Page 1

Original Article

A new PAPR reduction in OFDM systems using PTS combined

with APPR for TWTA nonlinear HPA

Chusit Pradabpet1* and Kobchai Dejhan2

1 Faculty of Science and Technology,

Phra Nakhon Si Ayutthaya Rajabhat University, Phra Nakhon Si Ayutthaya, 13000 Thailand.

2 Faculty of Engineering,

King Mongkut’s Institute of Technology Ladkrabang (KMITL), Bang Sue, Bangkok, 10520 Thailand.

Received 4 April 2007; Accepted 1 May 2008

Abstract

In this paper, we propose a new Peak-to-Average Power Ratio (PAPR) reduction technique using a partial transmit

sequence (PTS) combined with adaptive peak power reduction (APPR) methods. This technique is used in a system based on

Orthogonal Frequency Division Multiplexing (OFDM). In order to reduce PAPR, the sequence of input data is rearranged

by the PTS for the reduction of PAPR and then fed to the APPR process in the proposed system. The APPR method controls

the peak level of the modulation signal by an adaptive algorithm. The proposed method shows the improvement on PAPR,

on the power spectrum density (PSD) and on the high performance on bit error rate (BER) of an OFDM system.

Keywords: OFDM, PAPR, adaptive peak power reduction (APPR), PTS, nonlinear HPA

Songklanakarin J. Sci. Technol.

30 (3), 355-360, May - Jun. 2008

1. Introduction

Orthogonal Frequency Division Multiplexing (OFDM)

has many well known advantages such as robustness against

frequency selective fading or narrowband interference, high

bandwidth efficiency, and efficient implementation. Recently,

OFDM is mainly used in digital audio broadcasting (DAB),

digital video broadcasting-terrestrial (DVB-T), and mobile

multimedia access communication (MMAC), IEEE802.11a,

IEEE802.16 and IEEE 802.20. (Nee et al., 2000; Han et al.,

2005)

One major drawback of the OFDM is the large Peak-

to-Average Power Ratio (PAPR). It is causes nonlinear

distortions after amplified by a power amplifier. Several

techniques to reduce PAPR have been proposed. These tech-

niques have been known as amplitude clipping, clipping and

filtering, coding, tone reservation (TR), tone injection (TI),

active constellation extension (ACE), selected mapping

(SLM), partial transmit sequence (PTS). (Nee et al., 2000;

Tellado, 2005) binary tree based PTS (Wu et al., 2006),

clipping and PTS (Wen et al., 2006)

In the TR approach, the transmitter does not send

data on a small subset of tones in order to optimize the PAPR

reduction. In the TI approach, the substitution of the points in

the basic constellations by new points in the larger constella-

tion is equivalent to the injection of appropriate tone and

phase in the OFDM signal. In the ACE approach, some of

the outer signal constellation points in the data block are

dynamically extended towards the outside of the original

constellation for the PAPR reduction. In the SLM approach,

an input sequence is weighted by each phase rotations in

order to generate some alternative input sequences. These

alternative input sequences are transformed by IFFT and

then the optimum sequence with the low PAPR is selected

for transmission. In the PTS approach, the input data block is

partitioned into disjoint sub-blocks and then it is transformed

by IFFT. The sub-carriers in each sub-block are weighted by

*Corresponding author.

Email address: pchoos@aru.ac.th, c_pradabpet@hotmail.com

http://www.sjst.psu.ac.th

Page 2

356

C. Pradabpet & K. Dejhan I Songklanakarin 1. Sci. Technol. 30 (3),355-360,2008

phase rotations. The phase rotations are selected such that

the PAPR of the combined signal is minimized. The binary

tree based PTS approach supplies good selections on the

tradeoffs of implementation complexity and PAPR reduction

performance In the clipping and PTS approach, the PAPR of

the input OFDM signal are compared with a preset threshold,

in order to judge whether the operation of PTS is needed. If

the PAPR exceeds the preset threshold, PTS is performed.

Then, clipping with is performed to the ultimate signal.

In this paper, we propose a new PAPR reduction

technique. This technique using a PTS combined with APPR

methods. In the proposed method, for the first PAPR reduc

tion, an input data block is partitioned into d isjoint sub

blocks. The sub-carriers in each sub-block are weighted by a

phase rotations. The modified input data are fed to the APPR

process for the second PAPR reduction. The APPR method

adaptively controls the gain based on a minimum least-mean

square (LMS) error. It reduces modulation signals over a

predefined range. Using these two methods at the same time,

a high efficiency of PAPR reduction with lower out-of-band

radiation can be obtained, and simultaneously a high BER

properlY can be realized.

2. OFDM Signal and PAPR Reduction

Let LIS define N frequency domain signals in OFDM

as{X, n = 0, 1,2 ... , N-I}. These N signals construct 1

OFDM block. A set of N sub-carriers, i.e., {I", n = 0, 1,2 ...,

N-I}, is used for these symbols in the OFDM. The sub

carriers are chosen to be orthogonal, which is, In ::: n4f

in the frequency domain, where f;.I =I!NT and T and is

the OFDM symbol duration The OFDM signal is expressed

as

_1_1\-:-1 X

t --. r.-;

\IN n=O

j21rInt

ne

0

T

(1)

x ( )

L

,

S; t S;

The PAPR is defined as (Tellado, 2000; Choe et al., 2004)

(2)

where E {.} denotes an expectation. In some blocks of the

OFDM signals, large PAPR happens, since the structure of

the given symbols may cause this peak.

High PAPR is a serious issue in RF analog circuits, in

particular, at high power amplifiers (HPA). The nonlinearity

of HPA causes inter-carrier interferences (ICI) and thus out

of-band radiation. Accord ingly, the BER performance is

degraded.

3. Model of Nonlinear High Power Amplifiers (HPA)

jrp

x = p.e

(3)

The complex output signal is thus expressed by

g(x) = F[p].ej(rp+<D[p])

(4)

where F[p] and cD[p] represent the AMIAM and AMIPM

conversion characteristics of the nonlinear amplifier, respec

tively. In this paper, a Traveling Wave Tube Amplifiers

(TWTA) model is used for our simulation. The input-output

relationship of the TWTA can be model as

p

F(p) =

(5)

cD[p]=1r. p2

(6)

3 p2 + 4A 2

Figure I shows the characteristic of the TWTA non

linear HPA. The value of A2 is defined as the input saturation

power to the HPA model. The input back off (IBO) at a non

Iinear device is defined in terms of AZ as

(7)

where E {lxI2} is the average of the input power to the HPA

model.

4. Partial Transmit Sequence

In Partia] Transmit Sequence (PTS) approach, the

input data block is partitioned into disjoint sub-blocks. The

sub-carriers in each sub-block are weighted by phase rota

tions. The phase rotations are selected such that the PAPR is

-AWM'l

...... AMIP1'tf

oO · l - . . ' O ' : D . l ~ I U ' : - : : ' : O ~ ' - - - - - - : O - ' - .• - - - - : ' : ~ . ! , - - - - - - : o : ' ; - •• ----:':0.,=--= .. :'::-.---:C"'=--=':';-,.-----:",I:--:'C:-"-----:" ~ : - - : i ~

Normalh.od It\pl,ll.mpHtddt

loS 1.6

A nonlinear HPA can be modeled a memory-less

device. The complex input signal to the HPA is represented

as (Santella et aI., 1998; Tellado, 2000; Zheng et aI., 2004)

Figure 1. Characteristic ofTWTA nonlinear HPA

Page 3

357

C. Pradabpet & K. Dejhan / Songklanakarin J. Sci. Technol. 30 (3), 355-360,2008

minimized. At the receiver, the original data are recovered

by applying inverse phase rotations. A block diagram of the

PTS technique is shown in Figure 2 (Muller el at., 1997 ;

Cimini ef al., 2000; Han et al., 2003)

S.. h ~ l

T,

r"'l" ..l I l ~ 1

A""

1':u1.11l'"

In In

: . ~

] ' ) a l ~

. ~ ' ' ' ' ' ' ' ~

C l ' L ~ I ~ n

Figure 2. Block diagram of the conventional PTS technique.

Define the data block as a vector

T

X =[ Xo XI'" XN-l]

The vector X is partitioned into M disjoint sets. it is re

presented by vectors {Xn"m=I,2,3 ..,M}:

M

X = L Xm

m=1

An IFFT is employed as

(8)

(9)

x = IFFT{X}

Applying phase rotations to sub-blocks allows the

optimization of combining the weighted partial transmit

sequence. The combined sequence as

M

x'::: L: bm xm

m:::l

where {bm , m =1,2,3 ... , M} is the weighting phase rotations

for each sub-block. Choosing bm E {±l,±i)(W = 4) is very

interesting for an efficient imp lementation. In add ition, we

can set b = I without any loss of performance. The PAPR

l

can be mlllimized by the exhaustive search for an appro

priate combination of each sub-block and its corresponding

phase rotation.

(10)

( 11 )

5. Adaptive Peak Power Reduction (APPR)

The Adaptive Peak Power Reduction (APPR) method

controls the peak level of the modulation signal. An adaptive

algorithm reduces the amplitude of modulation signals over

a predefined range. A block diagram of APPR scheme is

shown in Figure 3. (Sano et af., 2006)

The value of xU) is an OFDM signal and it is con

sidered as an input of the APPR. The Ix(i)1 is fed into the

clipping module where the amplitude component Id(i)1 is

generated by

!

--~--

b(J)

J_

FIR

bU>

DIVider

,,(IY'(I)

_1.

i----.J..

0'

-J FIR

'(I)

......__...1

M_ ,..

r g(l)

• ,.....~ < :-. ....

Figure 3. Block diagram of conventional APPR

If Ix(i)1 is smaller than the target value d'h' then Id(i)1 takes

the same value as Ix(i)I. On the other hand, if Ix(i)1 is larger

than d'h' then Id(i)1 is chosen as d'h' Next, Id(i)1 and IX(i)1 are

multiplied together and the result is fed to a finite impulse

response (FIR) filter. The cross-correlation between comp lex

target signals and complex modulation signals weighted by

b(j) is calculated by

I

P/2

L

*

u(i) = -

b(p + P 12) xCi - p).d (i - p) (13)

P+ 1 p=-P/2

where the weighting coefficient b(j) is given from the

Blackman-Harris window function:

b(j) = 0.35875 - 0.48829 cos(2nj / P) + O. I4128 cos(4nj / P)

0.01 168cos(6nj / P)

(14)

At the same time, Ix(i)1 goes to the module of "(i" and

(P+l) then is fed to an stage FIR filter. The autocorrelation

function of xCi) weighted by b(j) is calculated by

I

P/2

2::

>«

v(l)=- b(p+P/2)x(i-p).x (l-p) (15)

P + I p=-PI2

Finally, the gain g(i) is calculated by Equation (16) and

multiplied by the complex modulation signal for reduction

of the signal's peak level

f ~

v(i»0

g(i) =l1v(i)

(16)

v(i) = 0

If d'h is determined small, low PAPR is obtained. In other

words, the high efficiency of the PAPR reduction can be

realized when cI'h is small. However, in this case, the OFDM

signal is considerably distorted. it yields a large out-of-band

rad iation.

6. The Proposed Method

A new technique using PTS combined with APPR

method is proposed in this paper. Figure 4 shows the block

diagram of the proposed method Using this method, both

the high PAPR reduction and the suppression of the o u t - o f ~

dthexP{J.arg(xU» }

IxU)I) dth

d(i) =

(12)

x(i)

IX(i)1 :;:; dth

Page 4

C. Pradabpet & K. Dejhan / Songklanakarin J. Sci. Technol. 30 (3), 355-360, 2008

358

band radiation can be realized. Its performance is higher

than of conventional methods.

First, a sequence of the input data is rearranged using

a PTS method. An input data block is partitioned into dis-

joint sub-blocks. The sub-carriers in each sub-block are

weighted by phase rotations. Since we can select many phase

rotations for its weighting, many sets of weighted input data

are obtained. Among them, the input data with a minimum

PAPR are selected after the APPR is applied to the OFDM

signals.

Using this method, even if large dth is used in the

APPR, the PAPR becomes low. In addition, an out-of-band

radiation can be suppressed because of a large dth.

7. Simulation Results and Discussions

To evaluate and compare the performance of the con-

ventional APPR methods and the proposed methods here,

simulation results are presented. The simulation parameters

are listed in Table 1. (Engles, 2002) The modulation signal

( )x i is used in the APPR is normalized to maximum equal

“1”, the definition of dth as the target value is normalized

varying to 0.80 and 0.90 respectively. The total system is

described in Figure 5.

7.1 PAPR Performance

Figure 6 and 7 illustrate the PAPR performance,

where CCDF is complementary cumulative distribution func-

tion (Han et al., 2005). In Figure 6, the proposed method can

be reduce the PAPR more than the conventional APPR with

a maximum of 3.40 dB. In Figure 7 the proposed method

can reduce the PAPR more than the conventional APPR by

3.52 dB. In case of P=32(P = filter order), the improvement

is maximal compared with the APPR. When the number

of filter orders (P) becomes large, the proposed method

suppresses the out-of-band radiation efficiently.

7.2 Bit Error Rate

Figure 8 and 9 show the BER of the proposed tech-

Figure 4. Block diagram of the proposed method

Table 1. The parameter simulation

Modulation

Number of data subcarriers

Number of FFT points

Number of sub-blocks(M)

64 - QAM

48

64

4

?

Phase rotations (φ)

3

0,, ,

?

22

?

Target value (dth)

Number of filter coefficients (P)

Window function

HPA Model

Channel Model

Coding rate

Decoding

0.80 , 0.90

16 , 32

Blackman-Harris

TWTA

AWGN

3/4

Soft – Decision Viterbi

Zero

Padding

and

IFFT

Serial

To

Parallel

&

Partition

Into

Clusters

Data

Map-

ping

Data

Source

Weighting Factor Optimization

Zero

Padding

and

IFFT

Zero

Padding

and

IFFT

X1

X2

.

.

.

.

.

.

XM

b1

b2

bM

X’

X

APPR

Figure 5. Block diagram of the total system used for the simulation

CodingAPPR

Guard

Interval

Insertion

IFFT

&

PTS

Mapping

Interleave

Deinterleave

FFT

&

IPTS

DemappingDecoding

HPA

Guard

Interval

Removal

Channel

Transmitter

Receiver

.

.

.

.

.

.

Page 5

355

C. Pradabpet & K. Dejhan / Songklanakarin J. Sci. Technol. 30 (3), 355-360, 2008

34567

PAPR(dB)

89101112

10

−4

10

−3

10

−2

10

−1

10

0

CCDF

PAPR Performance

Original

APPR(dth=0.80)

APPR(dth=0.90)

Proposed(dth=0.80)

Proposed(dth=0.90)

34567

PAPR(dB)

89101112

10

−4

10

−3

10

−2

10

−1

10

0

CCDF

PAPR Performance

Original

APPR(dth=0.80)

APPR(dth=0.90)

Proposed(dth=0.80)

Proposed(dth=0.90)

345678910

10

−4

10

−3

10

−2

10

−1

10

0

IBO(dB)

BER

BER Performance

Original

APPR(dth=0.80)

APPR(dth=0.90)

Proposed(dth=0.80)

Proposed(dth=0.90)

345678910

10

−4

10

−3

10

−2

10

−1

10

0

IBO(dB)

BER

BER Performance

Original

APPR(dth=0.80)

APPR(dth=0.90)

Proposed(dth=0.80)

Proposed(dth=0.90)

Figure 6. PAPR performance of the OFDM signal (filter order =

16)

Figure 7. PAPR performance of the OFDM signal (filter order =

32)

Figure 8. BER performance of the OFDM signal (filter order =

16)

Figure 9. BER performance of the OFDM signal (filter order =

32)

−0.5−0.4−0.3−0.2−0.1

Normalized Frequency

0 0.10.20.30.40.5

−25

−20

−15

−10

−5

0

PSD(dB)

Power spectrum density

Original

APPR

Proposed

−0.5−0.4−0.3 −0.2−0.1

Normalized Frequency

0 0.10.20.30.40.5

−25

−20

−15

−10

−5

0

PSD(dB)

Power spectrum density

Original

APPR

Proposed

Figure 10. PSD of the OFDM signal (IBO = 3dB)

Figure 11. PSD of the OFDM signal (IBO = 7dB)

niques. The definition of IBO is shown in Equation (7). It is

also compared with the APPR. The conventional APPR

presents more wrong property than the OFDM system with-

out the APPR method. The proposed method shows better