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&prod=JNL&arnumber21929&arnumber21929&arSt+56&ared=+65&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee>
&prod=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&prod=JNL&arnumber42491&arnumber42491&arSt=+4
652&ared=+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y>
&prod=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&prod=JNL&arnumber81458&arnumber81458&arSt=+9
3&ared=+96&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+
Lim%3B+Habong+Chung>
&prod=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&prod=JNL&arnumber76955&arnumber76955&arSt=+1
19&ared=+127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K>
&prod=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&prod=JNL&arnumber97931&arnumber97931&arSt=+9
19&ared=+928&arAuthor=+Litsyn%2C+S.%3B++Yudin%2C+A>
&prod=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&prod=JNL&arnumber15665&arNumber15665&arSt+425&ared=+427&arAuthor=+Jayalath%2C+A.D.S.%3B++Athaudage%2C
+C.R.N>
&prod=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&prod=JNL&arnumber43990&arnumber43990&arSt=+8
87&ared=+890&arAuthor=+Han%2C+S.H.%3B++Lee%2C+J.H>
&prod=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&prod=JNL&arnumber37204&arNumber37204&arSt=+1
440&ared=+1443&arAuthor=+Freiman%2C+G.%3B++Litsyn%2C+S.%3B++
Yudin%2C+A>
&prod=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&prod=JNL&arnumber56203&arnumber56203&arSt=+1
916&ared=+1926&arAuthor=Ochiai%2C+H>
&prod=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&prod=JNL&arnumber30745&arnumber30745&arSt=+4
53&ared=+456&arAuthor=+Wang%2C+L.%3B++Tellambura%2C+C>
&prod=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&prod=JNL&arnumber95841&arnumber95841&arSt=+1
243&ared=+1247&arAuthor=+Sharif%2C+M.%3B++Florens%2C+C.%3B++
Fazel%2C+M.%3B++Hassibi%2C+B>
&prod=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&prod=JNL&arnumber06718&arnumber06718&arSt+832&ared=+834&arAuthor=+Wulich%2C+D>
&prod=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&prod=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>
&prod=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&prod=JNL&arnumber84389&arnumber84389&arSt+65&ared=+67&arAuthor=+Sezginer%2C+S.%3B++Sari%2C+H>
&prod=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&prod=JNL&arnumber21929&arnumber21929&arSt+56&ared=+65&arAuthor=+Seung+Hee+Han%3B++Jae+Hong+Lee>
&prod=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&prod=JNL&arnumber42491&arnumber42491&arSt=+4
652&ared=+4660&arAuthor=+Wang%2C+C.-L.%3B++Ouyang%2C+Y>
&prod=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&prod=JNL&arnumber81458&arnumber81458&arSt=+9
3&ared=+96&arAuthor-Woon+Lim%3B+Jong-Seon+No%3B+Chi-Woo+
Lim%3B+Habong+Chung>
&prod=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&prod=JNL&arnumber76955&arnumber76955&arSt=+1
19&ared=+127&arAuthor=+Mobasher%2C+A.%3B++Khandani%2C+A.K>
&prod=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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