A Weighted Ofdm Signal Scheme for Pea1

8/19/2019 A Weighted Ofdm Signal Scheme for Pea1

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A WEIGHTED OFDM SIGNAL SCHEME FOR PEAK-TO-AVERAGE POWER RATIO REDUCTION OF OFDM

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CHAPTER 1

INTRODUCTION

1.1 Overview

Orthogonal frequency-division multiplexing (OFDM) is a transmission technique that

modulates multiple carriers simultaneously. Although their spectra overlap the transmitted

multiple carriers can !e demodulated orthogonally provided that correct time "indo"ing is used

at the receiver. #ince the OFDM-!ased system has high spectral efficiency and is ro!ust against

inter sym!ol interference and frequency-selective fading channels it has !een "idely chosen for

$uropean digital audio%video !roadcasting and "ireless local% metropolitan area net"or&

standards and no" it is used in most !road!and "ireless communication systems. 'o"ever one

of the maor pro!lems of OFDM-!ased systems is the high pea&-to-average-po"er ratio (A*)

of a transmitted signal "hich causes a distortion of a signal at the nonlinear high-po"er

amplifier ('A) of a transmitter. +hus the po"er efficiency of the 'A is seriously limited to

avoid nonlinear distortion, other"ise the high A* results in significant performance

degradation. ecause of the practical importance of this pro!lem a num!er of algorithms for

reducing the high A* have !een developed such as clipping and filtering (/F) coding

adaptive sym!ol selection such as selected mapping, partial transmit sequence and interleaving

tone reservation%inection active signal constellation extension companding and others.

1.2 Problem outline

A A* reduction scheme !ased on a "eighted OFDM signal is proposed to reduce the

A* "ithout distortion in removing the "eight at the receiver side. +his method is motivated

!y a circular convolution process i.e. the modulated OFDM signal is convoluted "ith a certain

&ind of signal 0 for smoothing the pea& of the OFDM signal !efore the 'A. 'ere "e choose

the signal 0 to satisfy that the Fourier transform φ of 0 has no 1ero on the real line. +he

convoluted signal can !e "ritten as a simple "eighted OFDM signal. 2hen the discrete data

{ak φ(k )}k =0 N −1

is given "e consider "eighted data {ak φ(k )}k =0 N −1

and form an OFDM signal

"ith this "eighted discrete data. +hen this "eighted OFDM signal is the same as the given

convoluted signal. #ince "eightφ

is non-uniform the !it-error-rate ($*) performance

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could !e degraded. 3n practice to improve the $* performance "e modify the "eight !y

adding a suita!le positive constant to the original "eight. +he A* of the "eighted OFDM

signal "ith the modified "eight is smaller than that of the /F method and the $*

performance is improved compared "ith the /F method.

1.3 Objective

+he effectiveness of the proposed scheme is evaluated "ith computer simulations. 3n

this "eighted OFDM method "ith modified "eight the time duration needed to transmit the

"eighted OFDM signal is the same as the time duration for the original OFDM signal. Moreover

the original discrete data can !e recovered completely at the receiver side "ith additional 4 N

complex multiplications of computational complexity "ithout extra cost in transmission.

+he "eighted OFDM scheme "as introduced in "here the 5aussian function sine

function and some other functions "ere used as "eighted functions. 2hen the noise is not

present the A* of the "eighted OFDM system "ith 5aussian "eight is reduced remar&a!ly.

As mentioned in the conclusion ho"ever the noise "as not also considered for $*

performance. 3f the additive 5aussian noise is considered the $* performance of the "eighted

OFDM system "ith 5aussian "eight "ill !e even degraded. 3n this paper "e suggest the

"eighted OFDM system "ith modified "eight to improve the $* performance and "e also

provide the condition for a function to !e a "eight function and a mathematical reason for the

merit of the "eighted OFDM system derived from a circular convolution system.

1.! T"ei outline

+he complete thesis of this "or& is outlined in six chapters6

hapter7 gives the details a!out the overvie" of the proect. 3t also gives the !rief description

a!out the pro!lem formulation and main o!ectives of proposed "or&.

hapter 4 gives the complete details a!out the literature survey. +his chapter descri!es the details

a!out the earlier methods proposed on "eighted OFDM on A* of OFDM.

hapter 8 gives the complete details a!out the system model of proposed approach. 3t also gives

the details a!out the OFDM system description.

hapter 9 gives the complete details a!out design and implementation of proposed "eighted

orthogonal frequency division multiplexing method.



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hapter : illustrates the performance evaluation of proposed approach. +his chapter gives the

results evaluation of performance comparison of DF of the /F and proposed methods of

different samples. Finally chapter ; concludes the thesis.

CHAPTER 2#ITRATURE $UR%E&

'igh ea&-to-Average o"er *atio has !een recogni1ed as one of the maor practical

pro!lem involving OFDM modulation. 'igh A* results from the nature of the modulation

itself "here multiple su!carriers % sinusoids are added together to form the signal to !e

transmitted. 2hen < sinusoids add the pea& magnitude "ould have a value of


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performance. On comparing !et"een these t"o domain methods frequency domain A*

reduction technique is the most efficient one !ecause of its a!ility to compress the A* "ithout

distorting the transmitted signal no production of in !and distortion and out of !and radiation in

OFDM signals.

roadly A* reduction techniques are classified into four sections.

• loc& coding

• #elective >evel Mapping (#>M)

• artial +ransmit #equences (+#)

#ignal scram!ling techniques "or& "ith side information "hich minimi1ed the effective

throughput since they commence redundancy. #ignal distortion techniques introduce !and

interference and system complexity also. #ignal distortion techniques minimi1e high pea&

dramatically !y distorting signal !efore amplification.

+he signal distortion techniques are6

• lipping

• ea& "indo"ing

• ea& cancellation

• ea& po"er suppression

•

2eighted multicarrier transmission

2.1.1 $i(n)l $cr)mblin( Tec"ni*ue

2.1.1.1. Pre+'itortion tec"ni*ue

+he pre-distortion technique is !ased on the reorientation or spreading the energy of

data sym!ol !efore ta&ing 3FF+. +he pre-distortion scheme includes DF+ spreading pulse

shaping or pre-coding and constellation shaping.

2.1.1.2 Co'in( tec"ni*ue

+he coding technique employed some error correcting codes for the A* reduction.

+hese methods are applied !efore the generation of OFDM signal (!efore 3FF+). 2hen signals

are added "ith the same phase they produce a pea& po"er "hich is times the average po"er.

+he !asic idea of all coding schemes for the reduction of A* is to reduce the occurrence

pro!a!ility of the same phase of many signals. +he coding methods select such code "ords that

minimi1e or reduce the A*. 3t causes no distortion and creates no out of !and radiation !ut it



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suffers from !and"idth efficiency as the code rate is reduced. 3t also suffered from the

complexity to find the !est codes and to store large loo&up ta!les for encoding and decoding

especially for a large num!er of su!carriers. +he error correcting codes li&e !loc& codes cyclic

codes 5olay complementary sequence *eed-#olomon (*#) code *eed-Muller (*M) code

'adamard code and >o" Density arity hec& (>D) code can !e used.

2.1.1.3 ,loc- Co'in( Tec"ni*ue

oding techniques can !e applied for signal scram!ling M sequences 5olay

complementary sequences #hapiro-*udin sequences codes can !e used to reduce the A*

efficiently.

+his loc& coding technique has !een proposed !y 2il&inson and ?ones in 7@;: for the

minimi1ation of the pea& to mean envelope po"er ratio of multicarrier communication system.

+he &ey o!ect in this paper is that A* can !e minimi1ed !y !loc& coding the data. +he !loc&

coding techniques have three stages for the development. +he first stage "or&s "ith the

collection of appropriate sets of code "ords for any num!er of carriers any M-ary phase

modulation method and any coding rate. +he second stage "or&s "ith the collection of the sets

of code "ords "hich ena!le proficient implementation of the encoding%decoding. +he third stage

offers error deduction and correction potential.

+here different methods for the collection of the sets of code "ords. +he mainly

insignificant method order to search the pea& envelope po"er ($) for all possi!le code "ordsfor a certain length of given num!er of carriers. +his technique is simple and accurate for short

codes !ecause it needs extreme computation. arge A* reduction can !e achieved if the long information sequence is separated

into different su! !loc&s and all su! !loc& encoded "ith #ystem on a rogramma!le hip

(#O). +here are many li&ely spaces "here the odd parity chec&ing !its can !e put into each

frame to minimi1e A*. For further minimi1ation of A* redundant !it location optimi1ed

su!-!loc& coding (*>O-#) optimi1es these locations redundant om!ination optimi1ed su!-



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!loc& coding scheme (O#) optimi1es the com!ination of the coded su!-!loc&s "here t"o

coding schemes instead of one is used to encode the same information source.

2.1.1.! ,loc- Co'in( $c"eme wit" Error Correction

+his loc& coding scheme "ith $rror orrection has !een proposed !y Ahn and et.al in

to introduce a ne" !loc& coding proposal for minimi1ation of pea& to average po"er ratio

(A*) of an Orthogonal Frequency Division Multiplexing (OFDM) system. loc& coding has

error correction capa!ility. 3n !loc& coding method the OFDM sym!ol can !e reduced !y

selecting only those code "ords "ith lo"er A*. 3n this paper the &ey o!ect of the method is

proposed that properly designed !loc& codes can not only minimi1e the A* !ut also give

error correction capa!ility. A & !it data !loc& (e.g. 9-!it data) is encoded !y a (n &) !loc& code

"ith a generator matrix 5B in the transmitter of the system. Follo"ed !y the phase rotator vector

! to produce the encoded output xCa.5!(mod 4).

+o achieve the accurate generator matrix and phase rotator vector that ma&e sure the

minimum A* for the OFDM system chec& all the 4n codes and choose only 4& codes that

o!tain the minimum A*. After that generator matrix 5B and the phase rotator vector !B are

produced, "hich are used mapping !et"een these sym!ols com!ination and input data vector aB.

+he converse functions of the transmitter are executed in the receiver system. +he parity chec& matrix 'B is achieved from the generator matrix 5B "ith an exception that the effect of the

phase rotator vector ! is removed !efore calculations of syndromes.



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Figure 4.7 loc& diagram of !loc& coding "ith error correction scheme

ontrasting the method in "hich only presents error detection, this method can

improve the overall system performance and provides error correction capa!ility.

2.1.1. $i(n)l cr)mblin( /Prob)bilitic0 tec"ni*ue

#ignal #cram!ling technique scram!le each OFDM sym!ol "ith different scram!ling

techniques and select the sequence that gives the smallest A* value. 3t includes methods li&e

#elective Mapping (#>M) and artial +ransmit #equence (+#).

2.1.1. $electe' )in( /$#0

#elective Mapping (#>M) approaches have !een proposed !y auml in 7@;:. +his

method is used for minimi1ation of pea& to average transmit po"er of multicarrier transmission

system "ith selected mapping. A complete set of candidate signal is generated signifying the

same information in selected mapping and then concerning the most favora!le signal is selected

as consider to A* and transmitted. 3n the #>M the input data structure is multiplied !y

random series and resultant series "ith the lo"est A* is chosen for transmission. +o allo" the

receiver to recover the original data to the multiplying sequence can !e sent as side

informationB.



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Figure 4.4 loc& diagram of #elected Mapping +echnique

One of the preliminary pro!a!ilistic methods is #>M method for reducing the A*

pro!lem. +he good side of selected mapping method is that it doesnBt eliminate the pea&s and

can handle any num!er of su!carriers. +he dra"!ac& of this method is the overhead of side

information that requires to !e transmitted to the receiver of the system in order to recover

information.

2.1.1.4 P)rti)l Tr)nmit $e*uence /PT$0

artial +ransmit #equence (+#) technique has !een proposed !y Muller and 'u!!er in

7@@E. +his proposed method is !ased on the phase shifting of su!-!loc&s of data and

multiplication of data structure !y random vectors. +his method is flexi!le and effective for

OFDM system. +he main purpose !ehind this method is that the input data frame is divided into

non-overlapping su! !loc&s and each su! !loc& is phase shifted !y a constant factor to reduce

A*.

+# is pro!a!ilistic method for reducing the A* pro!lem. 3t can !e said that +#

method is a modified method of #>M. +# method "or&s !etter than #>M method. +he main

advantage of this scheme is that there is no need to send any side information to the receiver of

the system "hen differential modulation is applied in all su! !loc&s.

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Figure 4.8 loc& diagram of +# technique

2.1.1.5 Interle)vin( Tec"ni*ue

3nterleaving technique has !een proposed !y ?ayalath and +ellam!ura for reduction

pea& to average po"er ratio of an OFDM transmission. A data randomi1ation technique has

proposed for the minimi1ation of the A* in this paper.

+he notion that highly correlated data structures have large A* can !e reduced if

long correlation pattern is !ro&en do"n. Also this paper proposes an additive method to

minimi1e the complexity.

+he !asic idea in adaptive interleaving is to set up an initial terminating threshold.

A* value goes !elo" the threshold rather than see&ing each interleaved sequences. +he

minimal threshold "ill compel the adaptive interleaving (A>) to loo& for all the interleaved

sequences. +he main important of the scheme is that it is less complex than the +# technique

!ut o!tains compara!le result. +his method does not give the assurance result for A*

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reduction. 3n this circumstance higher order error correction method could !e used in addition to

this method.

2.1.1.6 H)')m)r' Tr)n7orm

+he technique of 'adamard +ransform is !ased upon the relationship !et"een

correlation property of OFDM input sequence and A* pro!a!ility. +he average po"er of the

input sequence represents the pea& value of the autocorrelation. 'ence the pea& value of

autocorrelation depends on the input sequence provided that num!er of su! carriers remains

unchanged. +he !loc& diagram of 'adamard +ransform is illustrated !elo".

Figure 4.9 loc& diagram of an OFDM system using 'adamard +ransform

2.1.1.18 Dumm9 $e*uence Inertion /D$I0

3n Dummy sequence insertion (D#3) !efore 3FF+ stage in input data a dummy sequence

is added. +he sequences "hich are used may !e complementary correlation or any other

sequence. #ince dummy sequence is not used as side information hence any transmission error

does not increase $*. D#3 technique is united "ith A* threshold method. After 3FF+ if

A* is !elo" specific threshold then signal is transmitted !ut if it is more than this specific

level then insertion of dummy sequence is done to achieve the required results. +he !loc&

diagram of D#3 system is sho"n in figure 4.:

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Figure 4.: loc& diagram of D#3 system

+he main advantage of this technique is that $* is not degraded due to transmission

errors in the dummy sequence. #o far amongst different sequences use of complementary

sequence produces !etter results.

2.1.1.11 A''itive Corrective :unction

As the name suggests additive correcting function achieves reduction in A* through

addition of suita!le corrective function in OFDM signal. +he amplitude pea&s are in this

approach the amplitude pea&s are manipulated in such a manner that after the correction the

amplitude of the signal does not go !eyond a specified threshold.

3n this method the reduction in A* is achieved !y manipulation of OFDM signal at

transmit side. +he correct functions "hich can !e added include additive #inc functions and

multiplicative 5aussian function. +his technique can !e employed for ar!itrary num!er of

carriers "ithout requiring increased redundancy. 3n this method after correction the out of !and

interference is reduced !ut in !and interference is increased leading to increase in !and

distortion. 'ence the correcting function "hich is added should have minimal po"er to &eep

interference po"er "ithin the OFDM !and to minimum.

2.1.1.12 Pe)- ;in'owin(

ea& 2indo"ing is !ased upon the fact that frequency of high pea&s is infrequent

hence these can !e removed !y minimal increase in self-interference. 3n this technique signal



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pea&s are multiplied "ith certain "indo"s. +hese include osine 'amming 5aussian shaped

and aiser 2indo"s. +he used "indo" must !e shortest possi!le in time domain and at the same

time must !e narro"!and. Another example of A* reduction technique "hich is !ased upon

self-interference is clipping. +he A* reduction performance as "ell as spectral efficiency of

pea& "indo"ing technique is !etter as compared to clipping. +he maor advantage of pea&

"indo"ing is that A* reduction is achieved "ith minimal complexity for any num!er of su!

carriers. +he disadvantages include an increase in out-of-!and interference and $*.

2.1.1.13 Enveloe $c)lin(

3n envelop scaling the input envelopes of su! carriers are scaled prior to 3FF+. +he !ase

for this scheme is the facts that "ith # modulation all the su! carriers input envelops are

equal. 'ence input envelop of some su! carriers is scaled in such a "ay that minimum A* is

achieved at 3FF+ output. +he input "hich yields minimum A* is fed into the system. +he

phase information of the input sequence is similar to original ho"ever envelops are not the same.

'ence decoding of sequence can !e done !y receiver "ithout any requirement for side

information. +he maor dra"!ac& of this method is that it can only !e used "hen OFDM is

employing # modulation. On the other hand if "e use this method "hen GAM modulation is

implemented !y OFDM then there is severe degradation in $* performance results.

2.1.1.1! R)n'om P")e U')tin(

+he random phase updating technique for reduction of A* has !een proposed. 3n thistechnique for each carrier the phase is generated randomly and assigned. +his process of

updating phases &eeps running until the A* is reduced !elo" a specified threshold level. +he

A* reduction performance is independent of num!er of carriers and depends mostly upon the

chosen threshold level. Although this level can !e dynamic ho"ever there is an upper limit for

the num!er of iterations "hich can !e used for updating of phases.

#ince the receiver must !e provided "ith the information a!out change of phases that

are applied hence the amount of side information "hich needs to !e provided to the receiver

!ecomes quite significant.

2.1.1.1 D)t) ,e)rin( Pe)- Re'uction C)rrier

Data !earing pea& reduction carriers (*s) have !een proposed to achieve reduction of

A*. 3n this scheme the sym!ol of lo"er order modulation is represented !y a scheme of higher



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order modulation. 'ence the phase and amplitude of these carriers remains inside the

constellation area "hich represents the data sym!ols !eing transmitted.

Amongst dra"!ac&s of *s one is that the overall data transmission efficiency of the

system is compromised if "e try to achieve maximum A* reduction efficiency. At the same

time the $* performance is also affected adversely !ecause of employing constellation of

higher order for carrying sym!ols of lo"er order results in higher pro!a!ility of error.

2.1.1.1 Com)n'in( Tec"ni*ue

ompanding technique "as proposed !ased upon the assumption that the OFDM signal

has 5aussian distri!ution and occurrence of high pea&s is infrequent. 3n OFDM system on

transmitter side after 3FF+ the signal undergoes companding and quanti1ation "hile on receiver

side the signal is first digiti1ed and then expanded. +he !loc& diagram of OFDM system "ith

companding technique is sho"n in figure 4.;.

Figure 4.; loc& diagram of OFDM system "ith companding

ompanding "as initially employed for speech processing !ecause of infrequentoccurrence of pea&s. #ince the OFDM signal also sho"s infrequent pea&s hence the authors

planned to apply the technique for reduction of pea&s in OFDM system. #ince frequency of small

signals is much more as compared to large ones hence there is improved quanti1ation resolution

for small signals as compared to large signals.



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+he overall $* performance is considera!ly degraded !ecause the quanti1ation error

is increased nota!ly for large signals. 'ence the overall improvement in A* "hich is achieved

!y companding is at the cost of $* performance.

2.1.1.14 Tone Reerv)tion /TR0

+one *eservation (+*) method is proposed for A* reduction. +he main idea of this

method is to &eep a small set of tones for A* reduction. +his can !e originated as a convex

pro!lem and this pro!lem can !e solved accurately. +he amount of A* reduction depends on

some factors such as num!er of reserved tones location of the reserved tones amount of

complexity and allo"ed po"er on reserved tones.

+his method explains an additive scheme for minimi1ing A* in the multicarrier

communication system. 3t sho"s that reserving a small fraction of tones leads to large

minimi1ation in A* ever using "ith simple algorithm at the transmitter of the system "ithout

any additional complexity at the receiver end. 'ere < is the small num!er of tones reserving

tones for A* reduction may present a nonHnegligi!le fraction of the availa!le !and"idth and

resulting in a reduction in data rate. +he advantage of +* method is that it is less complex no

side information and also no additional operation is required at the receiver of the system. +one

reservation method is !ased on adding a data !loc& and time domain signal. A data !loc& is

dependent time domain signal to the original multicarrier signal to minimi1e the high pea&. +his

time domain signal can !e calculated simply at the transmitter of system and stripped off at thereceiver.

2.1.1.15 Tone Injection /TI0

+one 3nection (+3) method has !een recommended !y Muller #.'. and 'u!er ?..

+his technique is !ased on general additive method for A* reduction. Ising an additive method

achieves A* reduction of multicarrier signal "ithout any data rate loss.


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of the proper phase and frequency in the multi-carrier sym!ol. +he dra"!ac&s of this method are,

need to side information for decoding signal at the receiver side and cause extra 3FF+ operation

"hich is more complex.

2.1.1.16 Active Contell)tion E


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+his technique can also !e used "ith M# and GAM. +he main advantages of

technique include significant reduction of A* "ithout compromising data rate and no need for

side information. +here is additional slight decrease in $* also. +he dra"!ac& is that the

technique is useful for larger constellation si1e modulations only.

2.1.1.28 Ot"er Tec"ni*ue

+here are some other techniques "hich cannot !e categori1ed in any one class of

reduction techniques. +hese are !riefly descri!ed !elo".

Clutere' O:D tec"ni*ue clustering of su! carriers into a num!er of smaller !loc&s

is done !efore transmitting them on different antennas. A* reduction is achieved !ecause the

num!er of su!-carriers for each transmitter is reduced. +he main disadvantage is that num!er of

po"er amplifiers is increased.

Two+'imenion)l ilot 9mbol )ite' mo'ul)tion /2D+P$A0 is a distortion free

technique for reduction of A* and can also !e used for channel estimation. Although the

scheme is complex ho"ever it can !e reduced if the sequence used is properly designed.

C)rrier+Inter7erometr9 O:D /CI=O:D) reduces A* !y utili1ing 3 phase

codes for transmitting each !it on every < carriers. +he phase codes applied to the < carriers

result in one !itBs po"er reaching a maximum "hen the po"ers of the remaining


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2.1.2.1 Pe)- ;in'owin(

+he pea& "indo"ing method has !een suggested !y =an


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2.1.2.3 Pe)- Re'uction C)rrier

ea& *eduction arrier has !een proposed !y +an and 2assell to use of the data !earing

pea& reduction carriers (*s) to reduce the effective A* in the OFDM system.

+his scheme includes the use of a higher order modulation scheme to represent a lo"er

order modulation sym!ol. +his permits the amplitude and phase of the * to !e positioned

"ithin the constellation region sym!oli1ing the data sym!ol to !e transmitted.

For example to use a * that employs a 7;-# constellation to carry G# data

sym!ol the 7;-phases of the 7;-# constellations are divided into four regions to represent the

four different values of the G# sym!ol.

+his scheme is appropriate for # modulation, "here the envelopes of all su!carriers

are equal. 2hen the GAM modulation scheme "ill !e implemented in the OFDM system the

carrier envelope scaling "ill result in the serious $* degradation. +o limit the !it error rate

($*) degradation amount of the side information "ould also !e excessive "hen the num!er of

su!carriers is large.

2.1.2.! Cliin( )n' :ilterin(

'igh A* is one of the most common pro!lems in OFDM. A high A* !rings

disadvantages li&e increased complexity of the AD and DA and also reduced efficiency of

radio frequency (*F) po"er amplifier.

One of the simple and effective A* reduction techniques is clipping "hich cancelsthe signal components that exceed some unchanging amplitude called clip level. 'o"ever

clipping yields distortion po"er "hich called clipping noise and expands the transmitted signal

spectrum "hich causes interfering. lipping is nonlinear process and causes in-!and noise

distortion "hich causes degradation in the performance of !it error rate ($*) and out-of-!and

noise "hich decreases the spectral efficiency.

lipping and filtering technique is effective in removing components of the expanded

spectrum. Although filtering can decrease the spectrum gro"th filtering after clipping can

reduce the out-of-!and radiation !ut may also cause some pea& re-gro"th "hich the pea& signal

exceeds in the clip level. +he technique of iterative clipping and filtering reduces the A*

"ithout spectrum expansion. 'o"ever the iterative signal ta&es long time and it "ill increase the

computational complexity of an OFDM transmitter.



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ut "ithout performing interpolation !efore clipping causes it out-of-!and. +o avoid

out-of-!and signal should !e clipped after interpolation. 'o"ever this causes significant pea&

re-gro"th. #o it can use iterative clipping and frequency domain filtering to avoid pea& re-

gro"th.

3n the system used serial to parallel converter converts serial input data having different

frequency component "hich are !ase !and modulated sym!ols and apply interpolation to these

sym!ols !y 1ero padding in the middle of input data. +hen clipping operation is performed to cut

high pea& amplitudes and frequency domain filtering is used to reduce the out of !and signal !ut

caused pea& re-gro"th. +his consists of t"o FF+ operations. For"ard FF+ transforms the clipped

signal !ac& to discrete frequency domain. +he in-!and discrete components are passed

unchanged to inputs of second 3FF+ "hile out of !and components are null. +he clipping and

filtering process is performed iteratively until the amplitude is set to the threshold value level to

avoid the pea& out-of !and and pea& re-gro"th.

2.2 :)ctor 7or electin( t"e PAPR re'uction tec"ni*ue

#everal factors should !e considered for selecting the technique that can reduce the

A* effectively as "ell as can maintain high quality performance. +hese follo"ing factors are

to !e considered as6

• 2ithout introducing in-!and distortion and out-of-!and radiation A* reduction

techniques should !e ena!le to reduce the A*.

• >o" average po"er6 +he raise in po"er requires a high linear operation region in

'A and hence degrades the $* performance.

•


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threshold level. 3f OFDM signals are clipped it "ill introduce in-!and distortion and out-of-!and

radiation (adacent channel interference) into the communication system as a result $*

performance of the system degrades. 'ence the !est solution is to reduce the A* !efore

formation of OFDM sym!ols as "ell as prior transmitted OFDM sym!ols into nonlinear 'A

and DA.

+he most of the factors mentioned a!ove for selecting the A* reduction technique

are almost satisfied !y frequency domain method (i.e. signal scram!ling and pre-distortion

methods) !ecause they are distortionless

+a!le 4.7 different techniques

2.3 O:D

Orthogonal frequency division multiplexing (OFDM) is an attractive technique for

"ireless communication applications. 'o"ever an OFDM signal has a large pea&-to-mean

envelope po"er ratio "hich can result in significant distortion "hen passed through a nonlinear

device such as a transmitter po"er amplifier. 3nvestigate through extensive computer

simulations the effects of clipping and filtering on the performance of OFDM including the

po"er spectral density the crest factor and the !it-error rate. Our results sho" that clipping andfiltering is a promising technique for the transmission of OFDM signals using realistic linear

amplifiers.

3t is sho"n that repeated clipping and frequency domain filtering of an orthogonal

frequency division multiplexing (OFDM) signal can significantly reduce the pea&-to-average



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SIGNALS

po"er ratio (A*) of the transmitted signal. +he technique causes no increase in out-of-!and

po"er. #ignificant A* reduction can !e achieved "ith only moderate levels of clipping noise

2.! Cliin( )n' :ilterin(

3terative clipping and filtering (3F) is a "idely used technique to reduce the pea&-to-

average po"er ratio (A*) of orthogonal frequency division multiplexing (OFDM) signals.

'o"ever the 3F technique "hen implemented "ith a fixed rectangular "indo" in the

frequency-domain requires many iterations to approach specified A* threshold in the

complementary cumulative distri!ution function (DF). 3n L8 "e develop an optimi1ed 3F

method "hich determines an optimal frequency response filter for each 3F iteration using

convex optimi1ation techniques. +he design of optimal filter is to minimi1e signal distortion such

that the OFDM sym!olJs A* is !elo" a specified value. #imulation results sho" that our

proposed method can achieve a sharp drop of DF curve and reduce A* to an accepta!le

level after only 7 or 4 iterations "hereas the classical 3F method "ould require N to 7;

iterations to achieve a similar A* reduction. Moreover the clipped OFDM sym!ols o!tained

!y our optimi1ed 3F method have less distortion and lo"er out-of-!and radiation than the

existing method. A !loc& coding scheme using the maximum-length shift-register sequences (m-

sequences) is suggested for orthogonal frequency division multiplexing (OFDM). +he scheme

"ith a very simple implementation can significantly reduce the pea&-to-average po"er ratio of OFDM signals and provide error-correcting capa!ility at the same time. For any code defined

over an equal energy constellation it is first sho"n that at any time instance the pro!lem of

determining code "ords of "ith high pea&-to-average po"er ratios (A*) in a multicarrier

communication system is intimately related to the pro!lem of minimum-distance decoding of .

#u!sequently a method is proposed for computing the A* !y minimum-distance decoding of

at many points of time. Moreover an upper !ound on the error !et"een this computed value

and the true one is derived. Analogous results are esta!lished for codes defined over ar!itrary

signal constellations. As an application of this computational method an approach for reducing

the A* of proposed !y ?ones and 2il&inson (7@@;) is revisited. +his approach is !ased on

introducing a specific phase shift to each coordinate of all the code "ords "here phase shifts are

independent of the code "ords and &no"n !oth to the transmitter and the receiver. 2e optimi1e

the phase shifts offline !y applying our method for computing the A* for the coding scenario



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SIGNALS

proposed !y the $+#3 *A< #tandardi1ation ommittee. *eductions of order 9.: d can !e

freely o!tained using the computed phase shifts. $xamples are provided sho"ing that most of the

gain is preserved "hen the computed optimal phase shifts are rounded to quantenary phase-shift

&eying (#) N-# and 7;-# type phase shifts. 2e present a range of coding schemes for

OFDM transmission using !inary quaternary octary and higher order modulation that give high

code rates for moderate num!ers of carriers. +hese schemes have tightly !ounded pea&-to-mean

envelope po"er ratio (M$*) and simultaneously have good error correction capa!ility. +he

&ey theoretical result is a previously unrecogni1ed connection !et"een 5olay complementary

sequences and second-order *eed-Muller codes over alpha!ets 4h. 2e o!tain additional

flexi!ility in trading off code rate M$* and error correction capa!ility !y partitioning the

second-order *eed-Muller code into cosets such that code "ords "ith large values of M$*

are isolated. For all the proposed schemes "e sho" that encoding is straightfor"ard and give an

efficient decoding algorithm involving multiple fast 'adamard transforms. #ince the coding

schemes are all !ased on the same formal generator matrix "e can deal adaptively "ith varying

channel constraints and evolving system requirements the first lo"er !ound on the pea&-to-

average po"er ratio (A*) of a constant energy code of a given length n minimum $uclidean

distance and rate is esta!lished. onversely using a no constructive =arshamov-5il!ert style

argument yields a lo"er !ound on the achieva!le rate of a code of a given length minimum

$uclidean distance and maximum A*. +he derivation of these !ounds relies on a geometricalanalysis of the A* of such a code. Further analysis sho"s that there exist asymptotically good

codes "hose A* is at most N log n. +hese !ounds motivate the explicit construction of error-

correcting codes "ith lo" A*. ounds for exponential sums over 5alois fields and rings are

applied to o!tain an upper !ound of order (log n) 4 on the A*s of a constructive class of codes

the trace codes. +his class includes the !inary simplex code duals of !inary primitive ose-

haudhuri-'ocquenghem (') codes and a variety of their non-!inary analogs. #ome open

pro!lems are identified +he authors propose a method for the reduction of pea&-to-average

transmit po"er ratio of multicarrier modulation systems called selected mapping is presented

"hich is appropriate for a "ide range of applications. #ignificant gains can !e achieved !y

selected mapping "hereas complexity remains quite moderate



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SIGNALS

+he authors propose a very effective and flexi!le pea& po"er reduction scheme for

orthogonal frequency division multiplexing (OFDM) "ith almost vanishing redundancy.


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SIGNALS

OFDM%DM+ sym!ols. 3n this report "e focus on methods "hich try to reduce the impulsiveness

of the OFDM%DM+ process !y adding redundancy or signal transformation at the transmitter. 3n

another report "e "ill study methods that ta&e into account a model for the nonlinear amplifier

in order to compensate for its distortions LDecl@@!. 2e "onJt study either the techniques

involving coded versions of OFDM in "hich the goal is to end codes that exhi!it good pea&s

properties.


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SIGNALS

A general companding transform method is proposed to effectively reduce pea&-to-

average po"er ratio (A*) of orthogonal frequency division multiplexing (OFDM) signals. y

compressing large signals "hile enhancing small signals along "ith ta&ing into account their

statistical characteristics this method can achieve significant reduction in A* "ith lo"

implementation complexity. #pecifically presents the design criteria of the transform "hich

ena!le effective tradeoff !et"een reduction in A* and !it-error rate performance of the

OFDM system. 3t is sho"n !y simulations that the proposed method may significantly improve

the performance of OFDM systems in radio channels !y carefully choosing the companding

form and parameters.

A ne" nonlinear companding technique called Sexponential compandingS is proposed

to reduce the high ea&-to-Average o"er *atio (A*) of Orthogonal Frequency DivisionMultiplexing (OFDM) signals. Inli&e the T-la" companding scheme "hich enlarges only small

signals so that increases the average po"er the schemes !ased on exponential companding

technique adust !oth large and small signals and can &eep the average po"er at the same level.

y transforming the original OFDM signals into uniformly distri!uted signals ("ith a specific

degree) the exponential companding schemes can effectively reduce A* for different

modulation formats and su!-carrier si1es. Moreover many A* reduction schemes such as T-

la" companding scheme cause spectrum side-lo!es generation !ut the exponential companding

schemes cause less spectrum side-lo!es. omputer simulations "hich consider a !ase!and

OFDM system "ith Additive 2hite 5aussian


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SIGNALS

resents a "eighted cyclic prefix orthogonal frequency-division multiplexing (2-

OFDM) transceiver as a generali1ation of traditional cyclic prefix ()- OFDM. 3n time-variant

channels this multicarrier transmission scheme may mitigate inter-channel interference (33)

than&s to the use of non-rectangular pulse shapes. A pre-coding step may !e required in order to

reduce the pea&-to-average po"er ratio (A*) at the transmitter output. For instance a discrete

Fourier transform (DF+) pre-coder leads to a single carrier transmission scheme "ith frequency

domain equali1ation. 2e analy1e the consequences of such a pre-coding in terms of

performances in the context of a time-frequency selective channel.



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SIGNALS

CHAPTER 3

O:D $&$TE DE$CRIPTION

3.1O:D

OFDM has !ecome a popular technique for transmission of signals over "ireless

channels. OFDM has !een adopted in several "ireless standards such as digital audio

!roadcasting (DA) digital video !roadcasting (D=-+) the 3$$$ NK4.77a >A< standard and

the 3$$$ NK4.7;a MA< standard. OFDM is also !eing pursued for dedicated short-range

communications (D#*) for road side to vehicle communications and as a potential candidate

for fourth generation (95) mo!ile "ireless systems. OFDM converts a frequency-selective

channel into a parallel collection of frequency flat su!-channels. +he su!carriers have the

minimum frequency separation required to maintain orthogonality of their corresponding time

domain "aveforms yet the signal spectra corresponding to the different su!carriers overlap in

frequency. 'ence the availa!le !and"idth is used very efficiently. 3f &no"ledge of the channel is

availa!le at the transmitter then the OFDM transmitter can adapt its signaling strategy to match

the channel. Due to the fact that OFDM uses a large collection of narro"ly spaced su!-channelsthese adaptive strategies can approach the ideal "ater pouring capacity of a frequency-selective

channel. 3n practice this is achieved !y using adaptive !it loading techniques "here different

si1ed signal constellations are transmitted on the su!carriers.

OFDM is a !loc& modulation scheme "here a !loc& of < information sym!ols is

transmitted in parallel on < su!carriers. +he time duration of an OFDM sym!ol is < times larger

than that of a single-carrier system. An OFDM modulator can !e implemented as an 3DF+ on a

!loc& of < information sym!ols follo"ed !y an AD. +o mitigate the effects of 3#3 caused !y

channel time spread each !loc& of 3DF+ coefficients is typically preceded !y a or a guard

interval consisting of 5 samples such that the length of the is at least equal to the channel

length.

Inder this condition a linear convolution of the transmitted sequence and the channel is

converted to a circular convolution. As a result the effects of the 3#3 are easily and completely



28/65


SIGNALS

eliminated. Moreover the approach ena!les the receiver to use fast signal processing transforms

such as a fast FF+ for OFDM implementation. #imilar techniques can !e employed in single

carrier systems as "ell !y preceding each transmitted data !loc& of length < !y a of length

"hile using frequency-domain equali1ation at the receiver.

OFDM systems are attractive for the "ay they handle 3#3 "hich is usually introduced

!y frequency selective multipath fading in a "ireless environment. $ach su!-carrier is modulated

at a very lo" sym!ol rate ma&ing the sym!ols much longer than the channel impulse response.

3n this "ay 3#3 is diminished. Moreover if a guard interval !et"een consecutive OFDM

sym!ols is inserted the effects of 3#3 can completely vanish. +his guard interval must !e longer

than the multipath delay. Although each su!-carrier operates at a lo" data rate a total high data

rate can !e achieved !y using a large num!er of su!-carriers. 3#3 has very small or no effect on

the OFDM systems hence an equali1er is not needed at the receiver side.

OFDM has many advantages compared "ith other transmission techniques. One of such

advantages is high spectral efficiency (measured in !its%sec%'1). +he orthogonal in OFDM

implies a precise mathematical relationship !et"een the frequencies of the su!-channels that use

in the OFDM system. $ach one of the frequencies is an integer multiple of a fundamental

frequency. +his ensures that a su!-channel does not interfere "ith other su!-channels even

though the su!-channels overlap. +his results in high spectral efficiency.

OFDM has !een adopted in the 3$$$NK4.77a >A< and 3$$$NK4.7;a >Aine (D#>) modems and ca!le modems. *ecently "ireless systems such as



29/65


SIGNALS

85 >+$ have also adopted OFDM !ased transmissions to overcome the challenges of ine Of #ight (O#) propagation !ecause OFDM is a technology that has !een sho"n to !e

"ell suited to the mo!ile radio environment for high rate and multimedia services.

OFDM achieves high data rate and efficiency !y using multiple overlapping carrier

signals instead of ust one carrier. +he &ey advantage of OFDM over single carrier modulation

schemes is the a!ility to su!divide the !and"idth into multiple frequency su!-carriers "hich

carry the information streams are orthogonal to each other and deliver higher !and"idth

efficiency. +herefore OFDM allo"s higher data throughput even in the face of challenging

scenarios such as O# lin&s suffering from significant degradation !ecause of multipath

conditions. +herefore a guard time is added in each OFDM sym!ol to com!at the channel delay

spread. +he term delay spread descri!es the amount of time delay at the receiver from a signal

traveling from the transmitter along different paths. +he delay induced !y multipath can cause a

sym!ol received along a delayed path to interfere "ith su!sequent sym!ol arriving at the receiver

via a more direct path. +his effect is referred to as inter-sym!ol interference (3#3).

+he guard time may !e divided into a prefix (inserted at the !eginning of the useful

OFDM sym!ol and called cyclic prefix ()) and a postfix (inserted at the end of the previous

OFDM sym!ol). +he introduction of the can eliminate 3#3 in the time domain as long as the

duration is longer than the channel delay spread. +he is typically a repetition of the last

samples of data portion of the OFDM !loc& that is appended to the !eginning of the data payloadand ma&es the channel appear circular in order to permit lo"-complexity frequency domain

equali1ation.

OFDM signal generation consists of multiplexing the original data stream into


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SIGNALS

+he su!carrier pulse used for OFDM transmission is chosen to !e rectangular and this

has the advantage that the tas& of pulse forming and modulation can !e performed !y a simple

3nverse Discrete Fourier +ransform (3DF+) at the transmitter. 3n practice the 3DF+ is

implemented very efficiently as an 3nverse Fast Fourier +ransform (3FF+) and the 3FF+ &eeps

the spacing of the su!carriers ortoghonal and not requires intra-cell interference cancellation.

Accordingly at the receiver "e only need a FF+ to reverse this operation !ut the receiver and the

transmitter must !e perfectly synchroni1ed. +herefore according to the theorems of the Fourier

+ransform the rectangular pulse shape "ill lead to a sinc type of spectrum of the su!carriers that

are overlap !ut the information transmitted can still !e separated !ecause of the orthogonality

relation !et"een su!carriers. Figure 8.7 sho"s the !loc& diagram of a OFDM !ased transmission

system "ith only one single antenna at the transmitter and one at the receiver and ho" to

characteri1e a multipath radio channel for OFDM systems is descri!ed. +hen ho" to create the

mo!ile channel models to !e used for 85 deployment evaluation is explicitly descri!ed "here

simplifications in order to reduce the computational cost and the complexity of the simulations

are presented.

Fig.8.7 !loc& diagram of an #3#O OFDM !ased transmission system.

3.1.1 $in(le C)rrier o'ul)tion $9tem



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SIGNALS

A single carrier system modulates information onto one carrier using frequency phase

or amplitude adustment of the carrier. For digital signals the information is in the form of !its

or collections of !its called sym!ols that are modulated onto the carrier. As higher !and"idths

(data rates) are used the duration of one !it or sym!ol of information !ecomes smaller. +he

system !ecomes more suscepti!le to loss of information from impulse noise signal reflections

and other impairments. +hese impairments can impede the a!ility to recover the information

sent. 3n addition as the !and"idth used !y a single carrier system increases the suscepti!ility to

interference from other continuous signal sources !ecomes greater. +his type of interference is

commonly la!eled as carrier "ave (2) or frequency interference.

3.1.2 :re*uenc9 Diviion ultile


32/65


SIGNALS

"ireless channels offers much more unpredicta!ility and other challenges than their "ire line

(li&e t"isted "ire pairs or coaxial ca!les) counterparts due to the presence of multipath Doppler

spread etc. +his difficulty in the "ireless channels is mainly due to the frequent change in the

environment and other factors !ecause of the mo!ility of the user and presence of different

environment conditions.

3.1.! O:D 7or ultic)rrier Tr)nmiion

3n a "ireless communication system the signal is carried !y a large num!er of paths

"ith different strengths and delays. #uch multipath dispersion of the signal is commonly referred

as Uchannel-induced 3nter #ym!ol 3nterference (3#3).V 3n fact the multipath dispersion leads to

an upper limitation of the transmission rate in order to avoid the frequency selectivity of the

channel or the need of a complex adaptive equali1ation in the receiver.

3n order to mitigate the time dispersive nature of the channel single-carrier serial

transmission at a high data rate is replaced "ith a num!er of slo"er parallel data streams. $ach

parallel stream "ill !e then used to sequentially modulate a different su!carrier. y creating <

parallel su! streams "ill !e a!le to decrease the !and"idth of the modulation sym!ol !y the

factor of


33/65


SIGNALS

transform essentially correlates its input signal "ith each of the sinusoidal !asis functions. 3f the

input signal has some energy at a certain frequency there "ill !e a pea& in the correlation of the

input signal and the !asis sinusoid that is at that corresponding frequency. +his transform is used

at the OFDM transmitter to map an input signal onto a set of orthogonal su!carriers i.e. the

orthogonal !asis functions of the DF+. #imilarly the transform is used again at the OFDM

receiver to process the received su!carriers.

+he signals from the su!carriers are then com!ined to form an estimate of the source

signal from the transmitter. +he orthogonal and uncorrelated nature of the su!carriers is exploited

in OFDM "ith po"erful results. #ince the !asis functions of the DF+ are uncorrelated the

correlation performed in the DF+ for a given su!carrier only sees energy for that corresponding

su!carrier. +he energy from other su!carriers does not contri!ute !ecause it is uncorrelated. +his

separation of signal energy is the reason that the OFDM su!carriersB spectrums can overlap

"ithout causing interference. 3n OFDM the orthogonal su!carriers are separated !y a frequency

interval of f C 7%+s "here +s is the OFDM sym!ol duration as sho"n in Fig. 8.4.

Fig6 8.4 Frequency spectrum of OFDM transmission



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SIGNALS

+he frequency spectrum of the adacent su! channel overlap "ith one another !ut the

orthogonality of su!carriers "ill eliminate in principle the 3nter-hannel 3nterference (33#.

3.1. Ort"o(on)lit9 o7 i(n)l

A sinusoidal "ave !ehaves as an $igen functions for a linear time invariant (>+3)

system and is less suscepti!le to interference. 'ence a sine "ave is suita!le for transmission on a

multi-tap channel. +he sine "aves used for transmission should !e over sufficiently long

intervals of time in order to preserve the eigen property. +herefore distinct multiple sinusoids of

sufficient duration modulated !y data sym!ols can !e used to transmit data "ith a lesser

degradation in performance. 'o"ever adacent su!-carriers in frequency should !e separated !y

guard !ands to prevent overlap of information !et"een them resulting in poor !and"idth

efficiency.

+he main concept in OFDM is Orthogonality of the su!-carriers. #ince the carriers are

all either sin or cosine "aves "e &no" that the area under the sine "ave or cosine "ave is 1ero

as sho"n in Figure 8.8

Fig6 8.8 the area under a sine "ave over one period



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SIGNALS

Fig6 8.9 the area under a cosine "ave over one period

>etBs ta&e a sine "ave of frequency m and multiply it !y a sinusoid (sine or cosine) of a

frequency n "here !oth m and n are integers. +he integral or the area under this product is given

!y

f ( t )=sin (mwt )∗sin ( nwt ) (8.7)

y the simple trigonometric relationship the equation 4.4.7 is equal to sum of t"o

sinusoids (n-m) and (n+m), if n>m

1

2cos (n−m )−

1

2cos (n+m)

(8.4)

Again these t"o components are sinusoids each so the integral over one period is 1ero

(n−m )

(¿t )−∫0

2π 1

2 cos ( (n+m ) t ) dt

∫0

2π 1

2 cos ¿

(8.8)

K H K C K

3.1.6 DFT



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SIGNALS

+hough Multi carrier technique "as introduced in the 7@:K the main reason that

hindered the OFDM expansion for a very long time "as practical. As it seemed difficult to

generate such a signal and even harder to receive and appropriately demodulate such a signal.

Also this technique required a very large array of sinusoidal generators and also a large array of

coherent demodulators to ma&e the system "or&. +herefore the hard"are solution canBt !e

practical. As a consequence of the explosive development of digital signal processors (D#)

"hich can !e used for generating and demodulating an OFDM signal "as to use Fast Fourier

+ransform (FF+) a modern D# technique. FF+ merely represents a rapid mathematical method

for computer applications of Discrete Fourier +ransform (DF+). +he a!ility to generate and to

demodulate the signal using a soft"are implementation of FF+ algorithm is the &ey of OFDM

current popularity. 3n fact the signal is generated using the 3nverse Fast Fourier +ransform

(3FF+) the fast implementation of 3nverse Discrete Fourier +ransform (3DF+). +here is a

mysterious connection !et"een this transform and the concept of multicarrier modulation.

According to its mathematical distri!ution 3DF+ summari1es all sine and cosine "aves of

amplitudes stored in WL& array forming a time domain signal

kπ 2 n

N

X [k ] .(cos (¿)+ jsin(kπ 2 n

N ))n=0,1,… .. N −1

X [ k ] . e jkπ

2n

N =¿∑k =0 N −1

¿

[n ]=∑k =0

N −1

¿

(8.9)

3.1.4 Alic)tion o7 O:D

+he Orthogonal Frequency Division Multiplexing (OFDM) transmission scheme has the

follo"ing applications.

• 2orld"ide 3nteropera!ility for Micro"ave Access (2iMAW).

• +errestrial Digital Audio roadcasting (D=-+).

• 2ireless Metropolitan Area A


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SIGNALS

3$$$ NK4.77a.

3$$$ NK4.77g.

• Digital Audio roadcasting (DA).

• Digital =ideo roadcasting (D=).

• 'igh Definition +elevision ('D+=).

• road!and 3nternet Access.

• 2ireless


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SIGNALS

+he challenging pro!lem in a MM system is to implement !an& of modulators at the

transmitter side and demodulators at the receiver side. +he concept of UData transmissionV can !e

efficiently implemented using 3FF+ and FF+ instead of !an& of modulators at the transmitter side

and demodulators at the receiver side respectively.

E)9 E*u)li>)tion+

3n a single carrier system equali1ation ma&e frequency channel flat !ut equali1ation

amplify noise greatly in frequencies domain "here channel response is poor. As a result single

carrier performance is affected due to high attenuation in some !ands since all used frequencies

are given equal importance. 3n OFDM system "ide!and channel are divided into flat fading su!-

channels it reduces the equali1ation complexity in the receiver. #o it is possi!le to use

maximum li&elihood decoding "ith reasona!le complexity.

$ucetible to 7re*uenc9 elective 7)'in(+

Due to capa!ility of parallel transmission (each su!-carrier has narro" !and"idth to

overall !and"idth of signal) OFDM is highly suscepti!le to frequency selective fading. OFDM

converts a frequency selective fading channel into several flat fading channels.

Protection )()int Inter 9mbol inter7erence+

+he extended sym!ol time (due to lo"er data rate) ma&es the signal less suscepti!le to

effect the channel such as multipath propagation "hich introduces 3nter #ym!ol 3nterference

(3#3). +he use of cyclic prefix !et"een consecutive OFDM sym!ols ma&es it immune to 3#3.

Also it is less sensitive to sample timing offsets than single carrier system.

3.3 )jor Problem o7 O:D $9tem

Despite of several advantages the OFDM systems also have some maor pro!lems li&e-

Hi(" Pe)- to Aver)(e Power R)tio /PAPR0 o7 tr)nmitte' i(n)l+

resence of a large num!er of su!carriers "ith varying amplitude results in a high pea& to

average po"er ratio (A*) of the system "ith large dynamic range "hich in turn effects

on the efficiency of the *F amplifier. #9nc"roni>)tion /timin( )n' 7re*uenc90 )t t"e receiver+

#ym!ol +iming Offset (#+O) and arrier Frequency Offset (FO) affects on the

performance of OFDM system. orrect timing !et"een FF+ and 3FF+ is required at the receiver

side. OFDM system is highly sensitive to Doppler shifts "hich affect the carrier frequency

offset resulting in 33. .



39/65


SIGNALS

3.3.1 Ort"o(on)l :re*uenc9 Diviion ultile


40/65


SIGNALS

frequency division multiplexing. DF+ !ased frequency division multiplexing can !e fully

implemented in digital !ase!and. FF+ for highly efficient processing a fast algorithm for

computing DF+ can even further reduce the num!er of arithmetic operations to N log N from N2

(< if FF+ si1e).

A guard interval can !e used in !et"een consecutive sym!ols and the raised cosine

"indo"ing in the time domain to com!at the 3#3 and the 33. ut over a time dispersive channel

the system could not maintain perfect orthogonality !et"een su!carriers. +his pro!lem "as

tac&led "ith the use of cyclic prefix () or cyclic extension. 'ere they replaced the guard

interval "ith a cyclic extension of the OFDM sym!ol. +he 3#3 can !e eliminated totally if the

length of cyclic extension is longer than impulse response of the channel. Further this scheme

"ell simulates a channel performing cyclic convolution "hich ensures the orthogonality !et"een

su!carriers over a time dispersive channel. +he principle of OFDM system is to divide a single

high data rate !it stream into a num!er of lo"er data rate !it streams those are transmitted over

narro"er su! channels simultaneously. #o it is a modulation (frequency modulation) technique

and also a multiplexing (frequency division multiplexing) technique. +he difference !et"een

OFDM and conventional FDM is sho"n in figure 8.;.

Fig.8.; Orthogonal Frequency Division Multiplexing

3.! Eenti)l :e)ture in PAPR Re'uction Tec"ni*ue

A num!er of factors need to !e "ell thought-out in evaluation of any A* reduction

technique.

3.!.1 PAPR Re'uction er7orm)nce



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SIGNALS

A vital factor in selection of any technique is its performance as regards to A*

reduction. +his means ho" much capa!le the technique is as regards to reduction of A*. +his

capa!ility of any technique is algorithm dependent.

For example 3nter leaver technique A* reduction capa!ility is less than that of #>M.

'o"ever this A* reduction performance must !e udged "hile giving a cautious thought to

other detrimental effects "hich may result. +a&e an instance of clipping technique "hich has

very high performance as regards to A* reduction !ut the amount of resultant in-!and

distortion and out-of-!and radiation is intolera!le.

3.!.2 Tr)nmit $i(n)l ower incre)e

3t is necessary in a num!er of techniques that the po"er of transmit signal should !e

increased. +a&e an instance of +* "hich needs additional po"er !ecause *s employed in this

technique also need po"er. +he original constellation point is replaced !y equivalent

constellation points in +3. +hese equivalent constellation points need additional po"er as

compared to original point hence the po"er of transmit signal is increased in +3. +he

normali1ation of transmit po"er to original level results in degradation of $* performance.

3.!.3 Incre)e' ,ER )t t"e Receiver

An increase in $* at receiver end is another significant factor. +he increase in transmit

signal po"er and increased $* at receiver are interrelated. For instance in fe" techniques e.g.

A$ the $* is increased "hen transmit po"er is fixed. $* may also !e increased due toother reasons li&e errors inside information. For example the error inside information in +#

#>M and interleaving can result in loss of entire data !loc& hence a resultant increase in $*.

3.!.! D)t) R)te lo

Fe" techniques "hile tac&ling the A* result decrease in data rate. As sho"n in the

previous example the !loc& coding technique requires one out of four information sym!ols to !e

dedicated to controlling A*. 3n +# #>M and interleaving the loss in data rate is due to

transmission of side information utili1ing some of the carriers. #ince transmission of side

information "ithout errors is critical for retrieval of data sometimes channel coding is used to

protect against side information errors "hich further augments the pro!lem of data rate loss.

3.!. Comut)tion)l Comle


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SIGNALS

involved due to computations are of maor concern and have to !e evaluated against potential

increase in data !and"idth. 3n some schemes the signal processing needed for minimi1ing A*

may !e sufficiently complex that even leading edge technology gate arrays "ould not meet the

speed requirements for !road!and data transmission "ithin accepta!le !attery po"er and cost

constraints.

A* reduction may also incur an additional processor load in the receive path for

example "here a complex decoding or error-correction scheme is necessitated. #o to chec& the

applica!ility of any proposed technique employed for reduction of A* it is to !e seen that

ho" much penalty in terms of additional computations it "ill cost. For example the performance

for A* reduction is increased !y increasing the num!er of inter-leavers !ut "ith every

3nterleaver addition "e have additional computational cost. 5enerally more complex techniques

have !etter A* reduction capa!ility.

+a!le 8.7 omparison of A* reduction +echniques



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SIGNALS

3. :un')ment)l o7 PAPR

+here has !een momentous progress in the field of "ireless communication during last

t"enty years. +he internet and digital communication evolution has resulted in enormous

increase in methods of personal communication as "ell as commercial applications. +he ne"

paradigm of information access to every!ody every"here all the time is in ma&ing.

+o achieve the ever increasing demands of higher data transfer rates for ne" multimedia

applications the physical "ireless lin& of "ireless communication net"or&s is constantly under

trial. +he phenomenon of multipath fading mo!ility and the limited availa!ility of !and"idth are

maor precincts. >ately there have !een many !rea&throughs to triumph over these limitations.



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SIGNALS

Many modulation techniques compete for ne" solutions and future applications.

Modulation schemes can !e !roadly categori1ed in to single carrier and multi carrier. 2ide!and

code division multiple access (2-DMA) is single carrier modulation scheme. 2hile OFDM

Multi arrier ode Division Multiple Access (M-DMA) and multi carrier (M-3DMA) are

multi carrier schemes. 2-DMA "hich has !een adopted !y IM+# and it supports up to 4

LM!it%s at high mo!ility and large range. OFDM "hich is one of the multi-carrier techniques

and digital !roadcast systems li&e digital audio%video !roadcasting (DA%D=) are already

using this technique. 3t is also !eing used in "ireless local area net"or& (2>Aately OFDM has !een put into practice in DA digital television and high definition

television ('D+=)L78 high-!it-rate digital su!scri!er lines ('D#>) very high-speed digital

su!scri!er lines (='D#>) asymmetric digital su!scri!er lines (AD#>) and mo!ile "ide!and

data transmission (3$$$ NK4.77a 'iperlan 33). 3t is also used in the 3$$$ NK4.7; 2iMAW

standard.

+a!le 8.4 different standards



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SIGNALS

3n spite of all the advantages OFDM still has its shortcomings. One pro!lem is

vulnera!ility to carrier frequency estimation errors. $rror rate can increase drastically due to

small frequency offset !ecause it leads to loss of orthogonality !et"een the su! carriers. +he

second pro!lem is that OFDM signals suffer from high A*. 'igh A* requires a system to

accommodate an instantaneous signal po"er that is much larger than the signal average po"er

necessitating lo" operating po"er efficiency.

3..2 )t"em)tic)l o'el o7 O:D $9tem3n an OFDM system data is modulated in the frequency domain to < adacent su!

carriers. +hese < su! carriers span a !and"idth of '1 and are separated !y a spacing of X f C

%


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SIGNALS

3FF+ of these N samples is used to create the OFDM discrete-time sym!ol. +he parallel time-

domain samples are then converted to a serial stream and the is added.


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SIGNALS

As mentioned in the introduction the po"er efficiency of a system suffers "hen signal

that have large envelope variations is transmitted. +here have !een several metrics proposed that

quantify pea&y !ehavior. >ei >i and +ang pointed out that in practical systems signals are

frequently clipped to some lo" level even after envelope pea&s have !een minimi1ed.

Accordingly they propose that the envelope variation of a signal !e measured !y the clipping

noise po"er generated at some clipping level. Another metric to quantify the large envelop

variation is ea& to Average o"er *atio. 3ntuitively using some normali1ed measurement of the

pea& of a signal is appealing. +his is the idea !ehind the pea&-to-average ratio and is descri!ed in

detail in the next section.

3. PAPR ) etric o7 enveloe v)ri)tion

+he most popular quantification metric of envelope variation is the ea&-+o- Average

o"er *atio (A*)7. *ightfully so A* captures the most important aspect of a signal that

has to pass through a pea&-po"er limited device "hich is the pea& po"er. +he use of A* in

communications signals is a result of the use of A* in radar applications. A radar system shares

certain similarities "ith a communications system, namely they !oth have to transmit an

amplified radio signal of a certain spectrum. For radar the spectrum shape is often the only

signal constraint "hich ma&es "aveform shaping that minimi1es pea&s a relatively

straightfor"ard pro!lem. 'o"ever in an OFDM communication system there is the additional

constraint that each su! carrier (Fourier coefficient of the spectrum) is modulated "ith aninformation !earing complex num!er. +his additional degree of constraint significantly

complicates the pro!lem.

3..1 PAPR Curve b9 CCD:

OFDM systems com!ine multiple su!-carriers "hich causes increase in A*. +he

increase in A* is related to the num!er of su! carriers and their order of modulation.

omplementary umulative Distri!ution Function (DF) curves present vital information

regarding the OFDM signal to !e transmitted. +he DF curves are applied for many other

design applications such as to com!ine several signals through systems components visuali1e

the effects of modulation formats evaluate spread spectrum systems and design and test *F

components. +hese curves also provide the A* data needed !y component designer. +he main

use of po"er DF curves is to identify the po"er characteristic of the signals "hich are

amplified mixed and decoded.



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SIGNALS

+he plot of relative po"er levels of signal against their pro!a!ility of occurrence is

called DF curve. +his curve illustrates the amount of time the signal remains at or a!ove a

given po"er level. +he ratio !et"een po"er level and the average po"er is expressed in d.

Figure 4.4 sho"s all possi!le sym!ols for N-carriers # OFDM signal. +he plot sho"s po"er

levels of the sym!ols and the dotted hori1ontal line depicts the average po"er. +he pro!a!ility of

occurrence for any po"er level is percentage of time that signals spends at or a!ove that level.

Figure 8.N A "aveform to sho" a specific po"er level a!ove the average.

Figure 8.@ is a plot of the A* of x L


49/65


SIGNALS

Figure 8.@ DF of the discrete-time A* for various modulation orders.

For the derivation of cumulative distri!ution function (DF) fe" assumptions are made

considering only


50/65


SIGNALS

3.4.2 o'ul)tion Or'er

'igh data !and"idth efficiency (in terms of !%s%'1) may !e achieved !y using higher

order modulations !ased for example on GAM. 2hen the su! carrierBs modulation is a higher-

order GAM type the A* of the summed OFDM signal is increased !y the A* of the GAM

constellation used. 'o"ever the pro!a!ility of these higher pea&s occurring is correspondingly

less. Moreover since among advantages of OFDM one is that su! carriers can have their

modulation independently varied to adapt to channel conditions the com!ined A* in any

system using this technique may !e difficult to predict and control.

A* for an unfiltered !ase !and signal is listed in the follo"ing +a!le 8.8.

+a!le 8.8 A* for selected modulation formats

3.4.3 Contell)tion ")e

+he last entry in +a!le 8.8 is for a constellation o!tained !y modifying 4:;- GAM to

reduce A*. +his modified constellation shape is sho"n in figure 8.7K. 'o"ever there is an

additional processor load associated "ith encoding and decoding this constellation.



51/65


SIGNALS

Figure 8.7K 4:;-GAM constellations6 (a) regular and (!) modified mapping to reduce

A*

3.4.! Pule $")in(

3n terrestrial communications it is common to apply pulse shaping to the !ase !and

signal to reduce the !and"idth of the transmitted spectrum !ut this causes overshoot and could

increase the A* of the modulating signal !y 9-:d.

3.5 $9tem Decrition

Orthogonal multicarrier modulation is an efficient method of data transmission over

channels "ith frequency-selective fading. +his method has a relatively simple implementation

!ased on the inverse fast Fourier transform (3FF+).

+he simplified !loc& diagrams for an OFDM system "ith the convolution scheme and

the proposed "eighted scheme are sho"n in Fig. 8.77. As descri!ed in Fig. 8.77(a) the

modulated data stream is carried on the multi carriers !y the 3FF+ and the convolution !loc&

reduces the A* of signal "hich is corresponding to the "eight !loc& of the proposed scheme

as sho"n in Fig. 8.77(!). 3n the follo"ing !loc& the cyclic prefix is added !efore the 'A.



52/65


SIGNALS

(a)

(!)

Fig. 8.77 #implified !loc& diagrams for an OFDM system "ith (a) convolution scheme

and (!) proposed "eighting scheme.



53/65


SIGNALS

For a discrete data {ak }k =0 N −1

multicarrier-modulated signal x N ( t ) on LK ,NT is

represented !y

x N (

t )=

1

√ N ∑k =0 N −1

ak e

j2π f k t

(8.9)

"here N is the num!er of su!carriers T is the original sym!ol period∆ f =1/ NT and

f k =k ∆ f ,k =0,…, N −1 X f C 7 /NT . +he A* of x N over the time interval LK ,NT is

defined !y

PAPR ( x N )=max0≤ t ≤ N

T | x N (t )|

2

E(| x

N (t )

|

2) (8.:)

"here E (·) denotes the expectation operator.



54/65


SIGNALS

CHAPTER !

;EI?HTED ORTHO?ONA# :RE@UENC&+DI%I$ION

U#TIP#EIN? $&$TE

'ere "e provide the "eighted OFDM signal "here the "eight is derived from a

suita!le !and limited signal having no 1ero on the real line. +his method is motivated !y a

convolution method. +a&ing the circular convolution !et"een the multicarrier-modulated signal

xN and a suita!le signal 0 having compact support the A* of the convoluted signal can !e

reduced. 3n fact for p ∈ * "ith 7 ≤ p≤∞ from YoungBs in equality ‖ x N ∗Φ‖ p ≤‖ x N ‖1‖Φ‖ p,

and x N ∗Φ !elongs to L

p

Lp although x N ∈ L1

"here ‖f ‖ p=(∫ R

.

|f ( x)| p

dx )1

p

and the

space L p={f :‖f ‖ p 7 since L

p

is more tempered than L1

essentially the

A* of the convoluted signal can !e reduced. #imultaneously "e should consider carefully 0

to sustain the si1e of the expectation of x N ∗Φ .

First "e consider the convolution method and then derive the corresponding "eighted

OFDM signal.

!.1 Convolution et"o'

+he Fourier transform ! [ f ]

of f is defined !y

! [ f ] (" )≔∫ R

.

f ( x)e− j"x dx (9.7)

if the integral exists. +he inverse Fourier transform ! −1[ ! ] of F is defined !y



55/65


SIGNALS

! −1 [ ! ] ( x )≔

1

2 x∫ R

.

! (")e jx"d" (9.4)

provided that the integral exists. +hen ! −1 [ ! [ f ] ]=f "hen f and ! [ f ] are

integra!le and

! [ ! [ f ] ]=2π ~

f (9.8)

"here~

f ( x )=f (− x) .

2e consider signal φ as

φ ( x )=1−sin#( x)

π

2

x

2 (9.9)

2here

sin#x={sinπx

πx , x $0

1, x=0

y direct computation the Fourier transformΦ≔ ! [φ]

of ϕ is given !y

Φ (" )=

{1

2 (1−|"|π )

2

|"|≤ π 0,%t& e'wise .

+he signal ϕ is a !and limited signal "ith !and"idth π has no 1ero on the real line and

~φ=φ (9.:)

For more information a!outφ

see the Appendix at the end of this paper.

onsider the circular convoluted signal as follo"s6

( N (t )≔ 1

2π x N ∗Φ (t )=

1

2π ∫−π

π

x N (t −" )Φ ( " ) d" . (9.;)

+a&ing the Fourier transform in (9.;) "e have !y (9.8) and (9.:) that

! [ ( N ]= 1

2π ! [ x N ] ! [ Φ ]= ! [ x N ]φ (9.;)



56/65


SIGNALS

"here ! [ x N ] and ! [ ( N ] are the Fourier transforms in the sense of distri!ution.

#ince φ has no 1ero on the real line and

√ N 2π /¿∑

k =0

N −1

ak ) ("−2π f k ) ,

! [ x N ] (" )=¿ "e can recover the

discrete data so that. for k C K , . . . , N − 7 "e have

ak =√ N ! [ x N ](2π f k )

2π =

√ N ! [ ( N ](2 π f k )2πφ(2 π f k )

. (9.E)

!.2 ;ei("te' O:D $9tem2e sho" that the convoluted signal in (9.;) can !e "ritten as a simple "eighted OFDM

signal yN .

O!serving !y (9.8) (9.:) and (9.;) that

∫−π

π

e j2π f k (t −" )Φ (" ) d"=2πφ (2π f k )e

j 2π f k t

the convoluted signal in (9.:) can !e expressed as the follo"ing "eighted OFDM signal6

( N (t )= 1√ N ∑k =0 N −1

ak φ (2 π f k ) e j2 π f k t ,0≤ t ≤ N T (9.N)

!.3. ;ei("te' O:D $9tem ;it" o'i7ie' ;ei("t

+he demerit of the "eighted OFDM signal in (9.N) is the degradation of $*

performance since the "eight φ is non-uniform. +o overcome this o!stacle "e consider the

modified "eight "ith a positive constant α as follo"s6

φ* ( x )=φ ( x )+* /+%N (9.@)

"here α is a shift parameter and log


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SIGNALS

- N (t )= 1

√ N ∑

k =0

N −1

ak φ* (2π f k ) e j 2π f k t ,0≤t ≤NT (9.7K)

as a transmitted signal inste

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A Weighted Ofdm Signal Scheme for Pea1

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