PAPR Reduction Methods for Noncoherent OFDM-MFSK

3rd COST 289 WorkshopAveiro, Portugal, July 12-13, 2006

Matthias Wetz, Werner G. Teich, Jürgen Lindner

matthias.wetz@uni-ulm.dehttp://it.e-technik.uni-ulm.de

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Motivation

• Fast time variant channels for data transmission to and from high speed trains• Security relevant data requires robust transmission scheme• Combination of OFDM and noncoherently detected MFSK offers high data rate and robustnes• A problem of multicarrier transmission is a high PAPR

Use the phases to reduce the PAPR

Subcarrier phases for noncoherent OFDM-MFSK are

arbitrary

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Outline

• Motivation

• Basic OFDM Transmission Model

• A Robust Transmission Scheme - OFDM-MFSK

• PAPR Reduction Algorithms

• Influence on the Spectrum of the Transmit Signal

• Conclusions

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OFDM Transmission Model

CODmod

ser

par

IDFTcyclicext.

ser

par

iΔt

s(i)

x(k)

TFs(t)

h(t)Channel

AWGN

RFiΔt

n(t)

g(t)DFT

rem.cyclicext.

ser

parser

par

DET

Coding

Detection(Decoding)

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OFDM-MFSK

…

OFDM-Subcarriers(Frequency)

Δf

00 01 11 10 00 01 11 10

• OFDM-4FSK: Subcarriers are grouped into groups of four• 4FSK modulation over each group • One out of four carriers is occupied• Gray coding• Coherent and noncoherent detection possible

+ For noncoherent detection no CSI is necessary+ Very robust against time variant channels+ Subcarrier phases are arbitrary and can be used for PAPR reduction

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Noncoherently detected OFDM-MFSK Subcarrier phases can be chosen arbitrarilyso that PAPR is reducedNo side information necessary

Peak-to-Average Power Ratio

Definition PAPR:

Unfavourable superposition of subcarriers in OFDMVery high PAPR of time domain signal

Problem: Transmit amplifier has saturation limitNonlinear distortion (Out of Band Radiation)High backoff necessary (amplifier inefficient)

T

t

dttsT

ts

0

2

2

1max

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PAPR Reduction

Goal: Find optimum subcarrier phases for each possible OFDM symbol, so that PAPR is minimum

Problem: N=256 and OFDM-4FSKpossible OFDM symbols,possibilities to assign phase, if two phases foreach subcarrier are considered

Exhaustive search impossible

Worst case: All subcarrier phases are the sameSubcarriers add coherentlyPAPR = N/M = 256/4 = 18 dB

4/2564642

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PAPR Reduction Methods

5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z

)= P

(PA

PR

<z)

random continuous phases [0, 2π)

random discrete phases 0 or π

First approach:• Random phases• Allow only 0 or π

Cumulative Distribution Function (CDF)

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• Introduced by Bäuml, Fischer and Huber (´96)

• Assign random subcarrier phases to each symbol several times

• Transmit OFDM symbol with lowest PAPR

• When applied to noncoherently detected OFDM-MFSK, no side information is needed

Selected Mapping

5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z

)

random continuous phases [0, 2π)

random discrete phases 0 or π

Selected Mappingbest of 2 symbols

Selected Mappingbest of 4 symbols

Selected Mapping

best of 10 symbols with discrete random phases (0 or π)is chosen

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• Introduced by Ouderaa et al. (´88)

• Swapping between time and frequency domain

• Iterative reduction of PAPR

• Stop when PAPR is not decreasing any more

• Parameter: time domain clipping level CL

Time-Frequency Domain Swapping

random startingphases

build spectrum withfixed amplitudes andvariable

IFFT

amplitude clipping in time domain

FFT

determine phasesn n

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Time-Frequency Domain Swapping (cont´d)

3 4 5 6 7 8 9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z

)

random phases 0 or π

selected mapping best of 10 symbols

CL=0.8

CL=0.95

CL=0.9

swapping algorithm time-frequency domain

• Good performance

• Very high complexity: up to several hundred iterations per symbol

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Sequential Algorithm

random starting phases

IFFT

PAPR evaluation

flip φn

PAPRnew < PAPR ?

next subcarrier n

PAPR=PAPRnew

accept φn

discard changes

IFFT

yes no

• Subcarrier phases are systematically changed to reduce PAPR

• Subcarrier phases are flipped sequentially

• One extra IFFT per occupied subcarrier

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Sequential Algorithm (cont´d)

3 4 5 6 7 8 9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z

) swap algorithmCL=0.9

sequentialalgorithm

random phases 0/π

selected mappingbest of 65

selected mappingbest of 10

• Better performance than selected mapping

• Lower complexity than swapping algorithm

good trade offcomplexity / performance

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Complexity Comparison

In general, better performance means higher complexity

Remaining problem: PAPR reduction has to be done for each symbol

Random Phases:• PAPR 6-10.5dB

Selected Mapping (best of 10 symbols):• PAPR 5.8-7.8dB• 10 FFTs in total

Sequential Algorithm:• PAPR 5.1-6.9dB• 1 extra FFT per occupied subcarrier• 65 FFTs in total

Time-Frequency Domain Swapping (CL=0.8):• PAPR 3.8-6.5dB • About 200 FFTs in total

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Model of a Nonlinear Transmit Amplifier

NL Zonal Filters(t) s‘(t) s‘BP(t)

• Nonlinearity causes distortion at harmonic bands of carrier frequency

• Zonal filter limits signal to be a bandpass signal

• Nonlinearity can be modeled in the lowpass domain

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Model of a Nonlinear Transmit Amplifier

Soft limiter in bandpass domain: amplitude saturates

Transformation of thecharacteristics intolowpass domain

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

0 0.5 1 1.5 2 2.5 30

0.5

1

1.5

Ain Ain

Aou

t

Aou

t

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Transmit Spectrum with Nonlinear Distortion

-500 -400 -300 -200 -100 0 100 200 300 400 500-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

f/Δf

PS

D [

dB

r]

3dB IBO

6dB

9dB

random subcarrier phases 0/π

Simulation parameters:• Raised cosine transmit filter α=0.2• 160 used subcarriers• Reference point: Interference in next channel after neighbour channel < -70dBr

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Transmit Spectrum with Nonlinear Distortion

-500 -400 -300 -200 -100 0 100 200 300 400 500-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

f/ΔfP

SD

[d

Br]

3dB IBO

6dB

5dB

Sequential Algorithm

-500 -400 -300 -200 -100 0 100 200 300 400 500-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

PS

D [

dB

r]

f/Δf

3dB IBO

6dB

7dB

Selected Mapping (best of ten)

• Further reduction possible with swapping algorithm but improvement is small

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Summary and Conclusions

OFDM-MFSK was presented• Noncoherent detection possible• Robust transmission scheme• Subcarrier phases can be used for PAPR reduction

PAPR reduction algorithms were analysed• Selected Mapping• Time-frequency domain swapping• Sequential algorithm

Influence on the spectrum of the transmit signal• Effects of different PAPR reduction methods were compared