CCU Wireless Access Tech. Lab. The Peak-to-Average Power Ratio Problem Gwo-Ruey Lee.

CCU Wireless Access Tech. Lab.

The Peak-to-Average Power Ratio Problem

Gwo-Ruey Lee

Wireless Access Tech. Lab.


Outlines

The Peak-to-Average Power Ratio Problem The Peak-to-Average Power Ratio [1-7]

OFDM Signal Amplitude Statistics[4,13] The Distribution of The Peak-to-Average Power

Ratio [ 1,4,16]

Clipping and Peak Window [1,4,10,11] Clipping Amplifier Methods Clipping Amplifier Simulations

Peak Cancellation [1,4,8,9,14,15]PAP Reduction Codes [14,17,18.19]Symbol Scrambling [12,14,20,21]




It is plausible that the OFDM signal - which is the superposition of a high number of modulated subchannel signals – may exhibit a high instantaneous signal peak with respect to the average signal level.

An OFDM signal consists of a number of independently modulated subcarriers, which can give a large peak-to-average power (PAP) ratio.

High peak-to-average power ratio Problem 1. It increased complexity of the analog-to-

digital and digital-to-analog converters Problem 2. It reduced efficiency of the RF power

amplifier The PAPR puts a stringent requirement on the power

amplifier and reduces the efficiency in the sense that a higher input backoff factor is needed before the peaks in the signal experience significant distortion due to power amplifier nonlinearity.

1/3




0 0.5 10

0.5

1

1.5

2

time

Ampl

itude

waveform 1

0 0.5 1-1

-0.5

0

0.5

1

time

Ampl

itude

waveform 2

0 0.5 1-1

-0.5

0

0.5

1

time

Ampl

itude

waveform 3

0 0.5 1-1

-0.5

0

0.5

1

time

Ampl

itude

waveform 4

0 0.5 10

0.5

1

1.5

2

time

Ampli

tude

waveform 1

0 0.5 10

0.5

1

1.5

2

time

Ampli

tude

waveform 1+ 2

0 0.5 1-1

0

1

2

3

time

Ampli

tude

waveform 1+ 2+ 3

0 0.5 1-1

0

1

2

3

4

time

Ampli

tude

waveform 1+ 2+ 3+ 4

PAPR ~ number of subcarriers =N

2/3




The existing solutions of PAPR 1. Signal distortion techniques,which reduce the peak

amplitudes simply by nonlinearly distorting the OFDM signal at or around the peaks.

Clipping Peak window Peak cancellation

2. Coding techniques that using a special forward-error correct code

PAP reduction code 3. It is based on scrambling each OFDM symbol with different scrambling sequences and selecting that sequence that

gives the smallest PAP ratio.

Adaptive subcarrier selection (ASUS) Selected mapping (SLM) Partial transmit sequence (PTS)

3/3



The Peak-to-Average Power Ratio

Signal expression Let and denote the real and imaginary parts of the

output signal. A complex baseband signal, defined over the time interval

, can be expressed as

where is the complex data of the kth subcarrier and is the OFDM symbol period.

0, st T

kA sT

1/17

1

2

0

1s

Nj k T t

kk

s t x t jy t A eN

x t y t




PAPR Definition

OFDM bandpass signal

is the carrier frequency of RF signals.

The peak power is defined as the power of a sine wave with

an amplitude equal to the maximum envelope value.

The PAPR of the baseband OFDM signals can be defined as

2 cos2 sin 2cj f tc cs t s t e x t f t y t f t

cf

2

0

2

max t T s s t

E s t

2/17




If all the subcarrier are modulated by phase-shift keying (PSK), the theoretical upper bound of the PAPR in OFDM signals with N subcarriers is N.

For example It can be shown that for an M-ary PSK OFDM system,

there are at most patterns that yield the highest PAPR, namely, N.

The probability of observing such a PAPR is .

2M

22 N

N

MM

M

3/17




Basic waveforms of OFDM signal with 4-DFT BPSK

0 0.5 10

0.5

1

1.5

2

time

Am

plitu

de

waveform 1

0 0.5 1-1

-0.5

0

0.5

1

time

Am

plitu

de

waveform 2

0 0.5 1-1

-0.5

0

0.5

1

time

Am

plitu

de

waveform 3

0 0.5 1-1

-0.5

0

0.5

1

time

Am

plitu

de

waveform 4 Maximum PAPR case

[1,1,1,1] [4,0,0,0]

[ 1, 1, 1, 1] [ 4,0,0,0]

[1, 1,1, 1] [0,0,4,0]

[ 1,1, 1,1] [0,0, 4,0]

x X

x X

x X

x X

Re

Im

1-1

4/17




OFDM signal with 4-DFT BPSK

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 1 1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 1 1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 1 -1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 1 -1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 -1 1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 -1 1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 -1 -1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=1 -1 -1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 -1 -1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 -1 -1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 -1 1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 -1 1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 1 -1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 1 -1 1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 1 1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plit

ude

symbol=-1 1 1 1

5/17




The histogram of peak amplitude of 4-DFT BPSK

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

8

9

10

PAPR

cou

nt n

um

be

r

2.8284

8

4 4

6/17




0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=1 1 1 1

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=1 -1 1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=1+0i 0+1i -1+0i 0-1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=1+0i 0-1i -1+0i 0+1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0+1i 0+1i 0+1i 0+1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0+1i 0-1i 0+1i 0-1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0+1i -1+0i 0-1i 1+0i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0+1i 1+0i 0-1i -1+0i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0-1i 0-1i 0-1i 0-1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0-1i 0+1i 0-1i 0+1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0-1i 1+0i 0+1i -1+0i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=0-1i -1+0i 0+1i 1+0i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=-1 -1 -1 -1

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=-1 1 -1 1

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=-1+0i 0-1i 1+0i 0+1i

0 0.5 1-4

-2

0

2

4

time

Am

plitu

de

symbol=-1+0i 0+1i 1+0i 0-1i

4-DFT QPSK with max peak amplitude

7/17




4-DFT QPSK

3 2

01 2 30 2 2 224 4 4

, 1, 2,3.

0 1 2 3

nkjN

nk k kk j j jj

N

kX k x n e

x e x e x e x e

[1,1,1,1] [4,0,0,0]

[ 1, 1, 1, 1] [ 4,0,0,0]

[ , , , ] [4 ,0,0,0]

[ , , , ] [ 4 ,0,0,0]

[1, 1,1, 1] [0,0,4,0]

[ 1,1, 1,1]

x X

x X

x i i i i X i

x i i i i X i

x X

x

[0,0, 4,0]

[ , , , ] [0,0,4 ,0]

[ , , , ] [0,0, 4 ,0]

X

x i i i i X i

x i i i i X i

[1, , 1, ] [0, 4,0,0]

[ 1, ,1, ] [0, 4,0,0]

[ , 1, ,1] [0, 4 ,0,0]

[ ,1, , 1] [0, 4 ,0,0]

[1, , 1, ] [0,0,0,4]

[ 1, ,1, ]

x i i X

x i i X

x i i X i

x i i X i

x i i X

x i i

[0,0,0, 4]

[ ,1, , 1] [0,0,0,4 ]

[ , 1, ,1] [0,0,0, 4 ]

X

x i i X i

x i i X i

Re

Im

1-1

i

-i

8/17




0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

10

20

30

40

50

60

70

80

90

100

110

120

130

140

128

80

32

16

3.1623 2.8284

The histogram of peak amplitude of 4-DFT QPSK

9/17




N-point DFT M-ary PSK

It can be shown that for an M-ary PSK OFDM system, there are at most patterns that yield the highest PAPR, namely, N.

The probability of observing such a PAPR is .

2M2

2 NN

MM

M

10/17



OFDM Signal Amplitude Statistics

The time domain OFDM signal is constituted by the sum of complex exponential functions, whose amplitudes and phases are determined by the data symbols transmitted over the different carriers.

Assuming random data symbols, the resulting time domain signal exhibits an amplitude probability density function (PDF) approaching the two-dimensional or complex Gaussian distribution for a high number of subcarriers.

Figure listed below explicitly shows that the measured amplitude histogram of the (a) in-phase component/Quadrature component and (b) amplitude of the a 256-subcarrier OFDM signal obeys a (a) Gaussian distribution and (b) Rayleigh distribution with a standard deviation of .

1

2

11/17




The observed amplitude histogram of the 256-subcarrier OFDM signal is correspond to Rayleigh distribution.

Note that the standard deviation of the probability density function is independent of the number of subcarriers employed, since the mean power of the signal is normalized to 1.

12/17




-4 -3 -2 -1 0 1 2 3 40

0.002

0.004

0.006

0.008

0.01

0.012

amplitude

prob

abili

ty

0 1 2 3 4 50

0.002

0.004

0.006

0.008

0.01

9dB 6dB 3dB 12dB 0dB

(a) in-phase component/Quadrature component histogram (b) Amplitude histogram

The distribution of I/Q component and amplitude

13/17




Signal Amplitude CDF0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

10-5

10-4

10-3

10-2

10-1

100

amplitude

pro

ba

bili

ty

0dB 3dB 6dB 9dB 12dB

The distribution of Measured amplitude which the value is large than threshold

14/17



The Distribution of The Peak-to-Average Power Ratio

For one OFDM symbol with N subcarrier, the complex baseband signal can be written as

For large N, the real and imaginary values of become Gaussian distributed, each with a mean of zero and a variance ½.

The amplitude of the OFDM signal therefore has a Rayleigh distribution, while the power distribution becomes a central chi-square distribution given by

1

1n

Nj t

nn

x t a eN

x t

1 zF z e

15/17




Cumulative distribution function Assuming the samples are mutually uncorrelated – which i

s true for non-oversampling – the probability that the PAPR is below some threshold level can be written as

Assuming the distribution of N subcarriers and oversampling can be approximated by the distribution for

subcarriers without oversampling with larger than one.

(1 )N z Np PAPR z F z e

1Nzp PAPR z e

N

16/17




PAPR distribution without oversampling for a number of subcarriers of (a) 16 (b)32 (c) 64 (d) 128 (e) 256 and (f) 1024

0 2 4 6 8 10 12 14 1610

-6

10-5

10-4

10-3

10-2

10-1

100

PAPR[dB]

log

(CD

F)

(a )N=16 (b) N=32 (c) N=64 (d) N=128 (e) N=256 (f) N=1024

(f)

(e)

(d)

(c)

(b)

(a)

17/17



Clipping and Peak Window

Clipping the signal The simplest way to reduce the PAPR The peak amplitude becomes limited to some desired

level By distorting the OFDM signal amplitude, a kind of self-

interference is introduced that degrades the BER. Nonlinear distortion increases out-of-band radiation

Peak windowing To remedy the out-of-band problem of clipping To multiply large signal peaks by nonrectangular window To minimize the out-of-band interference, ideally the

window should be as narrowband as possible. The windows should not be too long in the time domain,

because that implies that many signal samples as affected, which increases the BER.

1/6



Clipping Amplitude Methods

Clipping – a example of reducing the large peaks in OFDM with the use of windowing

2/6

0 10 20 30 40 50 60 70 800

0.05

0.1

0.15

0.2

0.25

Time

Am

plit

ud

e

Original Signal Clipped Signal Cplipping Threshold

Peak




The difference between clipping the signal and windowing the signal

3/6




The spectral distortion can be decreased by increasing the windowing

4/6



Clipping Amplitude Simulations

Symbol error rate versus Eb/N0 in AWGN. OFDM signal is clipped to PAPR of (a) no distortion (b) 5 (c) 3 and (d) 1 dB.

5/6

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

100 Eb/N0 Vs BER

Eb/N0

BE

R

QP S K AWGNCR=5 CR=3 CR=1



Clipping Amplitude Simulations

Symbol error rate versus Eb/N0 in AWGN. Peak windowing is applied with a window width of 1/16 of the FFT durat

ion.

6/6

0 5 10 15 2010

-6

10-5

10-4

10-3

10-2

10-1

100 Eb/N0 Vs BER

Eb/N0

BE

R

QP S K AWGNrcos ine ka ise r hamming



Peak Cancellation

The undesired effect of nonlinear distortion can be avoided by doing a linear peak cancellation technique, whereby a time-shifted and scaled reference function is subtracted from the signal, such that each subtracted reference function reduced the peak power of the least one signal sample.

By selecting an appropriate reference function with approximately the same bandwidth as the transmitted signal, it can be assured that the peak power reduction does not cause any out-of-band interference.

Peak cancellation can be done digitally after generation of the digital OFDM symbols.

1/7



Peak Cancellation

The peak cancellation was done after parallel-to-serial conversion of signal.

2/7

SignalMapping

S/P IFFT Cyclic PrefixP/SPeak

CancellationD/A

Up-Converter

Input Data



Peak Cancellation

The peak cancellation is identical to clipping followed by filtering

Supposed the clipped signal is filtered by an ideal LPF with impulse response of .

are the amplitude, phase, and delay of the correction that is applied to the ith sample in order to reach the desired clipping level.

, , ,i i ia and

3/7

iji i

i

r n x n a e n

sinciji i

i

r n x n a e n sinc nT



Peak Cancellation

It is also possible to do the cancellation immediately after the IFFT that is done on a symbol-by-symbol basis.

An efficient way to generate the cancellation signal without using a stored reference function is to use a lowpass filter in the frequency domain.

4/7



Peak Cancellation

It shows an example of the signal envelopes of one arbitrary OFDM symbol and corresponding reference signal.

(a) OFDM symbol envelope (b) corresponding reference signal envelope

5/7

310 320 330 340 350 360 370 3800

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Sample

Am

plit

ud

e

a Original Signal b corresponding reference signal

a

b



Peak Cancellation

After subtraction, the peak amplitude is reduced to a maximum of 3dB above the RMS value.

(a) OFDM symbol envelope (b) signal envelope after peak cancellation

6/7

310 320 330 340 350 360 370 3800

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Sample

Am

plit

ud

e

a Original Signal b Signal After Peak Cancellation

a

b



Peak Cancellation

Simulated power spectral densities of an OFDM system with 32 carriers by using peak cancellation technique

(a) undistorted spectrum, PAPR=15dB (b) spectrum after peak cancellation to PAPR=4dB (c) clipping to PAPR =4dB

7/7



PAP Reduction Codes

Coding techniques that using a special forward-error-correction code Golay complementary sequence Linear block code [17,18]

1/7



PAP Reduction Codes Golay complementary sequence

Golay complementary sequence Golay complementary sequences are sequence pairs for w

hich the sum of auto-correlation function is zero for all delay shifts unequal to zero.

The correlation properties of complementary sequences translate

into a relatively small PAPR of 3 dB when the codes are used to modulate an OFDM signal.

2/7



PAP Reduction Codes Golay complementary sequence

For this case of 16 channels, the PAPR is reduced by approximately 9 dB in comparison with the uncoded case.

(a) Square root of PAPR for a 16 channel OFDM signal, modulated with the same initial phase for all subcarrier

((b) Square root of PAPR for a 16 channel OFDM signal, modulated with a complementary code.

3/7

0 2 4 6 8 10 12 14 160

0.5

1

1.5

2

2.5

3

3.5

4

Time

Am

plit

ud

e

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

Time

Am

plit

ud

e



PAP Reduction Codes Linear block code

Linear block code[17,18] A block coding scheme provides error correction

capability, and also achieves the minimum PAPR for the OFDM system utilizing QPSK modulation and 4 subcarriers.

Block coding approach : by selecting only those codewords with small PAPR. Well-designed block codes provide error correction capability.

4/7




Block diagram of the OFDM signal with the proposed block coding scheme

The 8 bit vector x becomes 4 complex anti-podal symbols 2 2 12 1 2 1 ( 0,1,2,3)i i iy x j x i

5/7




(a) Instantaneous power of an uncoded OFDM system with BPSK modulation and N=4 subcarriers.

(b) Instantaneous power of an uncoded OFDM system employing the block coding scheme.

10

1610log ( ) 6.0205 ( )

4PAPR dB 10

7.0710log ( ) 2.4735 ( )

4PAPR dB

6/7




Instantaneous power of an uncoded OFDM system with BPSK modulation and N=4 subcarriers.

7/7



Symbol Scrambling

The basic idea of symbol scrambling is that for each OFDM symbol, the input sequence is scrambled by a certain number of scrambling sequence, and the output signal is transmitted with the smallest PAPR.

Symbol scrambling techniques Adaptive subcarrier selection

With the subcarrier allocation scheme

Selected Mapping (SLM) The transmitter selects one favorable transmit signal from a set of sufficiently

different signals which all represent the same information.

Partial Transmit Sequence (PTS) The transmitter constructs its transmit signal with low PAR by coordinated

addition of appropriately phase rotated signal parts.

The difference between SLM and PTS is that the first applies independent scrambling rotations to all subcarriers, while the latter only applies scrambling rotations to group of subcarriers.

1/10



Symbol Scrambling - ASUS

OFDM system using ASUS (adaptive subcarrier selection) [20,21]

2/10



Symbol Scrambling - SLM

Selected Mapping (SLM) Generate U transmit sequences , representing the sam

e information for each OFDM symbols. Select the lowest PAPR in time-domain of U sequences to t

ransmit Define U distinct vectors , , (number of subcarriers) , .

Each OFDM frame is multiplied carrierwise with U vectors:

ua

1 ,...,u u u

NP P P u

vu jVP e

0,2uv

, 1: , 1:

uvu jA v A v e v N u U

1:v N 1:u U

3/10




Selected Mapping (SLM)

4/10




Selected Mapping (SLM) SLM requires U IDFT’s in the transmitter, while the

receiver still needs only one DFT. bits are required to explicitly represent the

side information. Moderate complexity. For arbitrary number of carriers and any signal

constellation. Distortionless.

2log U

5/10




Performance of SLM Known side information

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

100 Eb/N0 Vs BER

Eb/N0

BE

R

6/10



Symbol Scrambling - PTS

Partial Transmit Sequence (PTS) The information bearing subcarrier block is subdivide i

nto V pairwise disjoint carrier subblocks . All subcarrier positions in which are already represented i

n another subblock are set to zero .

Rotation factor for each subblock v and the modified subcarrier vector represents the same information as .

The subblocks are transformed by V separate IDFTs. Choose the rotation factor that minimize PAPR. Optimum transmitted sequence .

1

optimum rotation factor

vV

v

v

ba a

1

Vv

v

A A

A

, 1, , .vA v V

, 0,2vjv vb e

1

Vv v

v

A b A

A

7/10




Partial Transmit Sequence (PTS)

8/10




Partial Transmit Sequence (PTS)

9/10




Performance of PTS Known phase rotation

10/10

0 5 10 15 2010

-5

10-4

10-3

10-2

10-1

100 Eb/N0 Vs BER

Eb/N0

BE

R




ReadingsOchiai, H. and Imai H. ,“On the distribution of t

he peak-to-average power ratio in OFDM signals,” Communications, IEEE Transactions on , Vol. 49, Issue: 2, pp. 282 –289, Feb. 2001.

S. Müller and J. Huber, “A Comparison of Peak Power Reduction Schemes for OFDM,” In IEEE Global Telecommunications Conference (GLOBECOM '97), Phoenix, Arizona, USA, pp. 1-5, Nov. 1997.



References

[1] Richard van Nee, Ramjee Prasad, OFDM wireless multimedia communication, Artech House Boston London, 2000.

[2] Ahmad R. S. Bahai and Burton R. Saltzberg, Multi-carrier digital communications - Theory and applications of OFDM, Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow 1999.

[3] Ramjee Prasad, “OFDM based wireless broadband multimedia communication,” Letter Notes on ISCOM’99, Kaohsiung, Taiwan, Nov. 7-10, 1999.

[4] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadrature amplitude modulation – Principles and applications for personal communications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2000.

[5] Mark Engels, Wireless Ofdm Systems: How to Make Them Work? Kluwer Academic Publishers.

[6] Lajos Hanzo, William Webb, Thomas Keller, Single and Multicarrier Modulation: Principles and Applications, 2nd edition, IEEE Computer Society.

[7] John A. C. Bingham, ADSL, VDSL, and Multicarrier Modulation, Wiley-Interscience. [8] S. Müller and J. Huber, “A Novel Peak Power Reduction Scheme for OFDM,” In IEEE I

nt. Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '97), Helsinki, Finland, pp. 1090-1094, Sep. 1997.

[9] S. Müller and J. Huber, “A Comparison of Peak Power Reduction Schemes for OFDM,” In IEEE Global Telecommunications Conference (GLOBECOM '97), Phoenix, Arizona, USA, pp. 1-5, Nov.1997.

[10] Ochiai, H.; Imai, H, ”Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems, “Selected Areas in Communications, IEEE Journal on , Vol. 18 Issue: 11, pp. 2270 –2277, Nov. 2000.



References

[11] Wulich, D.; Dinur, N.; Glinowiecki, A,“Level clipped high-order OFDM,” Communications, IEEE Transactions on , Vol. 48 Issue 6, pp. 928 –930, June 2000.

[12] S. Müller and J. Huber, “OFDM with Reduced Peak-to-Average Power Ratioby Optimum Combination of Partial Transmit Sequences, ” Electronics Letters, Vol. 33, no. 5, pp. 368-369, Feb. 1997.

[13] S. Müller, R. Bäuml, R. Fischer, and J. Huber, “OFDM with Reduced Peak-to-Average Power Ratio by Multiple Signal Representation,” Annals of Telecommunications, Vol. 52, no. 1-2, pp. 58-67, Feb. 1997.

[14] S. Müller and J. Huber, “A Comparison of Peak Power Reduction Schemes for OFDM,” In IEEE Global Telecommunications Conference (GLOBECOM '97), Phoenix, Arizona, USA, pp. 1-5, Nov. 1997.

[15] M. Breiling, S. Müller-Weinfurtner, and J. Huber, “SLM Peak-Power Reduction without Explicit Side Information,” In IEEE Communications Letters, Vol. 5, no. 6, pp. 239-241, Jun. 2001.

[16] Ochiai, H. and Imai H. ,“On the distribution of the peak-to-average power ratio in OFDM signals,” Communications, IEEE Transactions on , Vol. 49 Issue 2, pp. 282 –289, Feb. 2001.

[17] Hyo-Joo Ahn, Yoan Shin and Sungbin Im, “A block coding scheme for peak-to-average power ratio reduction in an orthogonal frequency division multiplexing system,” Vehicular Technology Conference Proceedings, 2000. VTC 2000-Spring Tokyo. 2000 IEEE 51st , Vol. 1, pp. 56 –60, 2000.

[18] Pingyi Fan; Xiang-Gen Xia, “Block coded modulation for the reduction of the peak to average power ratio in OFDM systems,” Consumer Electronics, IEEE Transactions on, Vol. 45. Issue 4. Pp. 1025 -1029, Nov. 1999.



References

[19] Fernando, W.A.C.; Rajatheva, R.M.A.P. “Performance of turbo and trellis coded OFDM for LEO satellite channels in global mobile communications “Communications, 1998. ICC 98. Conference Record. 1998 IEEE International Conference on , Vol. 1, pp. 412 –416, 1998.

[20] Rohling, H.; Grunheid, R. “ Performance of an OFDM-TDMA mobile communication system ” Vehicular Technology Conference, 1996. Mobile Technology for the Human Race., IEEE 46th , Vol. 3, pp. 1589 -1593. 1996.

[21] Schmidt, H. and Kammeyer, K.-D., “Reducing the peak to average power ratio of multicarrier signals by adaptive subcarrier selection,” Universal Personal Communications, 1998. ICUPC '98. IEEE 1998 International Conference on , Vol. 2, pp. 933 -93 , 1998.

CCU Wireless Access Tech. Lab. The Peak-to-Average Power Ratio Problem Gwo-Ruey Lee.

Documents

peak power

ccu wireless access

average power pap ratio

average power ratio

high peak

peak window peak cancellation

peak amplitudes

large peak