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 Authors : Khyati K. Desai
 Paper ID : IJERTV3IS061413
 Volume & Issue : Volume 03, Issue 06 (June 2014)
 Published (First Online): 27062014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparison of SLM and PTS method for PAPR reduction in OFDM
Khyati K. Desai
Lecturer in Electronics & Communication Engg., Government Polytechnic,
Valsad, Gujarat, India
Abstract Orthogonal frequency division multiplexing (OFDM) also referred to as multicarrier communication systems, have become a key technology in current and for future communication systems. Due to OFDMs immunity to many channel imperfections, it is the ideal modulation scheme for many applications which transmit signals in hostile environments. A major drawback of OFDM is the high peakto averagepower ratio (PAPR) problem, which can lead to low power efficiency and nonlinear distortion at the transmitter power amplifier. Selected mapping (SLM) and Partial transmit sequences (PTS) are powerful and distortion less peak power reduction schemes for OFDM. In SLM the transmitter selects one favourable transmit signal from a set of sufficiently different signals which all represent the same information , while in PTS the transmitter constructs its transmit signal with low PAPR by coordinated addition of appropriately phase rotated signal parts. In this paper the technique of SLM is simulated for OFDM and it is found that using this technique with 8 alternative sub carrier vectors, PAPR is reduced to approximately 4 dB whereas using PTS with 8 sub block partitions, PAPR is reduced to approximately 5 dB.
Keywords Orthogonal frequency division multiplexing (OFDM), peaktoaverage power ratio (PAPR), selected mapping, partial transmit sequences.

INTRODUCTION
Orthogonal Frequency Division Multiplexing has many advantages including resistance to multipath fading and high data rates. It has therefore been chosen as the modulation
transmit sequences (PTS) are powerful and distortion less peak power reduction schemes for OFDM. In SLM the transmitter selects one favourable transmit signal from a set of sufficiently different signals which all represent the same information, while in PTS the transmitter constructs its transmit signal with low PAPR by coordinated addition of appropriately phase rotated signal parts[2].

PAPR IN OFDM
OFDM signals have a higher PeaktoAverage Power Ratio (PAPR) than single carrier signals. The reason for this is that in the time domain, a multicarrier signal is the sum of many narrowband signals. At some time instances, this sum is large, at other times it is small, which mean that the peak value of the signal is substantially larger than the average value. This high PAPR is one of the most important implementation challenges that face OFDM because it reduces the efficiency and hence increases the cost of the RF power amplifier.
Let A = [A0A1..AN1] denote an input symbol sequence in the frequency domain, where AK represents the complex data of the kth subcarrier and N the number of sub carriers of OFDM signal. Let T be a period of input symbol and NT a period of OFDM signal. The OFDM signal is generated by summing all the N modulated subcarriers each of which is separated by 1/T.
Then the complex OFDM signal in time domain is expressed as
standard for IEEE802.11a/g WLAN, Worldwide Interoperability for Microwave Acess (WiMax), Digital Video
at
1 N 1
Ane
i 2 nt / NT
,0 t NT
(1)
Broadcasting (DVB). However a major drawback of OFDM is the manner in which the phases can align in the frequency domain causing high peaks to result in the time domain [1].
N n0
Where, t is continuous time index. The OFDM signal sampled at Nyquist rate can be written as
High peak values cause saturation of the power amplifier and both inband and outofband distortion when limiting effects
ak
1 N 1
Ane
j 2 k / N
, k 0,1,…, N 1
(2)
occurs. To prevent such phenomena amplifiers are normally backed off by approximately the PAPR. This however severely impacts power amplifier efficiency, making it
N n0
Which can also be in a vector form, called an OFDM signal
preferable to reduce the PAPR of the signal before it enters the power amplifier [1]. For PAPR reduction number of
sequence, as
a a0 a1 a
N 1
. In fact, a correspond to
techniques have been developed e.g. Clipping, Coding, Selected Mapping, Partial Transmit Sequences, Tone Injection, and Tone Reservation. Selected mapping (SLM) & Partial
inverse fast Fourier transform (IFFT) of A. The PAPR of
OFDM signal sequence a is defined as the ratio between
maximum instantaneous power and its average power, which can be written as,
in a set of U different subcarrier vectors
A u
with
2
max ak
(3)
components,
u u
PAPR a 0 k N 1 2
ak
A,v
A,v Pv
,0 v N,1 u U
(7)
Then, all U alternative subcarrier vectors are transformed into
Statistically it is possible to characterize the PAPR
distribution (probability that PAPR exceeds given threshold
0 ) using its cumulative distribution function (CDF) or complementary cumulative distribution function (CCDF). For the case of OFDM, the following expression for the CCDF holds,
N
r PAPR 0 1 – 1 – exp 0
transmit sequence a a u with the lowest PAPR is
chosen. The SLMOFDM transmitter is depicted in Fig. 1 where it is visualized that one of the alternative subcarrier vectors can be the unchanged original one. Optionally, differentially encoded modulation may be applied before the IDFT and right after generating the alternative OFDM
CCDFPAPR 1 CDFPAPR

SELECTED MAPPING
(4)
symbols. At the receiver, differential demodulation has to be implemented right after the DFT [2][5].

PARTIAL TRANSMIT SEQUENCES
In this most general approach it is assumed that U statistically
In this method ,the subcarrier vector A
is partitioned into V
independent alternative transmits sequences
u
a
represent
pair wise disjoint subblocks
A ,1 V.All subcarrier
the same information. Then, that sequence
a a
u
positions in
A ,which are already represented in another
with the lowest PAPR, denoted as
, is selected for
V
transmission. The probability that
exceeds
0 is
subblock are set to zero, so that
A A
approximated by,
Pr
0 1 1 e
0
N U
(5)
1
P1
1
IDFT
Serialtoparallel conversion of user bit stream
Coding & Interleaving
Mapping
Subblock Partitioning
Optionally Differential Encoding
A
1
a
b
1
Serialtoparallel conversion of user bit stream
Coding & Interleaving Mapping
P2
A
PU
Bit source
A 1
Optionally Differential Encoding
Optionally Differential Encoding
A2
Optionally Differential Encoding
A
U
IDFT
IDFT
IDFT
1
a
a
2
a
U
a
2
IDFT
A
IDFT
Bit Source
2
a
a
2
b
b
a
Peak value optimization
+
If necessary Side information
Selection of a desirable symbol
If necessary Side information
Fig. 2 PAPR reduction in PTSOFDM [2]
We introduce complex valued rotation factors
Fig. 1 PAPR reduction in SLMOFDM [2]
b e j , 0, 2 ,1 V ,
enabling a
Because of the selected assignment of binary data to the
transmit signal, this principle is called selected mapping. A set of U markedly different, distinct, pseudorandom but fixed
modified subcarrier vector
A
V
1
b A
, which
vectors,
Pu P u,, P
u
represents the same information as A , if the set
b ,1 V(as side information) is known for each Âµ.
0 D1
P u e jvu , u 0, 2 ,0 v N,1 u U , (6)
v v
Clearly, simply a joint rotation of all subcarriers in sub block
by the same angle arg b is performed. To
must be defined. The subcarrier vector A is multiplied
subcarrier wise with each one of the U vectors Pu , resulting
calculate a
IDFT A , the linearity of the IDFT is
exploited. Accordingly, the subblocks are transformed by V
separate and parallel Dpoint IDFTs, yielding
U alternative sub carrier vectors: 16 V sub block partitions: 8
(8)
Data rate: 54 Mbps
a
V
1
b IDFT A
V
1
b a
Channel Mode: AWGN
Total no. of symbols to TX. : 10000
Where the V socalled partial transmit sequences
a IDFT A have been introduced. The PTSOFDM
transmitter is shown in below Fig. 2 with the hint, that one PTS can always be left unrotated [2]. Based on them a peak value optimization is performed by suitably choosing the free
The 64 point IFFT mapping is shown in Fig. 3. For generation of real output, IFFT mapping is done by taking its conjugate.
parameters
b
such that the PAPR is minimized for
b
.The
b
may be chosen with continuousvalued
32
26
1 0 1 26 31
phase angle, but more appropriate in practical systems is a restriction on a finite set of W (e.g. 4) allowed phase angles.
DC
Zeros subcarriers
subcarriers
Zeros
The optimum transmit sequence then is,
Fig.3 IFFT mapping for Complex time output OFDM signal
a
V
1
b a
. (9)
The results are shown in Fig. 4, 5 and 6. In Fig. 4 with N = 64 & U=16 PAPR reduction is 4.6 dB. In Fig. 5 with V=8 PAPR
Both scheme require, that the receiver has knowledge about
the generation of the transmitted OFDM signal in symbol
reduction is 5 dB. Fig. 6 shows comparison of both methods. It follows from this figure that PTS with W = 4 rotations and
period Âµ. Thus, in PTS the set with all rotation factors
b
V = 8 IFFTs achieves a slightly better performance than SLM with U = 8 IFFTs. With PTS PAPR reduction achieves 5 dB
u
and in SLM the number u of the selected P has to be
transmitted to the receiver unambiguously so that this one can denote the subcarriers appropriately. The number of bits required for canonical representation of this side information is the redundancy Rap introduced by the PAPR reduction scheme with PTS & SLM. As this side information is of
highest importance to recover the data, it should be carefully protected by channel coding. In PTS the number of admitted
and redundancy Rap= (V1)log2W = 14 bits / OFDM symbol ,whereas with SLM PAPR reduction achieves 4 dB and redundancy Rap = log2U = 3 bits / OFDM symbol. From Fig.7 and Fig.8, 5 dB PAPR reduction can be achieved with SLM using U=32 alternative sequences (no. of IFFTs) and 5 bits of redundancy whereas with PTS using V= 8 subblock partitioning (no. of IFFTs) and 14 bits of redundancy.
combinations of rotation angles
b
should not be
0 SLM METHOD FOR PAPR REDUCTION
10
Orignal U=2 U=4 U=8 U=16
Theoritical
excessively high, to keep the explicitly transmitted side
information within a reasonable limit. If in PTS each b is
CCDF (Pr[PAPR>PAPR0])
exclusively chosen from a set of W admitted angles, then Rap 101
2
= (V1) log2W bits per OFDM symbol are needed for this purpose. In SLM Rap = log2U bits are required for side information. In PTS the choice b 1, j (W = 4) is
very interesting for an efficient implementation, as actually no 10
multiplication must be performed, when rotating and
combining the PTSs
a
to the peakoptimized transmit
u 103
sequence a
in Eq.9. For SLM, choosing
P from the
latter set has the same advantage, when generating the alternative subcarrier vectors by applying Eq.7 [2][4].

DESIGN AND SIMULATION RESULT
The OFDM system is implemented using MATLAB to allow various parameters of the system to be varied and tested. The
following OFDM system parameters are considered.
Mapping: 16 QAM
Number of data subcarriers: 52 Number of FFT points: 64
4
10
0 2 4 6 8 10 12
PAPR0 [dB]
Fig. 4 Plot of SLM technique for different values of U
0 PTS METHOD FOR PAPR REDUCTION
10
PAPR reduction vs System Complexity
12

U=1

V=2 SLMOFDM
PTSOFDM
11
1
CCDF (Pr[PAPR>PAPR0])
10 10

U=2
PAPR0 [dB]
9
2
10
8 V=4

U=4
103 Orignal
V=2
V=4 V=8
Theoritical
4
7 U=8
6 V=8
5
U=16

U=32

U=64

10
0 2 4 6 8 10 12
PAPR0 [dB]
Fig. 5 Plot of PTS technique for different values of V
0 SLM & PTS METHOD FOR PAPR REDUCTION
10
1
CCDF (Pr[PAPR>PAPR0])
10
2
10
Orignal U=2 U=4
103 U=8
V=2 V=4 V=8
Theoritical
4
10
0 2 4 6 8 10 12
PAPR0 [dB]
Fig. 6 comparison of SLM & PTS technique
PAPR reduction performance vs. redundancy
12
0 10 20 30 40 50 60 70
Additional System Complexity
Fig. 8 PAPR reduction performance vs. additional system complexity for different values of U and V




CONCLUSION
SLM & PTS both schemes utilize several IFFTs instead of one and choose one signal from a multiplicity of transmit sequences. SLMOFDM and PTSOFDM can work with arbitrary numbers of subcarriers and any symbol mapping scheme. SLM outperforms PTS in terms of PAPR reduction vs. redundancy, but PTS is considerably better with respect to PAPR reduction vs. additional system complexity
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SeokJoong Heo,HyungSuk Noh, JongSeon No, DongJoon Shin., A modified SLM scheme with low complexity for PAPR reduction
of OFDM systems, The 18th Annual IEEE International Symposiumon Personal, Indoor and Mobile Radio

U=1
11

V=2
PTSOFDM
Communication(PIMRC07).



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U=2
PAPR0 [dB]
9
8 U=4
7 U=8

U=16

V=4
1997.




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6 U=32

U=64

5

V=8
0 2 4 6 8 10 12 14
Rap [ bit]
Fig. 7 PAPR reduction performance vs. redundancy for different values of U and V