PAPR Reduction Techniques

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INTRODUCTION

1.1 Background of the Problem

This chapter covers the material on thesis background, objectives, scope and the thesis ou

Introduction on this chapter covers about the MIMO OFDM implementation method

description on the available software for implementation. The problem statement will als

carried out in this chapter.

ith the rapid growth of digital communication in recent !ears, the need for high"speed d

transmission has been increased. The mobile telecommunications industr! faces the proble

providing the technolog! that is able to support a variet! of services ranging from vocommunication with a bit rate of a few kbps to wireless multimedia in which bit rate up

Mbps.

$owada!s, third generation %&'( mobile communication s!stems have became popular

around the world. )owever, its services cannot provide a ver! big d!namic range of data rate

nor can it meet the re*uirements of a variet! of business t!pes. +esides, voice transportati

in &' still relies on circuit switching technolog!, rather than pure Internet rotocol %

approach. Thus, based on consideration listed above, man! countries have alread! carr

out research on the ne-t completel! evolutionar! fourth generation % '( communicati

s!stems which provide a comprehensive and secure I solution where voice, data, a

multimedia can be offered to users at /an!time, an!where/ with higher data rates tha

previous generations 012. 3ince bandwidth resource in ' mobile communications is still scarce, in order t

improve spectrum efficienc! and achieve as high as 144Mbps wireless transmission rate

re*uires more advanced techni*ues to be emplo!ed. The limitation of modulation schemes


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e-isting communication s!stems has become an obstruction in further increasin

the data rate. )ence, ne-t generation mobile communication s!stems need more

sophisticated modulation scheme and information transmission structure.

Multiple input multiple output %MIMO( and orthogonal fre*uenc! division multiple-ing

DM( have therefore been adopted due to their superior performance. The! promise to beco

ke! high"speed wireless communication technologies and combining them can provi

wireless industr! evolution from &' to ' s!stem.

1.2 Theoretical oundation

This project is the continuation from the previous master student project which entitled 5ware 7arge"3cale Multiuser MIMO"OFDM downlink which investigate an orthogo

fre*uenc!"division multiple-ing %OFDM("based downlink transmission scheme for large

multi"user %M8( multiple"input multiple"output %MIMO( wireless s!stems012. The use of

causes a high peak"to"average %power( ratio % 56(, which necessitates e-pensive and p

inefficient radio"fre*uenc! %6F( components at the base station. In this paper, present a n

downlink transmission scheme, which e-ploits the massive degrees"of"freedom availabl

large"scale M8"MIMO"OFDM s!stems to achieve low 56. 3pecificall!, it proposes to join

perform M8 pre"coding, OFDM modulation and 56 reduction b! solving a conv

optimi9ation problem. It develops a corresponding fast iterative truncation algorithm %FI

and show numerical results to demonstrate tremendous 56"reduction capabilities. T

significantl! reduced linearit! re*uirements eventuall! enable the use of low"cost 6components for the large"scale M8"MIMO"OFDM downlink.

In MIMO"OFDM s!stem, the output is the superposition of multiple sub"carriers. In this c

some instantaneous power outputs might increase greatl! and become far higher than


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mean power of the s!stem when the phases of these carriers are same. This is also defined

large eak"to"5verage ower 6atio % 5 6(. )igh 5 6 is one of the most serious problems

MIMO"OFDM s!stem. To transmit signals with high 5 6, it re*uires power amplifiers w

ver! high power scope. These kinds of amplifiers are ver! e-pensive and have low

efficienc!"cost. If the peak power is too high, it could be out of the scope of the linear po

amplifier. This gives rise to non"linear distortion which changes the superposition of the si

spectrum resulting in performance degradation. If there are no measures to reduce the h

5 6, MIMO"OFDM s!stem could face serious restriction for practical applications.

1.! Ob"ecti#e$The aim of the thesis is:"

%i( To anal!9e transmission and reception of OFDM using ; 3< modulation in Matlab.

%ii( To anal!9e +=6 and capacit! performance of MIMO OFDM s!stem.

%iii( To stud! and implement clipping as a 5 6 reduction techni*ue in MIMO OFDM 3!ste

%iv( To stud! and implement T3 as a 5 6 reduction techni*ue in MIMO OFDM 3!stem.

%v( To stud! and implement 37M as a 5 6 reduction techni*ue in MIMO OFDM 3!stem.

%vi( To compare performance of 5 6 reduction techni*ues in MIMO OFDM 3!stem

%viii( To anal!9e Multiuser MIMO downlink in terms of 5 6 6eduction Techni*ue.

1.% &ignificance

7arge 3cale multiple"input multiple"output %MIMO( wireless communication is a prom

means to meet the growing demands for higher throughput and improved *ualit!"of"servic

ne-t"generation multi"user %M8( wireless communication s!stems 0#2. The vision is that a

number of antennas at the base"station %+3( would serve a large number of users concur

and in the same fre*uenc! band, but with the number of +3 antennas being much larger than


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number of users 0&2, sa! a hundred antennas serving ten users. 7arge"scale MIMO s!stem

have the potential to reduce the operational power consumption at the transmitter and enabl

use of low"comple-it! schemes for suppressing M8 interference %M8I(. 5ll these proper

render large"scale MIMO a promising technolog! for ne-t"generation wireless communica

s!stems.

hile the theoretical aspects of large"scale M8"MIMO s!stems have gained significa

attention in the research com"munit!, e.g., 0#2>0?2, much less is known about pra

transmission schemes. 5s pointed out in 0@2, practical reali9ations of large"scale MIMO s!

will re*uire the use of low cost and low"power radio"fre*uenc! %6F( components. To thisreference 0@2 proposed a novel M8 pre"coding scheme for fre*uenc!"flat channels, which

on per"antenna constant envelope %A=( transmission to enable efficient implementation

non"linear 6F components. Moreover, the A= pre"coder of 0@2 forces the peak"to"av

%power( ratio % 56( to unit!, which is not necessaril! optimal as in practice there is alw

trade"off between 56, error"rate performance, and power amplifier efficienc!. ract

wireless channels t!picall! e-hibit fre*uenc! selective fading and a low" 56 pre"coding solut

suitable for such channels would be desirable. referabl!, the solution should be such that

comple-it! re*uired in each %mobile( terminal is small %due to stringent area and p

constraints(, whereas heavier processing could be afforded at the +3. Orthogonal fre*uen

division multiple-ing %OFDM( 0B2 is an efficient and well"established wa! of dealing

fre*uenc! selective channels. In addition to simplif!ing the e*uali9ation at the receiver, OF

also facilitates per"tone power and bit allocation, scheduling in the fre*uenc! domain,

spectrum shaping. )owever, OFDM is known to suffer from a high 56 0C2, which necessit

the use of linear 6F components %e.g., power amplifiers( to avoid out"of"band radiatio


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signal distortions. 8nfortunatel!, linear 6F components are, in general, more costl! and le

power efficient than their non"linear counterparts, which would eventuall! result in e-orbi

costs for large"scale +3 implementations having hundreds of antennas. Therefore, it is

paramount importance to reduce the 56 of OFDM"based large"scale M8"MIMO s!stems

facilitate corresponding low"cost and low"power +3 implementations. To combat the challen

linearit! re*uirements of OFDM, a plethora of 56"reduction schemes have been proposed

point"to"point single"antenna and MIMO wireless s!stems, e.g., 0142>01?2. For M8"M

s!stems, however, a straightforward adaptation of these schemes is non"trivial, mainl! bec

M8 s!stems re*uire the removal of M8I using a pre"coder 01@2. 56"reduction schemes suifor the M8"MI3O and M8"MIMO downlink were described in 01B2 and 01C2, respective

rel! on Tomlinson")arashima pre"coding. +oth schemes, however, re*uire speciali9ed sig

processing in the %mobile( terminals %e.g., modulo reduction(, which prevents their

conventional MIMO"OFDM s!stems, such as I=== B4#.11n 0#42.

'IT(R)TUR( R(*I(+


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2.1 Introduction

ith the rapid growth of digital communication in recent !ears, the need for high"speed d

transmission has increased. The mobile telecommunications industr! faces the problem

providing the technolog! that be able to support a variet! of services ranging from vo

communication with a bit rate of a few kbps to wireless multimedia in which bit rate up

Mbps. Man! s!stems have been proposed and OFDM s!stem based has gained much attent

for different reasons. 5lthough OFDM was first developed in the 1C?4s, onl! recentl! has it b

recogni9ed as an outstanding method for high"speed cellular data communication wher

implementation relies on ver! high"speed digital signal processing, and this has onl! rece become available with reasonable prices of hardware implementation.

MIMO signaling is a groundbreaking development pioneered b! ack inters o

+ell 7aboratories in his 1CB article 0#2. 3everal different antenna configurations are us

defining space"time s!stems.

2.2 'iterature &ur#e,$

OFDM started in the mid ?4s. There were man! people who took an initiative and perf

work on this field. OFDM, first introduced in 1C?? 0142 and patented few !ears later 01

known for high"speed data transmission. =arl! on OFDM gained attention because data was

in parallel on different sub carriers, hence high speed e*uali9ation was no longer re*uired. O

incentives of OFDM were high spectral efficienc! and immunit! to the effects of multip

fading. In 1C@1 the idea of using the discrete Fourier transform in the modulationEdemod

process was introduced 01#2. rior to this breakthrough, OFDM s!stems were prohibit

comple- because arra!s of sinusoidal generators and coherent demodulators were necessar

the implementation. ith special"purpose Fast Fourier transform %FFT( chips, now it be


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possible to implement the entire OFDM s!stem digitall! and efficientl!. 7atel!, OFDM has be

put into practice in D5+, digital television and high definition television %)DT (01&2, hig

rate digital subscriber lines %)D37(, ver! high"speed digital subscriber lines % )D3

as!mmetric digital subscriber lines %5D37(, and mobile wideband data transmission %

B4#.11a, )iperlan II(. It is also used in the I=== B4#.1? iM5G 01 2 standard. 3om

contributions of some personalities are described below:"

%i( Ahang 0#2 proposed a method to s!nthesis band limited signals for multi ch

transmission. The idea is to transmit signals simultaneousl! through a linear band limi

channel without inter channel %IAI( an inter s!mbol interference %I3I(.%ii( 5fter that, 3alt9berg 0&2 performed an anal!sis based on AhangHs work and he conclu

the focus to design a multi channel transmission must concentrate on reducing crosstalk %

1C@1, einstein and =bert 0 2 made an important contribution to OFDM. Discrete Fo

transform %DFT( method was proposed to perform the base band modulation and demodu

DFT is an efficient signal processing algorithm. It eliminates the banks of sub carrier oscilla

The! used guard space between s!mbols to combat IAI and I3I problem. This s!stem did

obtain perfect orthogonalit! between sub carriers over a dispersive channel.

%iv( It was eled and 6ui9 0 2 in 1CB4 who introduced c!clic prefi- %A ( that sol

orthogonalit! issue. The! filled the guard space with a c!clic e-tension of the OFDM s!mbol

is assume the A is longer than impulse response of the channel.

%v( In 1CB4, )irosaki introduced an e*uali9ation algorithm to suppress both inter s!mb

interference %I3I( and IAI 0?2, which ma! have resulted from a channel distor

s!nchroni9ation error, or phase error. In the meantime, )irosaki also applied ;5M modulation


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pilot tone, and trellis coding techni*ues in his high"speed OFDM s!stem, which operate

voice"band spectrum.

%vi( In 1CB , Aimini introduced a pilot"based method to reduce the interference emanating

the multipath and co"channels 0@2.

%vii( In the 1CC4s, OFDM s!stems have been e-ploited for high data rate communications.

I=== B4#.11 standard, the carrier fre*uenc! can go up as high as #. ')9 or ')9. 6esearchers

tend to pursue OFDM operating at even much higher fre*uencies nowada!s. For e-ample,

I=== B4#.1? standard proposes !et higher carrier fre*uencies ranging from 14 ')9 to ?4 ')9.

%viii( . 5hn and ). 3. 7ee,0B2 in 1CC& anal!9e Fre*uenc! domain e*uali9ation of OFDMover fre*uenc! nonselective 6a!leigh fading channels

%i-( $.5. Dhahi.,studied 0C2 Optimum finite"length e*uali9ation for multicarrier transceive

1CC? was developed

%-( 6. 7i and '. 3tette, 0142 in 1CC? studied Time"limited orthogonal multicarrier modul

schemes

%-i(J. Khao and 3. '. )aggman,0 112 in #441 made contribution to Intercarrier interference s

cancellation scheme for OFDM mobile communication s!stems

%-ii( 7. ang and J. Aao, 0#B2 made contribution to 3ub"optimum T3 for 5 6 reductio

OFDM signals in #44B

%-iii( F. 6usek, D. ersson, +.


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Orthogonal Fre*uenc! Division Multiple-ing %OFDM( is a multi"carrier transmis

techni*ue, which divides the available spectrum into man! carriers, each one being modulate

a low rate data stream. OFDM is similar to FDM5 in that the multiple user access is achieved

subdividing the available bandwidth into multiple channels that are then allocated to us

)owever, OFDM uses the spectrum much more efficientl! b! spacing the channels much clo

together. This is achieved b! making all the carriers orthogonal to one another, prevent

interference between the closel! spaced carriers.

2.!.2 Orthogonalit, Defined

Orthogonalit! is defined for both real and comple- valued functions. The functions N1%tN#%t( are said to be orthogonal with respect to each other over the interval a t b if the!

the condition.

OFDM splits the available bandwidth into man! narrowband channels %t!picall! 144"B4

each with its own sub"carrier. These sub"carriers are made orthogonal to one another, mea

that each one has an integer number of c!cles over a s!mbol period. Thus the spectrum of e

sub"carrier has a null at the centre fre*uenc! of each of the other sub"carriers in the s!stem

demonstrated in Figure #.4 below. This results in no interference between the sub"carr

allowing then to be spaced as close as theoreticall! possible. +ecause of this, there is no g

need for users of the channel to be time"multiple-ed, and there is no overhead associated w

switching between users. This overcomes the problem of overhead carrier spacing re*uire

FDM5.


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Figure #.4: Orthogonalit! of 3ub"carriers

2.!.! O D- &ub/Carrier$ in re0uenc, Domain

5s for mentioned, OFDM is a special form of Multi Aarrier Modulation %MAM( and the O

time domain waveforms are chosen such that mutual orthogonalit! is ensured even though

carrier spectra ma! over"lap. ith respect to OFDM, it can be stated that orthogonalit! is

implication of a definite and fi-ed relationship between all carriers in the collection. It me

that each carrier is positioned such that it occurs at the 9ero energ! fre*uenc! point of all o

carriers. The sinc function, illustrated in Figure #.1 e-hibits this propert! and it is used a

carrier in an OFDM s!stem.

Figure #.1: OFDM 3ub carriers in the Fre*uenc! Domain


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2.!.% eneration of O D- &ignal$

To implement the OFDM transmission scheme, the message signal must first be digit

modulated. The carrier is then split into lower"fre*uenc! sub"carriers that are orthogonal to

another. This is achieved b! making use of a series of digital signal processing operations.

The message signal is first modulated using a scheme such as + 3


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The underl!ing principle here is that the FFT can keep tones orthogonal to one another if

tones have an integer number of c!cles in a s!mbol period. In the e-ample figure #.& below

see signals with 1,# and c!cles to form orthogonal set.

Figure #.&: 5 3et of Orthogonal 3ignals

To convert the sub"carriers to a set of orthogonal signals, the data is first combined into fr

of a suitable si9e for an FFT or IFFT. 5 FFT should be alwa!s in the length of #$ %where $ i

integer(. $e-t, an $"point IFFT is performed and the data stream is the output of the transmit

Thus when the signals of the IFFT output are transmitted se*uentiall!, each of the $ channel

appears at a different sub"carrier fre*uenc!. In order for this orthogonalit!, the receiver and

transmitter must be perfectl! s!nchroni9ed. This means the! both must assume e-actl! the sa

modulation fre*uenc! and the same time"scale for transmission. 5t the receiver, the ions

performed to recover the data. 3ince the FFT is performed in this stage, the data is back in

fre*uenc! domain. It is then demodulated according to the block diagram below.

2.!. uard Period


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This is especiall! important if the signal fs sub"carriers are to retain their orthogonalit! add

Figure #. : +lock Diagram for OFDM Aommunicationsguard period between transmitted s!mbols can be used to accomplish this. The guard the spa

of a an! c!clic prefi-, which is appended at the front of ever! OFDM signal. The c!clic pre

imposes a penalt! on bandwidth efficienc!, it is often the best compromise between performa


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and of that at the fre*uenc! where the received signal is evaluated, all other signals is 9ero.

period allows time for multipath signals from the previous s!mbol to dissipate before forma

from the current s!mbol is recorded. The most effective guard period is a efficienc! in

presence of inter"s!mbol interference. The c!clic prefi- is a cop! of the last part of the OFD

s!mbol, and is of e*ual or greater length than the ma-imum dela! spread of the channel %

Figure #. (.

Figure #. : Implementation of A!clic refi-

2.!.3 )d#antage$ of O D-

OFDM has several advantages compared to other t!pe of modulation techni*ue implemente

wireless s!stem. +elow are some of the advantages that describe the uni*ueness of OFDcompared to others:

i. +andwidth =fficienc!ii. OFDM overcome the effect of I3I

iii. OFDM combats the effect of fre*uenc! selective fading and burst error

2.!.4 The 5eakne$$ of O D-

5lthough OFDM is e-cellent in combating fading effect, it does not mean at OFDM is f

from an! weaknesses. +elow are some of the weaknesses for the OFDM s!stem.

i. eak"to"Mean ower 6atioii. 3!nchroni9ation

2.!.6 ) lication$ of O D-.


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OFDM has been chosen for several current and future communications. In addition to h

speed wireless application has also been adopted into several =uropean wireless communica

applications such as:".

i. Digital +roadcastingii. Terrestrial Digital ideo +roadcasting Terrestrial Television +roadcasting %DTT+(

iii. I=== B4#.11aE)iper75$# and MM5A ireless 75$iv. Mobile ireless Aommunication.

2.% -I-O &,$tem

MIMO signaling is a groundbreaking development pioneered b! ack inters o

+ell 7aboratories in his 1CB article 0#42. 3everal different antenna configurations are

in defining space"time s!stems.

2.%.1 Ba$ic &tructure of -I-O &,$tem

There e-ist several communication transmission models as follows %see Fig. #.?(:


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Figure #.?:" Different T!pes of Aommunication Models

1. 3ingle"input"and"single"output %3I3O( s!stem: It is uses onl! one antenna both at

transmitter and receiver.

#. 3ingle"input"and"multiple"output %3IMO( s!stem: It uses a single transmitting ant

and multiple receiving antennas 0&2.

&. Multiple"input"and"single"output %MI3O( s!stem: It has multiple transmitting ant

and one receiving antenna.

. Multiple"input"multiple"output %MIMO( s!stem: It uses multiple antennas both

transmission and reception. Multiple transmitting and receiving antennas will achie

antenna diversit! without reducing the spectral efficienc!.

In MIMO s!stem, a number of antennas are placed at the transmitting and receiving en

their distances are separated far enough. The distance between different base station anten

can be set as 14 times the carrier wavelength and mobile station antennas can be separated

half carrier wavelength. In this wa!, independent channels between the transmitting a

receiving ends are formed so as to achieve spatial diversit! or space division multiple-in

Theidea is to reali9e spatial multiple-ing and data pipes b! developing space dimensio


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which are created b! multi"transmitting and receiving antennas. The block diagram in Fig.

illustrates the antenna configuration in space"time s!stems.

2.%.2 -I-O Channel and Ca acit,

'enerall!, there are several kinds of channel impairments in wireless communication:"

1. Free space path loss %F3 7(: This refers to power loss of electromagnetic wave w

there is an unobstructed line"of"sight path e-ists between transmitter and receiver.

#. 3hadow fading: In realit!, big obstructions such as hills or large buildings obscure the m

signal path between the transmitter and the receiver, which will lead to shadowing and ampli

fluctuation of receiving signals. In fact, free"space path loss and shadow fading belong to lscale fading or slow fading.

&. 3mall"scale fading %multipath(: This refers to rapid fluctuation of amplitude and phase

short period of time or travel distance. 3mall"scale fading can be generall! related to reflec

diffraction and scattering. The interaction of these three different propagation mechanisms c

fading at a specific location 0 2. 6a!leigh fading is an applicable model to describe small"

fading when there is no dominant propagation along the line of sight between the transmitter

receiver. If there is a dominant propagation along the line of sight, 6ician fading ma! be m

applicable.

3!stem capacit! can be defined as ma-imum transmission data rate in condition of small er

probabilit!. +oth Telatar and Foschini in their papers state that in MIMO s!stem, s!stem capa

can be increased linearl! b! means of setting up multiple space sub"channels which connectransmitter and receiver 0 2 0?2. The transmitted signal bandwidth is so narrow that its fre*

response can be considered as being flat. Define the channel matri- ) is $r P$t comple- matri

elements of it are fading coefficients from the j"th transmit antenna to the i"th receive antenn


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2. -I-O/O D- &,$tem

2. .1 Introduction

In high"speed wireless communication, combining MIMO and OFDM technolog!, OFDM

be applied to transform fre*uenc!"selective MIMO channel into parallel flat MIMO chan

reducing the comple-it! of the receiver, through multipath fading environment can also ach

high data rate robust transmission. Therefore, MIMO"OFDM s!stems obtain diversit! gain

coding gain b! space"time coding, at the same time, the OFDM s!stem can be reali9ed w

simple structure. Therefore, MIMO"OFDM s!stem has become a welcome proposal for

mobile communication s!stems

Figure #.@:"MIMO OFDM 3!stem

2. .2 Ba$ic &tructure of -I-O/O D- &,$tem

5t the transmitting end, a number of transmission antennas are used. 5n input data bit streamsupplied into space"time coding, then modulated b! OFDM and finall! fed to antennas sending out %radiation(. 5t the receiving end, in"coming signals are fed into a signal detecto processed before recover! of the original signal is made. Fig. #.@ shows the basic structur


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amplitudes of various samples of -%t(. Due to s!mbol spaced output in the first e*uation we

some of the peaks missing which can be compensated b! oversampling the e*uation b! so

factor to give the true 5 6 value.

2.3.2 P)PR Reduction Techni0ue$

5 6 reduction techni*ues var! according to the needs of the s!stem and are dependent

various factors. 5 6 reduction capacit!, increase in power in transmit signal, loss in data r

comple-it! of computation and increase in the bit"error rate at the receiver end are vari

factors which are taken into account before adopting a 5 6 reduction techni*ue of the s!st

0&2. The 5 6 reduction techni*ues on which we would work upon and compare in our

stages are as follows:

1. 3ignal Distortion:" One of the most pragmatic and easiest approaches is clipping and filt

which can snip the signal at the transmitter so as to eliminate the appearance of high peaks a

a certain level. Alipping can be implemented to the discrete samples prior to digital"to"an

convertor %D5A( or b! designing analog"to"digital"convertor %D5A( andEor amplifie

saturation levels which are lower than the d!namic range 01@2. +ut due to the nonlinear dist

introduced b! this process, orthogonalit! will be destro!ed to some e-tent which results

serious in band noise and out of band noise. In"band noise cannot be removed b! filterin

decreases the bit error rate %+=6(. Out"of"band noise reduces the bandwidth efficienc

fre*uenc! domain filtering can be emplo!ed to minimi9e the out"of"band power. 5lthou

filtering has a good effect on noise suppression, it ma! cause peak re"growth. To overcome

drawback, the whole process is repeated several times until a desired situation is achieved.

#. 3ignal 3crambling Techni*ues:" The fundamental principle of this techni*ue is to scram

each OFDM signal with different scrambling se*uences and select one which has the sma


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5 60& 22 value for transmission. 5pparentl!, this techni*ue does not guarantee reductio

5 6 value below to a certain threshold, but it can reduce the appearance probabilit! of h

5 6 to a great e-tent. This t!pe of approach include: 3elective Mapping %37M( and ar

Transmit 3e*uences % T3(. 37M method applies scrambling rotation to all sub"car

independentl! while T3 method onl! takes scrambling to part of the sub"carriers. These

methods can be applied to an! scenarios without restriction on the number of sub"carriers

t!pe of modulation. )owever, for successful recover! of the signal at the receiver, additio

information is needed. That leads to low bandwidth utili9ation and high hardware comple-it

implementation.

&. Aoding Techni*ues:" The core of encoding method is to appl! special forward error corre

techni*ue to remove the OFDM signals with high 5 6. The classical schemes include lin

block code 0&?2, 'ola! codes and 6eed"Muller code 0&@2. 5s far as linear block code met

concerned, it is onl! suitable to the scenario which has a small number of sub"carriers, w

results in limited applications. 6eed"Muller code is a high efficienc! coding scheme, it obtai

lower 5 6 for the second order co"sets code b! classif!ing the alsh")adamard transform

% )T( spectrum of the code words. +! using 6eed"Muller code, 5 6 can be reduced to &d+

most with a good error correcting performance. )owever, all in all, the encoding method

limited to t!pes of constellation.

2.3.! Cumulati#e Di$tribution unction

The Aumulative Distribution Function %ADF( 0# 2 is one of the most regularl! used para

which is used to measure the efficienc! of an! 5 6 techni*ue. $ormall!, the Aomplementa

ADF %AADF( is used instead of ADF, which helps us to measure the probabilit! that the 5

a certain data block e-ceeds the given threshold.


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+! implementing the Aentral 7imit Theorem for a multi > carrier signal with a large numbe

sub"carriers, the real and imaginar! part of the time > domain signals have a mean of 9ero a

variance of 4. and follow a 'aussian distribution. 3o 6a!leigh distribution is followed for t

amplitude of the multi > carrier signal, where as a central chi"s*uare distribution with

degrees of freedom is followed for the power distribution of the s!stem.

Figure #.B AADF of 5 6 of Data +lock

The ADF of the amplitude of a signal sample is given b!

F%9(Q1"e-p%9( %&(

The AADF of the 5 6 of the data block is desired is our case to compare outputs of var

reduction techni*ues. This is given b!

% 5 6Y9(Q1" % 5 6V9(Q1"F%9( $Q1"%1"e-p%"9(( $ % (

2.3.% )m litude Cli ing and iltering


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5mplitude clipping is considered as the simplest techni*ue which ma! be under taken for 5

reduction in an OFDM s!stem. 5 threshold value of the amplitude is set in this case to limit

peak envelope of the input signal. 3ignal having values higher than this pre"determined valu

clipped and the rest are allowed to pass through un"disturbed 0&2.

+%-(Q -, W-WV5

5e-p%jZ%-( W-WY5 %

where, B(x) = the amplitude value after clipping.

x Q the initial signal value. A Q the threshold set b! the user for clipping the signal.

The problem in this case is that due to amplitude clipping distortion is observed in the s!s

which can be viewed as another source of noise. This distortion falls in both in"band and ou

band. Filtering cannot be implemented to reduce the in>band distortion and error perform

degradation is observed here. On the other hand spectral efficienc! is hampered b! out>of>b

radiation. Out>of>band radiation can be reduced b! filtering after clipping but this ma! resu

some peak re>growth. 5 repeated filtering and clipping operation can be implemented to s

this problem. The desired amplitude level is onl! achieved after several iteration of this proce

2.3. &elected -a ing

The techni*ue of selected mapping %37M( for 5 6 reduction was proposed in 1CC? 0&

37M from a set of candidate signals which are generated to represent the same information

signal with lowest 5 6 is selected and transmitted. The information about this selection a

needs to be e-plicitl! transmitted along with the selected signal as side information. The 37

s!stem block diagram is illustrated below. 37M needs to transmit the information to the recei


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about the selected signal, as side information. If there is a error in the received side informa

then the receiver cannot recover the information from the transmitted selected signal. ThatH

a strong protection against transmission errors is needed regarding side information. Onc

receiver has this side information then the decoding process is ver! simple. 37M is can

emplo!ed for larger number of sub"carriers with moderate comple-it!. The techni*ue uses co

onl! for 5 6 reduction and does not include error correction capabilities of codes. This sch

is aimed at decreasing the fre*uenc! of peak occurrence rather than elimination of peaks.

drawbacks include multiple numbers of IFFT operations leading to increased comple-it! and

need for transfer of side information to the receiver without an! margin for transmission er $ew e-tension techni*ues of 37M but with no need for transmission of side information h

been proposed 0.

Figure #.C +lock diagram of 3elected Mapping Techni*ue


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tone reservation as a linear programming problem that has an e-act solution %the OA3 m

is suboptimal(. The linear programming solution can be reached with comple-it! O 0$ log

The idea behind tone reservation is to isolate energ! used to cancel large peaks to a predef

set of tones. These tones do not bear an! useful information and are orthogonal to the d

bearing tones. This orthogonalit! makes recovering the data trivial.

The advantages of T6 techni*ue include:

1. $o need for side information#. Fewer comple-"multiplications as onl! one time IFFT operation is needed. +

multiple iteration operations are needed after IFFT operation.

&. $o special receiver operation is neededhile promising, tone reservation has several shortcomings. First the data rate is necessa

decreased because some tones are used strictl! for 56 reduction. The second problem is

difficult! of selecting which tones to reserve. 5 random search over all the possible sets,

would greatl! increase the comple-it! of tone reservation. Often the tones have to be cho

contiguousl! because fades often affect contiguous sets of sub carriers. These contiguous se

tones are known to have bad 56 reduction abilities. The third issue is a tradeoff between

*uantit! of reserved tones and the raise in average power due to tone reservation. More the t

that are reserved, lesser the power needs to be allocated for 5 6 reduction. On other ha

more reserved tones mean more unused bandwidth that could be data bearing.

2.3.6 Tone In"ection

Motivated b! the data rate loss of tone reservation, Tellado introduced a new techni*ue na

tone injection 0 2. It reduces the 5 6 without compromising the data rate. In this metho

si9e of the basic constellation is increased. )ence mapping of original constellation points

numerous corresponding points in the new stretched out constellation becomes possible.


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distance between these duplicate points can be calculated as D. where MQ constellation si9e.

There is no effect on +=6 and all we have to do is add a modulo"D subse*uent to FFT in

receiver side. 3ince mapping of each information unit into numerous corresponding constell

points is done, it gives a margin of free will which can be used reduction of 5 6.

2.4 actor$ (ffecting P)PR

Factors effecting 5 6 are as follows:

2.4.1 Number of $ub carrier$

In Multi"Aarrier 3!stems the comple- base band signal for one s!mbol in an OFDM s!stem m

be e-pressed as:G%t(Q1ER$ S ane-p%jwn t( %?(

here $ is the number of sub carriers and an is the modulating s!mbol. For moderatel! large

numbers of m" 3< sub carriers the *uadrature components of - %t( each tend towards a 'aus

distribution %giving the sum of their power amplitude a 6a!leigh distribution(. Aonse*ue

whilst the peak value possible is $ times the individual sub carrier peak, the probabilit! of

value close to that peak occurring is ver! low. For e-ample, with onl! # sub carriers, t

probabilit! of the 5 6 e-ceeding d+ is 14"# and of e-ceeding Bd+ is onl! 14" 0#@2.

2.4.2 -odulation Order

)igh data bandwidth efficienc! %in terms of bEsE)9( ma! be achieved b! using higher o

modulations based, for e-ample, on ;5M. hen the sub carrierHs modulation is a higher"or

;5M t!pe, the 5 6 of the summed OFDM signal is increased b! the 5 6 of the ;5M

constellation used.


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Table #.1 5 6 for an unfiltered base band signal

)owever, the probabilit! of these higher peaks occurring is correspondingl! less. Moreov

since among advantages of OFDM one is that sub carriers can have their modula

independentl! varied to adapt to channel conditions, the combined 5 6 in an! s!stem usithis techni*ue ma! be difficult to predict and control. 5 6 for an unfiltered base band signa

listed in the following Table #.1.

2.4.! Con$tellation $ha e

The last entr! in Table #.1 is for a constellation obtained b! modif!ing # ?" ;5M to redu

5 6. This modified constellation shape is shown in figure #. . )owever, there is an additio

processor load associated with encoding and decoding this constellation.


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Figure #.11 # ?";5M constellations: %a( regular and %b( modified mapping to reduce 5 6

2.4.% Pul$e &ha ing

In terrestrial communications it is common to appl! pulse shaping to the base band signa

reduce the bandwidth of the transmitted spectrum, but this causes overshoot and could inc

the 5 6 of the modulating signal b! " d+.

2.6 -ulti/U$er -I-O

2.6.1 Introduction

e have shown that the channel capacit! of the single"user $6[$T MIMO s!stems is

proportional to $min. In fact, MIMO techni*ue is an essential means of increasing capacit

the high 3$6 regime, providing at most $min spatial degrees of freedom. In the single"u

MIMO s!stem, a point"to"point high data rate transmission can be supported b! spa

multiple-ing while providing spatial diversit! gain. )owever, most communication s!stems de

with multiple users who are sharing the same radio resources. Figure #.1# illustrates a t!p

multi"user communication environment in which the multiple mobile stations are served

single base station in the cellular s!stem. In Figure #.1#, three out of four users are selectedallocated communication resource such as time, fre*uenc!, and spatial stream. 3uppose that

base station and each mobile station are e*uipped with $+ and $M antennas, respectivel!. 5s

independent users form a virtual set of < [ $M antennas which communicate with a single


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with $+ antennas, the end"to"end configuration can be considered as a MIMO s!stem

downlink.

Figure #.1# Multi"8ser MIMO 3!stem

In this multi"user communication s!stem, multiple antennas allow the independent user

transmit their own data stream in the uplink %man!"tone( at the same time or the base stat

transmit the multiple user data streams to be decoded b! each user in the downlink %on

man!(. This is attributed to the increase in degrees of freedom with multiple antennas as in

single"user MIMO s!stem. In the multi"user MIMO s!stem, downlink and uplink channels

referred to as broadcast channel %+A( and multiple access channel %M5A(, respectivel!. 3i

data streams of < independent users are available for a single receiver of the base station in

multiple access channels, the multi"user MIMO s!stem is e*uivalent to a single user MI

s!stem in the uplink.2.6.2 -athematical -odel for -ulti/U$er -I-O &,$tem

Aonsider < independent users in the multi"user MIMO s!stem. e assume that the +3 and ea

M3 are e*uipped with $+ and $M antennas, respectivel!. Figure #.1& shows the uplink chan


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known as a multiple access channel %M5A( for < independent users. 7et transmit signal from

u%th( user, u %\( 1] #] [ [ [ [


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!uQ )uD7-^9u, u Q 1,#,___,<

%B(

where 9u is the additive KMA3A' noise at the uth user. 6epresenting all user signals b! a single

vector, the overall s!stem can be represented as

! 1 ) 1D7 91

! # Q ) #D7 - ^ 9#

_ _. _.

! k ) k D7 9k

%C(

Figure #.1 Downlink channel model for multi"user MIMO s!stem: broadcast channel %+A(.

2.6.! Channel Ca acit, of -ulti/U$er -I-O &,$tem

+ased on the mathematical models in the previous section, we discuss some e-amples for

channel capacit! of M5A and +A in the 5 '$ channel. Aapacit! region of M5A was first

introduced in 0#B2. 7et u and 6 u denote the power and data rate of the uth user in the


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MIMO s!stem, u \ 1] #] [ [ [ ] #@2. In the multiuser MIMO scenario, channel inversion is the

processing as the KF pre"e*uali9ation discussed in Ahapter 1#. The onl! difference is th

replaced with )D7. 5s in the single user MIMO case, noise enhancement can be mitigated us


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the MM3= criterion. 5gain )D7 is used instead of ) which is referred to as a regulari9e

channel inversion in the conte-t of multi"user MIMO.

2.6.%.2 Block Diagonali7ation

In the previous subsection, we have seen channel inversion methods that deal with the mul

users, each with a single antenna. In the channel inversion methods, all signals other than ta

5 similar method can be applicable to multiple users, each with multiple antennas. 3ince

inter antenna interference in its own signal as well as other user interference are cancele

mitigated in the channel inversion processes, noise enhancement becomes more severe from

perspective of the target user.In this situation, a block diagonali9ation %+D( method is more suitable. In the +D method, u

in the channel inversion methods, onl! the interference from other user signals is canceled in

process of pre"coding. Then, the inter"antenna interference for each user can be cancele

various signal detection methods.

2.6.%.! Dirt, Pa er Coding 8DPC9

e alread! have illustrated an idea of dirt! paper coding %D A( in the course of deriving

channel capacit! of broadcast channel %+A(, showing that an interference"free transmissio

be reali9ed b! subtracting the potential interferences before transmission. In theor!, D A w

be implemented when channel gains are completel! known on the transmitter side. Dirt! pa

coding %D A( is a method of precoding the data such that the effect of the interference c

canceled subject to some interference that is known to the transmitter. More specificall!,

interferences due to the first up to %k"1( the user signals are canceled in the course of pre"c

the k th user signal.

2.6.%.% Tomlin$on/:ara$hima Precoding


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D A on the transmitter side is ver! similar to decision feedback e*uali9ation %DF=( o

receiver side. In fact, combination of D A with s!mmetric modulo operation turns out to

e*uivalent to Tomlinson")arashima %T)( precoding 012. T) precoding was originall! inven

for reducing the peak or average power in the decision feedback e*uali9er %DF=(, which s

from error propagation. The original idea of T) precoding in DF= is to cancel the post"cursor

in the transmitter, where the past transmit s!mbols are known without possibilit! of errors

fact, it re*uires a complete knowledge of the channel impulse response, which is onl! avail

b! a feedback from the receiver for time"invariant or slowl! time var!ing channel. To facili

e-position of the idea, consider the pre"coding in the one dimensional case, in which the s!mbol - is drawn from the M"ar! 5M constellation, M p. +! adding the data s!mbol -, wher

m is an integer, an e-panded s!mbol c can be defined as

AQ-^#5%m( %11(

In order to reduce the peak or average power, m must be chosen to minimi9e the magnitud

the e-panded s!mbol c in the transmitter. $ote that the original data s!mbol - can be recover

from the e-panded s!mbol c b! the s!mmetric modulo operation defined as order to address

pre"coding for the multi"user MIMO s!stem, we discuss the s!mmetric modulo operation fo

ar! ;5M modulated s!mbols.


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-(T:ODO'O ;

!.1 Introduction

This chapter describes the implementation of the objectives using Matlab software.

techni*ues used are e-plained through flow charts. 3imulation is carried out in Matlab 3oftw

!.2 &imulation of &'- &cheme

In this part, an evaluation of factors which could influence the 5 6 reduction performanc

performed using Matlab simulation. +ased on the principles of 37M algorithm, it

apparentl! that the abilit! of 5 6 reduction using 37M is affected b! the route number M

and subcarrier number N . Therefore, simulation with different values of M and N will be

conducted, and the results e-hibits some desired properties of signals representing the sa

information 0#12.

1. The probabilit! of high 5 6 is significantl! decreased. Increasing M leads to the

improvement of 5 6 reduction performance. If the probabilit! is set to 1 and then th

AADF curves with different M values are compared. The 5 6 value of case M Q# is about


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1d+ smaller than the unmodified one M Q1. 8nder the same condition, the 5 6 value of

case M Q1? is about &d+ smaller than the original one M Q1. )owever, from the comparison

of the curve M QB and M Q1?, we learned that the performance difference between these

two cases is less than 4. d+. This proves that we will not be able to achieve a linear growth

5 6 reduction performance with further increase the value of M %like M YQB(, the 5 6

reduction performance of OFDM signal will not be considerabl! improved. Furthermo

from the perspective of e-ecution time, we can see that e-ecution time will last longer w

the increase of M . Therefore, in practical application, we usuall! take M QB, thereb! not

onl! improve the s!stem performance, but also avoid introducing too.

YES

NO

START

Obtain theoptimized weighting

X is divided intoV nonoverlap s b!

#$%b&'b()bv*$&' thencalc late time domainse+ ence and its ,A,R val e

Set binde- $ 1& ' and thencalc late the new se+ ence andits ,A,R val e ,A,R-

,AR2,AR-


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YES

NO

3ig re &.1: Flowchart of sub"iterative algorithm

NO

YES

inde- $ inde-

inde- 5 inde-4& &

EN/

START

6nitialize relatedparameters7n mber of s b!carriers

8alc late corresponding ,A,REmpirical 8 m lative /istrib tion

:$:4&;enerate :6:O O3/: s mod lation

63 m2?/e0ne ro te n mbers : as a &@mdimensional matri- and set m $ &

EN/

8alc late and plot 8omplementar P A P R 0 ] )

Orignal M=2 M=4 M=8 M=16

Figure . 5 6 b! 3elective Mapping

%vii( 3imulation of 5 6 b! artial Transmit 3e*uence:"

The T3 method is emplo!ed for various values and compared for + 3< and ; 3< s!stem fo

iteration values. It is also studied for levels and 5 6 value is decreased for increase in lev


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%vii( 3imulation of Aomparison of 37M and T3 Techni*ues:"

The above mentioned techni*ues are compared and plotted on same graph and is anal!9ed

T3 techni*ue is better than 37M and will be emplo!ed in Multi"8ser MIMO Downlink 3!ste

5 6 7 8 9 10 11 1210

-3

10-2

10-1

100

PAPR0 [dB]

C C D F ( P r [ P A P R > P A P R 0 ] )

Orignal SLM PTS

Figure .@ 5 6 Aomparison b! Different Techni*ues

%vii( Multi"8ser MIMO Downlink:"The 73 and T) techni*ue is used and both are compared with each other. T) techni*ue is bett

as compared and +=6 versus 3$6 is plotted. 5lso the 5 6 is compared for both of them and

found that T) techni*ue is the best.


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0 1 2 3 4 5 610

-5

10-4

10-3

10-2

SNRdBs

S E R

Precoding with TMH

Precoding with LS

Figure .B %a( lot of 3=6 versus 3$6 for Multi"8ser MIMO Downlink

5 6 7 8 9 10 11 1210

-3

10-2

10-1

100

PAPR0 [dB]

C C

D F ( P r [ P A P R > P A P R 0 ] )

LSPTS-LSPTS-TMH


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Figure .B %b( lot of 5 6 for Multi"8ser MIMO Downlink

%.2 R(&U'T )N)';&I&

The MIMO"OFDM gives better +=6 performance over 3I3O>OFDM for high 3$6 value

MIMO channel capacit! increases b! a factor e*ual to the no. of antennas used over that o

3I3O

Table .1 Aomparison of var!ing 5 6 reduction proposals.

-ethod Di$tortion Po5er

increa$e

Data

rate

lo$$

O eration re0uired at

Tran$mitter 8T=9 > Recei#er 8R=9

Alipping J=3 $O $O T-:Alipping6-:$one

Aoding $O $O J=3 T-:Aoding6-:Decoding

T3 $O $O J=3 T-: times IDFTs operation6-:3ide Information =-traction,inverse T3

37M $O $O J=3 T-:M times IDFTs operation6-:3ide Info =-traction, inverse 37M

Interleaving $O $O J=3 T-: D times IDFTs operation, D"1times interleaving6-: 3ide information e-traction,deinterleaving

channel. MIMO s!stem uses spatial multiple-ing to increase the effective 3$6 of the s!stem

The MIMO"OFDM s!stem capacit! increases with increase in diversit!, i.e. no. of receiv

37M proposal can significantl! improve the 5 6 distribution of OFDM s!stem, that

significantl! reduce the presenting probabilit! of large peak power signal. The increasing


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the number of OFDM signal frames M will raise the comple-it! dramaticall!, but with benefit

of small improvement of 5 6 reduction performance. 37M algorithm adapted to an! length

FFT frame that means it can be used for different OFDM s!stems with different numbe

carriers. It is particularl! suitable for the OFDM s!stem with a large number of sub"carr

%more than 1#B(.

37M can significantl! improve the performance of OFDM s!stem b! reducing the 5 6, b

at the same time, the price is also ver! clear that is the comple-it! of it

implementation. =ver! time when appl!ing 37M algorithm, re*uires calculating the M group

IFFTs at the transmitter compared to onl! one on ordinar! OFDM s!stem.Thus, in practicalapplications, a tradeoff should be made between good performance and au-iliar! informat

From the discussion above, we can sa! that 37M algorithm is more suitable if s!stem c

tolerate more redundant information, otherwise, T3 algorithm is more acceptable w

comple-it! becomes the first considering factor. In brief, compromise will be made for a relia

s!stem. T) techni*ue used is far better than 73 as used in base paper.

PAPR Reduction Techniques

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