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A Survey on CF Method, PTS Approach, Companding Technique and

Time Domain Methods for PAPR Reduction in OFDM Systems 625

or Phase Shift Keying (PSK) or Quadrature Phase Shift Keying (QPSK). Since OFDM provides high

spectral efficiency, power efficiency, robustness to multipath fading and immunity to frequencyselective fading channel, it is widely used for high data rate wireless communication systems and in

many wireless communication standards such as Digital Audio and Video Broadcasting systems,

Wireless Local Area Network (WLAN), Very-High-Speed Digital Subscriber Loop (VDSL) and

Asymmetric Digital Subscriber Line (ADSL). In worst case the OFDM signal may add all the

sinusoidal signals constructively in phase and amplitude so that the amplitude is N times the averagepower[40].

1.1. Peak to Average Power Ratio (PAPR) Problem

Tasadduq and Rao (2002) stated that in OFDM transmission Systems when the number of subcarriers

increases the Gaussian distributed signal approaches to that of a sample function, Peak-to-average

power ratio (PAPR) is a good measure of the resulting occasional peaks. PAPR of an OFDM signal

is defined as the ratio of the maximum instantaneous signal power to the average signal power.

av

NTt

P

tx

txPAPR

]|)([|

)}(,{

2

0max

= (1)

In eqn. (1), Pav is the average powerT is the time period of an OFDM symbol

Even though large peaks occur very rarely, one of the main drawbacks of the OFDM system is

the high Peak to average Power ratio which leads to increase in complexity of Analog to DigitalConverters (ADC) and Digital to Analog Converters (DAC) while introducing intermodulation

distortion, spectral spreading and undesired out-of band radiation [20]. Large PAPR also leads to

Adjacent Channel Interference, degradation of Bit Error Rate (BER) performance and variation ofOFDM signal constellation [17]. The above mentioned issues can severely harm the OFDM system

performance and demands expensive transmitters for normal operation. Since the positive features of

OFDM can support the design of highly effective wireless commmunication systems, extensive

research activities were carried out in the late 1990s to study the distribution of PAPR and its reductionin OFDM systems. Eventhough coding schemes for reducing peak power were employed by Wulich

(1996) in multicarrier modulation systems and Eetvelt et al., (1996) in QPSK-OFDM systems, a major

break through in PAPR reduction methods started with Bauml et al., (1996) work on Selected mapping(SLM) technique, Muller and Hubers (1997) Partial Transmit Sequence (PTS) approach, Li and

Ciminis (1998) Clipping and filtering technique and Wang et al., (1999) article on Companding

Technique. The research community have proposed innovative methods to reduce PAPR of OFDMsignal, recently PAPR reduction is achieved in time domain directly with reduced computational

complexity avoiding the need for FFT operation.

he rest of the paper is organized as follows. Section 2 presents a survey on Clipping and

filtering methods which includes iterative clipping and filtering methods and non-iterative clippingmethods. Section 3 elaborates on Partial Transmit Sequence (PTS) approach with a brief review on

phase optimization methods, extended PTS approach, PTS based on DFT property and Algorithm

assisted PTS approach. Section 4 discusses on Companding schemes with emphasis on non-linear andlinear companding schemes. Section 5 examines the time domain based methods for PAPR reduction.

Section 6 concentrates on overview of survey and Scope for future work followed by conclusion in

Section 7.

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626 Arvind Chakrapani and V. Palanisamy

2. Clipping and Filtering MethodThe clipping operation can be viewed as the product of OFDM signal and a rectangular window

function that equals one if the OFDM signal amplitude is below a threshold and less than one if thepeak amplitude needs to be clipped. The conventional hard clipping introduces non-linear distortion

and out of band radiation which leads to spectral regrowth [16].

Li and Cimini (1998) introduced a post filtering operation to reduce the effects of out of bandradiation and spectral regrowth due to the clipping process, however the possibility of spectral

regrowth in the time domain is not addressed. Their work was the first to introduce filtering operationafter the clipping process inorder to reduce the spectral regrowth. Inorder to reduce the out of bandradiation, spectral regrowth and clipping noise involved in the PAPR reduction process, repeated

clipping and filtering methods were introduced while non-iterative clipping and filtering methods

reduced the computational complexity significantly.

2.1. Iterative Clipping and Filtering Methods

Armstrong (2002) performed a repeated clipping operation followed by an FFT - based frequency

domain filtering of an oversampled time domain OFDM signal to achieve a PAPR reduction with only

moderate level of clipping noise and no increase in out of band power. This method distorts the in

band spectral components to shrink the signal constellation and adds noise. While Leung et al., (2002)proposed an Iterative Clipping and Filtering(ICF) technique in time domain to achieve similar PAPR

reduction performance as that of Armstrongs method with reduced complexity requires no FFT/IFFToperation is presented in Table 1.

Table 1: Computational complexity of Armstrongs ICF and Leungs ICF technique.

Operation Armstrongs ICF technique Leungs ICF technique

Computational Complexity for K

iterations

Computation time in seconds 169 10

Where L oversampling rate

Deng and Lin (2007) introduced a Repeated Clipping and Filtering (RCF) method, where the

number of recursions is reduced by employing Smart Gradient Projection (SGP) algorithm and also

bounds or limits the distortion on each tone after each recursion to reduce the error rate and PAPR of

an OFDM signal.The iterative clipping process makes it difficult to estimate the BER performance. Bae et al.,

(2010) based on a noise enhancement factor suggested analytical expressions for the estimation of

attenuation factor, BER and Error Vector Magnitude (EVM). Their work also characterizes clippingnoise for iterative processes and the first to report an effective tradeoff between PAPR reduction and

BER performance in an ICF technique.Wang and Luo (2011) proposed a ICF technique where each iteration is expressed as a convex

optimization technique and the optimal frequency response filter is designed to minimize the signal

distortion so that PAPR is reduced for each of the OFDM symbol. This method achieves a PAPR

reduction in just one or two iterations while the same performance in a conventional technique requires

eight to sixteen iterations.

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2.2. Non Iterative Clipping Methods

A non iterative constrained clipping technique by Baxley et al., (2006) satisfies the in band metric

called Error Vector Magnitude(EVM) and the maximum permissible out of band spectral

constraints, so that PAPR of an OFDM signal is reduced.A computationally efficient single iteration clipping-filtering technique proposed by Wang and

Tellambura (2005) exploits the fact that the clipping noise obtained after several iterations of clippingand filtering is approximately equal to that generated in the first iteration. The simplified techniquescales the clipping noise generated during the first iteration and with just three FFT/IFFT operations it

achieves the same PAPR reduction as that of the existing iterative techniques with (2K+1) FFT/IFFT

operations where K is the number of iterations.Clipping methods introduce in-band and out of band radiation while the filtering process

reduces the out of band radiation due to clipping but cannot reduce the in-band distortion [29]. Even

though the ICF process reduces spectral expansion and eliminates peak re - growth, it is timeconsuming and increases the complexity of the transmitter.

3. Partial Transmit Sequence (PTS) ApproachMuller and Huber (1997) proposed a PTS approach where the subcarrier block is decomposed into

multiple disjoint sub blocks and each(other than the first sub block) of which is multiplied by acommon phase factor to generate a statistically independant new signal vectors that are optimally

combined to reduce PAPR of an OFDM signal. An exhaustive search over all the possible combination

of permissible phase factors is mandatory to find the optimal Phase factor but the search complexity

increases with the number of sub blocks exponentially [52]. The candidates generated using PTSapproach are interdependant and the required number of bits for transmitting the side information is

more compared to the Bauml et al., (1996) SLM scheme.

Figure 1: PTS based PAPR reduction in OFDM system (Muller and Huber, 1997)

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3.1. PTS Schemes Based on Phase Optimization Methods

Muller and Huber (1997) introduced an effective PAPR reduction scheme called Optimal Binary Phase

Sequence (OBPS) for OFDM systems with arbitrary number of subcarriers and unconstrained signal

set by optimally combining the partial transmit sequences.

Subcarrier block A is subdivided into V pair wise disjoint carrier sub blocks)(i

A where i =

1,2, V. An optimization parameter called rotation factor or phase factor { }=

2,0,)()()( iiji eb is

introduced to each sub block i and the peak power optimized PTS in time domain is

)(

1

)( iv

i

iab = = (2)

The above scheme works with almost vanishing redundancy and has a transmitter complexity

which increases exponentially with the number of sub carriers.

Tellumbura (1998) proposed a phase optimization criterion for several block phase factor inPTS approach for PAPR reduction in OFDM system with increase in complexity.

The new optimized criterion is derived as

==

1

032|)(|minarg],,....,[

N

kvk

Where (k) is the aperiodic autocorrelation of the information vector.

Hill et al. (2000) introduced an adaptation to OBPS to reduce PAPR by combining cyclic shiftof the IFFT sub block output with Partial Transmit Sequences. Cyclically shifted PTS increases the

number of alternative transmit sequences with trivial operations by cyclically shifting the data before

or after they are phase rotated

)(

1

)(~ ijv

i

ieaa

=

= (3)

Cyclic shift in Time Domain is performed as

=

+ =v

i

iji

v eaa1

)()(

)(~

(4)

In eqn. (4), )(v is cyclic shift in time domain.

Cimini and Sollenberger(2000) introduced sub-optimal iterative flipping algorithm (IFA) forcombining partial transmit sequences to reduce PAPR but it has a performance gap with ordinary PTS

technique, in other words the algorithm performs worse than conventional PTS with reduced

complexity.

Tellambura (2001) computed an optimal set of quantized phase factors and it achieves better

performance than the exhaustive search process of PTS approach. For small number of sub blocks the

proposed algorithm performs better than OBPS and when the number of sub blocks is large it performs

similar to OBPS.

Han and Lee (2004) suggested a gradient descent search algorithm to compute the phase factors

which leads to reduced PAPR statistics than the IFA with reduced search complexity and little

performance degradation.

3.2. Extended PTS Approach

Kang et al. (1999) proposed a concatenated pseudo-random Sub Block partition Scheme (SPS) for

PTS, it has the same PAPR reduction performance as that of the conventional pseudorandom SPS with

extensively reduced computational complexity. For M sub block partitioning, this method produces

candidates.

Chen and Pottie (2002) proposed a novel orthogonal projection based on PTS approach that

achieves significant PAR reduction at low redundancy.

Equation (2) can be rewritten in matrix form as

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],.......,[~ 221 NTTTTmbmbmbMba == (5)

Where mn nth column of Matrix M,

b Column phase vector of length V, b=[b1,b2 ..bv]

This geometrical interpretation in eqn. (5) forms the basis for finding the optimal phase rotation

vector b based on orthogonal vector function of the columns .1, Nnmn

Schenk et al. (2005) proposed a Spatial shifting based PTS scheme to transmit the partialtransmit sequences of the OFDM signal on the transmission branches with minimum PAPR, so that

significant PAPR reduction with limited complexity and signaling overhead is achieved. While Xiao et

al.(2007) presented a Low Complexity PTS(LC PTS) for reduction of PAPR by exploiting the

correlation among the candidate signals, the computational complexity of LC-PTS and PTS is given in

Table 2.

Table 2: Computational complexity of PTS and LC-PTS

Operation PTS LC-PTS Percentage

Complex Addition

Complex Multiplication

Computations

Where L Number of candidate signals

M Number of sub blocks

N Number of sub carriers

W Number of phase factors

P Number of highest amplitude positions

In 2010, Ghassemi and Gulliver employed the Autocorrelation function of PTS sub blocks to

develop a new PTS sub blocking scheme using error-correcting codes. This method minimizes the

number of repeated sub carriers within a sub block and provides better PAPR reduction thanpseudorandom or m-sequence sub blocking with low complexity.

3.3. PTS Approach Based on DFT Property

DFT property is employed to generate alternate candiadates of an OFDM signal, among which the

candidate with lowest PAPR is selected for transmission.

Lu et al. (2006) suggested to apply certain transformations on PTS (T-PTS) of a OFDM signal

to generate alternate frequency domain signals and transmit the signal which has a reduced PAPR than

that of the actual signal. Basic operations like complex conjugation, frequency reversal, circular shift

and their combinations are used either individually or jointly on different sub blocks to perform the

transformation. The alternative frequency domain signal can be expressed from eqn. (2) as

[ ]=

=v

t

iiiATbA

1

)()()( (6)

Where [ ])()( ii AT is a certain pre-defined transformation made on)(i

A . The time domain signal

of eqn.(6) is given as

[ ]{ })()()~

(

1~ iiiv

t ATIDFTba = = (7)T-PTS outperforms OBPS method for the same number of sub blocks and exhibits similar performance

for the same number of carriers with reduced complexity.

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A sub optimum PTS scheme introduced by Wang and Cao, (2008) combines an alternate

optimization method and linearity property of IDFT to reduce the computational complexity while

increasing the number of candidate signals, so that PAPR reduction performance of OPTS is attained

with dramatically reduced computational complexity.

Five novel simple transformations are proposed by Zhu et al., (2008) namely (i) circular time

shift of)(i

a (ii) circular frequency shift of)(i

A (iii) time reversal of)(i

a (iv) complex conjugate of)(i

a

(v) complex conjugate of

)(i

A employs DFT property on PTS in an iterative manner to reduce PAPR.For small number of sub blocks, some of the proposed transformations achieve better performance than

the IFA.

A PTS method by Yang et al., (2011) recursively combines the cyclically shifted sub block

sequences based on the linearity property of IFFT to generate a set of candidate signals in the time

domain with different phase constellation without employing multiplication. The phase detector

recovers the OFDM signal at the receiver. This method achieves PAPR reduction and maintains bit

error rate performance as that of the conventional PTS(OPTS) in both AWGN and Rayleigh fading

channel but requires a detector at the receiver.

When compared to conventional PTS approach, the DFT assisted PTS approach generates more

candidates of a OFDM signal and provides the liberty to select the candidate with lowest PAPR for

tramsmission.

3.4. Algorithm Assisted PTS Approach

Nguyen and Lampe (2008) preprocessed the data stream ahead of PAPR reduction so that side

information is embedded with minimal possible redundancy, maintaining the BER without causing

peak regrowth. The complexity in the search process of phase factor is formulated as a combinatorial

optimization problem enabling us to (i) unify different search strategies proposed in the PTS literature.

(ii) adapt different optimization algorithms known from the literature to assist the PTS approach.

Chen (2009) reduced the search complexity of PTS approach by combining the PTS with cross

entropy method and achieved the same PAPR reduction perfromance as that of Exhaustive Search

Algorithm (ESA). The PAPR problem is rewritten as a score or fitness function that is further

translated to a stochastic approximation problem which is effectively solved using a stochasticoptimization technique called cross entropy method.

Chen (2010a) expressed the PAPR reduction problem as a combinatorial optimization problem

which is effectively solved using Quantum Inspired Evolutionary Algorithm to find the optimal phase

factors that achieves significant PAPR statistics. While the search for optimal phase factors in a PTS

scheme is rewritten as a global optimization problem and is solved using a population based search

method called Electromagnetism - like (EM) Algorithm. The EM based PTS scheme by Chen (2010b)

follows a stochastic optimization approach and employs attraction repulsion mechanism to search the

optimal phase rotation factor so that the desired PAPR statistics is achieved with reduced complexity.

Wang et al, (2010) proposed a sub optimal method by combining a numeric function

optimization algorithm called Artificial Bee Colony Algorithm with PTS (ABC-PTS) to reduce the

search complexity of the allowable phase factors, such that PAPR reduction is achieved.Taspinar et al., (2011) proposed an iterative heuristic search method in which Parallel Tabu

search Algorithm is used in conjunction with PTS (Parallel TS-PTS) approach eliminates the iterations

that visits the solution obtained recently and selects the optimal phase rotation vectors to optimize the

PAPR statistics. The parallel information exchange between Tabu search algorithm is based on

crossover operator used in Genetic Algorithm (GA) combines good features of the parent to achieve

better performance. PAPR reduction and search complexity comparison of various PTS schemes

performed on a 16 QAM modulated OFDM signal with 256 subcarriers is presented in Table 3.

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Table 3: Comparision of various PTS schemes based on PAPR reduction

PTS schemes Number of searches (S) PAPR (dB)

Original OFDM 0 11.26

OPTS 6.74

IFA 1000 7.13

ABC-PTS 1000 6.98

Parallel TS-PTS 1000 6.93

Since Genetic Algorithm converges rapidly in changing channel conditions and provides

solution for Gradient based search method, Lixia and Murroni (2011) used it along with PTS approach

to reduce PAPR in multicarrier modulation(MCM) systems. Based on their study on OFDM and

Wavelet packets multicarrier modulation (WP MCM) in Additive White Gaussian Noise (AWGN)

channel, GA applied to PTS reduces PAPR more effectively in OFDM rather than for WP MCM.

4. Companding TechniqueThe first companding scheme was introduced based on the similarity between OFDM signal and

speech signal that large signal occurs infrequently by Wang et al. in 1999. He applied the idea of

companding in speech processing to reduce PAPR of an OFDM signal and to improve its transmission

performance. Companding scheme effectively compresses the large signals and enhances the small

signals to achieve PAPR reduction.

Figure 2: Block Diagram of a Companded OFDM system (X Wang et al., 1999)

4.1. Non Linear Companding Scheme

Wang et al., (1999) introduced a -Law companding technique to generate optimal companding

coefficients to limit PAPR of a OFDM signal and improves the BER performance. A companded

signal increases the transmitter signal power while the noise power remains constant and makes theHigh Power Amplifier(HPA) to operate in the non linear region. Mattsson et al. (1999) commented on

their work that Companding leads to spectral regrowth and raised a question whether the improvement

in BER is due to companding or increase in the transmit signal power. Later Wang et al. (1999)

compared the performance of a companded signal with that of the non companded signal with constant

transmission power to infer that in the region of high SWR the SER of a companded signal achieves

better results than that of an uncompanded signal. He also stated that the spectral regrowth due to

companding is minimal and is insensitive to the variations of companding coefficients. The

companding scheme shows better performance than clipping, but ignored the non-linear operation of

power amplifiers which leads to spectral side lobes growth.

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Huang et al., (2001) stated that the increase in the average input power of -Law companding

technique can be avoided and maintained constant by transforming the OFDM signal based on their

power distribution, so that the HPA operates in linear region. In -law companding transform, by the

proper selection of the companding form and its corresponding inflexion point the PAPR can be

reduced with reduced complexity and moderate degradation.

Jiang and Zhu (2004) introduced a Non-linear Companding Transform described by a single

valued function exploits the statistical characteristics of the OFDM signal to limit PAPR and exhibits

good BER performance in a AWGN channel.Huang et al. (2004) proposed the design criteria of Companding Transform (CT) based on the

statistical characteristics of OFDM signal to enable an effective tradeoff between PAPR reduction and

BER performance. He also discussed about the performance of four companding schemes namely (i)

Linear Symmetrical Transform (LST) (ii) Linear Nonsymmetrical Transform (LNST) (iii)Nonlinear

Symmetrical Transform (NLST) (iv) Nonlinear nonsymmetrical Transform (NLNST). The inflexion

point in NLST treats the large and small amplitude signals on different scales and achieves better

performance than the other three schemes and the clipping method.

Jiang et al., (2005) proposed an Exponential Companding (EC) technique that converts the

amplitude statistics of an OFDM signal into a uniformly distributed signal to limit the PAPR while

maintaining the average signal power constant.

The Exponential Companding function is given by

dx

axxh

=

2

2

exp1)sgn()( (8)

In equation (8), sgn(x) is sign function

[ ]

2

2

2

2

2

exp1

d

dn

n

sE

sEa

= maintains the average signal power constant.

The de-companding function at the receiver side is given by

=

d

e

xxxh 1log)sgn()( 21 (9)

The companding functions, eqn. (8) and eqn. (9) enhances the small signals and compresses the

large signals at the same time which is desirable when compared to the - law companding scheme

which enlarges the small signal and ignores the signal peaks. Hence the non-linear companding schemeattains better PAPR reduction, BER, Power Spectrum and Phase error than the -law companding

scheme. The main liability of EC scheme is that its performance remains unchanged for different levelsof companding.

Jiang et al. (2006) inferred that at the receiver side, a companded signal when undergoes only

inverse companding transform (ICT) the resultant spectrum exhibits severe out of band, in-band

distortion and peak regrowth due to excessive channel noise. Hence they proposed an iterative receiverwith slight increase in complexity to cancel out the channel noise and companding noise. Later in

2007, they proposed two novel nonlinear companding functions for MCM signals to transform the

Gaussian-distributed OFDM signal into a Trapezoidal-distributed signal. By proper selection of

parameters this method achieves PAPR reduction and maintains average power constant.The two novel companding functions introduced by Jiang et al. are

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10,2

.3)(1

= x

xerfxC is a LNST (10)

=

2.2).()(2

xerfxsgnxC is a NLNST (11)

Where nnn dttpthh )()( 2

1

12

= , maintains average power constant.

LNST scheme in eqn. (10), C1(x) achieves better tradeoff between BER and PAPR reduction

while NLNST scheme in eqn. (11), C2(x) provides result consistent with non linear compandingscheme for PAPR reduction. Table 4 compares the PAPR reduction and BER performance of the

Jiangs method with that of the EC scheme.

Table 4: PAPR reduction and BER performance comparison of the Jiangs method and EC scheme.

PAPR (dB)PAPR (dB)

PAPR (dB)

Original OFDM 6.98 8.58 10.80EC 9.67 11.42 4.80

EC* 7.43 9.08

Jiangs method 7.90 9.43 4.25

Jiangs method* 7.38 9.01

* without decompanding operation at the receiver

4.2. Linear Companding Scheme

Aburakhia et al., (2009) proposed a Linear Companding Transform (LCT) with two inflexion points toscale different signal levels independent of one another. Based on the simulation results of his

proposed LST and NLST on an AWGN channel it was inferred that LCT performs better in terms of

PAPR reduction and BER performance. The average value of PAPR reduction is 50% for LNST and70% for the proposed LCT.

Hou et al. (2009) introduced a Companding Scheme based on transformation of a Gaussian-

distributed OFDM signal to a Trapezoidal-distributed signal with proper selection of parametersachieves a better PAPR reduction and BER performance than the EC scheme.

Jiang (2010) proposed a new Companding Transform based on a smooth function called airy

special function which is given by

[ ]).()0().(.)( xaairyairyxsignxf = (12)In equation (12), airy(.) is an airy function of first kind

parameter to control the degree of companding

[ ]

= 2

2

.()0( xaairyairyE

xE

maintains the average signal power constant.

The decompanding function is given by

=

xairyairyxsign

xxf )0().(.

1)( 11 (13)

Eqn. (13) is computed based on Look-up table.The proposed Transform based on airy function is flexible, the degree of companding is varied

by changing which is reflected in the performance and this feature overcomes the liability of EC

scheme. The performance comparison of the Airy function based CT, EC technique and -law CT on

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four times oversampled 64 QPSK modulated OFDM signal in terms of Out of Band Interference

(OBI), PAPR and Signal to Noise Ratio (SNR) is given in Table 5.

Table 5: Performance Comparison of the Airy function based CT, EC scheme and -law CT.

Parameters Airy function based CT EC Scheme -law CT

OBI (dB) 47.5 45 39.7

PAPR (dB) 3.88 2.37 5.78

(dB) 8.9 10.4 11.7

* required to reach a BER of

While Hou et al. (2010) introduced a companding scheme which mainly compresses only the

large signals and even without decompanding function it maintains a good BER performance. ThePAPR reduction capability and Power spectrum obtained based on this method is superior to that of EC

scheme.

Companding Transform can be used to limit PAPR statistics for arbitrary number of carriers,irrespective of the frame format and constellation type [28]. Companding schemes achieve good PAPR

and BER performance with reduced complexity and no bandwidth expansion [29].

5. Time Domain Based PAPR Reduction TechniquesPAPR reduction is performed by employing some properties or methods in time domain to the originalOFDM signal so that the alternate candidate signals are generated and the candidate with lowest PAPR

is selected for transmission.

Lu et al. (2007) generated the candidate signals in time domain directly by computing theproduct of circular convolution of the OFDM data and IFFT of optimized cyclically shifted phase

sequences (OCSPS). Table 6 compares the PAPR reduction performance of OCSPS with SLM and

PTS.

Table 6: Comparison of various PAPR reduction methods on a OFDM signal with 1024 subcarriers

Method Number of Main Computations PAPR (dB)

Subblocks candidates

SLM = 4 10.14

PTS 2 10.4

4 9.08

OCSPS L = 4 One N-point IFFT 9.2

Where N refers to number of subcarriers and S refers to finite set of each element.

While a Low Complexity(LC) time domain-based PAPR reduction technique by Alsusa andYang, (2008) uses a linear symbol combining technique to consecutive OFDM symbols to create

several time domain representation of each OFDM symbol at the transmitter. The scheme requires one

IFFT block per OFDM symbol while PTS requires N IFFT blocks per OFDM symbol where N is the

number of sub sets. But Forward Error Correction(FEC) coding has to be performed on sideinformation to overcome the noise in the Channel, and to improve the BER performance at low SNR

values, which demands additional processing at the receiver. The BER performance is slightly reduced

due to its dependency on side information, symbols and multiblock combination.Yang et al., (2008) proposed a LC SLM scheme using Time Domain Sequence

Superposition(TDSS) to limit PAPR of an OFDM signal. Here two phase sequences generated are

multiplied with the input symbol to produce two intermediate sequences. Of this one time domainsequence is fixed and linearly combined with the cyclically shifted versions of the other sequence to

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produce new candidates. The computational complexity comparison of TDSS and SLM scheme is

presented in Table 7.

Table 7: Computational complexity of Bauml et al. SLM scheme and LC SLM TDSS scheme.

Operation Bauml et al. SLM Scheme LC SLM TDSS scheme

Number of Multiplications

Number of Additions

When M = 4, 8, 16 and 32PAPR reduction better than LC SLM

TDSS scheme

PAPR is 0.2 dB less than the

conventional SLM scheme

Where M refers to the number of phase sequences.

A selective time domain filtering technique suggested by Du et al., (2009) employs a filter bank

to generate candidate signals with different PAPR. Since scrambling is performed in time domain, the

need for additional IFFT block is eliminated.Wang et al., (2009) linearly combined the OFDM signal and its cyclically shifted version with

various allowable phase and time delays to produce candidate signals. The scheme has reduced

complexity than that of SLM scheme with some degradation in BER performance.

6. Overview of Survey and Scope for Future WorkThe comparative analysis on Iterative clipping and filtering technique, PTS Approach based on DFT

property, Algorithm assisted PTS scheme, Companding schemes and time domain based methods are

presented in Table 8, Table 9, Table 10, Table 11 and Table 12 respectively along with their scope forfuture work.

Table 8: Analysis of Iterative Clipping and Filtering Technique for PAPR reduction.

Author Methodology Merits Demerits Remarks

Armstrong

(2002)

Repeated clipping

and frequency

domain filtering

No increase in out

of band radiation

Two FFT operations

used

Peak regrowth

reduced

Moderate level of

clipping noise is

generated due to

distortion of in band

frequency components

Tradeoff between PAPR

reduction and BER

performance is not

addressed

Leung et al.,

(2002)

Repeated clipping

and time domain

filtering

Requires no FFT

operation

Clipping threshold is

increased by 5%

Deng et al.

(2007)

Distortion bounded

for each iteration Reduces error rate

Demands more reserved

tones to achieve better

error rate and PAPR

reduction

Occurrence of Constellation

shrinkage is not considered

Wang and Luo

(2011)

Convex

optimization

technique

PAPR reduction is

achieved in 1 or 2

iterations

Computational

complexity is high.

Processed OFDM symbols

are distortionless and

provides better out of band

radiation

Baxley et al.

(2010)

Noise enhancement

factor

Estimates BER,

EVM and

attenuation factor

Suppression of out of

band radiation by filtering

leads to peak regrowth

Reports tradeoff between

BER performance and

PAPR reduction

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6.1. Scope for Future Work I

The proposed PAPR reduction algorithm based on ICF technique will combine the positive features

like time domain filtering, distortion bounded for each iteration, expressing PAPR problem as a convex

optimization problem so that FFT operation is eliminated, BER is reduced and number of iterations isdrastically reduced while simultanously concentrating on clipping threshold, number of reserved tones

and computational complexity. This method is expected to achieve a significant tradeoff between

PAPR reduction, BER performance and reduction in computational complexity by reducing thenumber of iterations.

Table 9: Analysis of PTS approach based on DFT property for PAPR reduction.


Lu et al.,

(2006)

Transformation of

PTS using DFT

property

Complexity reduced

compared to PTS

scheme for same

number of sub blocks

Complexity is same as

that of PTS for same

number of candidatesOnly PAPR

reduction is

considered, BER

performance is

ignored

Wang and Cao

(2008)

Linearity property of

IDFT

Complexity less

compared to Lu and

PTS

Oversampled OFDM

signal is used to

capture the peaks

Zhu et al.,

(2008)

Five novel

transformation based

on Greedy algorithm

Performance betterthan iterative flipping

algorithm for small

number of sub blocks

Performance is poor

for large number of

sub blocks

Yang et al.,

(2011)

Phase constellation

varied

PAPR reduction and

BER performance

similar to that of PTS

For large M, the

PAPR reduction

performance is

degraded.

For M sub blocks,

independant

candidates are

produced

6.2. Scope for Future Work II

It is planned to generate candidates of a OFDM signal by combining the linearity and circular timeshift property, with a slight increase in computational complexity this method is expected to achieve

significant PAPR reduction. Since the DFT property based transformations are less complex, whendifferent sub block undergo different transformations, the additional candidates generated can outperform the conventional PTS scheme with less candidates.

Table 10: Analysis of Algorithm assisted PTS schemes for PAPR reduction.


Chen

(2009)

Cross Entropy

Algorithm

Performance similar

to ESA with low

complexityOFDM system with

64, 128 subcarriers

and QPSK modulated

signals are consideredfor simulation.

Tradeoff between

PAPR and BER

performance is

ignored.Chen(2010a)

Quantum Inspired

EvolutionaryAlgorithm

PAPR reduction better

than conventional

PTS with lowcomputational

complexity

Chen

(2010b)

Electromagnetism

like (EM) Algorithm

Unlike Genetic

Algorithm based

PTS approach,

Encoding and

decoding process is

not required.

At least 1200 samples

is needed to achieve

better PAPR reduction

performance

These schemes are

simulated for a

specific number of

subcarriers and

modulation type.

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Table 10: Analysis of Algorithm assisted PTS schemes for PAPR reduction. - continued

Wang et al.,

(2010)

Artificial Bee Colony

(ABC) Algorithm

PAPR reduction better

than conventional

PTS with low

computational

complexity

OFDM system with

256 subcarriers and 16

QAM modulatedsymbols are

considered for

simulation.Taspinar et al.,

(2011)

Parallel Tabu search

Algorithm

Better PAPR

reduction and BER

performance

compared to

conventional PTS and

ABC algorithm.

Input Back off (IBO)

value of HPA and its

relation to the BER

performance is

mentioned.

6.3. Scope for Future Work III

a) The PAPR problem is expressed as a optimization problem and different algorithms areemployed to assist the PTS scheme. Hence it is planned to represent the PAPR problem as a

combinatorial optimization problem and to find the optimal phase factors using a combinatorial

algorithm like Differential Evolution which is expected to achieve better PAPR statistics andBER performance.

b) To assign the permissible phase rotation factors generated based on PTS approach to the nodesof a tree structure and to propose an algorithm which performs a search to compute the optimalfactors effectively such that PAPR reduction is achieved.

Table 11: Analysis of Companding Techniques for PAPR reduction.


Wang et al.,

(1999)

Combines the

advantage of clipping

and companding

scheme

Performs better than

clipping method

Average input power

increasesIgnored the non

linear operation of

High power

amplifier(HPA)

Spectral side lobes are

generated.

Requires large dynamic

range for HPA

Companded OFDM

signal exhibits

quasi Gaussian

distribution.

Huang et al.,

(2001)

Transformation is

based on Power

distribution

Performs better than

CF scheme with

reduced complexity

Slight degradation in

PAPR reduction

performance

HPA operates in

linear region

Tradeoff between

PAPR and BER is

ignored

Huang et al.,(2004)

Inflexion point treats

the large and smallamplitude signals

differently

Tradeoff between

PAPR reduction andBER performance is

achieved

NLST companding

scheme performs betterthan LST, LNST,

NLNST and - Law

companding scheme

The efficiency of

Power amplifier is

increased withdecreased power

back off but no

evidence for

increased back off

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Table 11: Analysis of Companding Techniques for PAPR reduction. - continued

Jiang et al.,

(2005)

Gaussian distributed

Amplitude statistics is

transformed into

uniformly distributed

signal

Achieves better

PAPR reduction,

BER performance,

power spectrum and

phase error than the

- LawCompanding

Technique.

Average input power is

maintained constant

PAPR reduction

remains unchanged

for different levels

of companding

Uniform companding

increases the distribution

of large amplitude

signals which in turn

degrades the BERperformance when HPA

operates in non linear

region.

Aburakhia et al.,

(2009)

Two inflexion points

for scaling different

signals independently

PAPR reduction and

BER performance

better than NLST

When input signal

crosses the inflexion

threshold, the

transformed signal

jumps abruptly and

results in degraded

Power Spectral Density.

Uses 5 control

parameters while

NLST uses just two

parameters.

Hou et al.,

( 2009)

Transforms Gaussiandistributed signal to

Trapezoidal

distribution

PAPR reductionperformance better

than EC scheme.

BER is degraded by 0.5

dB

Proper selection of

companding

parametersprovides effective

tradeoff between

PAPR reduction

and BER

performance.

Jiang

( 2010)

CT using airy special

function

PAPR reduction

performance better

than - Law

companding scheme.PAPR reduction is 1.5

dB inferior to EC

scheme

Degree of

companding is

reflected in the

PAPR reduction

performance.

Better BER and out

of band radiation

performance than

EC and - Law CT.

Hou et al.,

(2010)

Mainly compresses

only large signals

PAPR and BER

performance better

than EC scheme.

BER performance is

slightly degraded

compared to the original

OFDM signal.

Even without

decompanding

operation better

BER performance

is achieved.

6.4. Scope for Future Work IV

a) The existence of Gaussian transform and its ability to compress Gaussian distributed signals issuggested by Alecu et al.,(2006) hence PAPR reduction of an OFDM signal by employing

Gaussian Transform in companding scheme is feasible. Since the amplitude of an OFDM signalis Gaussian distributed, this proposal is expected to achieve better tradeoff between PAPR

reduction and BER performance.

b) In Companding schemes, the Gaussian distributed OFDM signal is transformed into uniformdistribution by Jiang et al., (2005) and Trapezoidal distribution by Hou et al., (2009) to reducePAPR of OFDM signal. The above mentioned transformation opens avenues to find other

possible distribution based transformation methods which can be applied to OFDM signal so

that PAPR reduction is achieved without compromising on BER performance and PowerSpectral Density.

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Table 12: Analysis of Time domain based PAPR reduction methods.


Alsusa et al.,

(2008)

Linear Symbol

combining

Technique

One FFT operation /

OFDM symbol

BER performance is

slightly degraded

Achieves significant PAPR

reduction

Generates large number

of candidates

Latency is more due to

large number of symbolstorage

Number of multiplications

is reduced drastically

compared to PTS, SLM and

TR methods.

Yang et al.,

(2008)

SLM based

sequence

superposition

Two FFT operation /

OFDM symbol hence

computational

complexity is less

Inferior BER

performance compared

to conventional SLM

PAPR reduction is degraded

by about 0.2 dB compared

to conventional SLM

scheme

Du et al.,

(2009)

SLM based

Time domain

filtering

No FFT operation and

complex multiplication

required

PAPR reduction is

slightly degraded by 0.1

0.75 dB compared to

conv. SLM scheme

Demands one third to one

fourth of the number of

computations compared to

conventional SLM schemeRequires only complex

additions

Wang et al.,

(2010)

Linear

combination of

cyclically

delayed signals

Single FFT operation

required

PAPR reduction isslightly degraded

around 0.2 dB

compared to SLM Requires half the

complexity compared to LC

SLM scheme for similar

PAPR reduction and BER

performance

Requires additional

memory to store the

mapping sequences

6.5. Scope for Future Work V

Time domain transformations such as complex conjugation, time scaling, time reversal or theircombinations can be employed with existing time domain based PAPR reduction methods[54, 56, 57]

so that additional candidates can be generated and the candidate signal with lowest PAPR is selectedfor transmission.

7. ConclusionMost of the work discussed in the literature concentrates on parameters like PAPR reduction,

computational complexity, in band radiation, out of band radiation, peak regrowth, BER performanceand EVM in OFDM systems individually but an effective tradeoff between PAPR reduction and BER

performance which contributes to the overall betterment of the system is rarely addressed. In future

work, it is planned to perform research on the above mentioned proposals and to present a comparativestudy based on their result while maintaining the PAPR reduction and its corresponding BER

performance.

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