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Introduction Proposed Method Experimental Results Conclusion References

Partial Transmit Sequence (PTS) based PAPR reduction for OFDM using improved harmony search evolutionary algorithm

BICT 2014 Mangal Singh, Sarat Kumar Patra

Department of Electronics & Comm. Engg. National Institute of Technology, Rourkela, India

12/03/2014

1/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

2/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

3/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Introduction to OFDM

Basic Idea Use large number of parallel narrow-band sub-carriers instead

• f a single wide-band carrier to transport information.

Advantages Robustness against multipath fading . Low computational complexity & efficient hardware implemen- tation. Eliminates ISI through the use of cyclic prefix. Bandwidth efficient modulation scheme.

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Introduction to OFDM

Disadvantages Sensitive to frequency synchronization problems. It is also sensitive to Doppler Shift. The peak to average power ratio of OFDM is also very high. High PAPR increases the complexity of ADC & DAC converters. High PAPR reduces the power efficiency and battery life.

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Figure 1: The block diagram of OFDM system

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Figure 2: Effect of PAPR in OFDM system

7/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Peak to Average Power Ratio (PAPR)

Due to presence of large number of independently modulated sub- carriers in an OFDM system, the peak value of the system can be very high compared to the average of the whole system. As per the definition, PAPR of the transmitted signal is the ratio of peak power to the average power of the signal, i.e. PAPR = max |xn|2 E

• |xn|2

(1)

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Peak to Average Power Ratio (PAPR)

Complementary Cumulative Distribution Function (CCDF) is used to represent performance measure for PAPR reduction techniques. It calculates the probability that the PAPR of a data block exceeds a given threshold PAPR0. The CCDF of the PAPR of N symbols of a data block with Nyquist rate sampling is defined as Pr(PAPR ≥ PAPR0)= 1 − Pr(PAPR ≤ PAPR0) = 1−(1 − e−PAPR0)N (2)

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

PAPR Reduction Techniques

PAPR Reduction Techniques Power Increase Implementation Complexity Bandwidth Expansion BER degra- dation Tone Reservation Yes High Yes No Tone Injection Yes High Yes No Clipping No Low No Yes Selective Mapping No High Yes No Partial Transmit Sequence No High Yes No

10/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Partial Transmit Sequence Technique (PTS)

Basic Idea Among various PAPR reduction schemes, PTS is most suc- cessful technique for PAPR reduction, but the computational complexity is high due to searching of optimum phase factor. The complexity is proportional to the number of sub-blocks & phase factors used in PTS. Different optimization techniques can be used in PTS to reduce the searching complexity of the optimal phase factor. These optimization methods provides good PAPR reduction and computational complexity can be reduced simultaneously.

11/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Partial Transmit Sequence Technique (Conventional PAPR Reduction Scheme)

Partial Transmit Sequence is a method for reducing PAPR by divid- ing bit stream in to few sub-blocks, then multiply the sub-blocks with few combination of phase rotation vectors and then finally choose the lowest PAPR in each sub-blocks. The input signal (candidate signal) is the sum of the products of phase rotation vector and corresponding sub-block. Thus, the can- didate signal is given by xc =

M

• m=1

bc

mxm =

• xc

0 , xc 1 , ........, xc N−1

T (3) where c = 1, 2, ..C

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

Figure 3: Traditional Partial Transmit Sequence Technique

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Introduction Proposed Method Experimental Results Conclusion References Orthogonal Frequency Division Multiplexing Peak to Average Power Ratio PAPR Reduction Techniques Traditional Partial Transmit Sequence Technique

4 5 6 7 8 9 10 11 10

−3

10

−2

10

−1

10 PAPR

0 [dB]

Pr(PAPR>PAPR

0)

16−QAM CCDF of OFDMA, 256−point 3000−blocks No of subblocks= 1 No of subblocks= 2 No of subblocks= 4 No of subblocks= 8 No of subblocks=16

Figure 4: PAPR vs CCDF of Traditional Partial Transmit Sequence

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Introduction Proposed Method Experimental Results Conclusion References harmony search algorithm improved harmony search algorithm

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

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Introduction Proposed Method Experimental Results Conclusion References harmony search algorithm improved harmony search algorithm

Harmony Search Algorithm

The harmony search Algorithm idealizes the improvisation process by a skilled musician.When a musician is improvising, a musician has three possible choices [1]: Play any famous piece of music (a series of pitches in harmony) exactly from the memory which corresponds to harmony mem-

• ry.

Play something similar to a known piece (thus adjusting the pitch slightly) which corresponds to pitch Adjusting. Compose new or random notes which corresponds to random- ization.

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Introduction Proposed Method Experimental Results Conclusion References harmony search algorithm improved harmony search algorithm

Improved Harmony Search Algorithm

Improved Harmony Search Algorithm attempts to enhance accuracy and convergence rate of harmony search by adjusting PAR and bw to be up- dated dynamically as [2]- PAR(k) = PARmin + PARmax − PARmin K

• k

(4) bw(k) = bwmax exp ln (bwmin/bwmax) K

• k

(5)

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Introduction Proposed Method Experimental Results Conclusion References harmony search algorithm improved harmony search algorithm

Proposed Method

The steps of proposed IHS-PTS algorithm are as follows: Parameter initialization : The specified parameters are : harmony memory considering rate (HMCR) = 0.95; harmony memory size (HMS) i.e. number of solu- tions available in memory = 16; pitch adjustment rate (PAR) =0.05; number of musical instruments i.e. number of each phase factor vec- tor = M; pitch range of each instrument i.e. value range of each phase factor ={+1, −1} and stopping criterion K. Harmony Memory (HM) initialization : Harmony memory is initialized with possible set of phase vectors .Each row in the matrix is a set of solution by evaluating the objective func- tion between lower and upper bound values which results in randomly populating the solutions for each structure i(= 1, 2, ....HMS), the ob- jective function f (x) is evaluated, which will take the value from the collection {+1, −1}.

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Introduction Proposed Method Experimental Results Conclusion References harmony search algorithm improved harmony search algorithm

New solution construction : Harmony improvisation is done by creating a new harmony vector using IHS algorithm and updating the parameter values of PAR and bw in each iteration. Update HM : Updation of the harmony vector is done by comparing the new har- mony vector with the worst fit solution .If the new vector is better than the worst solution , then it is replaced by the new harmony vector. Stopping criterion : Above Algorithm is repeated till the total number of function evalu- ations K is reached, otherwise step 2 is repeated.

19/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References simulation parameters subcarrier variation iteration variation

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

20/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References simulation parameters subcarrier variation iteration variation

Table 1: Simulation Parameters

Simulation Parameters Type/Value Number of sub-carriers (N) 256, 512 Number of sub-blocks (M) 8, 16 OFDM Blocks 10,000 Oversampling Factor (L) 4 Bits per symbol (b) 4 PAPR in db 4 to 11 Harmony Memory Size (HMS) 16 Harmony Memory Consideration Rate (HMCR) 0.95 Pitch Adjustment Rate (PAR) 0.05 Bandwidth of adjustment (bw) 0.2 Constellation Size 16-QAM

• No. of iterations (K)

10, 20

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Introduction Proposed Method Experimental Results Conclusion References simulation parameters subcarrier variation iteration variation

4 5 6 7 8 9 10 11 10

−2

10

−1

10 PAPR

0[dB]

Pr(PAPR>PAPR

0)

HS−PTS FF−PTS IHS−PTS Original OFDM PTS

(a) N=256, M=8, b=4

4 5 6 7 8 9 10 11 10

−2

10

−1

10

PAPR0[dB] Pr(PAPR>PAPR

0)

HS−PTS FF−PTS IHS−PTS Original OFDM PTS

(b) N=512, M=8, b=4

Figure 5: CCDF vs PAPR performance of 16-QAM OFDM PTS system with variation in subcarriers

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Introduction Proposed Method Experimental Results Conclusion References simulation parameters subcarrier variation iteration variation

4 5 6 7 8 9 10 11 10

−2

10

−1

10 PAPR

0[dB]

Pr(PAPR>PAPR

0)

HS−PTS FF−PTS IHS−PTS Original OFDM PTS

(a) N=256, M=8, b=4, iter =10

4 5 6 7 8 9 10 11 10

−2

10

−1

10 PAPR

0[dB]

Pr(PAPR>PAPR

0)

HS−PTS FF−PTS IHS−PTS Original OFDM PTS

(b) N=256, M=8, b=4, iter =20

Figure 6: CCDF vs PAPR performance of 16-QAM OFDM PTS system with variation in iterations

23/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

24/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

Conclusion

From all the simulation results it is evident that IHS-PTS method provides optimum phase factor combinations with reduced PAPR per- formance as compared to HS-PTS & FF-PTS methods. The searching complexity is also less in HS-PTS and IHS-PTS as compared to T-PTS. The controlling parameters requirement are very less in HS PTS, so it is easily adjustable. IHS algorithm is one of the types of population based algorithms; this means that a number of harmonics groups can be used in parallel. Proper parallelism frequently leads to better implantation with higher efficiency.

25/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

Overview

1

Introduction

2

Proposed Method

3

Experimental Results

4

Conclusion

5

References

26/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

References I

[1]

• J. Gao, J. Wang, B. Wang, and X. Song, “A Papr Reduction Algorithm Based on Harmony Research for

Ofdm Systems,” Procedia Engineering, vol. 15, pp. 2665–2669, Jan. 2011. [Online]. Available: http://linkinghub.elsevier.com/retrieve/pii/S1877705811020029 [2]

• M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving
• ptimization problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567–1579, May 2007.

[Online]. Available: http://linkinghub.elsevier.com/retrieve/pii/S0096300306015098 [3]

• O. M. Alia and R. Mandava, “The variants of the harmony search algorithm: an overview,” Artificial

Intelligence Review, vol. 36, no. 1, pp. 49–68, Jan. 2011. [Online]. Available: http://link.springer.com/10.1007/s10462-010-9201-y [4] Ramjee Prasad, OFDM for Wireless Communications Systems. Artech House Universal Personal Communications Library, 2004. [5]

• S. G. Kang, S. Member, and J. G. Kim, “A Novel Subblock Partition Scheme for Partial Transmit Sequence

OFDM,” IEEE Transactions on Broadcasting, vol. 45, no. 3, p. 333, 1999. 27/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

References II

[6]

• M. Lixia, M. Murroni, and V. Popescu, “PAPR reduction in Multicarrier Modulations using Genetic

Algorithms,” in 12th International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2010, 2010, pp. 938–942. [7]

• J. Gao, J. Wang, B. Wang, and X. Song, “Minimizing PAPR of OFDM Signals Using Suboptimal Partial

Transmit Sequences,” 2012 IEEE International Conference on Information Science and Technology Wuhan, Hubei, China; March 23-25, 2012, pp. 776–779, 2012. [8]

• S. H. Muller, R. W. Bauml, R. E. H. Fischer, and J. B. Huber, “OFDM with reduced peak-to-average power

ratio by multiple signal representation *,” In Annals of Telecommunications,, vol. 52, pp. 58–67, 1997. [9]

• D. Shuyan, S. Ruo, L. Shibao, and G. Zhaozhi, “An Optimization Algorithm for PAPR Reduction in OFDM

System Based on Tabu Search,” pp. 317–320, 2013. [10]

• H. H. Y. Huang, H.-L. Hung, and Y.-F. Huang, “Peak-to-average power ratio reduction in orthogonal

frequency division multiplexing system using differential evolution-based partial transmit sequences scheme,” IET Communications, vol. 6, no. 11, p. 1483, 2012. [Online]. Available: http://digital-library.theiet.org/content/journals/10.1049/iet-com.2010.0997 28/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

Introduction Proposed Method Experimental Results Conclusion References

References III

[11]

• L. Cimini and N. Sollenberger, “Peak-to-average power ratio reduction of an OFDM signal using partial

transmit sequences,” IEEE Communications Letters, vol. 4, no. 3, pp. 86–88, Mar. 2000. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=831033 [12]

• E. M. Kermani, H. Salehinejad, and S. Talebi, “PAPR reduction of OFDM signals using harmony search

algorithm,” 2011 18th International Conference on Telecommunications, pp. 90–94, May 2011. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=5898991 [13] H.-l. Hung and T.-h. Tan, “Performance of Particle Swarm Optimization Techniques on PAPR Reduction for OFDM Systems,” in 2008 IEEE International Conference on Systems,Man and Cybernetics (SMC 2008), 2008, pp. 2390–2395. [14]

• C. Tellambura, “Improved phase factor computation for the PAR reduction of an OFDM signal using PTS,”

IEEE Communications Letters, vol. 5, no. 4, pp. 135–137, Apr. 2001. [Online]. Available: http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=917092 [15]

• S. H. Han, S. S. Member, and J. H. Lee, “PAPR Reduction of OFDM Signals Using a Reduced Complexity

PTS Technique,” IEEE Signal Processing Letters, vol. 11, no. 11, pp. 887–890, 2004. 29/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

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References IV

[16]

• Y. S. Cho, J. Kim, W. Y. Yang, and Chung G. Kang, MIMO-OFDM wireless communications with MATLAB.

John Wiley & Sons, Inc., 2010. [17]

• Y. Wang, W. Chen, C. Tellambura, and S. Member, “A PAPR Reduction Method Based on Artificial Bee

Colony Algorithm for OFDM Signals,” IEEE transactions on wireless communications, vol. 9, no. 10, pp. 2994–2999, 2010. [18]

• J. H. L. Seung Hee Han,, “An overview of peak-to-average power ratio reduction techniques for multicarrier

transmission,” IEEE Wireless Communications, vol. 45, no. April, pp. 56–65, 2005. [19]

• S. Muller and J. Huber, “OFDM with reduced peak-to-average power ratio by optimum combination of

partial transmit sequences,” Electronics Letters, vol. 33, no. 5, pp. 368–369, 1997. 30/31 Mangal Singh, Sarat Kumar Patra 12/03/2014 BICT 2014 Boston, Massachusetts, United States

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