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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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Golay Sequences (cont.)Spectral property: |DFT(X)|2+|DFT(Y)|2 = 2N
|DFT(X)|2 2NPeak to average power ratio:
1PAPR
2 (3 dB)Shapiro-Rudin code: 1 1 1 -1
apply (4): 1 1 1 -1 1 1 -1 1
apply (4): 1 1 1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 -1etcMultitone signals with low crest factor
by S. Boyd
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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