Kurzhanskiy.slides

8/10/2019 Kurzhanskiy.slides

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OFDMPeak to Average Ratio Problem

EE224B Project

Alex Kurzhanskiy(05/13/2004)


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Agenda

Peak to average ratio what is it?

Peak to average ratio reduction techniques OFDM simulation: study of high peak to

average ratio and the clipping method


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Peak to Average Power Ratio

0 1 2 3 4 5 6 7- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 2 3 4 5 6 7

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 2 3 4 5 6 7

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 2 3 4 5 6 7- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

+

+

+

0 1 2 3 4 5 6 70

0 .5

1

1 .5

2

2 .5

3

3 .5

4

Peak

Average


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PAPR

Transmitted signal: s(t), t2[0,T]

Crest factor:


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Narrowband ChannelTransmitted signal:

16-QAM constellation:

a


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Wideband CDMA

Transmitted signal:

If the spreading sequences ck = 1

then PAPR = 0 dB

Rectangular pulse shape:


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Wideband CDMA (cont.)Sinc pulse shape:

Discretize: t = /W,

= 0,,N-1PAPR performance:

- 3 - 2 - 1 0 1 2 3- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

0 1 0 2 0 3 0 4 0 5 0 6 0 7 06

7

8

9

1 0

1 1

1 2

1 3

1 4

1 5

1 6

N

PAPR(

dB)

For N = 16,

PAPR = 9 dB


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Wideband OFDMTransmitted signal:

PAPR depends on the number of carriers NIf N is small, upper bound for PAPR:

For N = 16, PAPR 12 dB


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Wideband OFDM (cont.)If N is large, by central limit theorem s(t) has

Gaussian distribution on [0,T], and |s(t)|2 isRayleigh distributed

PAPR cdf:

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PAPR0(dB)

cdf

N = 128

N = 256

N = 512

0 2 4 6 8 10-250

-200

-150

-100

-50

0

PAPR0(dB)

ln(cdf)

N = 128

N = 256

N = 512


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Methods of PAPR Reduction

Scrambling and carrier selection

Coding Signal distortion


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Selected Mapping (SLM)For each OFDM symbol, the input sequence is

scrambled by k scrambling sequences

The resulting signal with smallest PAPR istransmitted

Without SLM: Pr(PAPR>PAPR0) = pWith SLM: Pr(PAPR>PAPR0) = p

k

Reduces the probability of high PAPRReducing the peak-to-average power ratio ofmulticarrier modulation by selected mapping

by R.Buml, R.Fischer, J.Huber


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Partial Transmit Sequences (PTS)

OFDM with reduced peak-to-average ratio by optimumcombination partial transmit sequences

by S.Mller, J.Huber

Serial to Parallel

IFFT

IFFT

IFFT

X

X

X

Peak Value Optimization

+

r1

r2

rK

K non-overlapping blocks

K rotations


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Tone Reservation (TR)

On some subcarriers the data is not transmitted

They are used for PAPR reduction signal r(t)

Optimization problem:

Peak power reduction for multicarrier transmission

by J.Tellado, J.Cioffi


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Coding


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Golay Sequences

X, Y 2 {1}N are complementary sequences, if

Notation: X YN = 1: 1 1

N = 2: 1 1

1 -1N = 4: 1 1 1 -1 1 1 -1 1

N = 8: 1 1 1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 -1


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Golay Sequences (cont.)Such sequences exist if N is even and can

be represented as the sum of at most 2squares

N = 2, 4, 8, 10,16,18,20,26,32,34,36,40,50


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Golay Sequences (cont.)X Y ) Properties:

1. X Y2. Xi Y and X Yi , whereXi, Yi inversed sequences

3. A B, where ak = (-1)kxk and bk = (-1)kyk4. XY X(-Y) (concatenation)

5. x0y0xN-1yN-1 x0(-y0)xN-1(-yN-1)


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Signal Distortion


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OFDM Simulation

M ul t ipath

N o i s e

C h a n n e l

Q AM

modulationIFFT C lipping

Transmitter

FF TQAM

demodulation

Receiver


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Transmitted Signal

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0- 0 . 2

- 0 . 1 5

- 0 . 1

- 0 . 0 5

0

0 . 0 5

0 . 1

0 . 1 5

0 . 2B e f o r e c l i p p in g

PAPR = 10.7 dB

512 subcarriers

Target PAPR = 6 dB


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PAPR Performance

0 100 200 300 400 500 6006

6.5

7

7.5

8

8.5

9

9.5

10

10.5

11

Numbe r of s ubcarrie rs

PAPR(

dB)


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Text Transmission

Original textWireless communication, despite the

hype of the popular press, is afield that has been around for overa hundred years, starting around1897 with Marconis successful

demonstrations of wirelesstelegraphy. By 1901, radioreception across the AtlanticOcean had been established; thusrapid progress in technology hasalso been around for quite a while.

In the intervening hundred years,many types of wireless systemshave flourished, and often laterdisappeared.

Received textWireless communication, desqite thehype of the poyela press, is afield that has been aro d for overa hundred aps, starting around1897 with Marconi{*successful

demonstrat`Gn30of wirelesstelegraphy. By 1901, radlreception across thetlanticOcean had been established; thusrapid progress in tecnnology hasalso been around for quite a while.In the interveniv hundred years,many types of wireless systumshave flourished(and often laterdisappeared.

BER = 1.12 %

Without clipping


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Text Transmission

Original textWireless communication, despite the

hype of the popular press, is afield that has been around for overa hundred years, starting around1897 with Marconis successfuldemonstrations of wirelesstelegraphy. By 1901, radioreception across the AtlanticOcean had been established; thusrapid progress in technology hasalso been around for quite a while.In the intervening hundred years,many types of wireless systemshave flourished, and often laterdisappeared.

Received text

Wireless communication, de{qite thehype of the poyula press, is afIeld that has been aro_d forover a hundred fl ars, startingaro}nd 1897 withMarconiy,successfuldemonstrat)Onsifwireless$tElegraphy. By 1 01,rad Oreception acrossthg&Ptl!ntic Ocean had beenestablished; thus(rapid progress intekjnomogy has also feen aroundfor quite a while. In the interveni6hundred years, many types ofwireless(s9stems have flourishe`(aJMKften later$dmsappeared.

BER = 2 %

With clipping: more errors


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Image TransmissionOriginal

Received Image

Error

Gauss


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Out-of-band Radiation

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0- 0 .1

- 0 . 0 8

- 0 . 0 6

- 0 . 0 4

- 0 . 0 2

0

0 . 0 2

0 . 0 4

0 . 0 6

0 . 0 8

0 .1O FD M s ig n al

O rig in a l s ig n a l

C lip p e d s ig n a l

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 0-0 .0 2

-0 .0 1 5

-0 .0 1

-0 .0 0 5

0

0 .0 0 5

0 .0 1

0 .0 1 5

0 .0 2S ig n a l d iffe re n c e

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 00

0 .2

0 .4

0 .6

0 .8

1

1 .2

1 .4F re q u e n c y s p e c tru m

B e fo re c lip p in g

A fte r c lip p in g

0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 1 4 00

0 .0 1

0 .0 2

0 .0 3

0 .0 4

0 .0 5

0 .0 6

0 .0 7

0 .0 8

0 .0 9S p e c tru m d iffe re n c e


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Papers on Clipping Reducing the peak-to-average power

ratio of OFDM by R.van Nee, A.de Wild

Effects of Clipping and Filtering on thePerformance of OFDMby X.Li, L.Cimini Jr.


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Other Signal Distortion Methods Peak cancellation

Pulse shaping

Peak-to-average power ratio reduction of

OFDM signals using pulse shapingby B.Slimane

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