGA implementation.

Mathematical modeling and Matlab simulation of partial transmit sequence (PTS)

technique.

PAPR reduction with SCFDMA or DFT-spread techniques for IFDMA, DFDMA,

and LFDMA subcarrier mapping.

Reduction of PAPR and spectral growth on SCFDMA signal using raised-cosine

pulse shaping filter.

1.9 Achievements with Respect to Objectives

In the present research work, emphasis has been given to optimize the performance of the

proposed techniques with a reduction in computational complexity and hardware utilization.

In the case of linearization of power amplifiers with digital predistortion technique, 20 dB

reduction in adjacent channel power ratio (ACPR) has been achieved without (0 dBm)

reduction in amplitude while ensuring the best AM to AM and AM to PM characteristics.

The result obtained with this technique has not increased computational complexity and

hardware resources because of the exploitations of digital signal processing power. For the

case of PAPR reduction with clipping and filtering technique, while maintaining better bit

error rate (BER) performance, a significant reduction in PAPR has been achieved with

minimum hardware and computational complexity. Further, the result obtained with

mathematical modeling and Matlab simulations have been further verified with National

Instrument’s AWR commercial software and through FPGA implementation using Xilinx

Spartan 3 Protoboard XC 3S 400 board. When compared with original OFDM signal PAPR

with FPGA implementation of pre-filtering and post-clipping reduces by 10.4 dB, whereas

the reduction is 1.7 dB with FPGA implementation of pre-clipping and post-filtering. On the

other hand, these reductions are 2.0 and 1.9 dB with AWR and Matlab software simulations.

The result obtained with the proposed SLM technique with mathematical modeling and

Matlab simulations have been further verified with FPGA implementation and tested on

hardware co-simulation using Xilinx Spartan 3 Protoboard XC 3S 400 development board.

The PAPR of the SLM technique with Matlab simulation is 8.9 dB and it is 9.8 dB with FPGA

Introduction

12

implementation for the case of 4 QAM OFDM signal with 1024 number of subcarriers and

number of phase vector, V=4. The investigations in PTS technique have resulted with the

PAPR of 9.1dB for 4 number of sub-blocks with 1024 number of subcarriers. The PAPR

obtained is lowest with very low computational complexity as the number of IFFT operations

has been reduced. When the performance of the SCFDMA techniques are considered,

IFDMA gives the lowest PAPR of 0.4 dB at 10−2 of CCDF with 4 QAM baseband

modulation and 1024 number of subcarriers. The observed value is lowest as compared to

other PAPR reduction techniques available in the literature. Among many Nyquist pulses

used for the distortionless transmission without the presence of intersymbol interference,

raised cosine (RC) pulse is the most popular Nyquist pulse. From the result obtained it can

be observed that effect of pulse shaping is more on IFDMA than that of LFDMA. Further,

the PAPR value decreases with increase in the roll - off factor. For IFDMA system the PAPR

at 10−2 of CCDF with 1024 number of subcarriers with a change in the roll- off factor from

0.0 to 0.9, the reductions in PAPR value obtained is 4.8 dB for 4 QAM modulation format.

But it is only 1.0 dB for the case of LFDMA system.

1.10 Organization of the Remainder of Thesis

Chapter 2 deals with the literature review on effects of nonlinearity and their compensation

techniques in the multicarrier communication systems. It emphasizes on the research gap

available in the literature and finally concludes with the motivation behind the present

research work. Multicarrier OFDM communication systems and linearization of power

amplifier have been presented in chapter 3. In this chapter transceiver of OFDM

communication systems have been mathematically modeled and simulated with Matlab

software. Different power amplifier linearization techniques have been discussed and the

result obtained with National instrument’s AWR software have been presented. Chapter 4

presents PAPR reduction of multicarrier OFDM communication systems with four different

techniques, clipping and filtering, SLM, PTS, and SCFDMA. It discusses the effect of raised

cosine pulse shaping filter on SCFDMA signal. Chapter 5 gives the onclusion of the thesis.

13

CHAPTER -2

Literature Review

2.1 Introduction

Multicarrier OFDM communication systems possess high data rate transmission capability

but owing to its high PAPR causes power amplifiers to operate in the nonlinear region.

Nonlinear behavior of power amplifier causes inband signal distortions and out of band

spectral regrowth both of which are undesirable as it degrades the system performance.

There are two important challenges before the communication design engineer, first to

design a highly linear power amplifier with effective linearization technique and second to

reduce the PAPR of multicarrier OFDM communication systems with highly efficient PAPR

reduction techniques. Investigations on the nonlinearity effect in multicarrier OFDM

communication systems and their compensation techniques have been carried out by many

researchers in the past and important among them are discussed below.

2.2 Multicarrier OFDM Communication Systems

Investigation on nonlinear compensation techniques has been done by Ralph Hall [23]. The

intermodulation noise in a frequency-division multiplex system arises because of third-order

nonlinearity in the repeater amplifiers. He has observed that in order to reduce the effect of

nonlinearity a biased semiconductor diode can be used in the emitter feedback impedance at

the output stage of each repeater. It is stressed that although it is not possible to adjust the

bias of each diode for highest compensation, but a suitable standard bias can be chosen which

will give the required result because of the statistical distribution in the phase of third-order

intermodulation vectors of each repeater. In a practical 60-MHz system for the case of the

worst channel, he has obtained 6 dB reduction in third-order intermodulation noise. Pedro

and Carbalho [24] have reviewed major techniques for evaluating nonlinear distortion in

communication systems and discussed their major limitations. They have shown that the

theoretical value obtained with a third order nonlinear system, the multitone test

characteristics is directly related to two-tone test figures and noise power ratio gives an

optimistic measure of co-channel interference. They have proposed a new co-channel

Literature Review

14

standard characterization with a C-band amplifier circuit to overcome the disadvantages of

noise power ratio test and illustrated the usefulness of their suggested approach. Sevic, Steer,

and Pavio [25] have done a rigorous examination of the basic nonlinear analysis methods

for digital wireless communication systems. It has been pointed out that digitally modulated

system shows significant performance improvement over systems based on analog

modulation. At the same time, there is a change in the methods of characterization and

simulating system performance for the case of amplifier linearity. As the analog modulated

signals are represented as discrete spectra but the digitally modulated signals should be

represented as a power spectral density. But most of these discrete spectra nonlinear analysis

techniques are not suitable for simulating systems characterized by signals with power

spectral density representations for the case of digitally modulated signals. They have

examined common signals used in digital wireless communication systems, and their

representation and characterization methods. Various nonlinear analysis methods have been

explored and have described an alternative characterization method for the case of

microwave power amplifier simulation with the digitally modulated signal.

2.3 Linearization of Power Amplifier

Roblin et al [26] have presented a review on modeling and linearization of multiband power

amplifiers used for the amplification of signals with noncontiguous spectra. They have

presented supportive theories, simulation, and experimental results to demonstrate the

concept and practical implementation of multiband digital predistortion (DPD) systems.

With the increase in the number of noncontiguous bands, the algorithm complexity also

increases. Peak and average power envelopes should then prove useful for maintaining the

same order of complexity for multiband DPD systems. He has optimized the PAPR reduction

techniques for multiband applications which were used for composite multiband signals.

They have also explored power-added efficiency techniques such as envelope tracking.

Many of the techniques that have been developed for multiband DPD can also be used in the

single-band DPD systems of wide bandwidth applications. It is well known that the

bandwidth efficiency and power efficiency are the conflicting criteria for communication

systems and as per the system requirements, there has to be a trade-off between them.

Bandwidth efficiency is a major concern for the commercial products, as it tries to

accommodate as many users in the given system as possible. For a bandwidth-efficient

system, variable envelope signal with pulse-shaping filter is preferred over a constant

envelope signal. But, for mobile application the operating time of the system and in turn the

Linearization of Power Amplifier

15

battery life is also equally important. In order to have longer battery life constant envelope

signals with higher amplifier efficiency which reduce the overall processing power is often

a better choice. Liang et al [27], in their paper, have introduced a figure-of-merit to

investigate tradeoffs between amplifiers and modulation waveforms for the case of digital

communications systems. A variety of modulation schemes were investigated for the case

of class-AB power amplifiers in order to understand the relations between amplifier

efficiency, amplifier distortion, signal in-band and adjacent channel interference, and power

consumption to design low-energy communications systems. They have introduced a new

performance measure for optimizing communication systems power consumption and

developed a simulation tool that evaluates the performance of the nonlinear amplifier

interacting with modulated waveforms. Before including other parts of an overall system,

evaluation of the effect of nonlinearities on the modulation has been simulated and

optimized.

For the characterization of spectral regrowth at the output of a nonlinear amplifier, a

statistical technique for a digitally modulated signal in a digital communication system has

been investigated by Gard, Gutierrez, and Steer [28]. As a function of the statistics of the

quadrature input signal transformed into a behavioral model of the amplifier, this technique

gives an analytical expression for the autocorrelation function of the output signal. They

have used the amplifier model which is a baseband equivalent representation and derived

from a complex radio-frequency envelope model. The model has been developed from

measured or simulated amplitude modulation–amplitude modulation (AM/AM) and

amplitude modulation–phase modulation (AM/PM) available data. They have used this

technique to evaluate the spectral regrowth for a code division multiple access (CDMA)

signals. Frederick Raab et al, [29] in their classic paper have investigated power amplifiers

and transmitters for RF and microwave. They observed that RF and microwave generation

is not only required in wireless communications but in many other applications such as RF

heating, imaging, dc/dc converters and jamming, etc. But the requirement for bandwidth,

frequency, load, power, linearity, efficiency and cost differs from one application to another.

There are variety of techniques, implementations and active devices used to generate RF

power. Similarly, incorporation of power amplifiers in transmitters are done in a wide

variety of architectures such as linear, Kahn, envelope tracking, out phasing and Doherty.

They have also investigated and suggested different power amplifier linearization techniques

which include feedback, feedforward, and predistortion.

Literature Review

16

Allen Katz [30] in his classical paper concluded that for multicarrier application, in order to

increase power amplifier’s efficiency and power capacity, its linearization is essential. The

new linearizer design improves performance and bandwidths, alignment becomes simple

and also improves stability and linearity. In the case of traveling wave tube amplifiers

(TWTA), the linearizers are able to deliver four-fold additional power capacity and more

than double efficiency. It also increases power capacity and efficiency with improved

linearity for solid-state power amplifiers (SSPA). He has observed that for high linearity

requirement class AB and B amplifiers are more suitable which can deliver more than 3 dB

power capacity and double efficiency enhancement when used with SSPA. For the

applications which require high linearity, feedforward, and adaptive linearization is more

effective. On the other hand, indirect feedback method performance is good for limited

bandwidth. Predistortion is relatively simple, has the wider working bandwidth and suitable

for applications from the lowest to the highest linearity requirement. Pedro Safier, et al, [31]

have presented a methodology for using the results of physics-based frequency-domain

codes in a time-domain block model. Their approach allows them to directly relate the digital

performance of the device to its physical parameters. The result was validated by comparing

the block model design with 1-D/3-D multi-frequency parametric large-signal TWT code

CHRISTINE and their result is valid at a frequency higher than 5 GHz which is normally

used for high data-rate communication systems. But their code CHRISTINE is not suitable

for modeling multi-frequency signals in the presence of reflections, they have used single

tones to show that their approach to the modeling of internal reflections using a feedback

loop gives an accurate result. They have also simulated realistic modulated digital signals

without reflections and observed that their approach is robust, accurate and fast.

Christian Musolff, et al [32] in their paper titled linear and efficient Doherty power amplifier

revisited, have emphasized on the theoretical backgrounds behind the highly linear Doherty

PA design. They have shown a basic derivation of IMD products for reduced conduction

angle mode power amplifiers and IMD in Doherty power amplifiers. Their design strategy

does not improve the efficiency of an ideal Doherty power amplifier but offers a significant

improvement in average efficiency in comparison to a single-track class AB amplifier

because their design objective is focused on a sharp load modulation characteristic. They

have also observed that at comparatively low efficiency, a Doherty power amplifier which

is designed for high linearity can be made more linear compared to a single track design. It

was also emphasized that in the case of average efficiency, the two-tone signal is more


17

accurate than real-world communication signals. They have further reiterated that active load

modulation has a lot more to offer than the classical Doherty power amplifier.

Fehri and Boumaiza [33] have investigated a novel dual-band, dual-input dual-output

baseband equivalent Volterra series based behavioral model to linearize the dynamic

nonlinear behavior of a concurrently driven dual-band power amplifier. They have started

with a real-valued continuous-time passband Volterra series using some signal and system

transformations and derived a low-complexity, complex-valued, and discrete baseband

equivalent Volterra formulation. Their formulation included all possible distortion terms, it

used fewer kernels than the 2-D digital predistortion. Their model was applied to digitally

predistort and linearize a dual-band 45 W class AB GaN power amplifier which was driven

by different dual-band dual-standard test signals to reduce the adjacent channel leakage ratio

by up to 25 dB and requiring less than 25 coefficients. Aschbacher [34], in his thesis,

addressed digital predistortion for linearization of nonlinear and dynamic microwave power

amplifiers. His aim was for the development of a linearization algorithm which is capable of

linearizing a variety of power amplifiers. He has implemented the algorithm in a prototype

system in order to prove its practical value.

2.4 PAPR Reduction Techniques

Peak to average power ratio is a major limiting factor and needs to be addressed while

developing multicarrier OFDM transmission systems. Han and Lee [35], have described

some important PAPR reduction techniques for multicarrier OFDM transmission. Although

there are many techniques to reduce PAPR which have the potential to provide a substantial

reduction in PAPR at the cost of loss in data rate, increased transmitted signal power, BER,

computational complexity, etc. But, there is no specific PAPR reduction technique which

gives the best solution for all multicarrier OFDM transmission systems. They have

emphasized that the PAPR reduction technique should be carefully selected as per the system

requirement. Multiple factors such as the effect of the transmit filter, digital to analog

converter, transmit power amplifier, etc. must be taken into consideration while choosing an

appropriate PAPR reduction technique. Jiang and Wu [36] have observed that although

OFDM is an attractive technique owing to its spectrum efficiency and channel robustness

for wireless communications. It has one of the serious drawbacks of high PAPR when the

input sequences are highly correlated. They have described many aspects and have provided

a mathematical analysis, which included the distribution of the PAPR, in the multicarrier

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18

OFDM systems. They have elaborated and analyzed five important techniques in order to

reduce PAPR which have the potential to provide a reduction in PAPR but once again at the

cost of loss in data rate, an increase in transmit signal power, degradation in BER

performance, an increase in computational complexity, etc.

Ai Bo, et al [37] have observed that PAPR reduction may improve the high power amplifier

(HPA) efficiency, but very few have attempted to analyze the relation between PAPR

reduction and HPA linearization. In their paper, based on Saleh’s TWTA model, found that

all those data with amplitudes larger than Asat/2 can not be compensated for with a

predistorter. They have further concluded that when the HPA is working in such a linear

region as Asat ≥ 2Amax , for the case of HPA predistortion PAPR reduction process is not at

all necessary. But in order to improve HPA power efficiency, the PAPR reduction is

indispensable in the case of HPA working near or in the saturation. The methods discussed

can also be utilized to improve the adjacent channel interference and the BER performances

degradation caused by the PAPR reduction process.

2.4.1 Clipping and Filtering

Among the various PAPR reduction techniques proposed, clipping and filtering is the

simplest method for PAPR reduction. When compared to in-band distortion, out-of-band

radiation is more critical because it severely affects the communication in adjacent frequency

bands. By clipping the time-domain signal to a predefined level and subsequently filtering

eliminate the out-of-band radiation. Armstrong [38] in his letter emphasized that the

reduction of PAPR for an OFDM signal can be achieved without increasing the out-of-band

power first by clipping the oversampled time domain signal and then followed by filtering

the clipped signal using an FFT-based, frequency domain filter which is designed to reject

the out-of-band discrete frequency components. But filtering has an adverse effect of

regrowth of peak. But this regrowth can be further reduced by repeated clipping and filtering

operations. On the other hand, the distortions produced in-band signal results in an added

noise-like effect and shrinking of the signal constellation. Wang and Tellambura [39] have

proposed a new clipping and filtering technique with reduced computational complexity that,

in one iteration, obtains the same PAPR reduction as that of the iterative clipping and

filtering (CF) technique with several iterations. The computational complexity is, therefore,

significantly reduced. They have shown through the simulations that their proposed

technique has better PAPR reduction and out-of-band radiation and very close BER


19

performance to iterative clipping and filtering technique. They have further reiterated that

in deep clipping cases also their proposed technique performs similarly to iterative clipping

and filtering technique.

Li and Cimini [40] in their letter have investigated the effects of clipping and filtering on the

performance of OFDM. In order to better characterize the peakiness of an OFDM signal,

they have used the CF’s at various percentiles of the cumulative distribution function (CDF)

instead of using an absolute CF. They have observed that with a clipping ratio of 1.4 and

filtering, clipping and filtering of a bandpass OFDM signal with 128 tonnes at the 99.99%

point has been reduced to 9 dB from its initial value of 13 dB. The result obtained is almost

comparable to the absolute clipping and filtering of a raised cosine pulse-shaped bandpass

QPSK signal. But this reduction in PAPR has been obtained at the cost of only a 1-dB

degradation in the received signal to noise ratio. Further, they concluded that clipping and

filtering is an important technique to reduce the clipping and filtering of OFDM signals using

realistic linear amplifiers. Zhu, Pan, Li, and Tang [41] have investigated the clipped signal

and proposed a modified algorithm called optimized iterative clipping and filtering (OICF).

They could achieve required PAPR reduction with minimum in-band distortion and with

fewer iterations. They have changed the optimization problem equivalent to a problem with

the PAPR reduction vector as the optimization parameter, which has been solved by using

simple operations. They observed that the original and simplified algorithms have

comparable performance in terms of out-of-band radiation, BER, and PAPR reduction.

Further, they emphasized that their result performed with oversampling factor L = 4, is valid

for other value of oversampling factor also.

Based on the difference between cubic metric and PAPR, Zhu, Hu, and Tang [42] have

modified the conventional iterative clipping and filtering method and proposed a new

clipping and filtering method called descendent clipping and filtering for cubic metric

reduction. They verified through simulation results that the new proposed method has far

less computational complexity due to a reduction in iteration numbers and at the same time

demonstrates superiority when compared to iterative clipping and filtering method. In order

to reduce the PAPR of OFDM signals, Wang and Luo [43] have proposed a convex

optimization technique which has dynamically modified the filter response in an iterative

clipping and filtering method. Through simulation, they have demonstrated that their new

proposed technique possesses many advantages over the classic iterative clipping and

filtering method such as less out-of-band radiation, fewer in-band distortions and less

Literature Review

20

number of iterations required to obtain a given PAPR level. In order to simultaneously

reduce the PAPR and error rate of OFDM signal Deng and Lin [44] have proposed a

modified repeated clipping and filtering method by bounding the distortion after each

recursion of clipping and filtering. They have also proposed a smart gradient projection

algorithm to reduce the number of recursions with bounded distortion. They have compared

their results obtained with the proposed method than that of repeated clipping and filtering

using iteratively estimating and canceling the clipped noise (IECNC) and have concluded

that IECNC method does not promise that the resulting distortion would be bounded.

Effect of the clipping and adaptive symbol selection under the strictly band-limited condition

have been investigated by Ochiai and Imai [45] for PAPR reduction and the BER

performance degradation capability. They have observed that with a slight increase in

complexity, the significant PAPR reduction could be obtained with the combination of the

deliberate clipping and adaptive symbol selection. It has been pointed out that without any

compensation technique the deliberate clipping and erroneous symbol selection greatly

affects the BER performance and if powerful forward error correction codes such as turbo

codes are used, the performance degradation becomes less significant. They concluded that

in the case of a powerful forward error correction code, the deliberate clipping in

combination with the adaptive symbol selection can be used for the reduction of PAPR of

OFDM signals with a large number of subcarriers. Ryu, Jin, and Kim [46] have proposed a

new PAPR reduction technique using soft clipping and filtering. In their method, the clip

slope of the soft-clipping is not zero and have used additional FFT and IFFT transform stages

in order to remove the out-of-band clip noise. For QPSK baseband modulated signal with 16

number of subcarriers and clipping ratio of 0.8 and 1.0, they have been able to reduce the

PAPR up to 6.9 dB at 10−3 CCDF. They have also observed that with the new method the

spectrum after filtering is similar to the original OFDM spectrum and there is no spectral

regrowth causing the adjacent channel interference with the same level of BER degradation.

2.4.2 Selective Mapping Method

Selective mapping is one of the most important PAPR reduction technique as it is simple

from the implementation point of view, does not introduce distortion in the transmitted signal

and can achieve a significant reduction in PAPR value. Le Goff, et al [47, 48] have proposed

a quite simple SLM technique for PAPR reduction in OFDM system which does not require

the transmission of additional side information bits. Their investigations, based on QPSK


21

and 16 QAM baseband modulations, have revealed that their technique is most suitable for

systems having a large number of subcarriers. As a matter of fact if the extension factor or

the number of subcarriers are increased the probability of side information detection error

can be made very small. They have shown that BER performance difference between their

proposed technique and classical SLM technique using error-free side information is

negligible in the case where this probability have become sufficiently low and it is valid for

any number of subcarriers. But this has been achieved at the cost of a slight increase in the

system complexity in the receiver design owing to use of additional side information

detection block. Wang, Ku and Yang [49] have proposed search-and-partial-interpolation

scheme, a new low-complexity PAPR estimation technique, for discrete-time OFDM

signals. Their proposed scheme has the uniqueness of first finding the samples with power

higher than a preset threshold from the original discrete time OFDM signal, and then it

interpolates samples in the neighborhood with a higher sampling rate around each of the

searched samples. In order to estimate the PAPR, sample with the highest power among the

searched samples and the interpolated one is used. They have also demonstrated effective

criteria to determine the interpolation filter length and the threshold level which can be easily

combined with the SLM technique to form a low-complexity, high-performance PAPR

reduction technique. The result obtained by computer simulation have shown that their

proposed search-and-partial-interpolation scheme can achieve PAPR estimation

performance almost equal to that of the method with four times oversampled signal, with

50% reduced computational complexity. These features of low complexity and good

performance make their scheme attractive to be used for practical OFDM applications.

Bguml, Fischer and Huber [50] have proposed a scheme for the reduction of PAPR which

can be used for any numbers of subcarriers and any type of signal constellation and is

appropriate for all types of multiplexing techniques, which are used to transform data

symbols to the transmit signal. They have further reiterated that even in the case of single

carrier systems their method can be used with great advantage. FPGA implementation of

SLM technique have been investigated in [51-53] and the result obtained have shown a

similar trend with as that of obtained by mathematical modeling and simulations with

additional advantages of reduced hardware resource consumption and system complexity.

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22

2.4.3 Partial Transmit Sequence

Partial transmit sequence technique is an efficient technique for PAPR reduction of OFDM

signal by optimally combining signal subblocks, wherein the input symbol sequence is

partitioned into a number of disjoint symbol subblocks. Varahram and Mohd Ali [54] have

investigated a new phase sequence of PTS scheme wherein a matrix of possible random

phase factors are first generated which is multiplied point-wise with the input signal. In this

new technique, the number of IFFT operations have been reduced to 50 % so that the system

complexity has reduced compared with continuous PTS at the cost of a slight decrease in

PAPR. They have also examined the performance of the out-of-band distortion with

nonlinear Power Amplifier. With the application of digital predistortion and PAPR

reduction technique, the power spectral density of the output of the signal has been further

suppressed. In this way, they have exhibited enhancement of power efficiency and in turn

low power consumption and enhanced battery life which could be considered for application

in wireless communications systems such as long-term evolution and WiMAX. In optimum

PTS technique, the computational complexity increases extensively with an increase in the

number of sub-blocks. Yang, Chen, Siu, and Soo [55] have proposed a reduced complexity

PTS method and have given a derivation taking into account the relationship between the

transmitted signals and the weighting factors. They have demonstrated that the

computational complexity of their proposed method is only about the one (N-1)th of the

conventional PTS method, where N is the number of sub-blocks. With slight performance

degradation, the complexity of their proposed method has been greatly reduced which is

applicable for the number of transmitted signals to be searched at each stage using a preset

threshold level.

Hieu, Kim, and Ryu [56] have introduced a low complexity phase weighting method to

reduce the PAPR in OFDM communication system. In order to exploits characteristic of

DFT of periodical sequence, they proposed a technique which can reduce PAPR as

efficiently as partial transmit sequence or sub-block phase weighting (SPW) method. They

observed 2.15 dB reduction in PAPR for 64 number of subcarriers with the number of the

weighting factor, W = 2 and the number of sub-blocks, M=4. The reduction was increased

to 3.95 dB with an increase in weighting factor, W=4 and number of sub-blocks, M=4. Their

method used only one IFFT processor at one time which resulted in a reduction in complexity

of the system with remarkable improvement in the number of additions and multiplications.

For computing a good set of phase factors for PTS combining, Chintha Tellambura [57]


23

developed a new algorithm. His algorithm performs better than the optimal binary phase

sequence search for a small number of subblocks. In the case of an increase in the number

of subblocks, the performance difference between the two algorithms becomes almost equal

to zero, whereas the complexity of the optimal binary phase sequence solution increases

exponentially. It was also pointed out that the effect of 2-bit quantization on the performance

of the new algorithm was almost negligible.

Cimini and Sollenberger [58] observed that the SLM and PTS approaches provide a better

reduction in PAPR with a fewer loss in efficiency, but this comes at the cost of additional

system complexity. They described new algorithms which can combine partial transmit

sequences. Their simulation results revealed that the suboptimal strategies adopted was less

complex and more easily implemented and suffered very low-performance degradation.

Kang, Kim, and Joo [59] proposed a concatenated pseudo-random subblock partition scheme

for PTS-OFDM system, which has a form concatenation of interleaved partition and pseudo-

random scheme. As compared to pseudo-random subblock partition scheme their result has

shown the same reduction in PAPR with the reduction in computational complexity with the

number of concatenation factor, C = 2 and 4. Their scheme could be used in various systems

by carefully choosing the number of concatenation factor as per the required performance

and computational complexity. They further emphasized that for high quality and low

transmission rate communication system the number of concatenation factor can be low,

whereas it can be chosen high for the application requiring high transmission rate.

Park and Song [60] described a new estimator iterative PTS scheme (EI-PTS) with minimum

mean square error (MMSE) criterion to enhance BER performance by reducing nonlinear

distortion of the high power amplifier. Through simulation result they have validated that

keeping low subblock combining complexity, adaptive nonlinear estimator, EI-PTS gives

improved performance compared to that of with only iterative PTS. Baxley and Zhou [61]

investigated on SLM and PTS, two popular distortionless PAPR reduction techniques and

analyzed their computational complexity and PAPR reduction performance. It is to be

emphasized that SLM can produce multiple time-domain signals which are asymptotically

independent, whereas the alternative signals generated by PTS are interdependent and

because of that, PTS will have less PAPR reduction capability than that of SLM for a given

number of mappings. But the computational complexity of PTS is much lesser than that of

SLM which in turn outweigh the PAPR reduction capability of SLM. Using three different

selection criteria and metrics they have compared the performance of SLM and PTS

Literature Review

24

techniques and observed that in all three given metrics for a given amount of computational

complexity, SLM has better performance than PTS. Even PTS with an optimized non-

overlapping sub-blocks does not beat the performance of SLM in any of the metrics with all

complexities. They further reiterated that SLM is preferable over PTS owing to several

regions. First, SLM is simple in design second, SLM does not require any offline complexity

optimization and last but not the least SLM performs far better than that of the optimized

PTS.

Ryu and Youn [62], have investigated a new subblock phase weighting method for PAPR

reduction and proposed two kinds of side information insertion method in the feedback and

feedforward type. They have analyzed CCDF performance of PAPR and the reduction of

computational complexity. They have also solved the problem of the conventional PTS and

SLM which needed several IFFT blocks, with only one IFFT block using subblock phase

weighting method. Apart from that, they have revealed that with the use of side information

insertion method the required BER can be maintained with reduced computational

complexity. As the number of subblocks is increased PAPR reduction efficiency increases

but there is a small loss of the spectral efficiency due to the insertion of side information.

2.4.4 Single Carrier Frequency Division Multiple Access

Single carrier frequency division multiple access is a modified form of orthogonal frequency

division multiple accessing. It has a similar throughput performance and overall complexity

as OFDMA. It is a promising technique for high data rate uplink communications for future

cellular systems because of lower PAPR than that of OFDMA. Myung, Lim, and Goodman

[63] have investigated the effects of subcarrier mapping on throughput and PAPR. Among

the different subcarrier mapping approaches, they have observed that the localized FDMA

(LFDMA) with channel-dependent scheduling gives higher throughput than the interleaved

FDMA (IFDMA). But, the PAPR performance of IFDMA is better than that of LFDMA by

4 to 7 dB. They have also observed that in terms of PAPR performance with the pulse

shaping which is necessary to control adjacent channel interference, there was a narrower

difference between LFDMA and IFDMA. They also emphasized that the effective

scheduling depends on accurate information about the frequency response of the radio

channels linking terminals to an SCFDMA base station and the channel estimation errors are

caused by noise estimation and changes in channel properties which degrade the

performance of channel-dependent scheduling by causing incorrect adaptation of the


25

modulation technique and incorrect assignment of subcarriers to users. Through their

investigations, they have tried to quantify the effects of these errors.

Lin, Xiao, Vucetic, and Sellathurai [64] have derived frequency domain receiver algorithm

for the SCFDMA based uplink multiple inputs multiple outputs (MIMO) system with the

improper signal constellation. They have also derived mathematical expressions of the

received signal-to-interference-plus-noise ratio (SINR) for the considered MIMO systems.

Through simulation and analytical results, they observed that their scheme has a superior

BER and SINR performance compared to the conventional linear MMSE receiver for

SCFDMA MIMO uplink systems. In order to reduce the PAPR of SCFDMA systems,

Hasegawa, Okazaki, Kubo, Castelain, and Mottier [65] have studied a novel adaptive pilot

insertion method and through simulation results, they have demonstrated that their method

outperforms the conventional method of PAPR reduction in terms of BER and PAPR

performance.

Investigation on international mobile telecommunications-advanced (IMT-A) systems have

been carried out by Berardinelli, et al [66]. They have changed the subcarrier spacing and

kept slot duration constant of 3GPP LTE system. They have evaluated the performance of

OFDMA and SCFDMA scheme for uplink transmission and studied their performance for

diversity gain and PAPR. In order to get benefits of low PAPR only the localized distribution

of resource block should be considered but this consideration puts a limitation on the

flexibility of the resource allocation in the case of a multi-user environment. To overcome

this constraint, they proposed a new algorithm, which has low implementation and

computational complexity with better performance. When communicating over broadband

wireless channels, for increasing the achievable power-reduction, Zhang, et al [67] have

investigated a variety of cooperative relaying schemes designed for the SCFDMA uplink

and reviewed the principles of operation of SCFDMA methods. They have used a number

of inactive mobile terminals to act as potential relays, which have either time-variant or fixed

positions in a cell. While considering relay selection, subband allocation, power allocation

and novel signal processing algorithms at the relays, they have focused on the optimum

utilization of the available resources and their investigation demonstrated that power-

reduction and reliability of the SCFDMA systems can be improved significantly.

For studying the effect of proportional fairness scheduling in SCFDMA system Kim, et al

[68] have proposed a virtual MIMO version of the heuristic algorithm. They have further

Literature Review

26

reiterated that there was room to improve over the proposed algorithm, as the optimal PF

scheduling algorithm has not been known. Through simulation results, they have shown that

their algorithm was already very close to the optimal one. In order to reduce the effect of the

channel transition within the frequency domain equalization block, Kambara et al [69] have

proposed subblock processing. The investigation revealed that in fast fading environments

their proposed technique could effectively decrease the error floor, and for transmitted block

size of 256 symbols provided a 1.5-fold increase in a tolerable Doppler frequency for block

error rate of 10−2. They have also emphasized that in accordance with the block size, the

optimal number of subblocks has been shown to change.

Ciochina, et al [70] have studied the implementation of Alamouti based transmit diversity

schemes in an SCFDMA system and have reviewed the advantages and disadvantages of

existing schemes. They have shown that when combined with SCFDMA classical frequency

codes suffer from PAPR degradation while the space-time codes have implementation-

related limitations. They have proposed a family of PAPR-invariant mapping of space-

frequency codes suitable for SCFDMA with two transmit antennas and also derived an

extension of this technique for four antennas. Finally, they concluded that new mapping of

Alamouti-based space-frequency block code has shown better performance and

outperforming than its classical space-frequency block code counterpart. In order to increase

the coverage of SCFDMA systems, single-carrier space-frequency block code (SC-SFBC)

and single carrier quasi-orthogonal space-frequency block code (SC-QOSFBC) are more

flexible than space-time block code (STBC). Al-Kamali, et al [71] have considered the

design of a new transceiver scheme for the SCFDMA scheme using the wavelet transform

and have added no redundancy to the new system due to the discrete wavelet transform.

Because of that when compared to the conventional SCFDMA scheme its complexity has

slightly increased. Through simulation, they have shown that their proposed hybrid wavelet

SCFDMA (HW-SCFDMA) scheme provided better PAPR and BER performance than the

conventional SCFDMA scheme. They further emphasized that companding and the clipping

schemes must be designed carefully in order to limit the PAPR and provide a good BER

performance. Their proposed scheme was not very sensitive to the channel model used in

the simulation but it was more robust to the channel estimation errors than the conventional

SCFDMA system over a mobile wireless channel.


27

For SCFDMA systems Ma, Huang, and Guo [72] have proposed an interference self-

cancellation method and has improved the signal-to-interference ratio. While doing so they

have kept the bandwidth and the power level at a minimum level and maintained the PAPR

for SCFDMA scheme. Ma, et al [73] have presented a solution to the optimization problem

of designing a precoding matrix with minimum power leakage. They have constructed two

kinds of precoding matrices with multi-carrier and single-carrier properties to take

advantages of OFDM and SCFDMA respectively. They have used extra degrees of freedom

in the optimized matrix and because of that their proposed matrix design is flexible. The

proposed matrix could provide different side lobe roll-off performances at the same time

meeting the requirements of various systems as they have selected different optimization

region and redundancy. The result obtained revealed that the proposed precoding scheme

has decreased power leakage with only small bandwidth efficiency loss and the proposed

multi-carrier and single-carrier precoding schemes provided similar PAPR and BER to those

of OFDM and SCFDMA systems, respectively while maintaining low power leakage. The

investigation developed by Deng, Liao and Huang [74] for a new high-rate coded SCFDMA

transceiver system over frequency-selective fading channels have exploited several schemes.

Among those are the M-ary mapping and parallel spreading techniques which supported

communication at a very high data rate and the use of Chu-sequence for spreading could

ensure that the proposed system has a low PAPR and supports orthogonal despreading. The

ML detector with the interleaved time and the frequency equalizer enabled the system to

achieve frequency diversity and M-ary gain and finally the simulation result confirmed the

advantage of the low PAPR and better BER performance of their proposed coded SCFDMA

system.

For coded SCFDMA systems, Ji, Ren and Zhang [75] have proposed a simple and flexible

PAPR reduction technique. For the signal to noise ratio below 35 dB, their proposed

technique could achieve good PAPR reduction performance with same BER performance as

the conventional SCFDMA signals. In order to further reduce PAPR with very low

additional computational complexity, their proposed method could also be used with the

available pulse shaping methods with excess bandwidth.

2.4.5 Pulse Shaping Filter Technique

Pulse Shaping Filters in multicarrier OFDM communication systems with high data rate

transmission capability are used for better bandwidth utilization. There are many types of

Literature Review

28

Nyquist pulses which can be used for the distortionless transmission without the presence of

intersymbol interference. Among them, the most popular Nyquist pulse is the raised cosine

(RC) pulse which is basically a low-pass filter with odd symmetry around a cutoff frequency

and has a cosine shaped roll-off portion. In order to reduce the PAPR of the SCFDMA

systems, Feng et al [76] have investigated a novel piece-wise linear pulse shaping filter.

They have considered the optimal values of the design parameters that gives the minimum

value of PAPR. They have further observed that their proposed filter provide better

performance in terms of PAPR reduction and symbol error rate when compared with that of

the traditional filters and has much lower computational complexity. Using a spline

construction in the frequency domain Beaulieu and Damen [77] have investigated a new

parametric approach for constructing families of ISI-free pulses. When compared with raised

cosine pulses with the same value of excess bandwidth, their proposed technique has more

open pulse-sequence eye, smaller distortion, and a smaller average probability of error with

symbol timing error.

Assimonis, Matthaiou and Karagiannidis [78] have presented three alternative Nyquist

pulses: inverse-cosine inverse hyperbolic sine (acos[asinh]), inverse-cosine inverse-tangent

(acos[atan]) and sine inverse hyperbolic cosine (sin[acosh]) which are based on the concept

of inner and outer functions and exploited the inherent flexibility of using the concepts of

inner and outer functions. The result obtained with their proposed pulses were compared

with the farcsech pulse which is considered to be the most sophisticated two-parameter pulse

and demonstrated that there was an improvement in terms of maximum distortion and BER

performance. Using a piece-wise linear construction with segments of variable length and

slope in the frequency domain, Alexandru and Balan [79, 80] have presented a new

parametric approach for constructing families of inter-symbol interference (ISI) free pulses.

Their investigation revealed that with the same value of excess bandwidth the proposed new

parametric pulses for the specified values of design parameters exhibited smaller average

probability of error in the presence of symbol timing error compared to the previously

reported pulses. They further emphasized that in order to keep the ISI error probability at a

minimal value with increased time offset, the slope of the median segments must also be

increased. Meza, Lee, and Lee [81] have studied a novel Nyquist-I pulse and implemented

a linear combination between two ISI-free pulses. The result obtained with their proposed

filter has the same bandwidth for different values of the new design parameter, μ and a fixed

roll-off factor, α. For a given roll-off factor, α, and single carrier transmission scheme it


29

gives an additional degree of freedom to reduce PAPR. In order to minimize the PAPR of

the interleaved SCFDMA scheme, the optimum value of μ was observed to be 1.60 for α =

0.35. Their simulation result revealed that their proposed optimum filter has better PAPR

reduction capability than that of the existing filters available in the literature.

Assalini and Tonello [82] have proposed two new Nyquist pulses that have better error

probability performance in the presence of sampling errors than the popular raised cosine

and other pulses available in the literature. Their new proposed pulses, flipped-hyperbolic

secant (fsech) and flipped-inverse hyperbolic secant (farcsech) pulse are robust to the root

and truncation operations and asymptotically decay respectively as 𝑡−3and as 𝑡−2. It has

also been observed that the amplitude of the main sidelobes is smaller for the pulses with

𝑡−2 decay than for those with 𝑡−3 decay. These pulses show smaller error probability than

the popular raised-cosine pulse. They have also investigated the equivalent pulses that was

obtained with the auto-convolution of a “truncated root version” and for larger timing errors

the proposed pulse exhibited improved BER performance, a smaller maximum distortion

and a much wider eye opening, than the other available pulses. Analysis of the effect of time

and frequency selectivity in filtered multitoned (FMT) modulation have been investigated

by Tonello and Pecile [83] and obtained quasi-closed form expressions for the signal-to-

interference power ratio. Their result allowed them to characterize effect of fading channels

as a function of Doppler-delay spread. FMT uses a frequency confined prototype pulse that

makes the technique robust to the inter-carrier interference which are generated by the

channel time and frequency selectivity. It was emphasized that in FMT, a simple one tap

equalizer was sufficient to yield better signal-to-interference power ratio and BER

performance than OFDM in fast fading with a root-raised-cosine prototype pulse. Similar

performances were achieved in the case of frequency selective fading. Their result gave

guidelines on the design of the pulse, including length and roll-off factor of a root-raised

cosine pulse that yielded a required amount of inter carrier interference and inter symbol

interference in a time-frequency selective channel.

Kaiser and Hamming [84] have developed a general theory which indicated how to

interconnect multiple instances of the same filter transfer function in order to achieve an

overall filter performance which meets much tighter specifications using only gain factors,

adders, and delay elements. They have assumed that all instances of the filter are identical,

has a symmetric pulse response, and that the filter magnitude characteristics have unity in

Literature Review

30

the passband and zero in the stopband. They developed a simple but useful specialization

method called simple symmetric sharpening. The computational efficiency of the proposed

sharpened filter was compared with the best possible filter design. With examples of various

designs, they described three different cases of implementation technique and outlined a

number of properties of the method and various extensions and applications of the procedure.

Their technique added an important design technique in the field of signal processing and

developed an important method for multiprocessing using digital filters.

2.5 Research Gap

It has been observed in the literature review that there are very efficient techniques available

for linearization of power amplifiers and reduction of PAPR. Each technique has certain

merits and demerits and is suitable for a particular application only. In some techniques,

performance improvement in terms of BER and PAPR has been achieved at the cost of

increased computational complexity, inband distortions have been reduced at the cost of an

increase in the out of band radiation or increase in the adjacent channel power ratio and vice

versa. For example in the PAPR reduction with clipping and filtering technique, clipping of

signal results in the reduction of PAPR but at the cost of spectral regrowth. When the filtering

operation is performed ACPR decreases again at the cost of an increase in the PAPR.

Iterative clipping and filtering are used to check regrowth of both PAPR and ACPR once

again at the cost of an increase in hardware and computational complexity. Similar is the

case with other PAPR reduction techniques, such as selected mapping method, partial

transmit sequence, SCFDMA and pulse shaping with Nyquist filters.

2.6 Conclusion



distortion, phase distortion, adjacent channel interference, etc. Modern communication

systems use multicarrier OFDM which has high data rate transmission capability in addition

to robustness to channel impairments. One of its major disadvantages is having high peak-

to-average power ratio. High PAPR drives power amplifier into saturation region and causes

it to operate in the nonlinear region. Powerful techniques have been developed to mitigate

the harmful effects of nonlinearity, but are not effective when applied alone. There is a need

to address this issue at the transmitter and receiver simultaneously. At the transmitter, there

is a need to use the efficient modulation technique such as multicarrier OFDM system with

Conclusion

31

effective PAPR reduction techniques and utilization of effective power amplifier

linearization techniques. Similarly, effective pulse shaping filter and demodulation

technique are required to be used at the receiver.

32

CHAPTER – 3

Multicarrier OFDM Communication Systems

and Linearization of Power Amplifier

3.1 Introduction





etc. OFDM systems have many applications and are widely used in high-bit-rate digital

subscriber lines (HDSL), digital audio broadcasting (DAB), digital video broadcasting

(DVB) along with high-definition television (HDTV), terrestrial broadcasting [85]. Third

generation partnership project (3GPP) for long term evolution (LTE) and LTE advanced

(LTE-A) uses orthogonal frequency division multiple accessing (OFDMA) for the downlink

and SCFDMA technique for the uplink transmission [86].

3.2 OFDM Transceiver Model

The block diagram of the OFDM transceiver system is shown in Fig. 3.1. The baseband

modulated signal in the form of QPSK, QAM, etc. is fed to the serial to parallel converter.

N number of parallel signals generated from the serial to parallel converter which is termed

as subcarrier are multiplied with complex signal 𝑒𝑗2𝜋𝑛𝑘/𝑁 and added together. This

operation is known as inverse discrete Fourier transform (IDFT) and its equivalent algorithm

to be used with digital computer with higher speed and low computational complexity is

inverse fast Fourier transform (IFFT), is used as OFDM modulation [87]. It is to be noted

that with IDFT/IFFT operation now the complex signal is converted into time domain. In

order to prevent the intercarrier interference (ICI), intersymbol interference (ISI), interblock

interference (IBI), and to maintain orthogonality among the adjacent subcarriers cyclic

prefix is added with each block of data after the IFFT operation.

OFDM Transceiver Model

33

FIGURE 3.1 Block diagram of OFDM transceiver

The time domain signal is now converted into the serial form using serial to parallel

converter. DAC is used to convert these signals into the analog form before the passband

modulation is performed. In the passband modulation, the signal is up-converted to the

desired RF frequency for upward transmission. In the present work, the RF operating

frequency has been taken as 2 GHz. This passband signal is now transmitted through the

channel after passing through the transmit filter [88]. In the channel, the signal is mixed with

additive white Gaussian noise. In the receiver, the reverse process takes place as discussed

in the transmitter. After passing through low pass filter the signal is down-converted in the

passband demodulator before being converted back in the digital form with the help of

analog-to-digital converter (ADC) for digital processing. Serial to parallel converter is used

for converting the serial data into parallel form. Before using DFT/FFT block to demodulate

the OFDM signal cyclic prefix is removed and once again converted back into the serial

form using parallel to serial converter. Finally, the baseband signal is demapped and the

constellation diagram is obtained [89, 90].

Fig. 3.2 shows the concept of subdivision of bandwidth in the multicarrier OFDM

communication systems. A given larger frequency band is subdivided into N-number of

smaller bands which are known as subcarriers.

IX(f)I

0 ∆f W

f

FIGURE 3.2 Subdivision of bandwidth in OFDM modulation

Multicarrier OFDM Communication Systems and Linearization of Power Amplifier

34

The adjacent subcarriers are overlapping to each other in the frequency domain and do not

create interference as they maintain orthogonality among themselves. They are in the form

of sync pulses and have zero crossings at the multiples of the time period and as per the

Nyquist criteria, they are ISI free. Because of overlapping nature of adjacent carriers, it

preserves bandwidth and is considered to be spectrally efficient as depicted in Fig. 3.3.

The time domain signals are generated by multiplying the subcarriers with N number of

complex signal𝑠 𝑒𝑗2𝜋𝑛𝑘/𝑁 and adding together. The process of multiplication and addition

of subcarriers is known as IDFT/IFFT operation and is represented as in (3.1).

1

0.8

0.6

0.4

0.2

0

-0.2

-0.4100 200 300 400 5000 600

FIGURE 3.3 OFDM subcarrier arrangement

𝑥𝑛 = 1

𝑁∑ 𝑋𝑘

𝑁−1

𝑘=𝑜

𝑒𝑗2п𝑛𝑘

𝑁 (3.1)

Where, N is the symbol period, 𝑋𝑘 is the data symbol for the k-th subcarrier and the entire

process of (3.1) is equivalent to the N-point IDFT/IFFT operation. Care has to be taken to

maintain orthogonality among the subcarriers. Two signals, 𝑠1(𝑡) and 𝑠2(𝑡) are said to be

orthogonal to each other if condition depicted in (3.2) is satisfied [91, 92].

1

𝑇∫ 𝑠1(𝑡) 𝑠2(𝑡) 𝑑𝑡 = 0

𝑇

0 (3.2)

The subcarriers are in the form of sinc-shaped pulses whose zero crossings are located at the

multiples of time periods which helps in reduction of intercarrier interference and

intersymbol interference. The symbol duration of the OFDM signal is Tu seconds with Δω

of carrier spacing as represented in (3.3).

𝑇𝑢 = 2𝛱

𝛥𝜔 ↔ 𝛥𝜔 =

2𝛱

𝑇𝑢= 2𝛱𝛥𝑓 (3.3)


35

The Nth OFDM symbol is represented by Fourier series as shown in (3.4).

𝑥𝑘 = ∑ 𝑋𝑘

𝑁−1

𝑘=0

[𝑛] 𝛿𝑛(𝜔 − 𝑘 𝛥𝜔) (3.4)

The spectrum in (3.4) is inverse Fourier transformed and limited to a time interval of Tu

seconds in order to provide the OFDM symbol in the time domain. The time-domain signal

yn is given as in (3.5).

𝑦𝑛 = {1

𝑇𝑢

∑ 𝑋𝑛

𝑁−1

𝑛=0

[𝑛] 𝑒𝑗𝛥𝜔𝑛𝑡 0 ≤ 𝑡 ≤ 𝑇𝑢

0 otherwise

(3.5)

The cyclic prefix is added as given in (3.6) after summing up the signal and IDFT operation

is completed.

𝑣𝑛 = {

𝑦𝑛 (𝑡 + 𝑇𝑢 − 𝑇𝑔), 0 ≤ 𝑡 ≤ 𝑇𝑔

𝑦𝑛 (𝑡 − 𝑇𝑔), 𝑇𝑔 < 𝑡 < 𝑇𝑠

0 otherwise

(3.6)

In (3.6), Tg is the cyclic prefix duration and the total symbol duration Ts = Tu + Tg, where,

Tu is the useful symbol duration and Fig. 3.4 shows the addition of a cyclic prefix.

FIGURE 3.4 Addition of cyclic prefix


36

All OFDM symbols are linked together in order to form baseband signal for transmission as

shown in (3.7).

v(t) = ∑ 𝑣𝑛(𝑡 − 𝑠𝑇𝑠)

𝑁−1

𝑛=0

(3.7)

Before transmission into the channel, these signals are finally upconverted to an RF carrier

frequency as given in (3.8).

𝑚(𝑡) = 𝑅𝑒{𝑣(𝑡)𝑒𝑗2п𝑓𝑐 𝑡 } (3.8)

The signal m(t) is the transmitted RF passband signal and fc is its carrier frequency. For one

OFDM symbol starting at t = 𝑡𝑠 equation (3.8) can be further expanded as given in (3.9) and

(3.10).

𝑚(𝑡) = 𝑅𝑒 { ∑ 𝐷𝑛+𝑁 𝑒𝑗2п(𝑓𝑐− 𝑛+0.5

𝑇 )( 𝑡−𝑡𝑠 )

𝑁−1

𝑛=0

} , 𝑓𝑜𝑟 𝑡𝑠 ≤ 𝑡 ≤ 𝑡𝑠 + 𝑇 (3.9)

and,

𝑚(𝑡) = 0 𝑓𝑜𝑟 𝑡 < 𝑡𝑠 𝑎𝑛𝑑 𝑡 > 𝑡𝑠 + 𝑇 (3.10)

Where, 𝑡𝑠 is the symbol starting time, 𝐷𝑛 is the complex modulation symbol, N is the

number of subcarriers; T is the symbol duration, and fc is the carrier frequency. Equation

(3.11) is another version of the emitted signal as given in (3.9).

𝑚(𝑡) = 𝑅𝑒{𝑒𝑗2п𝑓𝑐 𝑡 ∑ ∑ ∑ 𝐶𝑚,𝑙,𝑛 𝑁𝑚𝑎𝑥𝑛=𝑁𝑚𝑖𝑛

67𝑙=0

∞𝑚=0 . 𝑄𝑚,𝑙,𝑛 (𝑡)} (3.11)

Where,

𝑄𝑚,𝑙,𝑛 (𝑡) = { 𝑒𝑗2п

𝑛′

𝑇𝑢 (𝑡−𝑇𝑔−𝑙.𝑇𝑠−68.𝑚.𝑇𝑠)

0 ; else (𝑙 + 68. 𝑚)𝑇𝑠 ≤ 𝑡 ≤ (𝑙 + 68. 𝑚 + 1)𝑇𝑠 (3.12)

The OFDM transmission system is described by (3.11) and (3.12). Where, n is the carrier

number, l is the symbol number, m is transmission frame number, N is the number of

transmitted subcarriers; 𝑇𝑠 is the symbol duration; 𝑇𝑢 is the useful symbol period; 𝑇𝑔 is the

duration of the cyclic prefix; 𝑓𝑐 is the operating frequency of the RF signal; 𝐶𝑚,0,𝑛 is the

complex symbol for carrier n of the data symbol number 1 in frame number m; 𝐶𝑚,1,𝑛

complex symbol for carrier n of the data symbol no. 2 in frame number m, etc.


37

TABLE 3.1 Numerical Values for the OFDM Simulation Parameters

Parameters Values

Carrier frequency 2 GHz

Number of subcarriers, N 1024

Useful OFDM symbol period, TU 5.12 μs

Guard Interval (Cyclic Prefix), (Tg = Tu /32) 0.16 μs

Total OFDM symbol period (TS = Tg + TU) 5.28 μs

2L- IFFT/ IFFT length, (L= 1024) 2048

We get (3.13) when (3.11) is considered for the period from t=0 to t=TS,

𝑚(𝑡) = 𝑅𝑒{𝑒𝑗2п𝑓𝑐 𝑡 ∑ 𝐶0,0,𝑛 𝑒𝑗2п

𝑛′ 𝑇𝑢

(𝑡−𝑇𝑔)

𝑁𝑚𝑎𝑥

𝑛=𝑁𝑚𝑖𝑛

(3.13)

With n′ = n – ( Nmax + Nmin) / 2

It is to be noticed that (3.13) is similar to the IDFT operation as given in (3.14).

𝑚𝑛 =1

𝑁∑ 𝑀𝑘 𝑒

𝑗2п𝑛𝑘 𝑁

𝑁−1

𝑘=0

(3.14)

The parameters of the OFDM signal are given in Table 3.1. The subsequent up-conversion

by passband modulation then gives the real signal m(t) centered at the carrier frequency fc

[93].

3.2.1 OFDM Transmitter Simulation with Matlab

Mathematical modeling and Matlab simulation has been carried out on OFDM transmitter

and its block diagram is depicted in Fig. 3.5. The simulation has been performed with the

parameters shown in Table 3.1 using (3.11). 4 QAM baseband modulated signal with 1024

number of subcarriers have been used at 2 GHz of operating frequency.


38

BASEBAND

QAM MOD

OFDM

SIGNAL

(IFFT)

PULSE

SHAPING

LOW PASS

FILTERX

Carrier Frequency, fc

Bandpass output

1 2 3 4 5

FIGURE 3.5 OFDM signal generation at transmitter

The Frequency response of baseband modulated 4 QAM signal at point 1 is shown in Fig.

3.6. After serial to parallel conversion, it is converted into time domain using IFFT operation.

FIGURE 3.6 Frequency response of signal

In order to reshape and avoid its leakage, the signal is passed through a pulse shaping filter

and its impulse response is shown in Fig. 3.7.

FIGURE 3.7 Impulse response of the D/A reconstruction filter

0 0.5 1 1.5 2 2.5 3 3.5 4

x 108

0

0.5

1

1.5

Frequency (Hz)

Ampli

tude

Frequncy response of Carrier FFT at point 1

0 50 100 150 200 250 300 350-120

-100

-80

-60

-40

Frequency (MHz)

PSD

(dB/

Hz)

Carrier Welch PSD estimate at point 1

0 0.5 1 1.5 2 2.5

x 10-9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time (second)

Ampli

tude

Pulse shape g(t)


39

The frequency response of the pulse shaping filter is reflected through Fig. 3.8. Then this

signal is passed through a digital to analog reconstruction filter.

FIGURE 3.8 Frequency response of filter

It is a Butterworth filter with 13 order and its cut-off frequency is approximately 1/T and its

frequency response is shown in Fig. 3.9.

FIGURE 3.9 Frequency response of D/A reconstruction filter

It is to be noted that the filter introduces approximately 50 μs delay. Then finally the signal

is passband modulated before being transmitted through the channel with 2 GHz operating

frequency and shown in (3.15).

m(t) = mi(t) cos(2Πfct) + mq(t) cos(2Πfct) (3.15)

The output of passband modulation in the time domain is shown in Fig. 3.10 and its

equivalent frequency response is depicted in Fig. 3.11.

0 1 2 3 4 5 6 7 8

x 109

0

10

20

30

40

Frequency (Hz)

Ampl

itude

Frequency Response of signal (FFT) at point 3

0 1 2 3 4 5 6 7-150

-100

-50

0

Frequency (GHz)

PSD

(dB/

Hz)

Welch PSD estimate at point 3

0 0.5 1 1.5 2 2.5 3 3.5 4

x 109

-700

-600

-500

-400

-300

-200

-100

0

100

Frequency (Hz)

Ampl

itude

(dB)

Frequency Response of D/A Reconstruction Filter


40

FIGURE 3.10 Time response of passband signal

It is to be emphasized that the passband signal contains large fluctuations in the amplitude and its

dynamic range is quite high. This is causing the high peak to average power ratio in the multicarrier

OFDM modulated signal.

FIGURE 3.11 Frequency response of passband signal

3.2.2 OFDM Receiver Simulation with Matlab

Mathematical modeling and Matlab simulations have been carried out for the OFDM

receiver depicted in Fig. 3.12. After receiving the signal its bandpass demodulation is carried

out. Then the demodulated signal is passed through the low-pass filter and converted back

into the digital domain with the help of sampler and quantizer. FFT is used to demodulate

the OFDM signal before finally obtaining the 4 QAM baseband signal.

0 1 2 3 4 5 6 7

x 10-8

-80

-60

-40

-20

0

20

40

60

80

Time (second)

Am

plitu

de

Time Response of Passband Signal at point 5

0 1 2 3 4 5 6 7 8

x 109

0

5

10

15

20

Frequency (Hz)

Ampl

itude

Frequency Response of passband Signal at point 5

0 0.5 1 1.5 2 2.5 3 3.5 4-150

-100

-50

Frequency (GHz)

PSD(

dB/H

z)

Welch PSD estimate at point 5


41

X LPFSAMPL

ERFFT

QAM

DEMOD

6 7 8 9 10

QAM CONST

Carrier, fc

RF Txr signal

FIGURE 3.12 Receiver model of OFDM systems

The impulse response function for the nth user, hn (t) of the channel baseband signal is

represented by (3.16). In order to estimate the signal at the receiver, side convolution is done

with the time domain complex baseband signal and the transmitted signal.

ℎ𝑛 (𝜏, 𝑡) = ∑ ℎ𝑛,𝑚 (𝑡) 𝛿𝑐(𝑡 − 𝜏𝑚) (3.16)

𝑀

𝑚=0

Where hn,m (t) is the representation of the complex gain of the mth multipath component

for the nth user at time t. It is to be noted that the channel has been assumed static for one

OFDM symbol duration. Equation (3.16) has been redefined for the static channel and is

represented by (3.17).

ℎ𝑛,𝑠 ( 𝑡) = ∑ ℎ𝑛,𝑚 (𝑠) 𝛿𝑐(𝑡 − 𝜏𝑚) (3.17)

𝑀

𝑚=0

Where ℎ𝑛,𝑚 (𝑠) = ℎ𝑛,𝑚 (𝑡) , 𝑠 𝑇𝑠 ≤ 𝑡 < (𝑠 + 1) 𝑇𝑠

Equation (3.18) is the representation of the corresponding frequency-domain channel

transfer function, Hn,s, which has been obtained using Fourier transformation.

𝐻𝑛,𝑠 ( 𝜔) = ∫ ℎ𝑛,𝑠 ( 𝑡)𝑒−𝑗𝜔𝑡∞

−∞

𝑑𝑡 (3.18)

There are multiple echoes of the transmitted signal present in the signal which has been

received at the receiver apart from interference and white Gaussian noise. Equation (3.19)

is the representation of the RF signal received by the nth user.

𝑚(𝑡) = 𝑅𝑒{𝑠(𝑡) ∗ ℎ𝑛,𝑠 ( 𝑡) 𝑒𝑗2𝛱𝑓𝑐 (𝑠)𝑡} + 𝑢(𝑡), 𝑠 𝑇𝑠 ≤ 𝑡 < (𝑠 + 1) 𝑇𝑠 (3.19)


42

FIGURE 3.13 Frequency response of bandpass signal

Where, u(t) is a real-valued, passband signal combined with additive white Gaussian noise

and interference. Now once again the receiver has to recreate the transmitted signal.

Frequency and timing error may also occur in the receiver apart from the occurrence of noise

and multipath effects [94]. N number of correlators are used to recreate the transmitted

subcarriers, each one correlating the incoming signal with the nth subcarrier frequency over

an OFDM symbol period as per (3.20). Fig. 3.13 is the representation of frequency response

of the bandpass signal at 2 GHz of the operating frequency.

𝑟𝑠 ( 𝑛) =1

√𝑇𝑢

∫ 𝑅𝑠 ( 𝑡) 𝑒𝑗∆𝜔𝑛𝑡𝑇𝑢

0

𝑑𝑡 (3.20)

The signal subjected to multipath effects and AWGN is down-converted to a baseband signal

at the receiver.

FIGURE 3.14 Frequency response of low pass filter

0 0.5 1 1.5 2 2.5 3 3.5 4

x 109

0

5

10

15

20

Frequency (Hz)Am

plitu

de

Frequency Response (FFT) of received signal at point 6

0 0.5 1 1.5 2 2.5 3 3.5-150

-100

-50

Frequency (GHz)

PSD(

dB/H

z

Frequency Response Welch PSD estimate of received signal at point 6

0 0.5 1 1.5 2 2.5 3 3.5 4

x 109

0

10

20

30

40

Frequency (Hz)

Ampli

tude


0 0.5 1 1.5 2 2.5 3 3.5-150

-100

-50

0

Frequency (GHz)

PSD(

dB/H

z

Frequency Response (PSD estimate) of received signal at point 7


43

From each block of the OFDM signal, the cyclic prefix is removed and it is correlated with

each subcarrier frequency. Fig. 3.14 is the representation of the response of the low pass

filter. Digital signal processing has been used to obtain the estimate of the transmitted

subcarriers by the OFDM receiver [95]. Sampling has been done of received signal using

Dirac impulse train and is represented by (3.21).

𝑟𝑠,𝑑 (𝑡) = ∑ 𝑦𝑠 (𝑛) 𝛿𝑐(𝑡 − 𝑛𝑇) (3.21)

𝑁−1

𝑛=0

T is the sample duration of the OFDM signal and is represented by equation (3.22).

𝑇 =𝑇𝑢

𝑁 (3.22)

FIGURE 3.15 Frequency response of sampler

Fig. 3.15 is the frequency response of the sampler. Now in order to demodulate the OFDM

signal FFT operation has been performed as given in (3.23).

𝐺𝑛 = {∑ 𝑟𝑠

𝑁−1

𝑛=0

[𝑛] 𝑒−𝑗𝛥𝜔𝑛𝑡, 0 ≤ 𝑡 ≤ 𝑇𝑢

0 otherwise

(3.23)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

x 108

0

0.5

1

1.5

Frequency (Hz)

Am

plit

ude


0 20 40 60 80 100 120 140 160 180-120

-100

-80

-60

-40

Frequency (MHz)

PS

D(d

B/H

z)

Welch PSD Estimate of received signal at point 8


44

FIGURE 3.16 Scatterplot of 4-QAM signal constellation

The constellation of 4 QAM baseband signal is obtained by the QAM demodulator and

shown in Fig. 3.16.

3.3 Peak to Average Power Ratio of Multicarrier OFDM Signal

Peak to average power ratio is the measure of the fluctuations in the envelope of OFDM

multicarrier signals. For the given sample {xn} the average power is represented by (3.24).

Pav = 1

Fs∑ xm

2

Fs−1

n=0

(3.24)

Whereas (3.25) is the representation of the peak power for the OFDM signal [95].

Ppeak = {xm2

mmax } (3.25)

It is defined as the ratio of peak power to average power of the complex passband discrete

time signal which is given by (3.26).

PAPR = Ppeak

Pav (3.26)

Sometimes, PAPR is also expressed in terms of crest factor (CF) and given by (3.27).

CF = √PAPR (3.27)

If the number of subcarriers is large, Gaussian distribution can be used to represent the

approximation of the baseband OFDM signal. Cumulative distribution function (CDF) is used

to find out the probability that the received signal zmax has an amplitude less than the

threshold value z and for N number of subcarriers, it is represented by (3.28).

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

Real axis

Imag

inary

axis

QAM Constellation at point 10

Peak to Average Power Ratio of Multicarrier OFDM Signal

45

Fzmax (z) = P (zmax ≤ 𝑧)

= P (z0 ≤ 𝑧) . P (z1 ≤ 𝑧) … … . P (zN−1 ≤ 𝑧) = (1 − e−z2)

N (3.28)

Whereas, (3.29) is the representation of the cumulative distribution function

Fzmax (z) = P (zN ≤ 𝑧) = ∫ f{zN (u)}z

−∞du, n = 0,1,2, … … . N − 1 (3.29)

In order to find out the PAPR of the OFDM signal complementary cumulative distribution

function (CCDF) is used to find out the probability that the PAPR exceeds a particular value

z, as given in (3.30).

F̃zmax (z) = P (zmax > 𝑧) = 1 − P (zmax ≤ z)

= 1 − Fzmax (z) = 1 − (1 − e−z2)

N (3.30)

FIGURE 3.17 PAPR of the original OFDM system with QPSK modulation

Peak to average power ratio for a different number of subcarriers of the OFDM signal has

been calculated for QPSK and 4 QAM baseband modulated signal and has been shown in

Figs. 3.17 and 3.18 respectively.

At 10−3 of CCDF, PAPR for QPSK baseband modulated signal are 10.5, 10.7, 10.9, 11.2 and

11.4 dB for N = 64, 128, 256, 512 and 1024 respectively. Similarly, for 4 QAM modulation,

these values are 11.5, 11.7, 12.0, 12.2, and 12.6 dB respectively. It is evident from figures

3.17 and 3.18 that value of PAPR increases with increase in the number of subcarriers and 4

QAM modulation has approximately 1.0 dB higher PAPR than that of QPSK modulation

format.

7 8 9 10 11 12 13 1410

-3

10-2

10-1

100

OFDM system with QPSK Baseband Modulation N-point FFT

PAPR [dB]

CC

DF

N= 256

N= 528

N= 1024

N= 64N= 128


46

FIGURE 3.18 PAPR of the original OFDM system with 4 QAM modulation

3.4 Linearization of Power Amplifier

With the application of OFDM power amplifier, nonlinearities become more vulnerable owing to

their high PAPR caused due to the large fluctuations in their signal envelope [96]. There are

different techniques for power amplifier linearization as nonlinearity introduces many

undesirable characteristics in the system which appear in the form of harmonic distortion,

gain compression, intermodulation distortion, phase distortion, adjacent channel

interference, etc. Linearization of the power amplifier is implemented for improving

linearity while maintaining high efficiency [97]. One of the simplest technique to reduce the

effect of nonlinearity of the power amplifiers is to operate it in the power back-off mode.

The power back-off mode technique results in lower efficiency. It also results in oversized

amplifier and has been found unsuitable for most of the practical applications. In order to

operate power amplifiers in its linear region, the input signals are attenuated and said to be

in power back-off mode. This operation is restricted to the system with low power efficiency

applications. In this input power back-off (IPBO) and output power back-off (OPBO) are

measured which are defined by (3.31) and (3.32) as given below.

𝐼𝑃𝐵𝑂 = 10 𝑙𝑜𝑔10

𝑃𝑖,𝑠𝑎𝑡

𝑃𝑖 (3.31)

and

𝑂𝑃𝐵𝑂 = 10 𝑙𝑜𝑔10

𝑃𝑜,𝑠𝑎𝑡

𝑃𝑜 (3.32)

7 8 9 10 11 12 13 1410

-3

10-2

10-1

100

OFDM system with QAM Baseband Modulation N-point FFT

PAPR [dB]

CC

DF

N= 64N= 128

N= 256

N= 512

N= 1024


47

Where, 𝑃𝑖,𝑠𝑎𝑡 and 𝑃𝑜,𝑠𝑎𝑡 are the input and output saturation powers and 𝑃𝑖 and 𝑃𝑜 are the

average power of the input and output signals. Generally, either OPBO or IPBO is used to

specify the power amplifier operating point. In order to quantify how much output power

the amplifier generates compared with the maximal available power, OPBO is used.

3.5 Power Amplifier Linearization Techniques

There are three different linearization techniques, such as feedback, feedforward, and

predistortion which are used to improve the linearity of power amplifiers. Feedback

technique is simple to implement but results in lowest efficiency. Feedforward technique is

used for wide bandwidths applications in multicarrier systems where feedback technique is

impractical. It gives improvements in distortion from 20 to 40 dB with 10-15% lower

efficiency. This technique also costs more due to the use of couplers, delay lines, error power

amplifier, etc. The predistortion technique does not use these RF components and improves

linearity with higher efficiency [98].

3.5.1 Feedback Technique

Feedback linearization is the simplest to implement and it can be applied either directly to

the RF amplifier or indirectly to the modulation. There are different feedback linearization

techniques such as envelope feedback, polar-loop feedback, and Cartesian loop feedback.

900

900

LOCALOSC.

Attentuator

Linearized Output

IINPUT

QINPUT

+

+

_

_

QOUTPUT

IOUTPUT

I-Q MODULATOR

I-Q DEMODULATOR

POWER AMPLIFIER

FIGURE 3.19 Block diagram of Cartesian loop feedback


48

In this technique, a portion of the output signal from the amplifier is fed back and subtracted

from the input signal. It reduces intermodulation distortions (IMD) but works best at the

low-frequency signal level and has poor performance at a higher frequency [99]. The block

diagram of the feedback loop is depicted in Fig. 3.19 and its simulation parameter is shown

in Table 3.2.

Power Amplifier Linearization with Feedback for 4 QAM, N = 1024

FIGURE 3.20 Simulation of feedback loop using AWR software

The overall gain, G of the amplifier with actual gain A and feedback factor β is represented

by (3.33).

DLY_SMPID=A9DLY=DelayIVAL=0

1

2

3

DIFFID=A12Y=0

TPID=WithFeedback

ATTENID=S4LOSS=15.8 dB

0

+90

1 2

3

QHYB_12ID=S3K=-23 dBKTYP=CouplingPHSBAL=0 DegLOSS=0 dBPHSTYP=0 deg/90 degVSWR=1.0NOISE=RF Budget onlyZ=_Z0 Ohm

PHASEID=A11SHFT=-90 Deg

LIN_SID=S5NET="Filter_Bandpass"INPORT={1}OUTPORT={2}NOISE=RF Budget only

LIN_SID=S1NET="Filter_Lowpass"INPORT={1}OUTPORT={2}NOISE=RF Budget only

AMP_BID=A1GAIN=35 dBP1DB=40 dBmIP3=50 dBmIP2=40 dBmMEASREF= OPSAT= NF=3 dBNOISE=RF Budget onlyRFIFRQ=

IN OUT

LO

MIXER_BID=A2MODE=SUMLOMULT=1FCOUT= RFIFRQ= GCONV=3-6 dBP1DB=30 dBmIP3=40 dBmLO2OUT=-130 dBIN2OUT=-130 dBLO2IN=-25 dBOUT2IN=-25 dBPLO=10 dBmPLOUSE=Spur reference onlyPIN=-10 dBmPINUSE=IN2OUTH OnlyNF=6 dBNOISE=RF Budget only

INOUT

LO

MIXER_BID=A6MODE=DIFFLOMULT=1FCOUT= RFIFRQ= GCONV=-3 dBP1DB=30 dBmIP3=40 dBmLO2OUT=-130 dBIN2OUT=-130 dBLO2IN=-25 dBOUT2IN=-25 dBPLO=10 dBmPLOUSE=Spur reference onlyPIN=-10 dBmPINUSE=IN2OUTH OnlyNF=6 dBNOISE=RF Budget only

TONEID=A3FRQ=2000 MHzPWR=10 dBmPHS=0 DegCTRFRQ= SMPFRQ= ZS=_Z0 OhmTN=_TAMB DegKNOISE=AutoPNMASK= PNOISE=No phase noise

RND_DID=A5M=2RATE=

QAM_MAPID=A4M=4SIGCNS= SCALE=

OFDM_MODID=A7OUTLVL=0OLVLTYP=No ScalingNC=1024CS= GI=1/8CTRFRQ=0 MHz


49

𝐺 = 𝐴

1+𝐴𝛽 (3.33)

The actual RF signal, 𝑋(𝑡) is given by (3.34).

𝑋(𝑡) = 𝐼(𝑡) 𝑐𝑜𝑠𝜔𝑐 𝑡 + 𝑄(𝑡) 𝑠𝑖𝑛𝜔𝑐 𝑡 (3.34)

TABLE 3.2 Simulation Parameter for Feedback Technique

Class of Amplifier Class B Power Amplifier

Power Amplifier Model Solid State Power Amplifier

Gain 35 dB

Noise Factor 3 dB

Operating frequency 2 GHz

3 dB Bandwidth 10 MHz

Modulation 64 QAM, OFDM

No of subcarriers 1024

Where, 𝜔𝑐 is the carrier frequency. Among different feedback linearization techniques,

Cartesian loop provides symmetry of gain and bandwidth in the two quadrature signal

processing path. The performance of feedback linearization technique has been simulated

using student evaluation copy of visual system simulator of National Instrument’s AWR

version 12.0 commercial software. The center frequency taken for simulation is 2 GHz. Fig.

3.20 depicts the simulation diagram of a feedback loop using visual system simulator of

National Instrument’s AWR software. Fig. 3.21 shows its performance in terms of power

spectral density.

FIGURE 3.21 Simulation result of feedback loop

1970 1980 1990 2000 2010 2020 2030

Frequency (MHz)

Power Spectrum

-90

-70

-50

-30

-10

10

30

Ampl

itude

(dBm

)

Without Feedback (dBm)

Without Feedback

With Feedback (dBm)

Cartesian Feedback


50

It can be deduced from Table 3.3 that with the application of feedback technique 5 dBm

reduction in amplitude and 30 dB reduction in ACPR has been achieved.

TABLE 3.3 Simulation Result of Feedback Technique

Parameters Without Feedback

With Feedback

Reduction

Amplitude

(dBm)

25 20 -5

ACPR

(dB)

0 -30 -30

3.5.2 Feedforward Technique

The feedforward technique is a very old method of linearization, dating back to 1928. The

feedforward linearization is used more in base stations and provides good linearization

performance [100]. This technique is mostly stable because there is no feedback path. In

this, the nonlinear distortions are corrected at the output level whereas it was done at input

level in feedback systems. In this technique, a highly linear and more power-inefficient error

amplifier is required and at the same time, precise analog RF-components are required [101].

The highly precise analog components are required in order to maintain accuracy over,

loading, time, and temperature. Figure 3.22 shows the block diagram of feedforward

technique.

Power devider

Error Amplifier

Main Amplifier

Delay Unit

Delay Unit

Input

_

+

Output

Combiner

Coupler Coupler

FIGURE 3.22 Block diagram of feedforward loop


51

For two carrier signal, input voltage, 𝑥𝑖𝑛 is given as in (3.35).

𝑥𝑖𝑛 = 𝑥 𝑐𝑜𝑠𝜔1 𝑡 + 𝑥 𝑐𝑜𝑠𝜔2 𝑡 (3.35)

Applying this input voltage to an amplifier with third-degree distortion, we get (3.36).

𝑥𝑜𝑢𝑡 = 𝑏1 𝑥𝑖𝑛 + 𝑏3 𝑥3𝑖𝑛 (3.36)

It gives output as in (3.37).

𝑥𝑜𝑢𝑡 = 𝑏1(𝑥 𝑐𝑜𝑠𝜔1 𝑡 + 𝑥 𝑐𝑜𝑠𝜔2 𝑡) + 𝑏3 (𝑥 𝑐𝑜𝑠𝜔1 𝑡 + 𝑥 𝑐𝑜𝑠𝜔2 𝑡 )3 (3.37)

From (3.37), the amplitude of two fundamental frequency components at 𝜔1 and 𝜔2 are

given as in (3.38).

𝑥𝑜, 𝜔1 , 𝜔2 = 𝑏1𝑥 + 𝑏3 9

4 𝑥3 (3.38)

The amplitude of third order intermodulation products is given in (3.39).

𝑥0, 2𝜔1− 𝜔2 ,2 𝜔2− 𝜔1 = 𝑏3

3

4 𝑥3

(3.39)

Now, the power amplifier output can be expressed as in (3.40).

𝑥0 = (𝑏1𝑥 + 𝑏3 9

4 𝑥3) 𝑐𝑜𝑠𝜔1 + (𝑏1𝑥 + 𝑏3

9

4 𝑥3) 𝑐𝑜𝑠𝜔2

+ 𝑏3 3

4 𝑥3 cos(2𝜔1−𝜔2) + 𝑏3

3

4 𝑥3 cos(2𝜔2−𝜔1) (3.40)

The input to error amplifier with sampling factor α is given by (3.41).

𝑥𝑒 = {(1 −𝑏1

𝛼) 𝑥 +

1

𝛼 𝑏3

3

4 𝑥3} 𝑐𝑜𝑠𝜔1𝑡 +{(1 −

𝑏1

𝛼) 𝑥

+1

𝛼

3

4 𝑏3 𝑥

3} 𝑐𝑜𝑠𝜔2𝑡- 1

𝛼

9

4 𝑥3 cos(2𝜔1−𝜔2) −

1

𝛼

9

4 𝑥3 cos(2𝜔2−𝜔1) (3.41)


52

FIGURE 3.23 Simulation of feedforward loop using AWR software

It is to be noted that the fundamental components are canceled out by suitably setting the

sampling factor α. Fig. 3.23 shows the simulation diagram of feedforward for 64 QAM

OFDM modulation technique with 1024 number of subcarriers.


PHASEID=A4SHFT=90 Deg


0

+90

1 2

3

QHYB_12ID=S2K=-33.035412 dBKTYP=CouplingPHSBAL=0 DegLOSS=-0.5 dBPHSTYP=0 deg/90 degVSWR=1.0NOISE=RF Budget onlyZ=_Z0 Ohm0

+90

1 2

3

QHYB_12ID=S3K=-10 dBKTYP=CouplingPHSBAL=0 DegLOSS=-0 dBPHSTYP=0 deg/90 degVSWR=1.0NOISE=RF Budget onlyZ=_Z0 Ohm

0

+90

1

2

3

QHYB_21ID=S4K=-10 dBKTYP=CouplingPHSBAL=0 DegLOSS=0 dBPHSTYP=0 deg/90 degVSWR=1.0NOISE=RF Budget onlyZ=_Z0 Ohm

RND_DID=A6M=2RATE=

TPID=Mod_Signal

SRC MEAS

VSAID=M1VARNAME=""VALUES=0

TPID=Error

SRC MEAS


TPID=With_Correction

SRC MEAS


TPID=Error_correction

TPID=Without_Correction


AMP_BID=A8GAIN=42.67 dBP1DB=55 dBmIP3=62 dBmIP2=100 dBmMEASREF= OPSAT= NF=3 dBNOISE=RF Budget onlyRFIFRQ=


1

2

3

COMBINERID=S1LOSS= SIGTYP=VoltageNIN=2CTRFRQ= PRIMINP=1ISOL=30 dBNOISE=Auto


OFDM_MODID=A2OUTLVL=0OLVLTYP=No ScalingNC=1024CS= GI=1/8CTRFRQ=0 GHz

Error Signal

Main Signal

Power Amplifier Linearization with Feed Forward for 4 QAM, N = 1024


53

TABLE 3.4 Simulation Parameter for Feedforward Technique



Gain Main Amplifier 1 15 dB

Gain Main Amplifier 2 11 dB

Gain Error Amplifier 42.67 dB

Noise Factor 3 dB


3 dB Bandwidth 1.2 GHz



The simulation has been carried out with visual system simulator of National Instrument’s

AWR student evaluation version 12.0 commercial software and the simulation parameters

are shown in Table 3.4.

FIGURE 3.24 Simulation result of feedforward loop

The simulation results using feedforward loop of the output of power amplifier and error

amplifier are depicted in Figs. 3.24 and 3.25 respectively. It can be observed that at 2 GHz

of operating frequency performance of the power amplifier using feedforward loop has been

improved compared to feedback technique.

0 1 2 3 4

Frequency (GHz)

Without and With Error Correction

-90

-70

-50

-30

-10

10

20

Am

plit

ud

e (

dB

m)

With Correction (dBm)

Without Correction (dBm)

Modulated Signal (dBm)


54

FIGURE 3.25 Simulation result of error amplifier

Fig. 3.26 shows the AM to AM characterization of the main amplifier with and without

feedforward correction.

FIGURE 3.26 Simulation result of AM to AM of the main amplifier

Similarly, Fig. 3.27 shows the AM to AM characterization of pre-amplifier with and without

feedforward correction.

0 1 2 3 4

Frequency (GHz)

Output of Error Amplifier

-120

-100

-80

-60

-40

Am

plitu

de (

dBm

)

Power Spectrum (dBm)

Feed Forward Correction

-20 0 20 40 60

Power (dBm)

AM to AM of Main Amplifier

-20

0

20

40

60

70

Am

plit

ude (

dB

m)

AM TO AM_PS (dBm)

Amplifier Characterization

AM TO AM _INST (dBm)



55

FIGURE 3.27 Simulation result of AM to AM of preamplifier

From Table 3.5 it can be observed that it gives 20 dBm reductions in amplitude because of

losses in the passive RF components with 25 dB reduction in ACPR.

TABLE 3.5 Simulation Result of Feedforward Technique

Parameters Without Feedforward With Feedforward Reduction

Amplitude

(dBm)

0 -20 -20

ACPR

(dB)

-60 -85 -25

3.5.3 Digital Predistortion Technique

The digital predistortion technique is one of the most efficient linearization technique in

which nonlinear element is inserted before the RF power amplifier in order to make the

power amplifier response linear [102, 103]. In the digital predistortion technique, the digital

signal processing is used to introduce predistortion in the digital data wherein only the data

symbols are distorted, not the transmit signal after transmit filtering and the pulse-shaping

is performed after the predistortion stage [104, 105].

The concept of predistortion technique is shown in Fig. 3.28.

-34 -24 -14 -4 6 16 26 34

Power (dBm)

AM TO AM of Pre Amplifier

-20

0

20

40

50

Am

plit

ud

e (

dB

m)

AM TO AM_ PS (dBm)

Amplifier Characterization

AM TO AM _INST (dBm)



56

+ =

Vin

VoutVout

Vin Vin

Vout

Predistortion Nonlinear distortionLinear Responce

FIGURE 3.28 Concept of predistortion

For the power amplifier having input voltage 𝑥𝑝 which is also the output of the predistorter,

its characteristics is represented as in (3.42).

𝑥𝑜 = 𝑏1 𝑥𝑝 + 𝑏3 𝑥3𝑝 (3.42)

The predistorter has the characteristics given by (3.43).

𝑥𝑝 = 𝑏1 𝑥𝑖𝑛 + 𝑏3 𝑥3𝑖𝑛 (3.43)

The power amplifier output including predistorter input signal 𝑥𝑖𝑛, is represented by (3.44).

𝑥𝑜 = 𝑏1 (𝑏1 𝑥𝑖𝑛 + 𝑏3 𝑥3𝑖𝑛) + 𝑏3(𝑏1 𝑥𝑖𝑛 + 𝑏3 𝑥3

𝑖𝑛)3 (3.44)

Which can be further expanded to as in (3.45).

𝑥𝑜 = 𝑏1𝑐1 𝑥𝑖𝑛 + (𝑏1𝑐3 + 𝑏3𝑐2) 𝑥2𝑖𝑛)

+ 3𝑏3 𝑐12𝑐2𝑥5

𝑖𝑛 + 3𝑏3 𝑐3

2𝑐1𝑥7𝑖𝑛

+ 𝑏3 𝑐33𝑥9

𝑖𝑛 (3.45)

Now, if we design the predistorter carefully as given in (3.46).

𝑐3 = − 𝑏3𝑐1

𝑏1 (3.46)

The third-degree distortion exhibited by the power amplifier can be eliminated, but it also

introduces some additional distortions extending up to the ninth degree. In order to cancel

this additional distortion, it has to generate some higher degree components [106].


57

DPD DAC

ESTIMATION OFCOEFICIENT

ADC

PA

Xin(n) Yout (t)

Ai

Xdpd (n)

Y(n)

Xrf(t)

Power Amplifier linearization with adaptive Digital Pre- Distortion

FIGURE 3.29 Block diagram of adaptive digital predistortion

Fig. 3.29 shows the block diagram of power amplifier digital adaptive predistortion

technique with input signal 𝑥𝑖𝑛(𝑛). It comprises of DPD module, DAC and power amplifier

(PA) all connected in series. A portion of the output signal is taken for estimation of

coefficient. Equation (3.47) is representation of the baseband signal.

𝑥𝐷𝑃𝐷(𝑛) = 𝑥𝑖𝑛(𝑛) + ∑ 𝑎𝑖𝑁𝑖=0 . 𝛽𝑖 (𝑛) (3.47)

Where 𝛽𝑖 (𝑛) are basis waveforms of nonlinear functions of 𝑥𝑖𝑛(𝑛), 𝑎𝑖 are complex DPD

coefficients and N is the number of basis waveforms used for DPD modeling [107]. The gain

polynomial of a basis waveform set is given by (3.48).

𝛽𝑖 (𝑛) = [𝑥(𝑛 − 𝑟)]𝑞−1. x(n) (3.48)

Here index i is the function of a polynomial of order q and memory offset r. The basis set is

written as a vector given in (3.49).

𝛼(𝑛) = [𝛽1 (𝑛) … … … … . . 𝛽𝑁 (𝑛)] (3.49)

The error in the DPD coefficients denoted by Δ𝑎𝑖 is estimated by minimizing as in (3.50).

𝑆𝐷𝑃𝐷 = ∑ ⎹ 𝐹{φ(𝑛)} − ∑ Δ𝑎𝑖 . 𝐹{𝛽𝑖 (𝑛)}⎹ 𝑁𝑖=0

2𝑛 (3.50)

Here F{ }is a linear filter as given in (3.51).

φ(n) = 𝐾𝑜−1𝑦(𝑛) − 𝑥(𝑛) (3.51)

Where, 𝐾𝑜 is the nominal gain.


58

The digital filter F{ } is designed to attenuate the allocated channel having input signal x(n).

In other words F{x(n)} ≈ 0. It is done in order to remove the biases in the least mean square

(LMS) estimate of Δ𝑎𝑖 which are present owing to modeled in-band errors. In the case of

adaptive DPD the coefficients 𝑎𝑖 are adjusted in order to minimize the residual distortions

in the output signal [108]. The sample of input signal with buffer size N is given by (3.52).

x = [𝑥(1) … … . . 𝑥(𝑁)]𝑇 (3.52)

The samples of the output signal with buffer size N is given by (3.53).

y = [𝑦(1) … … . . 𝑦(𝑁)]𝑇 (3.53)

The given basis set used by estimator is filtered by F{ }, which is denoted by (3.54).

𝛼𝐹 (𝑛) = [𝐹{𝛽1 (𝑛)} … … … . . 𝐹{𝛽𝑁 (𝑛)} ] (3.54)

If we assume that

𝑃𝐹 = 𝑀[𝛼𝐹 𝐶 (𝑛). 𝛼𝐹 (𝑛)] ≈

1

𝑁 ∑ 𝛼𝐹

𝐶 (𝑛).𝑁𝑛=1 𝛼𝐹 (𝑛) (3.55)

𝛼 𝐹 = 𝑀[𝛼𝐹 𝐶 (𝑛). 𝐹{𝜑(𝑛)}] ≈

1

𝑁 ∑ 𝛼𝐹

𝐶 (𝑛).𝑁𝑛=1 𝐹{𝜑(𝑛)} (3.56)

FIGURE 3.30 Simulation diagram of digital predistortion using AWR software

Fig. 3.30 shows the simulation diagram of digital predistortion using visual system simulator

of National Instrument’s AWR software for 4 QAM OFDM signal having 1024 number of

subcarriers. In (3.55) and (3.56), M[ ] is the mean value and ( )𝐶 is the conjugate transpose.

TPID=PA_onlyTP

ID=Source

TPID=PA+DPD

NL_SID=S6NET="AMP 2000"TOptimizeVariable=



TPID=PA+DPD_FxP

TPID=DPD

TPID=DPD_FxP

RND_DID=A1M=2RATE=


OFDM_MODID=A2OUTLVL=0OLVLTYP=No ScalingNC=1024CS= GI=1/8CTRFRQ=0 MHz

SUBCKTID=S5NET="LUT DPD"

SUBCKTID=S3NET="LUT DPD FxP"SigBW=12LUTBW=12

Power Amplifier only

Power Amplifier with DPD

Power Amplifier Linearization with Digital Pre-Distortion for 4 QAM, N = 1024

Power Amplifier with fixed-point DPD


59

The least mean square of the DPD coefficient error is given by (3.57). Table 3.6 depicts the

simulation parameters for digital predistortion technique.

𝛥𝑎 = 𝑅𝐹 . 𝜃 𝐹 (3.57)

Where, 𝛥𝑎 = [𝛥𝛼1 … … … 𝛥𝛼𝑁 ]𝑇 𝑎𝑛𝑑 𝑅𝐹 = 𝑃𝐹

−1. Now the updated DPD coefficients

are given by (3.58).

𝑎 (𝑡𝑓+1 ) = 𝑎 (𝑡𝑓) − 𝜎𝐷𝑃𝐷 . 𝛥𝑎 (3.58)

TABLE 3.6 Simulation Parameter for Digital Predistortion Technique



Gain Main Amplifier 15 dB

Noise Factor 3 dB


3 dB Bandwidth 10 MHz



As previously mentioned, 𝑎 = [𝛼1 … . . 𝛼𝑁 ]𝑇 , where 𝑡𝑓 indicates iteration number and

𝜎𝐷𝑃𝐷 < 1. In order to reduce distortions in the output, capturing of data, estimating

coefficients offsets and updating the coefficients are repeated.

FIGURE 3.31 Power amplifier AM to AM characteristics

-50 -40 -30 -20 -10 0 10 15

Input Power (dBm)

Power Amplifier AM to AM Characteristics

-50

-35

-20

-5

10

15

Out

put P

ower

(dBm

)

PA (dBm)

PA with DPD (dBm)


60

The AM to AM characteristics of the PA amplifier using DPD technique is shown in Fig.

3.31. Its corresponding AM to PM characteristics is depicted in Fig. 3.32.

FIGURE 3.32 Power amplifier AM to PM characteristics

Similarly, Fig. 3.33 shows the power spectral density of power amplifier at 2 GHz of the

operating frequency. It can be deduced from the figure that DPD has the highest efficiency

compared to feedback and feedforward technique.

FIGURE 3.33 Power amplifier power spectra using DPD

-50 -35 -20 -5 10 20

Input Power (dBm)

Power Amplifier AM to PM Characteristics

-180

-140

-100

-60

-20

20

60

100

140

180

Out

put P

hase

(D

eg)

Power Amplifier (Deg)

Power Amplifier with DPD (Deg)

1970 1980 1990 2000 2010 2020 2030

Frequency (MHz)

Power Amplifier Power Spectra at 2 GHz

-125

-100

-75

-50

-25

Am

plitu

de (d

Bm

)

Signal Source (dBm)

PA Output (dBm)

PA with DPD Output (dBm)

PA with DPD (FxP) (dBm)

Results and Discussion

61

TABLE 3.7 Simulation Result of Digital Predistortion Technique

Parameters Signal

Source

PA Output

Without DPD

PA Output

With DPD

PA Output with Fix

Point DPD

Reduction

Amplitude

(dBm)

-44 -24 -24 -24 0

ACPR

(dB)

--- -52 - 72 - 72 -20

The performance of digital predistortion technique is shown in Table 3.7 which indicates

that it has the highest efficiency without degradation of signal amplitude as there is 0 dBm

reduction in amplitude with 20 dB reduction in adjacent channel power ratio.

3.5.4 Comparative Performance of Power Amplifier Linearization Techniques

Table 3.8 gives the comparative performance of power amplifier linearization techniques.

From the table, it is evident that the performance of digital predistortion technique exhibits

better performance in terms of efficiency compared to other techniques as there is no

reduction in amplitude (0 dBm) and 20 dB reduction in ACPR with 3dB bandwidth of 10

MHz.

TABLE 3.8 Comparative Result of Power Amplifier Linearization Techniques

Parameters/

Linearization

Techniques

Feedback Feedforward Digital predistortion

Without

Feedback

With

Feed

back

Redu

ction

Without

Feed

Forward

With

Feed

Forward

Redu

ction

Without

DPD

With

DPD

Reduction

Amplitude

(dBm) 25 20 -5 0 -20 -20

-24 -24 0

ACPR

(dB) 0 -30 -30 -60 -85 -25

-52 - 72 -20

3.6 Results and Discussion

It has been observed that although OFDM system exhibits many advantages such as flat

fading frequency response and high data rate transmission capability it suffers from high

PAPR. Mathematical modeling and Matlab simulation has been carried out for the OFDM

transmitter and receiver for two different basebands modulated signal, QPSK, and 4 QAM.

It has been observed that for the case of QPSK baseband signal at 10−3 of CCDF, PAPR

are 10.5, 10.7, 10.9, 11.2 and 11.4 dB for N = 64, 128, 256, 512 and 1024 respectively.


62

Similarly for 4 QAM signal, these values are 11.5, 11.7, 12.0, 12.2, and 12.6 dB respectively.

It has been observed that PAPR increases with increase in the number of subcarriers and 4

QAM modulated signal has approximately 1.0 dB higher PAPR than that of QPSK

modulation format. It has also been observed that with the application of multicarrier OFDM

communication system power amplifier nonlinearities become more vulnerable owing to

their high PAPR. Linearization of power amplifiers is implemented for improving linearity

at the same time maintaining high efficiency. Among the three linearization techniques

investigated, feedback technique is simple to implement but results in lowest efficiency and

is not suitable at higher frequency. For the parameters used for simulation, it has resulted in

5 dBm reductions in amplitude and 30 dB reduction in ACPR at 10 MHz operating

bandwidth. Feedforward technique is used for wide bandwidths applications in multicarrier

systems where feedback technique is impractical. When simulated it has resulted in 20 dBm

reductions in amplitude with 25 dB reduction in ACPR but has a wide 1.2 GHz operating

bandwidth. This technique is also least preferred due to the high-cost of passive RF

components like couplers, delay lines, error power amplifier, etc. It has been observed that

the digital predistortion technique does not use these RF components and improves linearity

with higher efficiency. In this technique, the reduction in amplitude has been 0 dBm with 20

dB reduction in ACPR at 10 MHz of bandwidth.

63

CHAPTER 4

PAPR Reduction of Multicarrier OFDM

Communication Systems

4.1 Introduction

Multicarrier OFDM is one of the spectral efficient communication systems which promises

to deliver high data rate transmission apart from possessing other advantages. At the same

time, it has one of the major disadvantage of having high peak to average power ratio

(PAPR). The high PAPR drives microwave power amplifiers to operate in the nonlinear

region which produces inband distortions and out of band spectral regrowth. To improve the

quality of inband signal and reduce leakage of energy in the adjacent channel its PAPR has

to be reduced to a permissible value. There are many efficient PAPR reduction techniques

available in the literature and each has got its own merits and limitations. None of them are

useful for universal application and the careful decision has to be made for use of an

individual technique for the particular application [109-111]. In the present research work

clipping and filtering, selective mapping method (SLM), partial transmit sequence (PTS)

and single carrier frequency division multiple access (SCFDMA) / discrete Fourier

transform (DFT) spread technique have been investigated [112, 113]. Clipping and filtering

technique have been first investigated using mathematical modeling and Matlab simulations.

The PAPR obtained with Matlab simulations have been verified with National Instrument’s

AWR visual system simulator software simulations. The PAPR obtained have been further

verified by its FPGA implementation using Xilinx Spartan 3 Protoboard XC 3S 400

development board [114]. Selective mapping method is an efficient PAPR reduction

technique which has been analyzed using mathematical modeling and Matlab simulations

and the results obtained have been further verified with the hardware cosimulation using

Xilinx Spartan 3 Protoboard XC 3S 400 development board [115]. Partial transmit sequence

and SCFDMA have been analyzed using mathematical modeling and Matlab simulations.

Comparative study of the above mentioned four PAPR reduction techniques have been

studied with the same parameters and it has been observed that among the four techniques

PAPR Reduction of Multicarrier OFDM Communication Systems

64

discussed SCFDMA has lowest PAPR in its interleaved frequency division multiple access

(IFDMA) modes of operation [116]. On the other hand, clipping and filtering method is

simplest from an application point of view but gives distortions and spectral regrowth [117].

The effect of raised cosine pulse shaping filter has also been investigated in order to reduce

the out-of-band signal energy of SCFDMA system. From the result obtained it can be

observed that effect of pulse shaping is more on interleaved frequency division multiple

access (IFDMA) than that on localized frequency division multiple access (LFDMA)

techniques [118].

4.2 Clipping and Filtering Method

Clipping and filtering is one of the simplest PAPR reduction technique in which the passband

signal is passed through a clipper and then through a low-pass filter. Clipping operation

reduces PAPR depending upon the clipping ratio of the clipper but introduces distortions

because of which its BER gets increased. When the clipped signal is passed through a filter

its BER decreases but the filtering operation also increases its PAPR value. A trade-off has

to be made between PAPR and BER value desired and this can be achieved with repeated/

iterative clipping and filtering operations. The bandpass filter is required to reduce the out of

band radiation for oversampled signal but for a band limited signal sampled at Nyquist rate

a low pass filter is sufficient as all the distortions lie within the given band [119]. Filtering

operation can be performed both in time and frequency domain and for the over-sampled

signal clipping and frequency domain filtering is depicted in Fig. 4.1. To reduce peak

regrowth caused by filtering recursive/ iterative clipping and filtering technique has been used

[120, 121].

FIGURE 4.1 Clipping and filtering with oversampling factor

Clipping and Filtering Method

65

The signal received from serial to parallel converter has been oversampled to L-times by

increasing the length of IFFT. The signal x’ [m] generated from the IFFT is up-converted to

the desired transmission frequency fc by passband modulation to get xp [m]. The passband

signal is then passed through a clipper circuit whose clipping threshold is set at a particular

value A. the output of the clipper, xcP[m] is passed through a bandpass filter before being

transmitted as X′ [t]. xcP[m] is the clipped version of signal xp [m] and is given by (4.1)

where A is the threshold level of the clipper.

xcP[m] = {

−A xp [m] ≤ − A

xp [m] ⃒xp [m]⃒ < 𝐴

A xp [m] ≥ A

(4.1)

PAPR mainly depends upon the clipping ratio (CR) which is defined as the clipping threshold

level A, normalized by the RMS value σ of OFDM signal and is represented by (4.2).

CR = A

σ (4.2)

4.2.1 PAPR of Clipped and Filtered Signal with Matlab

Mathematical modeling and Matlab simulations have been performed on the multicarrier

OFDM passband signal using clipping and filtering operation [122]. The CCDF of PAPR of

the clipped signal has been plotted in Fig. 4.2 for 4 QAM signal with 1024 number of

subcarriers at 2 GHz of the operating frequency. At 10−2 of CCDF with a clipping ratio of

0.8, 1.0, 1.2, 1.4 and 1.6 the PAPR values of the clipped signal are 4.6, 5.0, 5.5, 5.9 and 6.5

dB respectively. It is to be noted that the PAPR depends upon the clipping ratio and its value

increases with increase in the value of the clipping ratio. Significant reduction in PAPR of

8.0 dB has been obtained at 0.8 clipping ratio with the clipping operation as the corresponding

value of original unclipped OFDM signal has been found to be 12.6 dB in chapter 3. The

price paid for this significant reduction in PAPR is an increase in its BER value [123].

When the clipped signal is passed through the filter circuit its PAPR gets increased with a

decrease in BER and spectral growth which is depicted in Fig. 4.3. The obtained PAPR for

the same parameters as mentioned above are 10.7, 11.0, 11.2, 11.4 and 11.7 dB with a clipping

ratio of 0.8, 1.0, 1.2, 1.4 and 1.6 respectively.


66

FIGURE 4.2 PAPR of clipped signals

Here the reduction in PAPR is 1.9 dB at 0.8 clipping ratio for the case of 4 QAM signal with

1024 number of subcarriers.

FIGURE 4.3 PAPR of clipped and filtered signal

The comparative value of PAPR of clipped and filtered signal with Matlab for different

number of subcarriers and the clipping ratio is shown in Table 4.1. It can be observed from

the table that PAPR increases with increase in the value of clipping ratio and the number of

subcarriers.

2 2.5 3 3.5 4 4.5 5 5.5 6 6.510

-2

10-1

100

PAPR (dB)

CD

F

PAPR OF CLIPPED SIGNAL; N= 1024

CR = 0.8

CR = 1.0

CR = 1.2

CR = 1.4

CR = 1.6

2 3 4 5 6 7 8 9 10 11 1210

-2

10-1

100

PAPR (dB)

CC

DF

PAPR OF CLIPPED AND FILTERED SIGNAL; N= 1024

CR= 0.8

CR= 1.0

CR= 1.2

CR= 1.4

CR= 1.6


67

TABLE 4.1 Comparative Value of PAPR of Clipped and Filtered Signal with Matlab

No of carriers (N) /

Clipping Ratio

(CR)

CR = 0.8

(dB)

CR = 1.0

(dB)

CR = 1.2

(dB)

CR = 1.4

(dB)

CR = 1.6

(dB)

64 7.2 7.7 8.0 8.2 8.5

128 8.4 8.8 9.1 9.2 9.6

256 9.1 9.5 9.8 10.0 10.4

512

9.9 10.3 10.5 10.8 11.2

1024 10.7 11.0 11.2 11.4 11.7

4.2.2 Bit Error Rate Performance of Clipped and Filtered Signal with Matlab

The BER performance for unclipped, clipped only, and clipped and filtered signal are shown

in Figs. 4.4, 4.5 and 4.6 respectively. It can be observed from Fig. 4.4 that the BER value for

an unclipped signal at 10 dB of Eb/ No is 0.0007.

FIGURE 4.4 BER performance of unclipped signal

Similarly Fig. 4.5 depicts the BER performance of clipped signal which once again depends

upon the value of clipping ratio (CR). At 10 dB of signal to noise power ratio, the BER values

are 0.041, 0.027, 0.019, 0.010 and 0.007 at CR value of 0.8, 1.0, 1.2, 1.4 and 1.6 respectively.

It is to be pointed out that as the value of clipping ratio increases its BER also increases. The

cause of the increase in the BER value is due to distortions caused during the process of

clipping operation [124, 125].

0 1 2 3 4 5 6 7 8 9 1010

-4

10-3

10-2

10-1

100

Eb / No (dB)

BE

R

BER OF UNCLIPPED 4 QAM OFDM SIGNAL, N= 1024


68

FIGURE 4.5 BER performance of clipped signal

Fig. 4.6 shows the BER performance of clipped and filtered signal for 4 QAM signal with

1024 number of subcarriers. The value of BER decreases when the signal is passed through

the filter circuit and it can be observed from the figure that at 10 dB of Eb/No the BER values

of clipped and filtered signal are 0.019, 0.013, 0.007, 0.005 and 0.003 with CR value of 0.8,

1.0, 1.2, 1.4 and 1.6 respectively. It has been observed that there is an improvement in BER

performance when the signal is passed through filter circuit.

FIGURE 4.6 BER performance with clipped and filtered signal

0 1 2 3 4 5 6 7 8 9 1010

-3

10-2

10-1

100

Eb / No (dB)

BE

R

BER OF CLIPPED AND FILTERED 4 QAM OFDM SIGNAL, N= 1024

CR = 0.8

CR = 1.0

CR = 1.2

CR = 1.4

CR = 1.6

0 1 2 3 4 5 6 7 8 9 1010

-3

10-2

10-1

100

Eb / No (dB)

BE

R

BER OF CLIPPED 4 QAM OFDM SIGNAL, N= 1024

CR = 0.8

CR = 1.0

CR = 1.2

CR = 1.4

CR = 1.6


69

4.2.3 PAPR of Clipped and Filtered Signal with AWR Software

In order to validate the result obtained with Matlab simulations the PAPR of 4 QAM OFDM

signal with 1024 number of subcarriers have also been obtained through student evaluation

license of National Instrument’s AWR visual system simulator software version 12. The NI’S

AWR design environment is a portfolio of software products which are used to design,

develop and realize microwave / RF components, circuits, and systems including monolithic

microwave integrated circuits, RF printed circuit boards, microwave modules, RF integrated

circuits, communication systems, radar systems, antennas, etc. The simulation diagram of

PAPR reduction using National Instrument’s AWR visual system simulator commercial

software is shown in Fig. 4.7.

FIGURE 4.7 Simulation diagram of PAPR reduction using AWR software

It can be observed from Fig. 4.8 that at CCDF of 10−5 the PAPR value obtained for the only

clipped signal is 4.2 dB which further increases to 10.6 dB after passing through the filter

circuit. When compared with the result obtained with Matlab simulations there is a decrease

in PAPR value of 0.4 dB with clipped signal and 0.1 dB for the clipped and filtered signal

when simulated with AWR software.

OFDM_MODID=A3OUTLVL=20OLVLTYP=Avg. Total Power (dBm)NC=1024CS=0.0003125 GHzGI=.125FCO=-32CTRFRQ=2 GHzOVRSMP=8


RND_DID=A1M=2RATE=

TPID=TP1

TPID=TP2 TP

ID=TP3LPFBID=F1LOSS=0 dBN=3FP=2 GHzNOISE=Auto

1 2

SUBCKTID=S1NET="Clipping"CLIPPING=80LPF_ORDER=6LPF_FP=2 GHz


70

FIGURE 4.8 Simulation result of PAPR using AWR software

4.2.4 BER Performance of Clipped and Filtered Signal with AWR Software

The simulation block diagram for the bit error rate performance using visual system

simulator of National Instrument’s AWR software for 4 QAM OFDM signal with 1024

number of subcarriers is shown in Fig. 4.9.

FIGURE 4.9 Simulation diagram of BER using AWR software

0 2 4 6 8 10 12 14 16

PAPR (dB)

CCDF 4 QAM, 1024 OFDM, Clipped & Filtered _AWR

1e-005

.0001

.001

.01

.1

1

CC

DF

PRE-CLIPPED & POST-FILTERED

CLIPPED ONLY

OFDM_MODID=A3OUTLVL=20OLVLTYP=Avg. Total Power (dBm)NC=1024CS=0.0003125 GHzGI=.125FCO=-32CTRFRQ=2 GHzOVRSMP=8


RND_DID=A1M=2RATE=

TPID=ID1

BER

BERID=BER1VARNAME=""VALUES= OUTFL=""

Xo Xn. . .

SWPVARID=SWP1VARNAME="ID1"VALUES=swpstp(,,)

Eb_N0 = sweep(stepped(0,10,1))


71

Fig. 4.10 shows the bit error rate simulation result of the OFDM system shown in Fig. 4.9.

It can be observed from the figure that the value of BER increases after clipping and filtering

operation is performed as compared with the original OFDM unclipped signal.

FIGURE 4.10 Simulation result of BER using AWR software

4.2.5 PAPR of Clipped and Filtered Signal with FPGA

In order to further validate the result of clipping and filtering technique obtained with Matlab

and NI’s AWR software simulations FPGA implementation using Xilinx Spartan 3

Protoboard XC 3S 400 board has been done. The parameters used are same as in the previous

case with 4 QAM signal and 1024 number of subcarriers. Clipping and filtering have been

investigated using two different approaches, first through pre-clipping and post-filtering and

second through pre-filtering and post-clipping technique [126]. The second approach, the

pre-filtering and post-clipping technique gives very low PAPR but is not used practically

because of its high BER value. Whereas the result obtained with pre-clipping and post-

filtering gives better BER performance with reasonable PAPR reductions.

4.2.6 PAPR of Pre-Clipped and Post-Filtered Signal with FPGA

Hardware cosimulation has been carried out using Xilinx Spartan 3 Protoboard XC 3S 400

development board for the case of the pre-clipped and post-filtered signal. Fig. 4.11 shows

its block diagram in which after the IDFT operation signal is first passed through a clipper

4 6 8 10 12 14 16

Eb/No (dB)

BER CURVE OF 4QAM OFDM USING AWR SOFTWARE

.001

.01

.1

1

BE

R

ORIGINAL OFDM SIGNAL

CLIPPED & FILTERED SIGNAL


72

and then to a low-pass filter circuit. The clipping level is set by the desired clipping ratio and

in this case, it is 0.8, 1.0, 1.2, 1.4 and 1.6.

FIGURE 4.11 Pre-clipping and post-filtering in time domain

The block diagram of system generator used for pre-clipping and post-filtering is shown in

Fig. 4.12. The main building block of the system generator are a Bernoulli binary generator,

a mapper for generation of 4 QAM baseband signal, S/P converter, a circuit for IFFT

operation, clipper circuit and finally the filter circuit. The filter circuit used is a finite impulse

response equi-ripple low pass filter.

FIGURE 4.12 Block diagram of pre-clipping and post-filtering


73

The internal block diagram of 4 QAM Mapper is shown in Fig. 4.13. Its output is a

constellation of 2-bit signal spaced in quadrature to each other. Then this signal is fed to the

serial to parallel converter which produces N number of parallel subcarriers.

FIGURE 4.13 Block diagram of 4 QAM mapper

N number of subcarriers are fed to the IFFT block for OFDM signal generation and the length

of the IFFT should be greater than or equal to the number of the subcarrier to prevent the

aliasing effect. In the case, over-sampling is done then additional zeros are padded in the

empty place. Fig. 4.14 shows the block diagram of IFFT.

FIGURE 4.14 Block diagram of IFFT


74

Similarly, Fig. 4.15 shows the block diagram of the clipper circuit and as stated the signals

have been clipped at different levels decided by the clipping ratio 0.8, 1.0, 1.2, 1.4 and 1.6.

FIGURE 4.15 Block diagram of clipper circuit

The block diagram of hardware cosimulator is shown in Fig. 4.16 to be used with Xilinx

Spartan 3 Protoboard XC 3S 400 development board for hardware cosimulation.

FIGURE 4.16 Block diagram of hardware cosimulator


75

Filter response of a 57 order low pass FIR equi ripple direct form-II structure is shown in

Fig. 4.17. Its operating parameters are 2 GHz passband, 5 GHz stopband, -1 dB passband

gain, -50 dB stopband gain and density factor, 20.

FIGURE 4.17 Low pass filter response

The system generator clip is shown in Fig. 4.18 which has been obtained after HDL netlist

compilation using above-stated development board.

FIGURE 4.18 System generator for pre-clipping and post-filtering


76

Fig. 4.19 shows the actual photograph of Xilinx Spartan 3 Protoboard XC 3S 400

development board.

FIGURE 4.19 Xilinx Spartan 3 Protoboard XC 3S 400 development board

The actual photograph of the hardware cosimulation is shown in Fig. 4.20 using a laptop,

Xilinx Spartan 3 Protoboard, and the connecting cable.

FIGURE 4.20 Hardware cosimulation on Xilinx Spartan 3 Protoboard


77

The PAPR obtained with FPGA implementation of 4 QAM baseband OFDM signal with

1024 number of subcarriers is depicted in Fig. 4.21 for the case of pre-clipping and post-

filtering technique.

FIGURE 4.21 PAPR value of pre-clipping and post-filtering with FPGA

The observed PAPR are 10.9, 11.2, 11.5, 11.8 and 12.1 dB with a clipping ratio of 0.8, 1.0,

1.2, 1.4 and 1.6 respectively. It is to mentioned that similar trend has been observed for the

case of FPGA implementation also, as PAPR increases with increase in the value of clipping

ratio. When compared with original unclipped OFDM signal there is 1.7 dB reduction in

PAPR with 0.8 value of the clipping ratio.

4.2.7 PAPR of Pre-Filtered and Post-Clipped Signal with FPGA

The block diagram of a pre-filtering and post-clipping method in time domain is shown Fig.

4.22.

IDFT Low Pass Filter ClipperData

FIGURE 4.22 Pre-filtering and post-clipping in time domain

5 6 7 8 9 10 11 12 1310

-3

10-2

10-1

100

PAPR Values Obtained after Pre-Clipping and Post-Filtering with FPGA Implementation

PAPR (dB)

CC

DF

CR = 0.8

CR = 1.0

CR = 1.2

CR = 1.4

CR = 1.6


78

Similarly Fig. 4.23 shows its FPGA implementation on Xilinx Spartan 3 Protoboard XC 3S

400 board. The baseband signal is 4 QAM with 1024 number of subcarriers with 0.8, 1.0,

1.2, 1.4 and 1.6 clipping ratio.

FIGURE 4.23 Block diagram of pre-filtering and post-clipping process

Fig. 4.24 depicts the PAPR values with different clipping ratio and the obtained PAPR are

2.2, 2.9, 3.6, 4.3 and 5.0 dB with 0.8, 1.0, 1.2, 1.4 and 1.6 clipping ratio respectively.

FIGURE 4.24 PAPR of pre-filtering and post-clipping with FPGA

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510

-3

10-2

10-1

100

PAPR Value obtained after Pre-Filtering and post-Clipping with FPGA Implementation

PAPR (dB)

CC

DF

CR = 0.8 CR = 1.0 CR = 1.2 CR = 1.4 CR = 1.6


79

It is interesting to note that PAPR obtained with the pre-filtering and post-clipping process

is significantly low but its BER value is quite high and this method is not used for practical

purposes.

4.2.8 Comparative Value of PAPR of Clipped and Filtered Signal

Fig. 4.25 gives the comparative value of PAPR of the clipped and filtered signal with

Matlab, NI’s AWR simulation, FPGA implementation and original unclipped OFDM signal.

At 10−3 of CCDF the PAPR obtained with FPGA implementation of the pre-filtered and

post-clipped signal is 2.2 dB. On the other hand, its corresponding value of the pre-clipped

and post-filtered signal is 10.9 dB with FPGA implementation. It is 10.6 dB with simulation

with NI’s AWR visual system simulator and 10.7 dB with Matlab simulations.

FIGURE 4.25 Comparative value of PAPR with different methods

The PAPR of original OFDM signal without clipping and filtering operation is 12.6 dB.

When compared with original OFDM signal PAPR with FPGA implementation of pre-

filtering and post-clipping reduces PAPR by 10.4 dB, whereas it is only 1.7 dB reduction

with FPGA implementation of pre-clipping and post-filtering. On the other hand, these

reductions are 2.0 and 1.9 dB with AWR and Matlab software simulations. Although pre-

filtering and post-clipping gives lowest PAPR but is not used practically because of worst

BER performance. On the other hand, a pre-clipping and post-filtering method is mostly

used for all practical purposes owing to its better BER performance.

0 2 4 6 8 10 12 1410

-3

10-2

10-1

100

Comparative PAPR of 4 QAM OFDM Signal with N= 1024 and 0.8 Clipping Ratio with

PAPR (dB)

CC

DF

Pre- Filtered and Post-Clipped with FPGA

Pre-Clipped and Post-Filtered with AWR

Pre-Clipped and Post-Filtered with Matlab

Pre-Clipped and Post-Filtered with FPGA

Original (Uncliiped and Unfiltered) OFDM Signal


80

4.3 Selective Mapping Method

SLM is an efficient technique for PAPR reduction. The 4 QAM baseband signal is converted

into N number of parallel subcarriers after passing through the serial to parallel converter.

Then each subcarrier is multiplied with a complex signal having different phase vector and

then its IFFT is taken. The PAPR is calculated for each phase vector and the one having

lowest PAPR is selected for transmission from the N available PAPR. In this way, a large

number of data vectors are generated in this process [127]. The information about the phase

vector which was responsible for producing minimum PAPR has to be transmitted to the

receiver as side information for detection of the signal. This additional information is an

overhead and marginally reduces the data transmission rate of the multicarrier OFDM

communication system [128].

The block diagram of SLM technique is depicted in Fig. 4.26. In this, the N number of

subcarriers are multiplied with N different phase vectors as shown in (4.3).

Input S/P

N- Point

FFT

N- Point

FFT

N- Point

FFT

X

X

X

Signal

with

min

PAPR

Q 1

Q N-1

M 0

M 1

M N-1

M[0]

M[1]

M[N-1]

Q o

M V 0

M V 1

M V N-1

W V 0

W V 1

W V N-1

W Minimum

Side Information

for transmission

FIGURE 4.26 Block diagram of Selected Mapping Method

Qv = [Q0v , Q1

v, … … QN−1v ]T (4.3)

Here, Qrv = e j θr

v and θr

v ∈ [0, 2π] for r = 0, 1, …….., N-1 and v = 1, 2,……N-1 and (4.4)

shows the modified data block produced from this process.

Selective Mapping Method

81

Mv = [Mv[0], Mv[1], … … . . Mv[N − 1]]T

(4.4)

As mentioned from the N data vectors, Wmin = WvN which has the lowest PAPR is selected

for transmission and represented by (4.5).

W = ( ⎸Wv [n] ⎸) n=0,1,…N−1

max

[v=1,2,…V]

arg min

(4.5)

Information about the phase vector which has produced minimum PAPR is selected and

transmitted to the receiver as side information. It requires N number of IFFT operation and

log2V bits of side information for each block of dataset [129].

4.3.1 PAPR of Selective Mapping Method with Matlab Simulation

In order to calculate PAPR with SLM technique mathematical modeling and Matlab

simulations have been performed for the case of 4 QAM signal with 1024 number of

subcarriers. Fig. 4.27 shows its PAPR with different number of phase vectors, V. At 10−2

value of CCDF the observed PAPR are 8.2, 8.4, 8.9, 9.7 and 10.6 dB with phase vectors, V

= 16, 8, 4, 2 and 1 respectively. Once again it is important to be noted that the PAPR is a

function of phase vector and decreases with increase in the number of phase vector.

FIGURE 4.27 PAPR of 4 QAM OFDM signal with SLM technique

PAPR for a different number of subcarriers with different phase vectors are depicted in Table

4.2 and it can be observed from the table that the PAPR increases with increase in the number

of subcarriers and decrease in the number of phase vectors.

4 5 6 7 8 9 10 11 1210

-2

10-1

100

PAPR (dB)

CC

DF

PAPR REDUCTION WITH SLM FOR N = 1024; 4 QAM

Phase vector = 4

Phase vector = 8

Phase vector = 16

Phase vector = 2

Phase vector = 1


82

TABLE 4.2 PAPR of Selective Mapping Method with Matlab

No of carriers (N) /

Phase vector (V)

V= 16

(dB)

V = 8

(dB)

V = 4

(dB)

V = 2

(dB)

V = 1

(dB)

64 5.8 6.3 7.5 8.1 9.3

128 6.4 7.0 8.1 8.4 9.7

256 7.1 7.5 8.5 8.9 10.1

512 7.6 8.1 8.8 9.2 10.3

1024 8.2 8.5 8.9 9.6 10.6

4.3.2 PAPR of Selective Mapping Method with FPGA

Fig. 4.28 shows the block diagram of a system generator using SLM technique for PAPR

reduction. The digital data is fed to the mapper which in turn generates 4 QAM signal. This

is converted into parallel form with the help of serial to parallel converter then after

multiplying with phase vectors IFFT is performed for each subcarrier. The block diagram of

4 QAM mapper and IFFT is depicted in Figs. 4.13 and 4.14 respectively. The real and

imaginary parts of the complex signal are separated and finally fed to the wave scope.

FIGURE 4.28 System generator for PAPR reduction using SLM technique

In the SLM technique the particular input data M[1] is multiplied by phase vectors, say 𝑄0 ,

𝑄1, 𝑄2 and 𝑄3.

Selective Mapping Method

83

FIGURE 4.29 Hardware cosimulator block diagram

For the given input data different PAPR is obtained with each phase factor and among

different PAPR obtained the minimum value is selected for transmission. Also, the phase

vector responsible for producing lowest PAPR is transmitted as side information to the

receiver. The hardware cosimulation is shown in Fig. 4.29 has been carried out using Xilinx

Spartan 3 Protoboard XC 3S 400 development board and Fig. 4.30 shows its corresponding

system generator status at the time of hardware cosimulation.

FIGURE 4.30 System generator of OFDM with SLM technique


84

For 4 QAM OFDM signal Table 4.3 gives the PAPR values obtained through hardware

implementation with four different phase vectors: Q0, Q1, Q2 and Q3 for 64, 128, 256, 512

and 1024 number of carriers.

TABLE 4.3 Value of PAPR of SLM with Different Methods

Phase vector / No of carriers N=64

(dB)

N=128

(dB)

N=256

(dB)

N=512

(dB)

N=1024

(dB)

𝑄0 11.3 11.5 8.9 9.7 10.8

𝑄1 9.4 10.9 11.6 11.2 12.1

𝑄2 7.8 10.9 9.6 10.9 9.8

𝑄3 9.1 8.4 11.0 9.2 11.5

Minimum PAPR with FPGA implementation 7.8 8.4 8.9 9.2 9.8

PAPR with Matlab simulation 7.5 8.1 8.5 8.8 8.9

PAPR without SLM (original OFDM signal) 11.5 11.7 12.0 12.2 12.6

As stated among four different PAPR obtained the minimum PAPR is selected for

transmission. The minimum PAPR obtained through FPGA implementation for the case of

64, 128, 256, 512 and 1024 number of subcarriers are 7.8, 8.4, 8.9, 9.2 and 9.8 dB

respectively. Whereas the PAPR obtained with Matlab simulations are 7.5, 8.1, 8.5, 8.8 and

8.9 dB, on the other hand, these values for original unclipped OFDM signals are 11.5, 11.7,

12.0, 12.2 and 12.6 dB for 64, 128, 256, 512 and 1024 number of subcarriers respectively.

4.3.3 Comparative Value of PAPR of SLM with Different Techniques

FIGURE 4.31 Comparative value of PAPR

4 5 6 7 8 9 10 11 12 13 1410

-3

10-2

10-1

100 COMPARATIVE PAPR OF SLM TECHNIQUE WITH FPGA IMPLEMENTATION OF 4 QAM OFDM SIGNAL; N= 1024

PAPR (dB)

CC

DF

PAPR of OFDM Signal (without SLM)

PAPR with FPGAImplementation

PAPR with

Matlab simulation

Partial Transmit Sequence

85

Fig. 4.31 shows the comparative value of PAPR with Matlab simulation, FPGA

implementation and original unclipped OFDM signal for the case of 4 QAM signal with

1024 number of subcarriers. It can be observed from the table that 3.7 dB reduction in PAPR

has been achieved with Matlab simulations whereas it is 2.8 dB with FPGA implementation.

A similar trend as observed in Matlab simulations have been obtained for the PAPR with

FPGA implementation, i.e. PAPR increases with increase in the number of subcarriers and

decrease in the number of phase vectors.

4.4 Partial Transmit Sequence

The partial transmit sequence (PTS) is a computationally inefficient technique for PAPR

reduction of multicarrier OFDM communication systems. It requires less number of IFFT

operations than that of SLM technique. The block diagram of PTS technique is shown in

Fig. 4.32 and from the figure it can be observed that the input data after serial to parallel

conversion is partitioned into M disjoint subblocks as represented by (4.6).

FIGURE 4.32 Block diagram of PTS for PAPR reduction


86

x = [x0 , x1, x2 , x3 , … … . . xM ]T (4.6)

Where, xi is the ith subblock and all subblocks are consecutively located and are of equal

size. In the PTS technique scrambling is applied to each subblock unlike the SLM technique

wherein scrambling is applied to all the subcarriers [130, 131].

Here the partitioned subblock is multiplied by a corresponding complex phase vector bn=

ejbn before taking its IFFT to yield (4.7) where, n =1, 2, …N.

x = IFFT{∑ bnNn=1 Xn} = ∑ bn. IFFT {v

v=1 Xn } = ∑ bnNn=1 xn (4.7)

In the above equation xn is known as partial transmit sequence (PTS) and its phase vector

is chosen such that the PAPR is minimized. Equation (4.8) is the time domain signal with

the lowest PAPR vector.

s′ = ∑ b−n

v

v=1

xn (4.8)

The phase vector {bm}N−1N is selected such that it reduces the search complexity. M number

of IFFT operations are required for each data block in the PTS technique and the length of

side information is [ log2Xn]. There are many factors on which the reduction of PAPR

depends and important among them are method of subblock partitioning, the number of

subblocks and number of phase vectors, etc. [132].

M-1

m

m

m

S(0)

S(1)

S(2)

Interleaved Method

FIGURE 4.33 Interleaved Method

Partial Transmit Sequence

87

In order to divide N number of subcarriers into M disjoint subbands, subblock partitioning

is done. Adjacent, interleaved and pseudo-random methods are generally used for the

subblock partitioning [133]. Fig. 4.33 shows the interleaved method of subblock partitioning

in which every subband signals spaced at the interval of N apart is allocated to the same

subband.

Adjacent MethodM-1 m

m

m

S(0)

S(1)

S(2)

FIGURE 4.34 Adjacent Method

In the adjacent method as shown in Fig. 4.34, N/M successive subbands are sequentially

allotted to the same subblock. Whereas, in the pseudo-random method of subblock

partitioning as shown in Fig. 4.35 any subband signal is randomly assigned into any one of

the subblocks. Among the three methods discussed, the pseudo-random method provides the

best PAPR performance [134, 135].

m

m

mM-1

S(0)

S(1)

S(2)

Pseudo- random

Method

FIGURE 4.35 Pseudo- random Method


88

It is to be noted that the number of IFFT operations have been reduced in the PTS technique

as it requires only one IFFT operation for each subblock [136, 137]. The number of complex

multiplication required for PTS technique are Nmultiplication =M

2log2 M and the number of

addition required are Naddition = M log2 M, where M is the number of subbands. It is clear

from the above discussion that the PTS technique has less computational complexity than

that of SLM technique at the cost of a marginal increase in PAPR [138].

4.4.1 PAPR of Partial Transmit Sequence using Matlab

Mathematical modeling and Matlab simulations have been carried out in order to investigate

the PAPR reduction using PTS technique in which pseudo–random method of block

partitioning has been used. Different subcarriers and subblocks have used to analyze the

PAPR performance of 4 QAM signal with 8000 number of blocks. As shown in Fig. 4.36,

with 1024 number of subcarriers and at 10−2 of CCDF with the number of subblocks, M =

16, 8, 4, 2 and 1 the value of PAPR obtained are 8.3, 8.6, 9.1, 9.8 and 10.6 dB respectively.

As usual, the PAPR increases with the decrease in the number of sub-blocks and increase in

the number of subcarriers.

FIGURE 4.36 PAPR reduction with PTS for 4 QAM signal

4 5 6 7 8 9 10 1110

-2

10-1

100

PAPR [dB]

CC

DF

PAPR REDUCTION WITH PTS FOR N=1024; 4 QAM

No of subblocks= 16

No of subblocks= 8

No of subblocks= 4

No of subblocks= 2

No of subblocks= 1

Single Carrier Frequency Division Multiple Access Technique

89

4.4.2 Comparative Value of PAPR of Partial Transmit Sequence using Matlab

Table 4.4 shows the comparative performance of PAPR for partial transmit sequence using

Matlab simulations for 4 QAM baseband signal with 64, 128, 256, 512 and 1024 number of

subcarriers and number of subblocks, M = 16, 8, 4, 2 and 1.

TABLE 4.4 PAPR Value with PTS Technique

No. of Sub- carrier

(N)

M= 16 (dB) M= 8 (dB) M= 4 (dB) M= 2 (dB) M= 1 (dB)

64 6.0 6.6 7.5 8.3 9.3

128 6.7 7.3 7.9 8.8 9.6

256 7.3 7.8 8.3 9.2 10.0

512 7.6 8.1 8.5 9.4 10.4

1024 8.3 8.6 9.1 9.8 10.6

For the case of 16 number of subblocks and 1024 subcarriers, the observed PAPR is 8.3 dB

which is 4.3 dB less than the corresponding PAPR of original OFDM signal and the PAPR

increases with increase in the number of subcarriers and decrease in the number of subblocks.

4.5 Single Carrier Frequency Division Multiple Access Technique

The single carrier frequency division multiple access (SCFDMA) is also known as discrete

Fourier transform (DFT) spread technique has been recommended by third generation

partnership project (3GPP) to be used for long-term evolution (LTE) and LTE advanced

(LTE-A). It uses orthogonal frequency division multiple access (OFDMA) for downlink

and SCFDMA for the uplink transmission [139, 140]. SCFDMA has many advantages over

OFDMA system as it has low BER, high throughput, high spectral efficiency and the lowest

PAPR. Because of the lowest PAPR, its power requirement is considerably low and is

suitable for mobile applications [141]. In SCFDMA system all symbols are present in all

subcarriers hence it allows frequency selectivity of the channel. It has one of the major

disadvantages of noise enhancement because of the fact that when DFT despreading is done

at the receiver noise is spread over the entire subcarriers [142, 143].

4.5.1 SCFDMA Transceiver Systems

Fig. 4.37 shows the transceiver of SCFDMA system in which two additional blocks have

been added in the transmitter and receiver to look it different from the OFDM transceiver.


90

In the transmitter DFT and subcarrier mapping block and in the receiver IDFT and subcarrier

mapping block have been added in the SCFDMA system. Hence both DFT spreading and

despreading is performed in the transmitter as well as in the receiver. Now if the length of

DFT and IDFT are same, it cancels each other and SCFDMA system virtually looks like a

single carrier system. It will have PAPR in the transmitter equivalent to a single carrier

system [144, 145].

FIGURE 4.37 Block diagram of SCFDMA system

The equivalent circuit model of SCDMA is shown in Fig. 4.38 which resembles its

appearance as a single carrier system instead of multiple carrier systems.

FIGURE 4.38 Equivalence of OFDMA systems with SCFDMA

Contrary to a conventional OFDMA system, wherein subcarriers are partitioned and

assigned to multiple mobile users, in the SCFDMA technique each user uses a subset of


91

subcarriers to transmit its own data and the particular subcarrier which is not used for the

data transmission is filled with zero [146, 147].

FIGURE 4.39 Subcarrier assignments to multiple users

Fig. 4.39 methods of mapping subcarriers to multiple users. Two different approaches of

assigning subcarriers are used among users, distributed FDMA (DFDMA) and localized

FDMA (LFDMA). L number of DFT outputs are distributed over the entire band of total M

subcarriers in the distributed mode of subcarrier mapping and zeros are filled in the

remaining L-M unused subcarriers. Whereas in the LFDMA, L number of DFT outputs are

allocated to consecutive subcarriers and the remaining L-M unused subcarriers are filled

with zeros. There is another way of subcarrier mapping known as interleaved FDMA

(IFDMA) in which distribution of DFT outputs are done uniformly with equal distance

[148].

Input data 𝑆′[𝑘] is DFT-spread to generate 𝑋𝑘 signals in the frequency domain as given in

(4.9).

𝑋𝑘 = ∑ 𝑆′[𝑘]𝑒−𝑗2𝛱𝑚𝑘/𝑀

𝑁−1

𝑘=0

(4.9)

These are allocated in the transmitter as depicted in (4.10).


92

𝑆′[𝑘] = {𝑆 [𝑘

𝑋] , 𝑘 = 𝑋. 𝑙1, 𝑙1 = 0,1,2,3 … … , 𝑙 − 1

0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (4.10)

Equation (4.11) shows the output of the IFFT sequence s’[m] with m = L . x + l for x

= 0, 1, 2, ………. , X-1 and l = 0, 1, 2, ………. , L-1.

𝑠′[𝑚] = 1

𝑋 ∑ 𝑆[𝑙]

𝐿−1

𝑙=0

𝑒−𝑗2𝛱𝑚𝑙/𝑀 (4.11)

Equation (4.11) is the repetition of the input signal s[l] which has been scaled by 1= X in the

time domain. But in the IFDMA system where the subcarrier mapping starts with the rth

subcarrier (r = 0, 1, 2, …X-1), the DFT-spread symbol is expressed as in (4.12).

𝑆′[𝑘] = {𝑆 [𝑘 − 𝑟

𝑋] , 𝑘 = 𝑋. 𝑙1 + 𝑟, 𝑙1 = 0,1,2, , 𝑙 − 1

0 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (4.12)

Equation (4.13) gives the corresponding IFFT output sequence.

𝑠[𝑚] = 1

𝑋 . 𝑒

𝑗2𝛱𝑚

𝑀𝑟 . 𝑆[𝑙] (4.13)

It is evident from these equations that the frequency shift in the subcarrier allocation with

the starting point of r subcarriers gives a phase rotation of 𝑒 𝑗2𝛱𝑚

𝑀𝑟 in IFDMA mapping. But

in the case of LFDMA mapping, the IFFT of the input signal 𝑆′[𝑘] at the transmitter is

expressed as in (4.14).

𝑆′[𝑘] = {𝑆[𝑘], 𝑘 = 0,1,2, … … , 𝐿 − 10 , 𝑘 = 𝐿, 𝐿 + 1, … … , 𝑀 − 1

(4.14)

Equation (4.15) shows the IFFT sequence 𝑠′[𝑚]with m= X.l + x for x = 0,1,2,….X-1.

𝑠′[𝑚] = 1

𝑋

1

𝐿 ∑ 𝑆[𝑘]𝑒

{𝑗2𝛱 (𝑋𝑙+𝑥)

𝑋𝐿 𝑘}

𝑀−1

𝑘=0

(4.15)

In the case of x= 0, (4.15) is now represented as in (4.16).

𝑠′[𝑚] = 1

𝑋 𝑠[𝑙] (4.16)

But when x ≠ 0, it is represented as in (4.17).


93

𝑆[𝑘] = ∑ 𝑆[𝑝]𝑒−𝑗2𝛱 𝑝𝐿

𝑘

𝐿−1

𝑝=0

(4.17)

Then (4.15) changes and is represented by (4.18).

s’[m] = 1

𝑋 𝑒𝑗𝛱

(𝐿−1)𝑥−𝑋𝑙

𝑋𝐿 . ∑

sin(𝛱𝑥

𝑋)

𝐿 sin(𝛱. 𝑋𝑙+𝑥

𝑋𝐿− 𝛱

𝑝

𝐿 )

𝐿−1𝑝=0 . (𝑒𝑗𝛱

𝑝

𝐿 𝑠[𝑝]) (4.18)

It can be observed from (4.16) and (4.18), that the time-domain LFDMA signal becomes the

1/X-scaled copies of the input sequence at the multiples of X. By adding all the input

sequences with the different complex-weight factor other values are calculated.

4.5.2 PAPR of 4 QAM SCFDMA Signal

Mathematical modeling and Matlab simulations of (4.18) have been done in order to obtain

the PAPR of 4 QAM signal for the case of SCFDMA signal. Fig. 4.40 shows the PAPR

performance with IFDMA, LFDMA, and OFDMA subcarrier mappings and its PAPR value

are 0.40, 6.90 and 10.50 dB for IFDMA, LFDMA, and OFDMA respectively. The PAPR

obtained with IFDMA subcarrier mapping is the lowest value obtained from any other PAPR

reduction techniques.

FIGURE 4.40 PAPR of IFDMA, LFDMA, and OFDMA for 4 QAM

0 2 4 6 8 10 1210

-2

10-1

100

PAPR OF DFT SPREAD SIGNAL; N =1024; 4 QAM

PAPR [dB]

CC

DF

OFDMA

LFDMA

IFDMA


94


The PAPR performance for the case of 16 QAM SCFDMA techniques is shown in Fig. 4.41

and it can be observed from the figure that at 10−2 of CCDF value the PAPR for IFDMA,

LFDMA, and OFDMA are 3.45, 7.80 and 10.55 dB respectively.



Similarly, for 64-QAM signal the corresponding values are found to be 4.55, 7.90 and 10.60

dB respectively for carrier mapping using IFDMA, LFDMA, and OFDMA methods

respectively as shown in Fig. 4.42.


0 2 4 6 8 10 1210

-2

10-1

100

PAPR[dB]

CC

DF

PAPR OF DFT SPREAD SIGNAL; N= 1024; 16 QAM

OFDMA

LFDMA

IFDMA

0 2 4 6 8 10 1210

-2

10-1

100

PAPR[dB]

CC

DF

PAPR OF DFT SPREAD SIGNAL; N= 1024; 64 QAM

OFDMA

LFDMA

IFDMA

Comparative Performance of all PAPR Reduction Techniques

95

4.5.5 Comparative value of PAPR for SCFDMA Signal

Table 4.5 indicates the comparative values of PAPR for SCFDMA signals for 4 QAM, 16

QAM and 64 QAM modulation format with the number of subcarriers, N=64, 128, 256, 512

and 1024 with IFDMA, LFDMA, and OFDMA carrier mapping at 10−2 of CCDF value. It

is clearly indicated that PAPR is lowest for IFDMA and highest for OFDMA and its PAPR

performance varies with modulation format and subcarrier allocation method. It is to be

noted that increase in the PAPR for LFDMA and IFDMA is considerable when number of

subcarrier is changing from 64 to 128, and thereafter with increase in the number of

subcarriers subsequent increase in the PAPR is very small. Whereas in the case of OFDMA

these variations are quite significant when the number of subcarriers are increased.

TABLE 4.5 PAPR Value of SCFDMA Signal

Mod Type SCFDMA

Mapping

PAPR

with

N=64

(dB)

PAPR

with

N=128

(dB)

PAPR with

N=256

(dB)

PAPR

with

N=512

(dB)

PAPR

with

N=1024

(dB)

4 QAM OFDMA 9.20 9.60 10.10 10.20 10.50

LFDMA 0.00 6.60 6.70 6.85 6.90

IFDMA 0.00 0.00 0.00 0.00 0.40

16 QAM OFDMA 9.30 9.70 10.18 10.25 10.55

LFDMA 3.30 7.65 7.70 7.74 7.80

IFDMA 3.30 3.35 3.38 3.42 3.45

64 QAM OFDMA 9.35 9.72 10.24 10.30 10.60

LFDMA 4.40 7.75 7.80 7.85 7.90

IFDMA 4.40 4.43 4.48 4.50 4.55

4.6 Comparative Performance of all PAPR Reduction Techniques

Fig. 4.43 depicts the comparative performance of all the four PAPR reduction techniques

discussed above for 4 QAM modulation format with 1024 number of subcarriers. The

observed PAPR values at 10−2 of CCDF with IFDMA technique is the lowest value of 0.4

dB, clipped signal with clipping ratio of 0.8 has 4.6 dB, LFDMA has its corresponding value

of 6.9 dB, SLM with 16 number of phase vectors has 8.2 dB, partial transmit sequence with

16 number of sub-blocks has 8.3 dB PAPR, OFDMA has its PAPR value of 10.5 dB, clipped

and filtered signal with clipping ratio of 0.8 has 10.7 dB and unclipped signal has PAPR

value of 12.6 dB. There has been a considerable reduction in PAPR of 12.2, 4.4, 4.3 and 1.9


96

dB with IFDMA, SLM, PTS and CF techniques respectively. It is to be emphasized that

IFDMA gives the lowest PAPR of 0.4 dB obtained so far in the literature at the cost of

marginal implementation complexity. On the other hand clipping and filtering method is one

of the simplest PAPR reduction technique from an implementation point of view but results

in spectral regrowth and degradation in BER performance.

FIGURE 4.43 Comparative value of PAPR with different reduction techniques

Selective mapping method has better performance than partial transmit sequence at the cost

of marginal computational complexity. All the PAPR reduction techniques discussed in this

work cannot be used for all applications and the use of particular reduction technique

depends upon the nature of the application and the system complexity involved.

4.7 Pulse Shaping Filter Technique

Pulse shaping is a linear filtering operation used to reduce the out-of-band signal energy, is

performed in the transmitter through convolution between the modulated subcarriers and the

filter's impulse response [149, 150]. Equation (4.19) is the representation of the response of

the baseband pulse amplitude modulation (PAM).

p(t) = ∑ an

∞

n=−∞

h(t − nT) (4.19)

Here, p(t) is output response, an is the transmitted symbol, the impulse response of the filter

is h(t) and T is the symbol period. It is to be noted that the impulse response of the filter has

to be selected in such a way that it should have zero inter-symbol-interference and should

have minimum bandwidth occupancy [151].

0 2 4 6 8 10 12 1410

-2

10-1

100

PAPR (dB)

CC

DF

COMPARATIVE VALUE OF PAPR; N = 1024, 4QAM SIGNAL

LFDMASLM

PTS

OFDMA

CLIPPED & FILTERED

UNCLIPPED SIGNAL

IFDMACLIPPED

ONLY

Pulse Shaping Filter Technique

97

As per the Nyquist criteria sampling of the waveform has to be done in such a way that zero

crossings occur at the multiples of symbol interval T, so that that the symbols can be

recovered correctly. Equation (4.20) represents the waveform sampled at the interval T.

p(kT) = ∑ an

∞

n=−∞

h(kT − nT) (4.20)

Equation (4.20) can be broken down in following two parts as shown in equation (4.21).

p(kT) = h(0)an + ∑ an

∞

n≠k

h(kT − nT) (4.21)

The second term in the equation (4.21) should be zero in order to have zero intersymbol

interference. For distortionless transmission as per the Nyquist first criteria, the impulse

response, h(t) of the filter is given by (4.22).

h(nT) = {1; n = 00; n = ±1, ±2, …

(4.22)

Here, T is the symbol period and the Nyquist pulse in the time domain is given by (4.23).

P (t) = sinc (t

T)

cosπαt/T

1 − 4α2t2/αT2 (4.23)

Where, sinc function sinc (t

T) is defined by (4.24).

sinc(x) ≅ (sin(πx))/(πx) (4.24)

Equation (4.25) gives the frequency domain representation of (4.23).

1

T∑ H (f +

k

T

∞

k= −∞

) = 1 (4.25)

The roll- off factor, α is used to determine the excess bandwidth of Nyquist ISI-free pulse

and value of α lies between 0 and 1.

The comparative response of the rectangular and sinc shaped pulse shaping filter is shown

in Fig. 4.44 which indicates that the sinc shaped filter does not have a band-limited response

in the frequency domain. With the increase in the value of roll-off factor, its bandwidth also


98

increases. When observed in time domain its wave shape is quite smooth and amplitude of

tail of the main lobe decreases with increase in the value of roll-off factor.

FIGURE 4.44 Response of rectangular and sinc shaped pulse shaping filter

This is one of the main reason of low PAPR with a large roll-off factor. Whereas in the case

of rectangular pulses there are more distortions at its edges compared to that there is

distortionless transmission by the sinc shaped pulses.

FIGURE 4.45 Raised cosine pulse shaping filter response in time domain

Figs. 4.45 and 4.46 show the time domain and frequency domain responses of the sinc

shaped pulse respectively with different roll-off factors.

-3 -2 -1 0 1 2 3-40

-30

-20

-10

0

10

20

Frequency, Hz

Po

we

r S

pec

tral

Den

sit

y

Rectangular and Sinc shaped Pulse Shaping Filter Response

Recatangular Pulse

Sinc shaped Pulse

-4 -3 -2 -1 0 1 2 3 4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

Am

plitu

de

Raised Cosine Pulse Shaping filter response in time domain

Roll - off Factor = 0.0




99

FIGURE 4.46 Raised cosine pulse shaping filter response in frequency domain

Fig. 4.44 shows that the amplitude of sidelobes (tails) decreases with increase in the value

of roll-off factor and this is the main cause of the decrease in PAPR but this decrease in

PAPR is obtained at the cost of a marginal increase in the bandwidth as depicted in Fig. 4.46.

FIGURE 4.47 Eye diagram with 0.5 roll-off factor

The eye diagram of the raised cosine filter with roll-off factor 0.5 and 1.0 are shown in

Figs. 4.47 and 4.48 respectively. It can be observed from the figure that when the value of

roll-off factor is 1.0, its eye is more open and it is less open with 0.5 roll-off factor. The

effect of ISI is less in the eye diagram with a value of roll-off factor being 1.0 than with that

of 0.5.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

1

2

3

4

5

6

7

8

9

10

Frequency

Am

pli

tu

de

Raised Cosine Pulse Shaping filter response in frequency domain

Roll off Factor = 0.0



0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1.5

-1

-0.5

0

0.5

1

1.5Eye Diagram with Roll-off Factor = 0.5

Time

Am

plitu

de


100

FIGURE 4.48 Eye diagram with 1.0 roll-off factor

Another important point to be noted that the raised cosine filters decays at a slower rate and

has a smaller amplitude of sidelobes with 1.0 roll-off factor than that with 0.5 roll-off factor.

It can be concluded that apart from low PAPR effect of intersymbol interference is low when

the value of the roll-off factor is high which has been obtained at the cost of a marginal

increase in bandwidth.

4.7.1 PAPR of SCFDMA Signal using Raised Cosine Pulse Shaping Filter

Equation (4.26) represents the even frequency spectrum of the raised cosine Nyquist pulse

with a roll-off factor, α.

S(f) = {

T; 0 ≤ f < 𝐵(1 − α)T

2 {1 + cos (

π

2Bα (f − B(1 − α)))} ; B(1 − α) ≤ f ≤ B(1 + α)

0; B(1 + α) < 𝑓

(4.26)

TABLE 4.6 Parameters used for Simulation

No of Subcarriers 1024

FFT Size 2048

Spreading Factor 2

No of Blocks for Iteration 5000

Oversampling factor 8

Roll-off factors of RC filter for pulse shaping 0.0, 0.3, 0.6, 0.9

Baseband modulation 4 QAM, 16 QAM, 64 QAM

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-1

-0.5

0

0.5

1

Eye Diagram with Roll - off factor = 1.0

Time

Am

pli

tu

de


101

Parameters used for the mathematical modeling and Matlab simulations for PAPR reduction

of the SCFDMA signal using raised cosine pulse shaping filter is shown in Table 4.6.

FIGURE 4.49 Effect of pulse shaping filter for 4 QAM signal

Effect of raised cosine pulse shaping filter on 4 QAM baseband modulated IFDMA and

LFDMA signal with 1024 number of the subcarrier is shown in Fig. 4.49. It can be observed

from the figure that at 10−2 of CCDF and 0.9 roll-off factor PAPR of IFDMA and LFDMA

signals are 2.4 and 7.7 dB respectively. When the value of the roll-off factor is reduced to

0.0, the PAPR value gets increased to 7.2 and 8.7 dB for IFDMA and LFDMA respectively.


Fig. 4.50 shows the result obtained for 16 QAM baseband signal with 1024 number of

subcarriers. For the case of IFDMA the PAPR obtained is 4.7 dB and for LFDMA it is 8.7

dB with 0.9 roll-off factor and PAPR increases with a decrease in value of the roll-off factor.

0 1 2 3 4 5 6 7 8 9 1010

-2

10-1

100

PAPR [dB] for 4-QAM

CC

DF

4-QAM CCDF of IFDMA/LFDMA, No. of Subcarriers = 1024, FFT Size = 2048 with Pulse shaping RC filter

IFDMA with no pulse shaping

LFDMA with no pulse shaping

IFDMA with a=0.0

LFDMA with a=0.9

IFDMA with a=0.3

LFDMA with a=0.6

IFDMA with a=0.6

LFDMA with a=0.3

IFDMA with a=0.9

LFDMA with a=0.0

LFDMAIFDMA

0 1 2 3 4 5 6 7 8 9 1010

-2

10-1

100

PAPR [dB] for 16-QAM

CC

DF




IFDMA with a=0.0

LFDMA with a=0.9

IFDMA with a=0.3

LFDMA with a=0.6

IFDMA with a=0.6

LFDMA with a=0.3

IFDMA with a=0.9

LFDMA with a=0.0

LFDMAIFDMA


102


Similar observations have been obtained in Fig. 4.51 for the case of 64 QAM signals with

1024 number of subcarriers. The corresponding PAPR with 0.9 roll-off factor are 5.7 and

8.9 dB for IFDMA and LFDMA respectively. Further, from the above figures it can be

concluded that the effect of pulse shaping is more on IFDMA than that on LFDMA and

PAPR decreases with increase in the value of roll-off factor.

4.7.2 Effect of Roll-off Factor on PAPR Performance

Table 4.7 gives the effect of the roll-off factor on PAPR performance on SCFDMA signal

and it can be concluded from the table that there are 4.8 dB reductions in PAPR for IFDMA

system when the roll-off factor is increased from 0.0 to 0.9 whereas the corresponding

reduction for LFDMA signal is only 1.0 dB for 4 QAM signal. A similar trend follows for

16 QAM and 64 QAM signals.

TABLE 4.7 Effect of Roll-off Factor on PAPR Performance

SCFDMA IFDMA LFDMA

Roll- off factor 4 QAM

(dB)

16 QAM

(dB)

64 QAM

(dB)

4 QAM

(dB)

16 QAM

(dB)

64 QAM

(dB)

Without Pulse Shaping 0.4 2.8 3.9 7.6 8.6 8.7

α= 0.0 7.2 8.4 8.6 8.7 9.7 9.9

α= 0.3 5.6 7.4 7.8 8.4 9.3 9.5

α= 0.6 3.8 5.9 6.7 8.0 8.9 9.2

α= 0.9 2.4 4.7 5.7 7.7 8.7 8.9

0 1 2 3 4 5 6 7 8 9 1010

-2

10-1

100

X: 9.8

Y: 0.018

PAPR [dB] for 64-QAM

CC

DF




IFDMA with a=0.0

LFDMA with a=0.9

IFDMA with a=0.3

LFDMA with a=0.6

IFDMA with a=0.6

LFDMA with a=0.3

IFDMA with a=0.9

LFDMA with a=0.0

IFDMA

LFDMA

Results and Discussion

103

4.8 Results and Discussion

Modern communication systems use multicarrier OFDM communication systems which

have high data rate transmission capability in addition to robustness to channel impairments.

One of its major disadvantage is having high PAPR. High PAPR drives power amplifier into

saturation region and causes it to operate in the nonlinear region. In order to reduce its PAPR

different reduction techniques such as clipping and filtering, selective mapping method

(SLM), partial transmit sequence (PTS) and single carrier frequency division multiple access

(SCFDMA) have been analyzed. Among different PAPR reduction techniques, SCFDMA

results in the lowest PAPR. The effect of raised cosine pulse shaping filter has also been

investigated in order to reduce the out-of-band signal energy of SCFDMA system.

For the case of PAPR reduction with clipping and filtering technique, while maintaining

better bit error rate (BER) performance, a significant reduction in PAPR has been achieved

with minimum hardware and computational complexity. Further, the result obtained with


Instrument’s AWR commercial software and through FPGA implementation. When

compared with original OFDM signal PAPR with FPGA implementation of pre-filtering and

post-clipping reduces by 10.4 dB, whereas the reduction is 1.7 dB with FPGA implementation

of pre-clipping and post-filtering. On the other hand, these reductions are 2.0 and 1.9 dB with

AWR and Matlab software simulations. The result obtained with the proposed SLM

technique with mathematical modeling and Matlab simulations have been further verified

with FPGA implementation and tested on hardware cosimulator using Xilinx Spartan 3

Protoboard XC 3S 400 development board. The PAPR of the SLM technique with Matlab

simulation is 8.9 dB and it is 9.8 dB with FPGA implementation for the case of 4 QAM

OFDM signal with 1024 number of subcarriers and number of phase vector, V=4. The

investigations in PTS technique have resulted with the PAPR of 9.1, dB for 4 number of sub-

blocks with 1024 number of subcarriers. The PAPR obtained is lowest with very low

computational complexity as the number of IFFT operations has been reduced.

When the performance of the SCFDMA techniques with 1024 numbers of subcarriers are

considered, the PAPR of 4 QAM signal with IFDMA, LFDMA, and OFDMA subcarrier

mappings at 10−2 of CCDF value are 0.40, 6.90 and 10.50 dB respectively. The PAPR

performance for the case of 16 QAM SCFDMA techniques for IFDMA, LFDMA, and

OFDMA are 3.45, 7.80 and 10.55 dB respectively. Similarly, for 64-QAM SCFDMA signal


104

the corresponding values are found to be 4.55, 7.90 and 10.60 dB respectively. IFDMA gives

the lowest PAPR of 0.40 dB at 10−2 of CCDF for 4 QAM baseband modulation with 1024

number of subcarriers. The observed value is lowest as compared to other PAPR reduction

techniques discussed. Among many Nyquist pulses used for the distortionless transmission

without the presence of intersymbol interference, raised cosine (RC) pulse is the most popular

Nyquist pulse. For IFDMA system the PAPR at 10−2 of CCDF with 1024 number of

subcarriers with a change in the roll-off factor from 0.0 to 0.9, the reductions in PAPR is 4.8

dB for 4 QAM modulation format. But it is only 1.0 dB for the case of LFDMA system. From

the result obtained it can be observed that effect of pulse shaping is more on IFDMA than

that on LFDMA. Further, the PAPR value decreases with increase in the roll-off factor.

105

CHAPTER – 5

Conclusion

5.1 Conclusion





etc. It has many applications and is widely used in high-bit-rate digital subscriber lines, digital

audio broadcasting, digital video broadcasting along with high-definition television,

terrestrial broadcasting, etc. OFDM has one of the major disadvantage of having high peak

to average power ratio and the power amplifier linearity has become more vulnerable due to

their high PAPR caused by large fluctuations present in the OFDM signal envelope. Many

powerful techniques have been developed to mitigate the harmful effects of nonlinearity in

the communication systems, but are not much effective when applied alone. There is a need

to address this issue at multiple levels simultaneously, such as reduction of PAPR of the

OFDM modulated signal, linearity improvement of the high power amplifier at the

transmitter and reduction of spectral growth by using pulse shaping filters, etc. In order to

reduce the effect of nonlinearity first, the transceiver of OFDM system has been analyzed

using mathematical modeling and Matlab simulations and its PAPR values have been

calculated. Second, to reduce the effect of high PAPR, linearization of the power amplifier

has been carried out using feedback, feedforward, and digital predistortion technique. Third,

PAPR reduction techniques, such as clipping and filtering, selective mapping method, partial

transmit sequence and single carrier frequency division multiple access techniques have

been investigated. At the end, pulse shaping filter technique has been analyzed for the case

of SCFDMA signals for reducing the spectral growth and out-of-band signal energy

radiation apart from reducing the PAPR.

Mathematical modeling and Matlab simulation have been carried out for the OFDM

transmitter and receiver for two different baseband modulated signals, QPSK, and 4 QAM.

Conclusion

106

It has been observed that for the case of QPSK baseband signal at 10−3 of CCDF, PAPR

are 10.5, 10.7, 10.9, 11.2 and 11.4 dB for N = 64, 128, 256, 512 and 1024 respectively.

Similarly for 4 QAM signal, these values are 11.5, 11.7, 12.0, 12.2, and 12.6 dB respectively.

It has been observed that PAPR increases with increase in the number of subcarriers and 4

QAM modulated signal has approximately 1.0 dB higher PAPR than that of QPSK

modulation format. It has also been observed that with the application of multicarrier OFDM

communication system power amplifier nonlinearities become more vulnerable owing to

their high PAPR. Linearization of power amplifiers is implemented for improving linearity

at the same time maintaining high efficiency. Among the three linearization techniques

investigated, feedback technique is simple to implement but results in lowest efficiency and

is not suitable for higher frequency. For the parameters used for simulation, it has resulted in

5 dBm reductions in amplitude and 30 dB reduction in ACPR at 10 MHz operating

bandwidth. Feedforward technique is used for wide bandwidths applications in multicarrier

systems where feedback technique is impractical. When simulated it has resulted in 20 dBm

reductions in amplitude with 25 dB reduction in ACPR but has a wide 1.2 GHz operating

bandwidth. This technique is also least preferred due to the high-cost of passive RF

components like couplers, delay lines, error power amplifier, etc. It has been observed that

the digital predistortion technique does not use these RF components and improves linearity

with higher efficiency. In this technique, the reduction in amplitude has been 0 dBm with 20

dB reduction in ACPR at 10 MHz of bandwidth.

For the case of PAPR reduction with clipping and filtering technique, while maintaining

better bit error rate (BER) performance, a significant reduction in PAPR has been achieved

with minimum hardware and computational complexity. Further, the result obtained with


Instrument’s AWR commercial software and through FPGA implementation. When

compared with original OFDM signal PAPR with FPGA implementation of pre-filtering and

post-clipping reduces by 10.4 dB, whereas the reduction is 1.7 dB with FPGA implementation

of pre-clipping and post-filtering. On the other hand, these reductions are 2.0 and 1.9 dB with

AWR and Matlab software simulations. The result obtained with the proposed SLM

technique with mathematical modeling and Matlab simulations have been further verified

with FPGA implementation and tested on hardware co-simulation using Xilinx Spartan 3

Protoboard XC 3S 400 development board. The PAPR of the SLM technique with Matlab

simulation is 8.9 dB and it is 9.8 dB with FPGA implementation for the case of 4 QAM

Conclusion

107

OFDM signal with 1024 number of subcarriers and number of phase vector, V=4. The

investigations in PTS technique have resulted with the PAPR of 9.1 dB for 4 number of sub-

blocks with 1024 number of subcarriers. The PAPR obtained is lowest with very low

computational complexity as the number of IFFT operations has been reduced. When the

performance of the SCFDMA techniques are considered for 1024 number of subcarriers, the

PAPR of 4 QAM signal with IFDMA, LFDMA, and OFDMA subcarrier mappings at 10−2

of CCDF value are 0.40, 6.90 and 10.50 dB respectively. The PAPR performance for the

case of 16 QAM SCFDMA techniques for IFDMA, LFDMA, and OFDMA are 3.45, 7.80

and 10.55 dB respectively. Similarly, for 64 QAM SCFDMA signal the corresponding

values are found to be 4.55, 7.90 and 10.60 dB respectively. IFDMA gives the lowest PAPR

of 0.4 dB at 10−2 of CCDF for 4 QAM baseband modulation with 1024 number of

subcarriers.

The comparative performance of all the four PAPR reduction techniques discussed above

for 4 QAM modulation format with 1024 number of subcarriers have been studied. The

observed PAPR at 10−2 of CCDF with IFDMA technique is the lowest value of 0.4 dB,

clipped signal with clipping ratio of 0.8 has 4.6 dB, LFDMA has its corresponding value of

6.9 dB, SLM with 16 number of phase vectors has 8.2 dB, partial transmit sequence with 16

number of sub-blocks has 8.3 dB PAPR, OFDMA has its PAPR value of 10.5 dB, clipped

and filtered signal with clipping ratio of 0.8 has 10.7 dB and unclipped signal has PAPR

value of 12.6 dB. There has been a considerable reduction in PAPR of 12.2, 4.4, 4.3 and 1.9

dB with IFDMA, SLM, PTS and clipping and filtering techniques respectively. It is to be

emphasized that IFDMA gives the lowest PAPR of 0.4 dB obtained so far in the literature at

the cost of marginal implementation complexity. On the other hand clipping and filtering

method is one of the simplest PAPR reduction technique from an implementation point of

view but results in spectral regrowth and degradation in BER performance. Selective

mapping method has better performance than partial transmit sequence at the cost of

marginal computational complexity.

Among many Nyquist pulses used for the distortionless transmission without the presence of

intersymbol interference, raised cosine (RC) pulse is the most popular Nyquist pulse. For

IFDMA system the PAPR at 10−2 of CCDF with 1024 number of subcarriers with a change

in the roll-off factor from 0.0 to 0.9, the reductions in PAPR is 4.8 dB for 4 QAM modulation

format. But it is only 1.0 dB for the case of LFDMA system. From the result obtained it can

be observed that effect of pulse shaping is more on IFDMA than that on LFDMA. Further,

Conclusion

108

the PAPR value decreases with increase in the roll-off factor. All the PAPR reduction

techniques discussed in this work cannot be used for all applications and the use of particular

reduction technique depends upon the nature of application and system complexity involved.

The techniques investigated in the present work to compensate the effect of nonlinearity in a

communication system are simple in design, requires fewer hardware resources, has less

computational complexity and better performance capability compared to available

techniques in the literature.

5.2 Scope of Future Work

Amplitude and phase distortions produced due to the effect of nonlinearity causes

loss of orthogonality among the subcarriers and results in the form of inter-carrier

interference in the transmitted signal. The problem of resolving ICI has not been

addressed in the present work and can be undertaken as future work.

The power amplifier linearization has been addressed for class B amplifier using

solid state power amplifier behavioral model, further study can be made using other

behavioral models such as Saleh model, Volterra model, Wiener model,

Hammerstein model, etc. with other classes of amplifiers.

In the present work only four PAPR reduction techniques, clipping and filtering,

SLM, PTS, and SCFDMA have been investigated. Other techniques like, coding

scheme, nonlinear companding transforms, tone reservation and tone injection

schemes, etc. can be taken for further study.

Pulse Shaping using raised cosine filter has been used for SCFDMA signal which

can be extended to other PAPR reduction techniques.

Other Nyquist pulse shaping filters such as piece-wise linear Nyquist filter, flipped-

exponential, flipped-hyperbolic secant, flipped-inverse hyperbolic secant, parametric

linear combination pulses, etc. can also be used for further study.

109

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120

List of Publications

Journal Papers

1. Yadav Shatrughna Prasad, Bera Subhash Chandra (2016), “FPGA Implementation of SLM

Technique for OFDM Communication Systems”, Indian Journal of Science and

Technology, Vol. 9, No. 48, pp. 1-6, ISSN: 0974-6846 (Print), 0974-5645 (Online).

DOI: 10.17485/ijst/2016/v9i48/91142.

2. Yadav Shatrughna Prasad, Bera Subhash Chandra (2016), “Hardware Implementation of PAPR

Reduction with Clipping and Filtering Technique for Mobile Applications”, International Journal of

Engineering and Technology (IJET), Vol. 8 , No. 5, pp. 2018-2033, ISSN: 0975-4024 (online), ISSN:

2319-8613 (print);

DOI: 10.21817/ijet/2016/v8i5/160805420.

3. Yadav Shatrughna Prasad, Bera Subhash Chandra (2016), “PAPR Reduction for Improved Efficiency of

OFDM Modulation for Next Generation Communication Systems” International Journal of Electrical and

Computer Engineering (IJECE), Vol 6, No 5, pp. 2310-2321, ISSN: 2088-8708.

DOI: 10.11591/ijece.v6i5.10878.

4. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “Reduction of PAPR in SC-FDMA System

using Pulse Shaping Technique", International Journal of Applied Engineering Research (IJAER),

Volume 10, Number 23, pp. 43509-43513 ISSN 0973-4562.

http://www.journalindex.net/visit.php?j=3560

5. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “PAPR Reduction using Selective Mapping

Method for OFDM Communication Systems” STM Journal of Communication Engineering & Systems;

Volume 5, Issue 3, pp. 50-57. ISSN: 2249-8613 (Online); 2321-5151 (Print)

http://stmjournals.com/index.php?journal=JoCES&page=article&op=view&path%5B%5D=6632

6. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “Investigations on PAPR Reduction using PTS

Technique for OFDM Communication Systems” STM Journal of Communication Engineering &

Systems; Volume 5, Issue 3, pp. 19-26. ISSN: 2249-8613 (Online); 2321-5151 (Print).

http://stmjournals.com/index.php?journal=JoCES&page=article&op=view&path%5B%5D=6505

7. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “OFDM Transceiver for Nonlinear

Communication Systems”, International Journal of Engineering Science and Innovative Technology

(IJESIT), Volume 4, Issue 1, pp. 185- 194, ISSN: 2319-5967.

http://www.ijesit.com/archive/20/volume-4issue-1january-2015.html

8. Yadav Shatrughna Prasad, Bera Subhash Chandra (2014), “PAPR Reduction using DFT-Spread

Technique for Nonlinear Communication Systems”, International Journal of Engineering and Innovative

Technology (IJEIT) Volume 4, Issue 6, pp - 178- 184, ISSN: 2277-3754.

http://www.ijeit.com/Vol%204/Issue%206/IJEIT1412201412_33.pdf

https://dx.doi.org/10.21817/ijet/2016/v8i5/160805420

http://www.iaesjournal.com/online/index.php/IJECE/issue/view/290

http://stmjournals.com/index.php?journal=JoCES&page=article&op=view&path%255

http://stmjournals.com/index.php?journal=JoCES&page=article&op=view&path%255

List of Publications

121

Conference Papers

1. Yadav Shatrughna Prasad, Bera Subhash Chandra (2016), “Linearity Improvement of Microwave Power

Amplifiers” 13th IEEE India International Conference, 2016 (INDICON 2016), Indian Institute of

Science, Bengaluru, pp. 1-6. ISSN: 2325-9418.

(Published in IEEE Xplore, DOI:10.1109/INDICON.2016.7838910).

2. Yadav Shatrughna Prasad, Bera Subhash Chandra (2016), “Hardware implementation of SLM technique

for OFDM Communication Systems”, IEEE International Conference on Power Electronics, Intelligent

Control and Energy Systems (ICPEICES 2016), Delhi Technological University, New Delhi. pp. 1-5.

ISBN: 978-1-4673-8586-2.

(Published in IEEE Xplore, DOI: 10.1109 / ICPEICES.2016.7853341 ).

3. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “Single Carrier FDMA for Wireless

Communication System”, 12th IEEE India International Conference, 2015 (INDICON 2015), Jamia

Millia Islamia, New Delhi, pp. 1-6. ISBN: 978-1-4673-7399-9.

(Published in IEEE Xplore, DOI:10.1109/INDICON.2015.7443655).

4. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “PAPR Analysis of Single Carrier FDMA

System for Uplink Wireless Transmission”, 10th IEEE International Conference on Information,

Communications and Signal Processing (ICICS 2015), Singapore, PP. 1-5. ISBN: 978-1-4673-7217-6.

(Published in IEEE Xplore, DOI: 10.1109/ICICS.2015.7459941).

5. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “PAPR Reduction using Clipping and Filtering

Technique for Nonlinear Communication Systems”, IEEE International Conference on Computing,

Communication and Automation (ICCCA-2015), Galgotias University, Greater Noida, Uttar Pradesh,

pp.1220-1225. ISBN: 978-1-4799-8890-7.

(Published in IEEE Xplore, DOI: 10.1109/CCAA.2015.7148590).

6. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “Selective Mapping and Partial Transmit

Sequence Techniques for PAPR Reduction in OFDM for Spectrum Efficient Multimedia Communication

Systems” International Conference on Telecommunication Technology & Management (ICTTM 2015),

pp.4, IIT Delhi, ISBN: 978-0-9926800-5-3.

7. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “Multicarrier OFDM Communication for High

Power Amplifiers”, IEEE International Conference on Computing, Communication, Control and

Automation (ICCUBEA-2015), Pune, Maharashtra, pp. 78- 82, ISBN: 978-1-4799-6893-0 (Received

best paper award).

(Published in IEEE Xplore, DOI: 10.1109/ICCUBEA.2015.22).

8. Yadav Shatrughna Prasad, Bera Subhash Chandra (2015), “PAPR Reduction techniques for OFDM

Communication Systems”, National Conference on Emerging Trends in Engineering, Technology &

Management (NCEETM), Ahmedabad, Gujarat, pp.37-38, ISBN: 978-93-80867-75-5.

9. Yadav Shatrughna Prasad, Bera Subhash Chandra (2014), “Nonlinearity Effects of Power Amplifiers in

Wireless Communication Systems” IEEE International Conference on Electronics, Communication and

Computational Engineering (ICECCE 2014), Hosur, Tamilnadu, pp.12-17. ISBN: 978-1-4799-5747-7.

(Published in IEEE Xplore, DOI: 10.1109/ICECCE.2014.7086613).

https://doi.org/10.1109/ICPEICES.2016.7853341

http://dx.doi.org/10.1109/INDICON.2015.7443655

http://dx.doi.org/10.1109/ICICS.2015.7459941

http://dx.doi.org/10.1109/CCAA.2015.7148590

http://dx.doi.org/10.1109/ICCUBEA.2015.22

http://dx.doi.org/10.1109/ICECCE.2014.7086613

122

10. Yadav Shatrughna Prasad, Bera Subhash Chandra (2014), “Nonlinearity Effect of High Power Amplifiers

in Communication Systems” IEEE International Conference on Advances in Communication and

Computing Technologies (ICACACT-14), Mumbai, Maharashtra, pp.1-6. ISBN: 978-1-4799-7319-4.

(Published in IEEE Xplore, DOI: 10.1109/EIC.2015.7230741).

http://dx.doi.org/10.1109/EIC.2015.7230741

GUJARAT TECHNOLOGICAL UNIVERSITY AHMEDABAD June 2017 D THESIS_SHATRUGHNA... · 2020. 9. 11. · The...

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