I have gone thtough some literature on PAPR reduction techniques. Boardly it can
be divided as:

1. Signal Processing

2. Coding (Random encoding, Golay Sequence, Cyclic Code)

3. Random Scrambling (Costellation Design, Selective Mapping, Partial Transmit
sequence)

Of which I am mostly interested in the first one because that do not need any
change in the inner transmitter functions and interoperability will not be an
issue. In this the following are done:

1. Clipping

2. Peak cancellation

3. Bandwidth Efficient Reduction of Crest

If you have come across any new techinques plz update.

Amit

Dear all,

>

> If anyone working on Pre-distortion techniques for OFDM or PAPR Reduction
Techniques for OFDM ...it is good idea if we get together and discuss the issues
and the literature through this forum...

> What do you think ?..

> Waiting for your earliest attention..

> Rgds,

> Jasan

# Re: PAPR Reduction or Pre-distortion Techniques for OFDM

Started by ●June 7, 2006

Reply by ●June 9, 20062006-06-09

Yeah, precoding is a possible solution to reduce PAPR. Giannakis has some

papers on it.

> >

> > If anyone working on Pre-distortion techniques for OFDM or PAPR

>Reduction Techniques for OFDM ...it is good idea if we get together and

>discuss the issues and the literature through this forum...

> > What do you think ?..

> > Waiting for your earliest attention..

> > Rgds,

> > Jasan

> >

> >

papers on it.

> >

> > If anyone working on Pre-distortion techniques for OFDM or PAPR

>Reduction Techniques for OFDM ...it is good idea if we get together and

>discuss the issues and the literature through this forum...

> > What do you think ?..

> > Waiting for your earliest attention..

> > Rgds,

> > Jasan

> >

> >

Reply by ●June 12, 20062006-06-12

Here are some papers that I collected on PAR reduction.

Note that you need subscription to IEEE digital library to

access the URL links below.

A review on the subject was provided by Han and Lee.[i]

They described a few techniques: clipping (the brute force

method, but not that trivial), coding (use a limited code

space that yields low PARs), partial transmit sequence

(modulate across sub blocks with phase, etc. to reduce PAR,

and send the side information so data can be recovered),

selected mapping (select one from the multiple legitimate

mapping from source data to modulated signal), interleaving

(select different interleaving schemes to reduce PAR, and

send the side information for data recovery), tone

reservation (reserve some subcarriers to send PAR-reduction

signal), tone injection (reverse of modulo-2 operation),

active constellation extension (if a constellation point is

at the boundary of constellation set, it can be moved

outwards, without affecting demodulation). The paper also

outlined the issues one should consider when selecting a

method: PAR reduction gain, TX power increase, BER increase,

overhead in data rate, etc. The review is not insightful,

but the description is rather clear, and many references are

provided.

Wang and Ouyang proposed a low complexity method for

selected mapping scheme.[ii] The bins are rotated by one of

the phase sequences. A lower PAR result is selected for

transmission. The paper focuses on the method of generating

the time domain results, without performing IFFT on every

possible phase rotation.

Lim et al. described a similar selected mapping scheme to

reduce PAR of OFDM. [iii] A phase rotation sequence is

multiplied to the constellation sequence, to reduce the PAR

of the output. The paper focuses on a low-complexity way to

come up with the phase rotation sequence. Of course,

another cost of the method is the redundancy capacity

required to communicate the phase rotation sequence to the

receiver.

Mobasher and Khandani studied a PAR reduction method, which

is similar to the modulo-2 expanding in Tomlinson

precoding.[iv] They presented a pretty mathematical

analysis of the problem, and proposed a different modulation

method based on Hadamard transform. I did not go through

the math in detail. The PAR reduction is about 4 dB.

Litsyn and Yudin studied some mathematical relationships

between the PAR in continuous and sampled time points.[v]

They gave an upper bound and a lower bound for the ratio of

the two PAR values, and a probably tighter upper bound for

the continuous PAR, given the sampled PAR and its derivative

against time. The issue of over-sampling was also

considered. The mathematics may be interesting, and the

results are helpful in estimating the continuous PAR.

However, the work assumes that the sub-carrier modulations

are constant-modulus. I suspect that under this constraint,

the PAR can be easily evaluated, anyhow.

Jayalath and Athaudage provided a brief analysis of the

problem.[vi] They studied the reduction of PAR by multiple

signal representation. However, the exact formulations

were omitted from this letter. Anyhow, their paper provides

a starting point, and some basic results.

Han and Lee reported PAR reduction based on PTS

technique.[vii] The method divides the frequency bins into

sub-blocks, and multiply each sub-block with a constant

phase shift. By choosing the phase shift values, one can

reduce the PAR. The key is how to search for the optimal

phase value combination. The paper proposed a simplified

search method, and evaluated the performance.

Freiman, et al. published a sufficient condition for

BPSK-OFDM, to have PAR below 3/4 of the maximum value.[viii]

They then proposed a coding scheme to ensure such condition.

This is an interesting mathematical exercise. However, it

is difficult to apply in practical systems.

Ochiai proposed an interesting shaping scheme for OFDM to

reduce PAR.[ix] First, he introduced a trellis

coding/shaping mechanism, where a convolutional coder

generates valid code words that will code to 0 by the

receiver's block coder. The output is thus added to the

constellation, to provide a degree of freedom that can be

used to reduce PAR. Next, he made the observation that PAR

is related to the autocorrelation in frequency domain (i.e.,

correlation between the signals for a given bin among the

various symbols). Therefore, we have an optimization target

without the time-domain feedback that is usually required

for a shaping scheme. Third, in order to avoid the

exhaustive search process, he developed a metric to

approximate the autocorrelation criteria. With this metric

the codeword that minimizes PAR can be found out by a

Viterbi decoder. Finally, simulation results were given.

Potential improvements can be big (up to 5 dB). It is an

interesting work, although some details were not presented

very clearly.

Wang and Tellambura proposed a "soft clipping" method, which

clips only the amplitude while preserves the phase.[x] They

spend a lot of effort characterizing the performance,

discovering some properties that help to simplify the task.

However, the benefit is only evaluated by simulation, which

is confined to a specific modulation scheme.

Sharif, et al. proposed a way to use sign and amplitude

adjustments to reduce PAR.[xi] By using the sign, one bit

per bin is lost from the data rate. The amplitude

adjustment is done by pushing the outer constellation points

outwards. This does not affect receiver processing, but

increases the power slightly. The problem is challenging.

The author came up with some practical optimization methods.

However the benefit of the whole scheme is questionable, as

it reduces system capacity significantly.

Wulich proposed an interesting concept: efficient PAR.[xii]

This applies to a situation where the transmit power is

limited by the power amplifier (instead of by regulation).

Given the power amplifier, increasing transmit power would

improve SNR at the receiver. On the other hand, increasing

transmit power also increases non-linearity and thus

distortion. The best transmit power can be found to

minimize the BER. This is a guide to select the PAR

setting. The paper also discussed the impact of several

popular PAR reducing techniques from this framework.

Garcia, et al. proposed a PAR reduction method based on 2D

pilot-symbol modulation.[xiii] They studied how to best

determine the pilot symbols for lower PAR, and how to detect

such transmission.

Sezginer and Sari proposed amplitude pre-distortion method.

The outer constellation points are moved outwards, to

provide the freedom needed for PAR reduction.[xiv]

Hope it helps.

Feng

_____

[i] Seung Hee Han; Jae Hong Lee, "Modulation, coding and

signal processing for wireless communications - An overview

of peak-to-average power ratio reduction techniques for

multicarrier transmission", Wireless Communications, IEEE

[see also IEEE Personal Communications], Vol.12, Iss.2,

April 2005, Pages: 56- 65, URL:

http://ieeexplore.ieee.org/iel5/7742/30716/01421929.pdf?isnu

mber0716

umber0716∏=JNL&arnumber21929&arnumber21929&arSt+56&ared=+65&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee>

∏=JNL&arnumber21929&arnumber21929&arSt=+56&ared=+6

5&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee,

[ii] Wang, C.-L.; Ouyang, Y., "Low-Complexity Selected

Mapping Schemes for Peak-to-Average Power Ratio Reduction in

OFDM Systems," Signal Processing, IEEE Transactions on [see

also Acoustics, Speech, and Signal Processing, IEEE

Transactions on] , vol.53, no.12pp. 4652- 4660, Dec. 2005

URL:

http://ieeexplore.ieee.org/iel5/78/32945/01542491.pdf?isnumb

er2945

ber2945∏=JNL&arnumber42491&arnumber42491&arSt=+4

652&ared=+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y>

∏=JNL&arnumber42491&arnumber42491&arSt=+4652&ared+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y.,

[iii] Dae-Woon Lim; Jong-Seon No; Chi-Woo Lim; Habong Chung,

"A new SLM OFDM scheme with low complexity for PAPR

reduction," Signal Processing Letters, IEEE , vol.12,

no.2pp. 93- 96, Feb. 2005, URL:

http://ieeexplore.ieee.org/iel5/97/30119/01381458.pdf?isnumb

er0119

ber0119∏=JNL&arnumber81458&arnumber81458&arSt=+9

3&ared=+96&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+

Lim%3B+Habong+Chung>

∏=JNL&arnumber81458&arnumber81458&arSt=+93&ared=+9

6&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+Lim%3B+Ha

bong+Chung,

[iv] Mobasher, A.; Khandani, A.K., "Integer-Based

Constellation-Shaping Method for PAPR Reduction in OFDM

Systems," Communications, IEEE Transactions on , vol.54,

no.1pp. 119- 127, Jan. 2006

URL:

http://ieeexplore.ieee.org/iel5/26/33336/01576955.pdf?isnumb

er3336

ber3336∏=JNL&arnumber76955&arnumber76955&arSt=+1

19&ared=+127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K>

∏=JNL&arnumber76955&arnumber76955&arSt=+119&ared=+

127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K.,

[v] Litsyn, S.; Yudin, A., "Discrete and Continuous Maxima

in Multicarrier Communication", Information Theory, IEEE

Transactions on, Vol.51, Iss.3, March 2005, Pages: 919- 928,

URL:

http://ieeexplore.ieee.org/iel5/18/30405/01397931.pdf?isnumb

er0405

ber0405∏=JNL&arnumber97931&arnumber97931&arSt=+9

19&ared=+928&arAuthor=+Litsyn%2C+S.%3B++Yudin%2C+A>

∏=JNL&arnumber97931&arnumber97931&arSt=+919&ared=+

928&arAuthor=+Litsyn%2C+S.%3B++Yudin%2C+A.,

[vi] Jayalath, A.D.S.; Athaudage, C.R.N. , "On the PAR

Reduction of OFDM Signals Using Multiple Signal

Representation", Communications Letters, IEEE, Vol.8, Iss.7,

July 2004, Pages: 425- 427, URL:

http://ieeexplore.ieee.org/iel5/4234/29157/01315665.pdf?isNu

mber)157

umber)157∏=JNL&arnumber15665&arNumber15665&arSt+425&ared=+427&arAuthor=+Jayalath%2C+A.D.S.%3B++Athaudage%2C

+C.R.N>

∏=JNL&arnumber15665&arNumber15665&arSt=+425&ared=+

427&arAuthor=+Jayalath%2C+A.D.S.%3B++Athaudage%2C+C.R.N.,

[vii]Han, S.H.; Lee, J.H., "PAPR Reduction of OFDM Signals

Using a Reduced Complexity PTS Technique", Signal Processing

Letters, IEEE, Vol.11, Iss.11, Nov. 2004, Pages: 887- 890,

URL:

http://ieeexplore.ieee.org/iel5/97/29592/01343990.pdf?isnumb

er)592

ber)592∏=JNL&arnumber43990&arnumber43990&arSt=+8

87&ared=+890&arAuthor=+Han%2C+S.H.%3B++Lee%2C+J.H>

∏=JNL&arnumber43990&arnumber43990&arSt=+887&ared=+

890&arAuthor=+Han%2C+S.H.%3B++Lee%2C+J.H., stored in

Z:\ofdm\01343990.pdf

[viii] Freiman, G.; Litsyn, S.; Yudin, A., "A Method to

Suppress High Peaks in BPSK-Modulated OFDM Signal",

Communications, IEEE Transactions on, Vol.52, Iss.9, Sept.

2004. Pages: 1440- 1443, URL:

http://ieeexplore.ieee.org/iel5/26/29496/01337204.pdf?isNumb

er)496

ber)496∏=JNL&arnumber37204&arNumber37204&arSt=+1

440&ared=+1443&arAuthor=+Freiman%2C+G.%3B++Litsyn%2C+S.%3B++

Yudin%2C+A>

∏=JNL&arnumber37204&arNumber37204&arSt=+1440&ared+1443&arAuthor=+Freiman%2C+G.%3B++Litsyn%2C+S.%3B++Yudin%2C+

A.,

[ix] Ochiai, H., "A novel trellis-shaping design with both

peak and average power reduction for OFDM systems",

Communications, IEEE Transactions on, Vol.52, Iss.11, Nov.

2004, Pages: 1916- 1926, URL:

http://ieeexplore.ieee.org/iel5/26/29784/01356203.pdf?isnumb

er)784

ber)784∏=JNL&arnumber56203&arnumber56203&arSt=+1

916&ared=+1926&arAuthor=Ochiai%2C+H>

∏=JNL&arnumber56203&arnumber56203&arSt=+1916&ared+1926&arAuthor=Ochiai%2C+H.,

[x] A Simplified Clipping and Filtering Technique for PAR

Reduction in OFDM Systems, Wang, L.; Tellambura, C. , Signal

Processing Letters, IEEE, Vol.12, Iss.6, June 2005, Pages:

453- 456, URL:

http://ieeexplore.ieee.org/iel5/97/30858/01430745.pdf?isnumb

er0858

ber0858∏=JNL&arnumber30745&arnumber30745&arSt=+4

53&ared=+456&arAuthor=+Wang%2C+L.%3B++Tellambura%2C+C>

∏=JNL&arnumber30745&arnumber30745&arSt=+453&ared=+

456&arAuthor=+Wang%2C+L.%3B++Tellambura%2C+C.,

[xi] Amplitude and Sign Adjustment for Peak-to-Average-Power

Reduction, Sharif, M.; Florens, C.; Fazel, M.; Hassibi, B. ,

Communications, IEEE Transactions on, Vol.53, Iss.8, Aug.

2005, Pages: 1243- 1247, URL:

http://ieeexplore.ieee.org/iel5/26/32145/01495841.pdf?isnumb

er2145

ber2145∏=JNL&arnumber95841&arnumber95841&arSt=+1

243&ared=+1247&arAuthor=+Sharif%2C+M.%3B++Florens%2C+C.%3B++

Fazel%2C+M.%3B++Hassibi%2C+B>

∏=JNL&arnumber95841&arnumber95841&arSt=+1243&ared+1247&arAuthor=+Sharif%2C+M.%3B++Florens%2C+C.%3B++Fazel%2C+

M.%3B++Hassibi%2C+B.,

[xii] Definition of efficient PAPR in OFDM, Wulich, D. ,

Communications Letters, IEEE, Vol.9, Iss.9, Sept. 2005,

Pages: 832- 834, URL:

http://ieeexplore.ieee.org/iel5/4234/32282/01506718.pdf?isnu

mber2282

umber2282∏=JNL&arnumber06718&arnumber06718&arSt+832&ared=+834&arAuthor=+Wulich%2C+D>

∏=JNL&arnumber06718&arnumber06718&arSt=+832&ared=+

834&arAuthor=+Wulich%2C+D.,

[xiii] Fernandez-Getino Garcia, M.J.; Edfors, O.;

Paez-Borrallo, J.M., "Peak power reduction for OFDM systems

with orthogonal pilot sequences," Wireless Communications,

IEEE Transactions on , vol.5, no.1pp. 47- 51, Jan. 2006

URL:

http://ieeexplore.ieee.org/iel5/7693/33321/01576525.pdf?isnu

mber3321

umber3321∏=JNL&arnumber76525&arnumber76525&arSt+47&ared=+51&arAuthor=+Fernandez-Getino+Garcia%2C+M.J.%3B++E

dfors%2C+O.%3B++Paez-Borrallo%2C+J.M>

∏=JNL&arnumber76525&arnumber76525&arSt=+47&ared=+5

1&arAuthor=+Fernandez-Getino+Garcia%2C+M.J.%3B++Edfors%2C+O.

%3B++Paez-Borrallo%2C+J.M.,

[xiv] Sezginer, S.; Sari, H., "OFDM peak power reduction

with simple amplitude predistortion," Communications

Letters, IEEE , vol.10, no.2pp. 65- 67, Feb. 2006

URL:

http://ieeexplore.ieee.org/iel5/4234/33437/01584389.pdf?isnu

mber3437

umber3437∏=JNL&arnumber84389&arnumber84389&arSt+65&ared=+67&arAuthor=+Sezginer%2C+S.%3B++Sari%2C+H>

∏=JNL&arnumber84389&arnumber84389&arSt=+65&ared=+6

7&arAuthor=+Sezginer%2C+S.%3B++Sari%2C+H.,

Note that you need subscription to IEEE digital library to

access the URL links below.

A review on the subject was provided by Han and Lee.[i]

They described a few techniques: clipping (the brute force

method, but not that trivial), coding (use a limited code

space that yields low PARs), partial transmit sequence

(modulate across sub blocks with phase, etc. to reduce PAR,

and send the side information so data can be recovered),

selected mapping (select one from the multiple legitimate

mapping from source data to modulated signal), interleaving

(select different interleaving schemes to reduce PAR, and

send the side information for data recovery), tone

reservation (reserve some subcarriers to send PAR-reduction

signal), tone injection (reverse of modulo-2 operation),

active constellation extension (if a constellation point is

at the boundary of constellation set, it can be moved

outwards, without affecting demodulation). The paper also

outlined the issues one should consider when selecting a

method: PAR reduction gain, TX power increase, BER increase,

overhead in data rate, etc. The review is not insightful,

but the description is rather clear, and many references are

provided.

Wang and Ouyang proposed a low complexity method for

selected mapping scheme.[ii] The bins are rotated by one of

the phase sequences. A lower PAR result is selected for

transmission. The paper focuses on the method of generating

the time domain results, without performing IFFT on every

possible phase rotation.

Lim et al. described a similar selected mapping scheme to

reduce PAR of OFDM. [iii] A phase rotation sequence is

multiplied to the constellation sequence, to reduce the PAR

of the output. The paper focuses on a low-complexity way to

come up with the phase rotation sequence. Of course,

another cost of the method is the redundancy capacity

required to communicate the phase rotation sequence to the

receiver.

Mobasher and Khandani studied a PAR reduction method, which

is similar to the modulo-2 expanding in Tomlinson

precoding.[iv] They presented a pretty mathematical

analysis of the problem, and proposed a different modulation

method based on Hadamard transform. I did not go through

the math in detail. The PAR reduction is about 4 dB.

Litsyn and Yudin studied some mathematical relationships

between the PAR in continuous and sampled time points.[v]

They gave an upper bound and a lower bound for the ratio of

the two PAR values, and a probably tighter upper bound for

the continuous PAR, given the sampled PAR and its derivative

against time. The issue of over-sampling was also

considered. The mathematics may be interesting, and the

results are helpful in estimating the continuous PAR.

However, the work assumes that the sub-carrier modulations

are constant-modulus. I suspect that under this constraint,

the PAR can be easily evaluated, anyhow.

Jayalath and Athaudage provided a brief analysis of the

problem.[vi] They studied the reduction of PAR by multiple

signal representation. However, the exact formulations

were omitted from this letter. Anyhow, their paper provides

a starting point, and some basic results.

Han and Lee reported PAR reduction based on PTS

technique.[vii] The method divides the frequency bins into

sub-blocks, and multiply each sub-block with a constant

phase shift. By choosing the phase shift values, one can

reduce the PAR. The key is how to search for the optimal

phase value combination. The paper proposed a simplified

search method, and evaluated the performance.

Freiman, et al. published a sufficient condition for

BPSK-OFDM, to have PAR below 3/4 of the maximum value.[viii]

They then proposed a coding scheme to ensure such condition.

This is an interesting mathematical exercise. However, it

is difficult to apply in practical systems.

Ochiai proposed an interesting shaping scheme for OFDM to

reduce PAR.[ix] First, he introduced a trellis

coding/shaping mechanism, where a convolutional coder

generates valid code words that will code to 0 by the

receiver's block coder. The output is thus added to the

constellation, to provide a degree of freedom that can be

used to reduce PAR. Next, he made the observation that PAR

is related to the autocorrelation in frequency domain (i.e.,

correlation between the signals for a given bin among the

various symbols). Therefore, we have an optimization target

without the time-domain feedback that is usually required

for a shaping scheme. Third, in order to avoid the

exhaustive search process, he developed a metric to

approximate the autocorrelation criteria. With this metric

the codeword that minimizes PAR can be found out by a

Viterbi decoder. Finally, simulation results were given.

Potential improvements can be big (up to 5 dB). It is an

interesting work, although some details were not presented

very clearly.

Wang and Tellambura proposed a "soft clipping" method, which

clips only the amplitude while preserves the phase.[x] They

spend a lot of effort characterizing the performance,

discovering some properties that help to simplify the task.

However, the benefit is only evaluated by simulation, which

is confined to a specific modulation scheme.

Sharif, et al. proposed a way to use sign and amplitude

adjustments to reduce PAR.[xi] By using the sign, one bit

per bin is lost from the data rate. The amplitude

adjustment is done by pushing the outer constellation points

outwards. This does not affect receiver processing, but

increases the power slightly. The problem is challenging.

The author came up with some practical optimization methods.

However the benefit of the whole scheme is questionable, as

it reduces system capacity significantly.

Wulich proposed an interesting concept: efficient PAR.[xii]

This applies to a situation where the transmit power is

limited by the power amplifier (instead of by regulation).

Given the power amplifier, increasing transmit power would

improve SNR at the receiver. On the other hand, increasing

transmit power also increases non-linearity and thus

distortion. The best transmit power can be found to

minimize the BER. This is a guide to select the PAR

setting. The paper also discussed the impact of several

popular PAR reducing techniques from this framework.

Garcia, et al. proposed a PAR reduction method based on 2D

pilot-symbol modulation.[xiii] They studied how to best

determine the pilot symbols for lower PAR, and how to detect

such transmission.

Sezginer and Sari proposed amplitude pre-distortion method.

The outer constellation points are moved outwards, to

provide the freedom needed for PAR reduction.[xiv]

Hope it helps.

Feng

_____

[i] Seung Hee Han; Jae Hong Lee, "Modulation, coding and

signal processing for wireless communications - An overview

of peak-to-average power ratio reduction techniques for

multicarrier transmission", Wireless Communications, IEEE

[see also IEEE Personal Communications], Vol.12, Iss.2,

April 2005, Pages: 56- 65, URL:

http://ieeexplore.ieee.org/iel5/7742/30716/01421929.pdf?isnu

mber0716

umber0716∏=JNL&arnumber21929&arnumber21929&arSt+56&ared=+65&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee>

∏=JNL&arnumber21929&arnumber21929&arSt=+56&ared=+6

5&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee,

[ii] Wang, C.-L.; Ouyang, Y., "Low-Complexity Selected

Mapping Schemes for Peak-to-Average Power Ratio Reduction in

OFDM Systems," Signal Processing, IEEE Transactions on [see

also Acoustics, Speech, and Signal Processing, IEEE

Transactions on] , vol.53, no.12pp. 4652- 4660, Dec. 2005

URL:

http://ieeexplore.ieee.org/iel5/78/32945/01542491.pdf?isnumb

er2945

ber2945∏=JNL&arnumber42491&arnumber42491&arSt=+4

652&ared=+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y>

∏=JNL&arnumber42491&arnumber42491&arSt=+4652&ared+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y.,

[iii] Dae-Woon Lim; Jong-Seon No; Chi-Woo Lim; Habong Chung,

"A new SLM OFDM scheme with low complexity for PAPR

reduction," Signal Processing Letters, IEEE , vol.12,

no.2pp. 93- 96, Feb. 2005, URL:

http://ieeexplore.ieee.org/iel5/97/30119/01381458.pdf?isnumb

er0119

ber0119∏=JNL&arnumber81458&arnumber81458&arSt=+9

3&ared=+96&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+

Lim%3B+Habong+Chung>

∏=JNL&arnumber81458&arnumber81458&arSt=+93&ared=+9

6&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+Lim%3B+Ha

bong+Chung,

[iv] Mobasher, A.; Khandani, A.K., "Integer-Based

Constellation-Shaping Method for PAPR Reduction in OFDM

Systems," Communications, IEEE Transactions on , vol.54,

no.1pp. 119- 127, Jan. 2006

URL:

http://ieeexplore.ieee.org/iel5/26/33336/01576955.pdf?isnumb

er3336

ber3336∏=JNL&arnumber76955&arnumber76955&arSt=+1

19&ared=+127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K>

∏=JNL&arnumber76955&arnumber76955&arSt=+119&ared=+

127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K.,

[v] Litsyn, S.; Yudin, A., "Discrete and Continuous Maxima

in Multicarrier Communication", Information Theory, IEEE

Transactions on, Vol.51, Iss.3, March 2005, Pages: 919- 928,

URL:

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