PAPR Reduction in OFDM SystemsHafeth

8/3/2019 PAPR Reduction in OFDM SystemsHafeth

1/29

1 Hafeth Hourani PAR Reduction in OFDM Systems 13.11.2003

PAPR Reduction in OFDM Systems

Hafeth Hourani

[email protected]

S-88.221

Postgraduate Seminar on Signal Processing I

Fall 2003


2/29


Contents

OFDM Overview

Introducing PAPR

PAR Reduction Solutions References

Abbreviations


3/29


OFDM Overview


4/294 Hafeth Hourani PAR Reduction in OFDM Systems 13.11.2003

What is ODFM

OFDM is a Multi-Carrier Transmission Scheme

ODFM is a good solution for high speed digital communications

OFDM concept: Spread the data to be transmitted over a large number oforthogonal carriers, each being modulated at a low rate.

The carriers can be made orthogonal by appropriately choosing the

frequency spacing between them.



OFDM vs. FDM

In contrast to the FDM, the spectral overlapping among subcarriers areallowed in OFDM

Advantages of OFDM overFDM

OFDM spreads out thefrequency selective fading overmany symbols

The distortion caused by theburst errors is distributed

among several symbol



OFDM Properties

OFDM benefits for wireless communication systems High Spectral Efficiency Robustness to channel fading

Immunity to impulse interferences Flexibility

Easy equalization



OFDM Problems

There are some obstacles in using OFDM

OFDM signal exhibits very high Peak to Average Power Ratio (PAPR)

Very sensitive to frequency errors (Tx. & Rx. offset)

Intercarrier Interference (ICI) between the subcarriers



OFDM Implementation: Tx & Rx

tje 1

tj Ne

g(t)

tj o

e

g(t)

g(t)

S/P RF

a0

a1

aN

xt[ ]ka

g*(-t)

tj oe

g*(-t)

tj

e1

g*(-t)

tj N

e

P/SRF

[ ]ka

The OFDM Rx is implementedusing DFT (FFT)The OFDM Tx is implementedusing IDFT (IFFT)

[ ] [ ] [ ]{ }kaIDFTekanxN

k

Nnkjb ==

=

1

0

2 [ ] [ ]{ }nxDFTka b=



OFDM Application

ADSL

Digital audio and terrestrial TV broadcasting

Wireless LANs High-speed cellular data


10/29


Introducing PAPR


11/29


What is PAPR . . .

Peak-to-Average ratio Describes the envelope fluctuation

The system should operate in the linear region

Large peaks cause saturation in the power amplifiers Amplifier saturation results in non-linear distortion

One particular problem with multicarrier is the large envelopefluctuation

The envelope variation is due to the superposition of multiple channels.

PAPR causes

Intermodulation Out-of-band radiation


12/29


PAPR and Carrier Orthogonality


13/29


PAPR of OFDM signals

The complex envelop of the OFDM signal, over T second interval isgiven by:

=

>>=

1

0

0),()(N

n

nnc TttwAtS

cA

where

nw is the element of N-elements parallel data vector [ ]110 ,...,,

=NwwwW

is the carrier amplitude, and

and the orthogonal carriers are

S/PW

0w

1w

1

N

w

tfjnnet 2)( =

where

= 2

11

)(

N

nTtfn


14/29


Quantifying the PAPR

The PAPR is defined by

=

NT

s

t

dttSNTE

tStSPAPR

0

2

2

)(1

)(max))((

From the central limit theorem; for large number of N, the real and

imaginary values of S(t) become Gaussain distributed The amplitude of PAPR, is therefore has a Rayleigh distribution, with

zero mean and variance N times the variance of one complex sinusoid

Assuming mutually uncorrelated samples, the CDF of PAPR per OFDMsymbol is given by:

{ } ( )N

ePAPR => 11Pr


15/29


PAPR Properties

From the previous two slides, we can conclude the following PAPRproperties:

PAPR results from the superposition of large number of subcarriers.

The PARP distribution is Rayleigh The large peaks do not occur very often

Large PAPR can cause In band noise => Increase BER Spectral spreading (out band) => ACI (adjacent carrier interference)

Possible solutions Amplifier back-off Reduce PAPR of OFDM signal


16/29


Overcoming PAPR Effect

Basically, there are two approaches to deal with PAPR in OFDM By Preventing the problem

Make use of redundancy

By Correcting the problem Make use of correction functions


17/29


PAPR Reduction Methods


18/29


1) Clipping

The simplest way is to clip (to limit) the max amplitude BUT, clipping is nonlinear process:

It may cause significant in-band distortion (degrades BER) . . .

and out-of-band noise (reduces the spectral efficiency)

Filtering after clipping mayreduce the spectral splatter


19/29


2) Peak Windowing

Multiply the large OFDM signal peaks with a Shaping Window

Any window can be used, e.g., Gaussian, Cosine, Kaiser.

The applied windows should be as narrow band as possible. Otherwise, the OFDM spectrum will be affected


20/29


3) Additive Correction Function

Instead of using multiplicative correction function (as the case inwindowing), we use an additive correction function

The OFDM signal is modified so that given amplitude threshold of the

signal is not exceeded after the correction The corrected signal can be written as:

The above correction limits the signal S(t) to at position ofamplitude peaks

0A nt

)()()( tktStc += , where

= )()(nn

ttgAtk

and( ))(

)()( 0

n

nn

tS

tSAtSA =

BtjeBtsiinctg )()(

The correction function should be chosen so that It has minimal power It does not interfere with the original OFDM signal anyhow


21/29


4) BERC Technique

Bandwidth Efficient Reduction of the Crest Factor (BERC)

Multiply the OFDM envelope S(t) with a weighting function b(t)

( ) ( ) ( )tbtStS = , where b(t) is composed of a sum of Gaussian pulses

The coefficients are chosen so that the envelope does no longercross the threshold Tr

( ) ( )

=

=

n

nn ttgatb 12

)( tetg =

nt : denotes the position of the local maximum of the envelope above acertain threshold (Tr) that is normalized to the root mean square

value )(tSEff( )tS

)(

)(.

1 tS

tSTr

aEff

n =

na

, : optimization factor, where

)


22/29


5) Scrambling

Usually, some bit streams may lead to high-magnitude peaks

By scrambling the input bit stream, we may reduce the probability oflarge peaks generated by those bit patterns

)


23/29


6) Coding

Nonlinear Map transmitted sequence into a larger sequence where high-peak

sequences are not used

Good performance with little overhead Error correction capability can be used as well

) S


24/29


7) Selective Mapping

Multiply the data signal with M different sequences

Generate the OFDM for each signal (M signals)

Select the OFDM signal with the lowest PAPR

The receiver has toknow which sequence

was used to generatethe signal, so that itcan recover the

original data The used sequence can

be transmitted as aside information

S/PData Source

Selector(selectt

helowestPAPR)

r1

IFFT

r2

IFFT

rM

IFFT

) P i l T i S (PTS)


25/29


8) Partial Transmit Sequence (PTS)

Divide the OFDM subcarriers into M clusters Generate the OFDM signals for each cluster

Combine the M output OFDM signals with weighting factors bi The weighting factors are generated with some optimization algorithm

The receiver

has to knowthe generationscheme(sequences) in

order torecover thedata

Optimization

DataSource

Partitionintosu

b-blocks

S

IFFT

IFFT

IFFT

S/PX

X1

X2

XM

b1

b2

bM

9) T R ti


26/29


9) Tone Reservation

This method describes an additive method for reducing PAPR

The basic idea is to reserve a set of subcarriers (tones) for PAPRreduction by optimizing the time-domain OFDM signal

The transmitter can add any data vector in the reserved subcarrier inorder to reduce the PAPR

Gradient algorithm can be used iteratively

This methods may reduce the system bit rate if many tones arereserved for PAPR reduction purposes


27/29


Thats itthank you !

R f


28/29


References

[1] J. Heiskala and J. Terry, OFDM Wireless LAN: A Theoretical and Practical Guide, SAMS Publishing,2001

[2] F. Kohandani, PAR Reduction in OFDM/CDMA Systems, 2002

[3] R. Nee and A. Wild, Reducing the Peak-to-Average Power Ration of OFDM, IEEE

[4] S.H. Muller and J.B. Huber, A novel peak power reduction scheme for OFDM, IEEE conferenceproceedings PIMRC, 1997

[5] A.E. Jones, T.A. Wilkinson, S.K, Barton, Block coding scheme for reduction of peak to mean envelopepower ration of multicarrier transmission schemes, Electronics Letters, Vol.30, No.25, pp.2098-2099, 1994

[6] X. Li, and J.A. Ritcey, m-sequence for OFDM PAPR reduction and error correction, Electronic Letters,Vol.43, No.5, 1998

[7] M. Pauli, and H.P. Kuchenbecker, On the reduction of the out of band radiation of OFDM signals, IEEEconference proceedings ICC, Vol.3, 1304-1308, 1998

Abb i ti


29/29


Abbreviations

BERC: Bandwidth Efficient Reduction of the Crest Factor DFT : Discrete Fourier Transform

FFT : Fast Fourier Transform

IDFT : Inverse Discrete Fourier Transform

IFFT : Inverse Fast Fourier Transform

PAR : Peak to Average Ratio

PAPR : Peak to Average Power Ratio

OFDM: Orthogonal Frequency Division Multiplexing

P/S: Parallel to Serial converter

S/P: Serial to Parallel converter

PAPR Reduction in OFDM SystemsHafeth

Documents

Transcript of PAPR Reduction in OFDM SystemsHafeth