Efficient Selective Mapping PAPR Reduction Technique - ScienceDirect

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ScienceDirect Procedia Computer Science 45 (2015) 620 – 627

International Conference on Advanced Computing Technologies and Applications (ICACTA2015)

Efficient Selective Mapping PAPR Reduction Technique Kavita Mhatrea, Uday Pandit Khotb a

Usha Mittal Institute of Technology, SNDT University, Mumbai-400049 , India St.Francis Institute of Technology, Mumbai University, Mumbai-400103, India

b

Abstract

OFDM is a form of multicarrier modulation technique with high spectral efficiency and immunity to interference. One major drawback of OFDM systems is the high peak to average power ratio (PAPR) which leads to power inefficiency and signal distortion with practical power amplifiers used at the transmitter. Selective Mapping (SLM) is a distortion less technique that can reduce PAPR efficiently without increase in power requirement and incurring data rate loss. The simulation result shows that proposed SLM technique has better PAPR reduction performance. © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2015 The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of scientific committee of International Conference on Advanced Computing Technologies and Peer-review under responsibility of scientific committee of International Conference on Advanced Computing Technologies and Applications (ICACTA-2015). Applications (ICACTA-2015). Keywords: Orthogonal Frequency Division Multiplexing(OFDM);Selective Mapping(SLM); Peak-to-Average Power Ratio (PAPR); Complementary CDF(CCDF).

1. Introduction Orthogonal Frequency Division Multiplexing is a special form of multicarrier modulation technique being used in many latest wireless standards. OFDM has been adopted for many broadcast standards, such as Digital Audio Broadcasting (DAB) standards, Digital Video Broadcasting (DVB) standards [1].It is also used in wireless local area standards such as 802.11g, 802.11n and also for standards such as WIMAX.OFDM is also used in cellular telecommunication standard, Long Term Evolution (LTE).An OFDM consists of a large number of closely spaced orthogonal carriers. The data to be transmitted is spread over these carriers and each orthogonal carrier is being modulated at low data rate[2].The most advantage of OFDM is high frequency spectrum efficiency as overlapping

1877-0509 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of scientific committee of International Conference on Advanced Computing Technologies and Applications (ICACTA-2015). doi:10.1016/j.procs.2015.03.117

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of carriers do not cause interference at receiver side. Orthogonality between carriers minimizes interference. This is achieved if the frequency separation between carriers (∆f) is equal to reciprocal of OFDM symbol period (1/Ts)[3].In spite of its numerous merits, OFDM systems have some drawbacks. One major drawback of OFDM systems is high peak-to-average power ratio (PAPR), which degrades the efficiency of power amplifier. Therefore, PAPR reduction is very important for OFDM systems [4].An OFDM signal consists of many individual sinusoidal carriers. When these sinusoids align in phase at the IFFT input, and are added coherently, OFDM signal can have large amplitude resulting in a high PAPR at the IFFT output. The large peak amplitude of the OFDM signal is due to N subcarriers and it is N times that of a single-carrier system. When these large peaks with high PAPR exceed the saturation region of power amplifier used at the transmitter and/or receiver, the OFDM signals will suffer from nonlinear distortion, out of band distortion and also inter-modulation interference among OFDM subcarriers [5]. Due to this, bit-error-rate (BER) increases at the receiver. Use of power-amplifiers with a large saturation region can reduce distortion or BER. However, it leads to high equipment cost and high battery power consumption. To deal with this problem, several algorithms have been introduced for reduction of high PAPR [7] such as clipping, coding, partial transmit sequences, selective mapping and tone reservation. Selective mapping technique for reducing PAPR is discussed in this paper. This paper is organized as follows. Section II describes Peak to Average Power Ratio of OFDM. Section III gives PAPR reduction techniques. Section IV presents Selective Mapping technique in brief. Section V shows simulation results and section VI concludes the whole paper. 2. Peak to Average Power Ratio of OFDM In the OFDM, the RF power amplifier cannot operate efficiently due to high PAPR. This amplifier must be used in its linear region to combat distortion, out-of-band noise and BER degradation. In addition, high PAPR requires a high-resolution digital-to-analog converter (DAC) and analog-to-digital converter (ADC). Low PAPR makes the power amplifier operate efficiently and also reduces the complexity of DAC and ADC.

Ppeak PAverage

PAPR

Where

(1)

Ppeak represents peak output power, PAverage means average output power.

ܲ‫ ܴܲܣ‬ൌ

௠௔௫೟ ȁ௫ሺ௧ሻȁమ ா೟ ሾȁ௫ሺ௧ሻȁమ ሿ

And for the discrete time signal

ܲ‫ ܴܲܣ‬ൌ

(2)

xn

௠௔௫೙ ȁ௫ሺ௡ሻȁమ ா೙ ሾȁ௫ሺ௡ሻȁమ ሿ

(3)

The input signal to the amplifier in the OFDM system is an analog signal and the time domain samples of the output from the inverse fast Fourier transform (IFFT) is xn which represents the transmitted OFDM signals obtained by taking IFFT operation on modulated input symbols. Mathematically xn is expressed as:

xn

1 N

N 1

¦XW k

nk N

k 0

For an OFDM system with sub-carriers, the peak power of received signals is N times the average power when phase values are the same.

(4)

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2.1. Probability Distribution function of PAPR Cumulative Distribution Function (CDF) is expressed as follows

F ( z) 1  e

z (5)

where Z is probability of PAPR. The probability distribution function for PAPR less than a certain threshold (z) is therefore expressed as

P( PAPR  z ) F ( z )

N

z N (1  e )

(6)

3. PAPR Reduction Techniques There are different techniques to reduce PAPR of OFDM. x x x x x x

Clipping Coding Schemes Partial Transmission Sequence(PTS) Selective Mapping(SLM) Tone Reservation Tone Injection

3.1. Clipping Clipping is the simplest technique that is used to reduce PAPR in OFDM system. The basic idea of this technique is to clip the parts of the signals that have high peak outside of the allowed region [8] 3.2. Coding Schemes When N signals that have the same phase added together results in the high peak power which is N times the average power. The main idea of coding schemes is to select codeword that will produce good PAPR.The good PAPR can be obtained by reducing occurrence probability of the same phase of the N signals. 3.3. Partial Transmission Sequence (PTS)[[9] Partial transmit sequences (PTS) is one of the most important methods that is used to reduce PAPR in the OFDM system. And it can be presented in two main steps. First, by dividing the original OFDM signal into a number of sub-blocks. Secondly, adding the phase rotated sub-blocks to develop a number of candidate signals to pick the one with smallest PAPR for transmission. There is another way which can also be used to express PTS method by multiplying the original OFDM signal with a number of phase sequences. 3.4. Tone Injection (TI) Tone Injection technique uses additive correction method for reducing PAPR. TI is based on mapping of original data that causes large peaks to several new positions which will not generate large peaks and thus reducing PAPR. The receiver must know how to map the redundant positions on the original one. TI is distortion less technique and does not exhibit data rate loss. However, transmitter is more complex as it requires additional IFFT operation [10]. TI technique also requires more signal power for transmission of signal.

Kavita Mhatre and Uday Pandit Khot / Procedia Computer Science 45 (2015) 620 – 627

3.5. Tone Reservation (TR) Tone Reservation technique is based on reserving small set of tones which are called as peak reduction carriers to reduce PAPR. These tones are orthogonal to each other and they are added to a data block or information signal to minimize the high peak. The amount of PAPR reduction depends on number of reserved tones and their position. The performance of TR also depends on allowed power on reserved tones and amount of complexity [10]. This technique can be applied to every type of MCM (Multi Carrier Modulation) system. TR method helps to achieve large minimization in PAPR just by reserving a small set of tones at the transmitter. This method is less complex. And transmission of side information is not necessary at the receiver of the system. Table1. Comparisons of Different PAPR Reduction Techniques [10]

Reduction Techniques

Power Increase

Implementation Complexity

Bandwidth Expansion

BER Degradation

Clipping

No

Low

No

Yes

Coding

No

Low

Yes

No

PTS

No

High

Yes

No

SLM

No

High

Yes

No

TR/TI

Yes

High

Yes

No

Table 1 shows comparison of different PAPR reduction techniques and it is observed from the Table 1 that Power requirement of TR/TI is much more compared to Selective Mapping Method. Though PTS and SLM have similar kind of benefits, SLM is better than PTS with respect to number of data vectors. As no of data vectors or sub blocks increases, complexity in PTS increases substantially.PTS method requires higher information redundancy compared to SLM algorithm[11] under same circumstances. Oversampling and filtering does not increase the PAPR dramatically as it does in PTS. 4. Selective Mapping Selective mapping (SLM) is a promising PAPR reduction technique of OFDM system. Figure 1 shows the basic principle of Selective Mapping.The basic idea of SLM is to produce U alternative transmit sequences from the same data source and then to select the transmit signal exhibiting the lowest PAPR. The idea stems from the fact that as the PAPR is determined by the sequence of the transmit data vectors; Xm multiplying the data vectors by some random phase will change the PAPR properties after the IFFT. Mathematically, a set of U markedly different, pseudo random fixed vectors are generated, Let us assume that the original input data X [X1, X2,…,XN-1 ] multiplied with independent phase sequences P=[P 1(u) P2(u),…,PN(u)]( u=0,1, U-1) , where U is the number of phase sequences. Both the input data and phase sequences have the same length N (u= 0, 1…, U-1). After multiplication, inverse fast Fourier transform (IFFT) will be applied on each sequence to convert the signal from frequency domain to the time domain. The result from multiplication will generate the data block of an OFDM system that has different time domain signals, with length of U, and different PAPR values, X(u)= [X 1(u) , X2(u),…,XN-1(u) ].The last step is comparing the PAPR among the independent data blocks and the candidate with the lowest PAPR will be selected for transmission. The following equation (8) expresses the optimal candidate that has the lowest PAPR and selected for transmission [11].

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Fig 1. Basic Principles of Selective Mapping [12]

The probability that PAPR of an OFDM signal exceeds threshold z, can be found by following CCDF,

FZ max( z )

P ( Z max ! z )

= 1  P( Z max  z ) = 1  FZ max( z )

(7)

If each mapping considered statically independent, then CCDF of PAPR will be

P( PAPR ! z )

F ( z)

N

z N U (1  (1  e ) )

(8)

where U is the number of phase sequences N is the number of subcarriers Z is threshold Z is any real no As it can be seen from equations (7) and (8), they derived when the number of subcarriers is large and the samples are independent with Nyquist sampling rate. But, both equations do not mention the effect of over-sampled and band limited process. It is because the sampled signal does not need to have the maximum point of the original signal. On other hand, the effect of over-sampling is approximated by adding certain number of extra bits i.e. independent samples to obtain better value of PAPR. Nee and Prasad [13] shows an approximation to explain the probability of PAPR, by approximated N sub-carriers and over-sampling distribution by α and they mention that for α=2.8, is the best value to reach better PAPR. The approximation is shown below [9],

P( PAPR ! z )

F ( z)

N

(1  (1  e

 z DN U ) )

(9)

5. Results and Discussions Figs 2 to 9 show the performance of Selective Mapping for different values of subcarriers N and phase sequences U. X axis of Figs 2 to 9 indicates probability of PAPR represented by z. Figs 2,3,4,5 show simulated results of PAPR's Complementary CDF distribution for SLM in MATLAB with values of sub carrier for N=64, N=128, N=256 and N=1024, respectively.

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Kavita Mhatre and Uday Pandit Khot / Procedia Computer Science 45 (2015) 620 – 627 0

0

10

10 U=1 U=2 U=4 U=8 U=16

-1

-1

10

P(PAPR>z)

P(PAPR>z)

10

-2

10

-3

-2

10

-3

10

10

-4

10

U=1 U=2 U=4 U=8 U=16

-4

4

5

6

7

8 z

9

10

11

10

12

4

5

Fig 2. PAPR Reduction for SLM where N=64 and U = 1, 2, 4,8,16

0

8 z

9

10

11

12

0

10 U=1 U=2 U=4 U=8 U=16

-1

U=1 U=2 U=4 U=8 U=16

-1

10

P(PAPR>z)

10

P(PAPR>z)

7

Fig 3. PAPR Reduction for SLM where N = 128 and U = 1, 2, 4,8,16.

10

-2

10

-3

-2

10

-3

10

10

-4

10

6

-4

4

5

6

7

8 z

9

10

11

Fig 4. PAPR Reduction for SLM where N = 256 and U = 1, 2, 4,8,16

12

10

4

5

6

7

8 z

9

10

11

12

Fig 5. PAPR Reduction for SLM where N = 1024 and U = 1, 2, 4,8,16

Figs 2 and 3 show that as N=64 increases to N=128, PAPR will increase by 0.9dB and substantial reduction in PAPR as phase sequences change from U=1, 2, 4,8,16. Figs 4 and 5 show that as N=256 changes to N= 1024, PAPR will increase only by 0.5dB and significant reduction in PAPR as the phase sequences change from U=1, 2, 4,8,16.

626

Kavita Mhatre and Uday Pandit Khot / Procedia Computer Science 45 (2015) 620 – 627 0

0

10

10

U=1 U=2 U=4 U=8 U=16

-1

-1

10

P(PAPR>z)

P(PAPR>z)

10

-2

10

-3

-2

10

-3

10

10

-4

-4

10

U=1 U=2 U=4 U=8 U=16

4

5

6

7

8 z

9

10

11

10

12

4

Fig 6. PAPR Reduction for SLM where N = 64, α = 2.8 and U = 1, 2, 4, 8, 16 0

7

8 z

9

10

11

12

0

10

U=1 U=2 U=4 U=8 U=16

-1

U=1 U=2 U=4 U=8 U=16

-1

10

P(PAPR>z)

10

P(PAPR>z)

6

Fig 7. PAPR Reduction for SLM where N =128, α = 2.8 and U =1, 2, 4,8,16

10

-2

10

-3

-2

10

-3

10

10

-4

10

5

-4

4

5

6

7

8 z

9

10

11

Fig 8. PAPR Reduction for SLM where N =256, α = 2.8 and U =1, 2, 4,8,16

12

10

4

5

6

7

8 z

9

10

11

12

Fig 9. PAPR Reduction for SLM where N =1024, α = 2.8 and U =1, 2, 4,8,16

Figs 6, 7, 8 and 9 show MATLAB simulated results by considering oversampling factor α=2.8 and for N=64, N=128, N=256 and N=1024 for the phase sequences U= 1,2,4,8,16.The results obtained by taking into account oversampling factor are similar with theoretical results shown in Figs 2, 3, 4, and 5. 6. Conclusions Simulation results of OFDM with SLM show that as value of N increases, PAPR increases. PAPR decreases with increase in phase sequences U [6][9]. Simulation results are compared with theoretical results to make sure that Simulated results give the valid and correct results [6][11].Proposed Threshold Selective Mapping method can be used to achieve significant reduction in PAPR. Acknowledgement The authors are thankful to the Management Usha Mittal Institute of Technology for providing all the necessary facilities.

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References 1. Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, IEEE Std. 802.11g, June 2003. 2. H. Chen, H. Liang. Combined Selective Mapping and Binary Cyclic Codes for PAPR Reduction in OFDM Systems, IEEE Transactions on Wireless Communications, vol.6, no.10, Oct. 2007. 3. G. Hill, Peak Power reduction in Orthogonal Frequency Division Multiplexing Transmitters, in school of Communication and Informatics: Victoria University, March 2011, p.13. 4. S. H. Han and J. H. Lee, An overview of peak-to-average power ratio reduction techniques for multicarrier transmission, IEEE Wireless Comm. Mag., vol. 12, pp. 56–65, Apr. 2005. 5. B. Wang, P. Ho, and C. Lin, OFDM PAPR Reduction by Shifting Null Subcarriers Among Data Subcarriers, IEEE Communication Letters, vol. 16. No.9, p. 1377-1379, Sep. 2012. 6. S. Eom, H. Nam, Y. Ko. Low-Complexity PAPR Reduction Scheme without Side Information for OFDM Systems, IEEE Transactions on Signal Processing, vol. 60, No. 7, p. 3657-3669, July 2012. 7. C. Shin, K. Rim, Y. Kim. A Weighted OFDM Signal Scheme for Peak-to-Average Power Ratio Reduction of OFDM Signals, IEEE Transactions on Vehicular Technology, vol. 62, No.3, p. 1406-1409, March 2013. 8. N. R. Rajan, S. Prabha, D. Meenakshi. Improved Performance in OFDM systems by PAPR reduction techniques, IEEE International Conference on Computer Communication Informatics (ICCCI-2013), p. 04-06, Jan 2013. 9. Di-xiao Wu. Selected Mapping and Partial Transmit Sequence Schemes to reduce PAPR in OFDM Systems, IEEE Transactions on Image analysis and signal processing, p.1-5, Oct 2011. 10. V. K. Singh, A. Goel, A. Sharma, Reducing Peak to Average Power Ratio of OFDM by Using Selective Mapping, International Journal of Research in Information Technology, vol. 2.No.4, p-400-407, April 2014. 11. M. Singh, V. Kumar. Signal scrambling Techniques for PARP reduction in OFDM system, International Journal of Engineering and Computer Science vol. 2, p. 311-317, Jan 2013. 12.B. K. Shiragapur, U. Wali, S. Bidwai, Novel Techniques to reduce PAPR in OFDM Systems Using Threshold SLM, IEEE International Conference on Advance Computing Conference (IACC), p.515-519, Feb 2013. 13. Richard van Nee, Ramjee Prasad. OFDM for wireless multimedia Communications. Artech house, 2000.

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