Comparison of SLM and PTS method for PAPR reduction in OFDM

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 peak-to- average-power 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), peak-to-average power ratio (PAPR), selected mapping, partial transmit sequences.

1. 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].

2. PAPR IN OFDM

   OFDM signals have a higher Peak-to-Average 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..AN-1] 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 in-band and out-of-band 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 SLM-OFDM 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

3. SELECTED MAPPING

   (4)

   symbols. At the receiver, differential demodulation has to be implemented right after the DFT [2][5].

4. 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

   Serial-to-parallel conversion of user bit stream

   Coding & Interleaving

   Mapping

   Subblock Partitioning

   Optionally Differential Encoding

   A

   1

   a

   b

   1

   Serial-to-parallel 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 PTS-OFDM [2]

   We introduce complex valued rotation factors

   Fig. 1 PAPR reduction in SLM-OFDM [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, pseudo-random 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 µ.

   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 D-point 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 so-called partial transmit sequences

   a IDFT A have been introduced. The PTS-OFDM

   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 continuous-valued

   -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 µ. 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= (V-1)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 sub-block 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 10-1

   -2

   = (V-1) 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 peak-optimized transmit

   u 10-3

   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].

5. 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 sub-carriers: 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 SLM-OFDM

   PTS-OFDM

   11

   -1

   CCDF (Pr[PAPR>PAPR0])

   10 10

   • U=2

     PAPR0 [dB]

     9

     -2

     10

     8 V=4

     • U=4

       10-3 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

       10-3 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

6. CONCLUSION

SLM & PTS both schemes utilize several IFFTs instead of one and choose one signal from a multiplicity of transmit sequences. SLM-OFDM and PTS-OFDM 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

REFERENCES

1. Carole Devlin, Anding Zhu, Thomas J. Brazil, PAPR reduction technique for OFDM signals using unused tones with phase

   information, Circuits and Systems for Communications, 2008. ICCSC 2008. 4th IEEE International Conference, pp.6-10.

2. Stefan H. Muller , Johannes B. Huber., A Comparison of peak power reduction schemes for OFDM, Proc. Of the IEEE Global

   Telecommunications Conference GLOBECOM97, Phoenix, Arizona, USA, pp.1-5, November 1997.

3. Seok-Joong Heo,Hyung-Suk Noh, Jong-Seon No, Dong-Joon 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

     PTS-OFDM

     Communication(PIMRC07).

4. S. Muller, R. Bauml, R. Fischer, and J. Huber, OFDM with Reduced Peak-to-Average Power Ratio by Multiple Signal Representation,

   Annals of Telecommunications, Vol. 52, No.1-2,pp. 58-67, February

   10

   • U=2

     PAPR0 [dB]

     9

     8 U=4

     7 U=8

     • U=16

       • V=4

       1997.

5. Van Eetvelt, P., Wade, G., Tomlinson, M., Peak to average power reduction for OFDM schemes by selective scrambling, Electronics

   Letters, Vol.32,No.21,pp.1963-1964,1996.

6. Seung Hee Han, Jae Hong Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE

   wireless commun., Vol. 12, No. 2, pp. 56-65, April 2005.

   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