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HIGH RATE TECHNIQUES FOR PAPR REDUCTION IN OFDM

SYSTEMS

_______________

A Thesis

Presented to the

Faculty of

San Diego State University

_______________

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

in

Electrical Engineering

_______________

by

Sudarshan M. Kannappan

Spring 2012

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Copyright 2012

by

Sudarshan M. Kannappan

All Rights Reserved

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DEDICATION

This thesis is dedicated to my parents Sriram M K and Padmini M K, my sisterSmitha M K, my aunt Mythili M K and my cousins Kiran Kannappan and Kishore Mandyam

and also my pet Brownie.

I would also like to dedicate this to my best friend Srinivas Anand.

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ABSTRACT OF THE THESIS

High Rate Techniques for PAPR Reduction in OFDM Systemsby

Sudarshan M. Kannappan

Master of Science in Electrical EngineeringSan Diego State University, 2012

Wireless communication has evolved so much today that it has greatly beenintegrated into everyones life. From listening to music using Bluetooth headset, accessing

information on the web on the move using WiFi or 3G to calling our loved ones who are on

the other side of the globe and locating our position when lost, can be done using a plethora

of wireless devices available today.This thesis addresses the problem of high peak-to-average power ratio (PAPR) found

in orthogonal frequency division multiplexing (OFDM) modems. The reason for high PAPR

in OFDM is the constructive addition of sinusoidal signals at different frequencies. HighPAPR increases the dynamic range of power amplifier operation, thereby resulting in

increased cost and chip area.

This thesis proposes several high rate techniques to reduce PAPR. One techniqueextends the efficiency of the well known complementary code keying (CCK) OFDM. The

second technique eliminates high PAPR by removing the periodicity which may exist

between the bits fed to the OFDM transmitter. This rate-12/16 technique is compared to other

techniques such as traditional OFDM and carrier-interferometry (CI) OFDM. Further, thisthesis integrates the proposed rate-12/16 technique and CCK to obtain an improved

rate-12/16 technique, which brings the PAPR value down to a new low. Bit error rates (BER)

are obtained for each coding technique for comparison. The proposed rate-12/16 techniqueachieves good BER performance due to the coding gain it provides. The improved

rate-12/16 outperformed all the techniques discussed in terms of PAPR.

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TABLE OF CONTENTS

PAGE

ABSTRACT ...............................................................................................................................v

LIST OF TABLES ................................................................................................................. viii

LIST OF FIGURES ................................................................................................................. ix

ACKNOWLEDGEMENTS ..................................................................................................... xi

CHAPTER

1 INTRODUCTION .........................................................................................................12 CHALLENGES IN WIRELESS COMMUNICATION ................................................53 CHANNEL MODELS ...................................................................................................8

3.1 Additive White Gaussian Noise (AWGN) Channel ..........................................83.2 Fading Channels.................................................................................................93.3 Multipath Fading ..............................................................................................11

3.3.1 Rayleigh Fading ..................................................................................... 123.3.2 Rician Fading ......................................................................................... 13

4 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM) ................144.1 Cyclic Prefix ....................................................................................................174.2 OFDM Symbol.................................................................................................174.3 Performance of OFDM Systems ......................................................................174.4 PAPR in OFDM ...............................................................................................19

5 EXISTING PAPR REDUCTION TECHNIQUES ......................................................235.1 Carrier Interferometry-OFDM .........................................................................235.2 Performance of CI OFDM Systems .................................................................245.3 Complementary Code Keying (CCK) OFDM .................................................245.4 PAPR Performance of CCK OFDM Systems ..................................................27

6 PROPOSED PAPR REDUCTION TECHNIQUES ....................................................296.1 Extension of CCK OFDM ...............................................................................296.2 PAPR Performance of Proposed CCK OFDM System ...................................306.3 Rate-12/16 Technique ......................................................................................30

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6.4 Performance of Rate-12/16 Technique ............................................................316.5 Improved Rate-12/16 Technique: Combination of Rate-12/16 and

CCK .......................................................................................................................336.6 PAPR Performance of Improved Rate-12/16 Technique.................................336.7 Comparison of Performance of All the Discussed Technologies ....................34

7 CONCLUSION AND FUTURE ENHANCEMENT ..................................................38BIBLIOGRAPHY ....................................................................................................................39

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LIST OF TABLES

PAGE

Table 4.1. Comparison of OFDM Systems ..............................................................................18Table 6.1. Comparison of OFDM, CI-OFDM, CCK, Rate-12/16 and Improved

Rate-12/16 Techniques ................................................................................................36

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LIST OF FIGURES

PAGE

Figure 3.1. Probability distribution function for Gaussian random variable for

different variance values. ...............................................................................................9Figure 3.2. Noise model in communication system. ................................................................10Figure 3.3. Large scale fading v/s small scale fading. .............................................................11Figure 3.4. Multipath fading. ...................................................................................................11Figure 3.5. Probability distribution function for Rayleigh fading for different

variance. .......................................................................................................................12Figure 3.6. Probability distribution function for Rician fading. ..............................................13

Figure 4.1. Comparison of the conventional FDM with OFDM. ............................................15Figure 4.2. Block diagram of OFDM transmitter. ...................................................................16Figure 4.3. Block diagram of OFDM receiver. ........................................................................16Figure 4.4. Cyclic prefix in OFDM. ........................................................................................17Figure 4.5. Typical OFDM symbol..........................................................................................18Figure 4.6. Bit error rate of OFDM for AWGN channel. ........................................................19Figure 4.7. (a) PAPR of OFDM and (b) is histogram of PAPR. .............................................21Figure 4.8. Transfer function of a typical power amplifier......................................................22Figure 5.1. Block diagram of CI-OFDM transmitter. ..............................................................24Figure 5.2. Block diagram of CI-OFDM receiver. ..................................................................24Figure 5.3. Bit error rate of CI-OFDM for AWGN channel. ...................................................25Figure 5.4. (a) PAPR of CI-OFDM and (b) is histogram of PAPR. ........................................25Figure 5.5. Block diagram of CCK OFDM transmitter. ..........................................................26Figure 5.6. Block diagram of CCK OFDM receiver. ..............................................................26Figure 5.7. (a) PAPR of CCK OFDM and (b) is histogram of PAPR. ....................................28Figure 6.1. Details of the 7/16 spreading sequence block. ......................................................29Figure 6.2. (a) PAPR of 7/16 CCK OFDM and (b) is histogram of PAPR. ............................30Figure 6.3. Block diagram of rate-12/16 transmitter. ..............................................................31Figure 6.4. Block diagram of rate-12/16 receiver. ...................................................................31Figure 6.5. Bit error rate of rate-12/16 technique. ...................................................................32

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Figure 6.6. (a) PAPR of rate-12/16 technique and (b) is histogram of PAPR. ........................32Figure 6.7. Details of 12/16 mapper block. .............................................................................34Figure 6.8. Block diagram of improved rate-12/16 transmitter. ..............................................34Figure 6.9. Block diagram of improved rate-12/16 receiver. ..................................................35Figure 6.10. (a) PAPR of improved rate-12/16 technique and (b) is histogram of

PAPR............................................................................................................................35 Figure 6.11. Bit error rate of OFDM, CI-OFDM, rate-12/16 techniques. ...............................36Figure 6.12. PAPR of OFDM, CI-OFDM, rate-12/16 and improved rate-12/16

techniques. ...................................................................................................................37Figure 6.13. Histogram of PAPR of OFDM, CI-OFDM, rate-12/16 and improved

rate-12/16 techniques. ..................................................................................................37

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ACKNOWLEDGEMENTS

I would like to take this opportunity to thank all of you who have supported methroughout my thesis.

First of all, I would like to thank my thesis advisor Dr. Santosh Nagaraj who is a

wonderful human being. His motivation, encouragement and support have helped me

complete my thesis successfully.

I would also like to thank Dr. Ashkan Ashrafi and Dr. Christopher Paolini for their

help in completing my thesis.

Thanks to my friends Vishak Neergund, Sagar Rao for having those technical

discussions which were thought provoking, this aided my thesis.

I would like to thank my parents, my sister, my aunt and my cousins who have been

with me giving their moral, emotional and financial support without which this thesis and

masters wouldnt have been possible. I love you guys!

Lastly, thank you Srinivas Anand who has been with me and encouraged me when I

was feeling low during my thesis period.

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CHAPTER 1

INTRODUCTION

Guglielmo Marconi in 1875, opened the way for modern wireless communications by

transmitting the three-dot Morse code for the letter S over a distance of three kilometers

using electromagnetic waves. From satellite transmission, radio and television broadcasting

to the now ubiquitous mobile telephone, wireless communications has revolutionized the way

societies function [1].

Wireless Communication is used for a wide range of services which are categorized

as:

Broadcasting services: AM, FM radio and terrestrial television. Mobile communications of voice and data: Maritime and aeronautical mobile for

communications between ships, airplanes and land; Terrestrial mobile

communications between a fixed base station and mobiles.

Fixed Services: Point to point, Point to multipoint services. Satellite: Broadcasting, Communications and internet. Other Uses: Military, radio astronomy, meteorological and scientific uses [1].

The history of mobile telephones can be loosely broken into four periods. In first

(pre-cellular) period, mobile telephones used a frequency band exclusively in a particular

area. These telephones had severe problems with congestion and call completion [1].

The introduction of cellular technology expanded the efficiency of frequency use of

mobile phones. A geographic area was broken down into small areas called cells and a band

of frequency was allocated to a particular cell, rather than exclusively allocating a band of

frequency to one telephone call in a large geographic area. Different users in different

(non-adjacent) cells were able to use the same frequency for a call without interference [1].

First generation cellular mobile telephone (1G) refers to wireless telecommunication

technology developed in 1980s which was based on analog signals. In 1G, a voice call was

modulated to a higher frequency of about 150 MHz and up as it was transmitted between

radio towers. This was done using a technique called Frequency-Division Multiple Access

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(FDMA). It had some disadvantages like low capacity, unreliable handoff, poor voice links

and no security at all.

Second generation (2G) mobile telephones used digital technology. It was developed

in 1990s. All phone conversations were digitally encrypted. 2G systems were significantly

more efficient on the spectrum and 2G also introduced data services for mobile with the

introduction of Short Message Service (SMS). 2G networks were built mainly for voice

services and slow data transmission. Groupe Speciale Mobile (GSM) was the first 2G

system. It was later standardized to Global System for Mobile Communication. GSM

allowed full international roaming, automatic location services, common encryption and

relatively high quality audio [1]. GSM is now the most widely used 2G system worldwide, in

more than 130 countries, using the 900 MHz frequency range. GSM uses Time Division

Multiple Access (TDMA) unlike FDMA scheme used in 1G.

The first major step in the evolution of GSM networks to 3G occurred with the

introduction of General Packet Radio Service (GPRS) which was called the 2.5G. It was

between 2G and 3G cellular wireless technologies. This technology implemented a

packet-switched domain in addition to the circuit-switched domain. GPRS could provide data

rates from 56 Kbit/s up to 115 Kbit/s. It was used for services such as Wireless Application

Protocol (WAP) access, Multimedia Messaging Service (MMS), and for Internet

communication services such as email and World Wide Web access.

GPRS networks evolved to EDGE networks with the introduction of 8PSK encoding.

EDGE was deployed on GSM networks beginning in 2003. Enhanced Data rates for GSM

Evolution (EDGE); Enhanced GPRS (EGPRS) was backward-compatible digital mobile

phone technology that allowed improved data transmission rates, as an extension on top of

standard GSM. EDGE provides a three-fold increase in capacity of GSM/GPRS networks.

The specification achieves higher data-rates (up to 236.8 Kbit/s) by switching to more

sophisticated methods of coding (8PSK), within existing GSM timeslots.

The third generation mobiles network uses spread spectrum technology, Code

Division Multiple Access (CDMA) in particular. These systems allow for significantly

increased speeds of transmission and are particularly useful for data services. WCDMA is

also found in 3G standard utilizes the DS-CDMA channel access method and the FDD

duplexing method to achieve higher speeds and support more users compared to most time

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division multiple access (TDMA).W-CDMA differs from CDMA in many aspects. One

among them is WCDMA transmits on a pair of 5 MHz-wide radio channels, while CDMA

transmits on one or several pairs of 1.25 MHz radio channels. There are evolutionary

standards (EDGE and CDMA) that are backwards-compatible extensions to pre-existing 2G

networks as well as revolutionary standards that require all-new network hardware and

frequency allocations. 3G offers a minimum data rate of 2 Mbit/s for stationary or walking

users, and 384 Kbit/s when in a moving vehicle. Also 3G networks offer greater security than

their 2G predecessors. The bandwidth and location information available to 3G devices gives

rise to applications which were not previously available to mobile phone users. Some of them

are:

Mobile TV Video on demand Video conferencing Tele-medicine Location-based services

High Speed Packet Access (HSPA) is combination of two mobile telephony

protocols, High Speed Downlink Packet Access (HSDPA) and High Speed Uplink Packet

Access (HSUPA) that improves the performance of existing WCDMA protocols. HSPA

supports increased peak data rates of up to 14 Mbit/s in the downlink and 5.8 Mbit/s in the

uplink. High-Speed Downlink Packet Access (HSDPA) is an enhanced 3G (third generation)

mobile telephony communications protocol which is called as 3.5G, which has increased data

transfer speeds and capacity. Current HSDPA support down-link speeds of 1.8, 3.6, 7.2 and

14.4 Megabits/s. Further speed increases are available with HSPA+, which provides speeds

of up to 42 Mbit/s downlink and 84 Mbit/s.

HSPA+ provides HSPA data rates up to 84 Megabits per second (Mbit/s) on the

downlink and 22 Mbit/s on the uplink through the use of a multiple-antenna technique known

as Multiple-Input Multiple-Output (MIMO) and higher order modulation (64QAM). MIMO

on CDMA based systems acts like virtual sectors to give extra capacity. The technology also

delivers significant battery life improvements.

With the introduction of OFDM, a new standard evolved called 4G which promises

very high data rates which increased data traffic by five-fold. A 4G system is expected to

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provide a comprehensive and secure all-IP based mobile broadband solution to laptop

computer wireless modems, Smartphone and other mobile devices. Facilities such as

ultra-broadband Internet access, IP telephony, gaming services and streamed multimedia are

provided to users. 4G has two parts:

WiMax (Wireless Interoperability for Microwave Access) LTE (Long Term Evolution)

WiMax is a telecommunications technology that provides fixed and fully mobile

internet access. It is based on IEEE 802.16 standard. Data rate of up to 70 Mbps can be

achieved. It uses frequency range of 10-66 GHz licensed bands, obtained at premium costs.

WiMax has two variants namely 802.16d and 802.16e which differs in their mobility. WiMax

offers higher speeds, extended range and supports greater number of users as compared to

WiFi standard, which is based on IEEE 802.11. WiMax has a scalable physical layer which

offers flexibility in choosing data rates. Unlike WiFi, WiMax is a connection oriented service

which establishes connection between the sender and receiver for offering the required

service.

On the other hand, LTE is a standard supports both voice and data traffic at high

speeds. LTE is often marketed as 4G even though they do not comply with the 4G standards.

The pre-4G standard is a step toward LTE Advanced, a 4th generation (4G) standard of radio

technologies designed to increase the capacity and speed of mobile telephone networks. LTE

Advanced is backwards compatible with LTE which uses the same frequency bands, while

LTE is not backwards compatible with 3G systems. LTE offers a peak data rate of 70 Mbps.

It uses SC-FDMA in the uplink and OFDMA in the downlink. OFDMA is a multiple access

technique for OFDM and SC-FDMA is single carrier frequency division multiple access

scheme used to overcome a high PAPR drawback in OFDM

This thesis contribution lies in reduction of PAPR (peak Average to Power Ratio) in

OFDM. The main short-coming of OFDM system is high PAPR. PAPR is the ratio of the

peak power and the average power of the OFDM signal. This consumes more power than

required and also forces one to use bulky power amplifiers. The issues might prove costly in

mobile devices as they are power hungry and portable. We have proposed couple of

techniques which deals with reducing PAPR by getting rid of periodicity which is the main

cause of high PAPR in OFDM systems.

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CHAPTER 2

CHALLENGES IN WIRELESSCOMMUNICATION

Wireless Communication has many advantages and challenges too which are

discussed in this chapter. Some of the challenges of wireless communication are given below

[2].

Developing reliable transmission and reception to send data through unfriendlywireless channel.

The most fundamental challenge for wireless communication comes from the

transmission medium itself. Wireless communication systems use radio wave propagation

mechanisms for transmission unlike wired communication channels which rely on a physical

connection such as copper wires etc. Several large and small obstructions, terrain

undulations, relative motion between the transmitter and the receiver, interference from other

signals, noise, and various other complicating factors together weaken, delay, and distort the

transmitted signal in an unpredictable and time-varying fashion [2]. It is a challenge to design

a digital communication system that performs well under these conditions, especially when

requirements are for very high data rates and high-speed mobility. Some of the impairments

contributed by the channel are:

1. Distance-dependent reduction in signal power2. Inter-symbol interference (ISI) due to time dispersion3. Doppler Spread due to frequency dispersion4. Noise (AWGN)5. Interference

Achieving high spectral efficiency and coverage with limited available spectrum.The second challenge to wireless communication comes from the scarcity of

bandwidth. The regulatory bodies around the world have allocated only a limited amount of

spectrum for commercial use. The need to accommodate an ever-increasing number of users

and offering bandwidth-rich applications using a limited spectrum challenges the system

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designer to continuously search for solutions that use the spectrum more efficiently [2]. The

most significant tool used to achieve higher spectral efficiency is the concept of a cellular

architecture, where several lower-power transmitters are used to cover a smaller area, called

a cell. The cells are again subdivided into sectors. The available frequency spectrum is

divided among the cells to minimize interference. This method of allocation is called

frequency reuse.

Supporting the required QoS (throughput, delay).QoS refers to the collective effect of service, as perceived by the user. QoS actually

refers to meeting certain requirements such as throughput, packet error rate, delay, and jitter.

Wireless communication networks must support a diversity of applications, such as

voice, data, video, and multimedia, which has different traffic patterns and QoS requirements

[2]. The diversity in the QoS requirements makes it a challenge to accommodate all these on

a single-access wireless network, where bandwidth is precious. The perceived quality is

based on the end-to-end performance of the network from a user perspective. Therefore QoS

has to be delivered end-to-end across the network, which may include both wired and

wireless infrastructure.

Supporting mobility through uninterrupted communication.Mobility is one of the significant features offered by wireless communication. Two of

the main challenges are roaming and handoff which are critical in providing a good user

experience.

Roaming includes maintaining the communication link between two users when both

or either of them is travelling within the same base station area or outside that area or outside

the country.

Handoff is required to support roaming. When there is change of base station

or change of network, then the communication shouldnt be hampered. Handoff takes

care of retaining the communication link by handing over the responsibilities to the

target base station without any interruption to the user. IP-based networks support

roaming and handovers across heterogeneous networks, such a WiMax network or a

WiFi network [2].

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Achieving low power consumption to handle mobile devices which are batteryoperated.

Portability is another unique aspect of wireless communication. Portability is desired

for full mobility and some nomadic applications. Portability requires the mobile device to be

battery powered and the battery to hold juice for a long time. Unfortunately, advances in

battery technology have been limited, especially when compared to processor technology.

The need for reducing power consumption translates to use of power-efficient modulation

and transmission schemes, computationally less intensive signal-processing algorithms,

low-power circuit-design, and battery technologies with longer life [2].

Unfortunately, there exists a trade-off between the power required and bandwidth.

Both are significant aspects for performance of any wireless communication link. This might

result in portable wireless systems offering asymmetric data rates on the downlink and theuplink. The power-constrained uplink supports lower bits per second per Hertz than the

downlink.

Providing security.Security is an important consideration in wireless communication systems. The fact

that connections can be established in untethered fashion makes it easier to intrude in an

inconspicuous and undetectable manner [2]. Therefore, a robust level of security must exist.

From the perspective of an end user, the primary security concerns are privacy and data

integrity. Users need assurance that no one can eavesdrop on their sessions and that the data

sent across the communication link is not tampered. This is usually achieved through the use

of encryption. From the service providers perspective, an important security consideration is

preventing unauthorized use of the network services. This is usually done using strong

authentication and access control methods [2].

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CHAPTER 3

CHANNEL MODELS

3.1ADDITIVE WHITE GAUSSIAN NOISE (AWGN)

CHANNEL

AWGN is a linear continuous memory-less and time invariant channel used to model

thermal noise in all communication links. Wideband Gaussian noise comes from many

natural sources, such as the thermal vibrations of atoms in conductors (referred to as thermal

noise or Johnson noise), shot noise, black body radiation from the earth and other warm

objects, and from celestial sources such as the sun.

The AWGN channel is a good model for many satellite and deep space

communication links. It is not a good model for most terrestrial links because of multipath,

terrain blocking, interference, etc. However, for terrestrial path modeling, AWGN is

commonly used to simulate background noise of the channel under study, in addition to

multipath, terrain blocking, interference, ground clutter and self interference that modern

radio systems encounter in terrestrial operation.

This model does not account for fading, frequency selectivity, interference,

nonlinearity or dispersion. However, it produces simple and tractable mathematical models

which are useful for gaining insight into the underlying behavior of a system before these

other phenomena are considered. Some of the set assumptions are:

The noise is additive, i.e., the received signal equals the transmit signal plus somenoise, where the noise is statistically independent of the signal.

The noise is white, i.e., the power spectral density is flat, and so the autocorrelation ofthe noise in time domain is zero for any non-zero time offset.

The noise samples have a Gaussian distribution.The graph of the associated probability density function is bell-shaped, and is

known as the Gaussian function or bell curve.

f (x) =

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where parameter is the mean (location of the peak) and2

is the variance (the measure of

the width of the distribution).

The distribution with = 0 and2

= 1 is called the standard normal. See Figure 3.1

for probability distribution function for Gaussian random variable.

Figure 3.1. Probability distribution function for Gaussian random

variable for different variance values.

Communication systems use the system model shown in Figure 3.2. X is the

transmitted signal from the transmitter. N, which is assumed to be AWGN, is the thermal

noise present in the channel added to X which yields Y. Y is the received signal at the

receiver which contains the transmitted signal X and noise N. The goal of the receiver is to

deal with the noise and decode the information with limited error. N includes only thermal

noise and does not contain fading, multipath and other channel impairments.

3.2FADING CHANNELS

Fading is deviation of the attenuation that a carrier-modulated telecommunication

signal experiences over certain propagation media. The fading may vary with time,

geographical position and/or radio frequency, and is often modeled as a random process. A

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Figure 3.2. Noise model in

communication system.

fading channel is a communication channel that experiences fading. Fading occurs due to

many reasons. They are:

Multipath propagation, referred to as multipath induced fading. Shadowing from obstacles affecting the wave propagation sometimes referred to asshadow fading.

Fading is classified into two types which are large scale fading and small scale

fading.

Large scale fading represents the average signal attenuation or path loss due to

motion over large areas. This is affected by prominent terrain contours such as hills, forest,

billboards etc. present between the transmitter and receiver. The statistics provide a way of

computing an estimate of path loss as a function of distance. This is described as mean path

loss and log normally distributed variation about the mean [3].

Small scale fading refers to dramatic changes in signal amplitude and phase that can

be experienced because of small changes. It manifests itself in two mechanisms- time

spreading of signal and time variation of channel. Time variation of channel is seen due to

motion of transmitter and receiver [3].

Figure 3.3 shows the comparison of large scale fading and small scale fading. m(t) is

large scale fading component and r0(t) is the small scale fading component. In Figure 3.3a,

the signal power received is a function of the multiplicative factor (t). Small-scale fadingsuperimposed on large-scale fading can be readily identified. The typical antenna

displacement between adjacent signal-strength nulls due to small-scale fading is

approximately half of wavelength. In Figure 3.3b, the large-scale fading or local mean m(t)

has been removed in order to view the small-scale fading r0(t). The log-normal fading is a

N

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Figure 3.3. Large scale fading v/s small scale fading.

relative slow varying function of position, while the Rayleigh fading is a relatively fast

varying function of position.

3.3MULTIPATH FADING

Multipath is a phenomenon that results in radio signals reaching the receiving antenna

by two or more paths. Some of the causes of multipath include atmospheric ducting,

ionospheric reflection and refraction, and reflection from water bodies and terrestrial objects

such as mountains and buildings. Figure 3.4 shows the phenomena of multipath fading.

Figure 3.4. Multipath fading.

TRANSMITTER RECEIVER

BUILDINGS

or ANY

OBJECT

Line of Sight

Direct Path

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Multipath can cause errors and affect the quality of communications. The errors are

due to introduction of inter-symbol interference (ISI) which causes smearing of the

neighboring symbol. Equalizers are used to correct the ISI. Alternatively, techniques such as

orthogonal frequency division modulation (OFDM) and rake receivers, which are used to

decode CDMA signals, may be used.

Multipath fading has two kinds viz Rayleigh and Rician which are discussed below.

3.3.1 Rayleigh Fading

Rayleigh fading models assume that the magnitude of a signal that has passed through

a communications channel will fade according to a Rayleigh distribution shown in

Figure 3.5. Rayleigh fading is viewed as a reasonable model for signal propagation in urban

environments. Rayleigh fading is most applicable when there is no dominant propagationalong a line of sight between the transmitter and receiver. If there is a dominant line of sight,

Rician fading is more applicable.

Figure 3.5. Probability distribution function for Rayleigh fading for

different variance.

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The Rayleigh probability density function is:

f (x, ) = x 0for parameter > 0.

3.3.2 Rician Fading

Rician fading is a stochastic model for radio propagation anomaly caused by partial

cancellation of a radio signal by itself the signal arrives at the receiver by several different

paths (hence exhibiting multipath interference), and at least one of the paths is changing.

Rician fading occurs when one of the paths, typically a line of sight signal, is much stronger

than the others. Rician fading is characterized by a Rician distribution which is discussed

below. Figure 3.6 shows Rician distribution.

Figure 3.6. Probability distribution function for Rician fading.

f (xv, ) =

whereI(z) is the modified Bessel function of the first kind with order zero. When v = 0, the

distribution reduces to a Rayleigh distribution.

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CHAPTER 4

ORTHOGONAL FREQUENCY DIVISIONMULTIPLEXING (OFDM)

Orthogonal Frequency Division Multiplexing (OFDM) is a technique in which a

high-bit-rate data stream is divided into several parallel lower bit-rate streams, modulating

each stream on separate carriers called subcarriers [4]. OFDM belongs to a family of

transmission schemes called multicarrier modulation. Each sub-carrier is modulated with a

digital modulation scheme such as Phase-Shift Keying (PSK) or Quadrature Amplitude

Modulation (QAM). The total data rate is similar to the conventional single-carrier

modulation scheme with the same bandwidth. It is used for high speed data transmission over

multipath fading channels [5].

OFDM is a combination of modulation and multiplexing. Multiplexing refers to

independent signals, produced by different sources. In OFDM the signal itself is first split

into independent channels, modulated by data using suitable modulation technique and then

re-multiplexed to create the OFDM carrier. However, OFDM signals are known to suffer

from a high PAPR when a number of independently modulated subcarriers are added upcoherently [6].

The primary advantage of OFDM over single-carrier schemes is its ability to cope

with severe channel conditions, for example interference and frequency-selective fading due

to multipath, without complex equalization requirement. Inter-symbol interference (ISI) is

eliminated by use of guard intervals which allow the echoes to die down before the next

symbols arrival. Frequency selective fading is taken care because of the inherent property of

OFDM which uses multiple carriers. The entire OFDM symbol isnt affected due to

frequency selective fading and hence only certain sub-carriers which are affected are

discarded. OFDM is the right fit for hostile channels.

Advantages of OFDM include:

Reduction in computational complexity due to the use of FFT.

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Exploitation of frequency diversity. Robust against narrowband interference. Usage of simple frequency domain equalizers instead of complex time domain

equalizers.

Well handling of Multipath propagation.Figure 4.1 shows the comparison of the conventional FDM with OFDM scheme.

Notice that there is 50% overlapping done in OFDM due to the presence of orthogonality.

Also notice a significant savings in bandwidth is achieved.

Figure 4.1. Comparison of the conventional FDM with OFDM.

OFDM has developed into a popular scheme for wideband digital communication. It

is used in variety of applications such as digital television and audio broadcasting, wireless

networking and broadband internet access. Some of them are listed below.

Applications of OFDM include:

WLAN radio interfaces IEEE 802.11a/g/n. Digital Radio systems such as DAB, HD radio. The terrestrial digital TV systems DVB-T. The terrestrial mobile TV systems DVB-H. A variant of OFDM in 4G systems such as WiMax, LTE.

The block diagram of OFDM transmitter and receiver are shown in Figure 4.2 and

Figure 4.3. Bits arrive serially to the serial to parallel converter which is converted to parallel

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4.1CYCLIC PREFIX

Cyclic prefix refers to the prefixing of a symbol with a repetition of the end. Some

samples at the end of the symbol is prefix to the starting of the symbol shown in Figure 4.4.

The receiver discards the cyclic prefix samples before decoding. Cyclic prefix is used for

three reasons discussed below. In order for the cyclic prefix to be effective, the length of the

cyclic prefix must be at least equal to the length of the multipath channel.

Figure 4.4. Cyclic prefix in OFDM.

To maintain orthogonality: Studies have shown that the echoes of the OFDM symbollast for 0.8 microseconds. Hence a gap called the guard interval of 0.8 microsecondsis created after each OFDM symbol. Creation of gap results in loss of orthogonality

and hence a cyclic prefix is added to compensate.

Frequency domain equalization: As a repetition of the end of the symbol, it allows thelinear convolution of a frequency-selective multipath channel to be modeled as

circular convolution, which in turn may be transformed to the frequency domainusing a Discrete Fourier transform. This approach allows for simple

frequency-domain processing, such as channel estimation and equalization.

Intersymbol interference (ISI): The creation of guard interval gets rid of ISI. ISI iscaused due to multipath fading.

4.2OFDMSYMBOL

Figure 4.5 shows a typical OFDM symbol. As discussed above OFDM symbol

consists of a bunch of sinusoidal waves of different frequencies created by the IFFT block.

Comparison of OFDM systems is shown in Table 4.1.

4.3PERFORMANCE OF OFDMSYSTEMS

The performance of any OFDM system can be assessed using two parameters which

are Bit Error Rate (BER) and PAPR.

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Figure 4.5. Typical OFDM symbol.

Table 4.1. Comparison of OFDM Systems

Standard Name DVB-T DVB-HIEEE 802.11a

(WiFi)

Frequency Range (MHz)470-862

174-230470-862 4915-5825

Channel Spacing (MHz) 6,7,8 5,6,7,8 20

FFT (K=1024) 2K,8K 2K,4K,8K 64

No of sub-carriers2K mode:17058K mode:6817

2K mode:1705

4K mode:34098K mode:6817

52

Sub-carrier Modulation

technique

QPSK, 16 QAM

64 QAM

QPSK, 16 QAM

64 QAM

BPSK,QPSK

16QAM,64 QAM

Symbol length

(microseconds)

2K mode:224

8K mode:896

2Kmode:2244K mode:448

8K mode:896

3.2

Guard Interval (Fractionof symbol length) , 1/8, 1/16, 1/32 , 1/8, 1/16, 1/32 1/4

Sub-carrier spacing(kHz)

2K mode:4.4648K mode:1.116

2K mode:4.464

4K mode:2.232

8K mode:1.116

312.5

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The bit error rate is found from the errors generated by comparing the data bits both

at the transmitter and receiver. The bit error rate varies depending on the Eb/No value where

Eb is the energy per bit and No/2 is the power spectral density of noise. Figure 4.6 which is

plotted by adding AWGN channel only, resembles the typical waterfall model which is

expected.

Figure 4.6. Bit error rate of OFDM for AWGN channel.

Disadvantages of OFDM include:

Sensitive to Doppler shift. Sensitive to frequency synchronization problems. Very susceptible to phase noise and frequency dispersion. High PAPR (Peak average to power ratio) which requires more power efficient

amplifiers.

Loss of efficiency caused by cyclic prefix.4.4PAPR IN OFDM

Peak-to-Average Power Ratio (PAPR) is the ratio of the peak power and average

power of a signal. It is a dimensionless quantity.

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where s1 contains signal voltages.

PAPR is a major issue in OFDM. OFDM signals have high PAPR when compared to

the single carrier modulation signals. When the OFDM signals super-positioned sinusoidal

subcarriers to be in-phase at the input of the transmitters inverse fast Fourier transform

(IFFT) operator, these sinusoids would add constructively, producing a high magnitude at the

IFFT output [7]. PAPR increases exponentially with increase in the number sub-carriers. The

peak power of a signal is a critical design factor for band limited communication systems,

and it is necessary to reduce it as much as possible [8]. Because of the high PAPR, the

transmitter power amplifier may be driven into saturation. This potentially contaminates the

adjacent channels resulting in the co-channel interference [9].

The disadvantages of high PAPR are:

1. Power Amplifiers at high ranges need linearization.2. Increases dynamic range of the power amplifiers which results in big, bulky and

expensive power amplifiers.

3. PAPR generates out-of-band energy (spectral re-growth) and in-band distortion(constellation tilting and scattering) [10].

4. High PAPR requires high resolution for both the transmitters DAC and thereceivers ADC [2].

5. High values of PAPR result in low efficient usage of the ADC and DAC wordlength [11].

6. Consumes more battery power in mobile devices which are power hungry [12].7. Inefficient amplification which leads to out-of-band noise.Figure 4.7 shows the graph of PAPR values versus the number of symbols in OFDM.

The first subplot shows various PAPR values for different OFDM symbols and the second

subplot show the histogram of PAPR in OFDM. Notice that the maximum PAPR appears to

be close to 16 which is very high.

Figure 4.8 shows the transfer function of a typical power amplifier. The region

between zero and peak is called the linear region and most of the functions of an amplifier

are carried out in this region. Exceeding the input voltage beyond peak introduces

non-linearity and causes non-linear distortion which should be avoided. One must make sure

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Figure 4.7. (a) PAPR of OFDM and (b) is histogram of PAPR.

PAPR is well within the limits of the peak shown or increase the dynamic range (ratio of max

and min at the input) of the amplifier, which in turn increases the peak limit, at the expense

of high cost. By increasing the resolution of both DAC and ADC due to increase in PAPR,

the system gets more complex, costs high, and requires high power.

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Figure 4.8. Transfer function of a typical power amplifier.

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CHAPTER 5

EXISTING PAPR REDUCTION TECHNIQUES

5.1CARRIER INTERFEROMETRY-OFDM

Carrier Interferometry (CI) is a type of spread spectrum technology which uses a

unique orthogonal complex spreading sequence (applied in the frequency domain) to spread

parallel data streams over all sub carriers in orthogonal frequency-division multiplexing

(OFDM) [13]. This creates frequency diversity benefits for each symbol stream leading to

high performance.

Additionally, the use of carefully selected complex spreading sequences eliminates

large peaks in power, thus reducing the Peak-to-Average Power (PAPR) of the transmitted

signal.

The transmitter and receiver block diagram of CI OFDM are shown in Figures 5.1

and 5.2, respectively which has all the blocks from OFDM along with spreading blocks after

encoders. The first N/2 subcarriers are spread using the upper spread block and the next N/2

subcarriers are spread using the lower spread block as shown in Figure 5.1. The formulae for

spreading are:

First N/2 subcarriers:

Next N/2 subcarriers:

where A is the output from encoders and N is the number of subcarriers.

The receiver had a block dispreading to despread the bits similar to the one in the

transmitter as shown in Figure 5.1. The despreader did the reverse and the formulae were

First N/2 subcarriers:

Next N/2 subcarriers:

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Figure 5.1. Block diagram of CI-OFDM transmitter.

Figure 5.2. Block diagram of CI-OFDM receiver.

5.2PERFORMANCE OF CIOFDMSYSTEMS

CI OFDM systems have bit error rate performance similar to traditional OFDM

systems. Figure 5.3 shows the bit error rate performance in AWGN channel only. Figure 5.4

shows the PAPR performance of CI OFDM. The reduction in PAPR can be seen as compared

to the traditional OFDM systems. In this case, the maximum PAPR value is limited to

10 which is certainly better when compared to traditional OFDM which had maximum PAPR

value of 16.

5.3COMPLEMENTARY CODE KEYING (CCK)OFDM

CCK is a modulation technique used in 802.11b WLAN standard. This technique is

based on polyphase complementary codes found by Golay. It was adopted to supplement

Barker code to increase the data rate in wireless networks. Golay sequences have the

property that the sum of their autocorrelation functions equals zero for all time shifts, except

SERIAL

TO

PARALLEL

PARALLEL

TO

SERIAL

N

POINT

FFT

DECODER

DECODER

DECODER

DECODER

LOW

DE-SPREA

DING FOR

1 TO N/2

DE-SPREADI

G FOR N/2+1

TO N

ADC

SERIAL

TO

PARALLEL

PARALL

EL

TOSERIAL

N POINT

IFFT

ENCODER

ENCODER

ENCODER

ENCODER

POWER

AMPLIFIER

SPREADING

FOR 1 TO N/2

SPREADING

FOR N/2+1 TO

N

DAC

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Figure 5.3. Bit error rate of CI-OFDM for AWGN channel.

Figure 5.4. (a) PAPR of CI-OFDM and (b) is histogram of

PAPR.

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zero. In other words, Golay sequences have a very good aperiodic autocorrelation property

which is useful to reduce the PAPR in OFDM system [14]. Wireless networks based on

802.11b specification employ CCK to operate at either 5.5 or 11 Mbit/s in band at 2.4 GHz.

A drastic reduction in PAPR can be seen by using complementary codes. The CCK

modulation used by 802.11b transmits data in symbols of eight chips, where each chip is a

BPSK at chip rate of 5.5 Mchip/s or a QPSK bit-pair at a chip rate of 11 Mchip/s. To

implement the 11 Mbps 802.1lb signal, a block of 8 data bits are mapped into a combination

of a unique 8-chip CCK codeword and a differential phase to form the nth symbol [15]. The

block diagram of transmitter and receiver is shown in Figures 5.5 and 5.6, respectively. The

spreading sequence block in the transmitter takes four bits as input giving eight values

(chips) which depend on the input bits as the following.

Figure 5.5. Block diagram of CCK OFDM transmitter.

Figure 5.6. Block diagram of CCK OFDM receiver.

SERIAL

TO

PARALLEL

PARALLEL

TO

SERIAL

DESPREADING

SEQUENCE

DESPREADINGSEQUENCE

DESPREADINGSEQUENCE

DESPREADINGSEQUENCE

LOW NOISE

AMPLIFIER

N

POINT

FFT

SERIAL

TO

PARALLEL

PARALLEL

TO

SERIAL

SPREADING

SEQUENCE

SPREADING

SEQUENCE

SPREADING

SEQUENCE

SPREADING

SEQUENCE

POWER

AMPLIFIERN POINT

IFFT

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Figure 5.7. (a) PAPR of CCK OFDM and (b) is histogram of

PAPR.

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CHAPTER 6

PROPOSED PAPR REDUCTION TECHNIQUES

6.1EXTENSION OF CCKOFDM

The CCK technique proposed extends the rate from 5/16 to 7/16 while retaining the

same performance. This technique increases the efficiency by 40% which is very significant

in todays data rate hungry systems. The same block diagram of CCK is used with replacing

the 5/16 spreading sequence with a 7/16 spreading sequence as shown in Figure 6.1. The rate

7/16 block consists of one rate 4/8 block as discussed above and a multiplexer which

contains two rate 4/8 with one of the bit replaced with either 0 or 1 depending on whichever

gives less PAPR value at the output. The upper block in the multiplexer takes 3 bits appends

a zero which results in 4 bits and acts as a rate 4/8 encoder, encoding 8 values given in the

CCK section above. The lower block in the multiplexer does the same but appends the 3 bits

with a one instead of a zero. The multiplexer makes sure that either of the blocks is switched

on depending on whichever gives least PAPR value at the output.

Figure 6.1. Details of the 7/16 spreading sequence block.

7-16 SPREADING

SEQUENCE

4-8

SPREADING

SEQUENCE

MULTIPLEXER

3&ZERO-8

SPREADING

SEQUENCE

3&ONE-8

SPREADING

SEQUENCE

=

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6.2PAPRPERFORMANCE OF PROPOSED CCKOFDM

SYSTEM

The simulation of the PAPR performance is shown in Figure 6.2. Notice that PAPR is

limited to a value of three which is very less compared to traditional OFDM. The PAPR

value is lesser than the 4/8 CCK OFDM system discussed earlier. The efficiency of the

system is sacrificed to obtain PAPR that low.

Figure 6.2. (a) PAPR of 7/16 CCK OFDM and

(b) is histogram of PAPR.

6.3RATE-12/16TECHNIQUE

The Rate-12/16 technique proposed can reduce PAPR while improving the

performance of bit error rate due to coding gain. This technique explorers the root cause of

PAPR which is periodicity of the bits which are fed to IFFT block after encoding and before

power amplifier. This technique eliminates the periodicity by introducing a block at the start

of the OFDM transmitter block diagram, which is the 3-4 mapper and demapper blocks as

shown in Figures 6.3 and 6.4, respectively. This block takes 3 bits as input and maps to one

of the 4 bit combinations which are non-periodic. This ensures elimination of periodicity of

the bits. For example: 000 can be mapped to either of the values such as 0001,0010,0100,

0110,0111,1000,1001,1011,1101, 1110 and not to 0000, 0011, 0101, 1010, 1100, 1111

because the latter values are periodic. PAPR is reduced by 55-60%, using this technique, as

compared to traditional OFDM whereas the efficiency is sacrificed by 25%. The tradeoff

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Figure 6.3. Block diagram of rate-12/16 transmitter.

Figure 6.4. Block diagram of rate-12/16 receiver.

lies between the efficiency and the scale of reduction of PAPR. The block diagram of this

proposed technique is shown in Figures 6.3 and 6.4 which resembles the block diagram of

OFDM except presence of an additional block which is 3-4 mapper. The receiver has a block

called pre-decoder, which finds the correct 4 bit word if there is an error introduced due tonoise. The receiver knows the eight aperiodic combinations which are mapped at the

transmitter. Each received 4 bit word is multiplied by all the eight combinations known at the

receiver and sum is calculated for all. The 4 bit word corresponding to the one which gives

the highest sum is considered as the perfect match for further processing. This involves

demapping the mapped word into the original data bits which is done by 3-4 demapper

shown in the block diagram.

6.4PERFORMANCE OF RATE-12/16TECHNIQUE

The performance of Rate-12/16 technique which consists of a Bit Error Rate (BER)

diagram and the PAPR diagram is shown in Figures 6.5 and 6.6, respectively. As we can see,

SERIAL

TO

ARALLEL

PARALLEL

TO

SERIAL

N

POINT

FFT

DECODER

DECODER

DECODER

DECODER

LOW

NOISE

AMPLIFIER

3-4

DEMAPADC

P

R

E-

D

E

CO

D

E

R

SERIAL

TO

PARALLEL

PARA-

LLEL

TO

SERIAL

N

POINT

IFFT

ENCODER

ENCODER

ENCODER

ENCODER

POWER

AMPLIFIER

3-4

MAPPE

DAC

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Figure 6.5. Bit error rate of rate-12/16 technique.

Figure 6.6. (a) PAPR of rate-12/16 technique and (b) is

histogram of PAPR.

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the bit error rate figure is similar to the one obtained in traditional OFDM indicating

similarity in the error performance. The PAPR performance is well below traditional OFDM.

The PAPR value is limited to 7 which is a reduction of more than 50% compared to

traditional OFDM.

6.5IMPROVED RATE-12/16TECHNIQUE:COMBINATION

OF RATE-12/16 AND CCK

Improved Rate-12/16 is a proposed technique which combines the previous

Rate-12/16 technique and the CCK (Complementary Code Keying) technique discussed

earlier. This combines the advantages obtained from both the techniques and reduces PAPR

even further giving the same performance. This technique replaces the 3-4 mapper block with

a 12/16 mapper which consists of two 3-4 mappers and 4-6 CCK encoder and a multiplexer

which contains four 2-2 encoders. The details of 12/16 codec is shown in Figure 6.7 between

the transmitter block diagram (Figure 6.8) and the receiver block diagram (Figure 6.9). The

3-4 mappers work similar followed by the 4-8 codec which also works similar as discussed.

The multiplexer, which has four 2-2 encoders, switches on any of the four encoders

depending on the one which gives least PAPR at the output. We get the best and the least

value of PAPR, which is the primary goal of all the techniques discussed. This technique also

has trade-off between the efficiency and the scale of PAPR reduction which existed in the

previous Rate-12/16 technique. This technique provides the same efficiency as the

Rate-12/16 technique but with reduced PAPR. The reduction when compared to the previous

Rate-12/16 technique is close to 30% which is pretty significant.

6.6PAPRPERFORMANCE OF IMPROVED RATE-12/16

TECHNIQUE

The PAPR performance of the improved rate-12/16 technique is shown in

Figure 6.10. The reduction of PAPR seen is enormous when compared to traditional OFDM.

The reduction seen is more than 65% while retaining the BER performance. The highest

PAPR value seen in this technique is less than five on the histogram which is way less than

the traditional OFDM which is 16. This technique has lesser PAPR than the Rate-12/16

technique while the efficiencies remained the same which is 75%.

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Figure 6.9. Block diagram of improved rate-12/16 receiver.

Figure 6.10. (a) PAPR of improved rate-12/16 technique and

(b) is histogram of PAPR.

and 6.13. Figure 6.12 shows comparison of the four technologies viz traditional OFDM,

CI-OFDM, Rate-12/16 technique and Improved Rate-12/16 technique. The Improved

Rate-12/16 technique wins the race as the PAPR is the least when compared to other

techniques discussed so far. The only drawback is the efficiency which is 75% whereas the

PAPR is reduced close to 70% compared to traditional OFDM. One can use Rate-12/16

technique for less complexity, if the obtained PAPR value is satisfied. The improved

rate-12/16 technique is a bit complex compared to Rate-12/16 technique but the PAPR

SERIAL

TO

PARALLEL

PARALLEL

TO

SERIAL

N

POINT

FFT

DECODER

DECODER

DECODER

DECODER

LOW

NOISEAMPLIFIER

12/16

DEMAP

ADC

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Figure 6.11. Bit error rate of OFDM, CI-OFDM, rate-12/16

techniques.

Table 6.1. Comparison of OFDM, CI-OFDM, CCK, Rate-12/16 and Improved

Rate-12/16 Techniques

Techniques BER @ Eb/No=5 Max PAPR Efficiency

OFDM 10-3

16 1

CI-OFDM 10-3

11 15-16 CCK-OFDM - 2 0.3125

7-16 CCK-OFDM - 3 0.4375

Rate-12/16 10-4

7 0.75

Improved Rate-12/16 10-4

5 0.75

performance is up by 30%. One can chose either of the two techniques depending on the

requirements. Figure 6.13 shows the histogram of the same technologies and notice that no

value exist greater than 5 in case of improved rate-12/16 technique. One can conclude that,there is a better performance in both BER and PAPR for a sacrificed efficiency.

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Figure 6.12. PAPR of OFDM, CI-OFDM, rate-12/16 and

improved rate-12/16 techniques.

Figure 6.13. Histogram of PAPR of OFDM, CI-OFDM,

rate-12/16 and improved rate-12/16 techniques.

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CHAPTER 7

CONCLUSION AND FUTURE ENHANCEMENT

High PAPR is the culprit for use of inefficient power amplifiers which lessens the

battery life in power hungry devices such as mobile phones. Even though many techniques

exist today which takes care of PAPR concerns, there is always scope for improvement. A

couple of improvements for PAPR were discussed and couple of them was proposed too. The

proposed techniques bring PAPR to a new low by making certain modifications. A trade-off

exists between the extent of reduction of PAPR and the efficiency. The trade-off also exists

between the complexity and extent of reduction of PAPR. All the simulations were carried

out in MATLAB.

Some of the future work involves:

Increasing the efficiency while retaining the same or getting better PAPRperformance.

Reducing the complexity by using some efficient techniques.

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