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  1. 1. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532Comparitive Study Of Papr Of Dht-Precoded Ofdm System With Dft & Wht BhanuPavanKumar.M B.Vinod Naik.M-Tech.,Assistant Prof.Abstract High Peak to Average Power Ratio candidate for Wireless Asynchronous Transfer(PAPR) is one of the major drawbacks in Mode (WATM).Orthogonal Frequency Division Multiplexing However, among others, the Peak to(OFDM). The High PAPR increases the Average Power Ratio (PAPR) is still one of thecomplexity of Analogue to Digital (A/D) and major drawbacks in the transmitted OFDM signalDigital to Analogue (D/A) convertors and also [2]. Therefore, for zero distortion of the OFDMreduces the efficiency of RF High Power signal, the HPA must not only operate in its linearAmplifier (HPA). In this paper we present the region but also with sufficient back-off. Thus, thecomparative PAPR Analysis of DHT-Precoded RF High Power Amplifier (HPA) with a largeOFDM system with other systems for Different- dynamic range are required for OFDM system.QAM. We compare the computer simulation These amplifiers are very expensive and are majorresults of DHT precoded OFDM system with cost component of the OFDM system. Thus, if weDFT precoded OFDM system, Walsh reduce the PAPR it not only means that we areHadamard Transform (WHT) precoded OFDM reducing the cost of OFDM system and reducingsystem, Selected Mapping (SLM) based OFDM the complexity of the Analogue to Digital (A/D)system and OFDM conventional. The results and Digital to Analogue (D/A) convertors, but alsoobtained show that the PAPR of DHT precoded increasing the transmit power, thus, for same rangeOFDM system is lower than WHT precoded improving received Signal to Noise Ratio (SNR),OFDM system, SLM-OFDM system and OFDM or for the same SNR mproving range.conventional. We also concluded in this paper A large number of PAPR reductionthat DFT precoded OFDM system has zero techniques have been proposed in the literature.PAPR. Which stands to be an ideal one for the Among them, schemes like constellation shapingtime being. [3], coding schemes [4,5], phase optimization [6], nonlinear companding transforms [7], ToneIndex Terms-- PAPR, DFT precoder, DHT Reservation (TR) and Tone Injection (TI) [8,9],precoder, HPA clipping and filtering [10], Partial Transmit Sequence (PTS) [11], Precoding based SelectedI. INTRODUCTION Mapping (PSLM) [12], precoding based techniques Orthogonal Frequency Division [13] and Selected Mapping (SLM) [14] areMultiplexing (OFDM) is a multicarrier popular.transmission scheme that has become the In [10] Wang and Tellambura proposed atechnology of choice for next generation wireless soft clipping technique which preserves the phaseand wireline digital communication systems and clips only the amplitude. They also put a lot ofbecause of its high speed data rates, high spectral effort to characterize the performance and discoverefficiency, high quality service and robustness some properties to simplify the job. However, theagainst narrow band interference and frequency PAPR gain is only estimated by simulations and isselective fading [1]. OFDM thwarts Inter Symbol limited to a specific class of modulation technique.Interference (ISI) by inserting a Guard Interval (GI) In [11] Han and Lee proposed a PAPRusing a Cyclic Prefix (CP) and moderates the reduction technique based on Partial Transmitfrequency selectivity of the Multi Path (MP) Sequence technique in which they divide thechannel with a simple equalizer. This leads to frequency bins into sub blocks and then theycheap hardware implementation and makes simpler multiply each sub-block with a constant phasethe design of the receiver. OFDM is widely shift. Choosing the appropriate phase shift valuesadopted in various communication standards like reduces PAPR. The most critical part of thisDigital Audio Broadcasting(DAB), Digital Video technique is to find out the optimal phase valueBroadcasting (DVB), Digital Subscriber Lines combination and in this regard they also proposed a(xDSL), Wireless Local Area Networks(WLAN), simplified search method and evaluated theWireless Metropolitan Area Networks (WMAN), performance of the proposed technique.Wireless Personal Area Networks (WPAN) and In [12] authors developed PSLMeven in the beyond 3G Wide Area Networks technique for PAPR reduction. In this technique(WAN) etc. Additionally, OFDM is a strong Zadoff-Chu based precoder is applied after the 527 | P a g e
  2. 2. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532 multiplication of phase rotation factor and before 2 max xn the IFFT in the SLM-OFDM system. The proposed PAPR  2              (2) PSLM technique is signal independent and it does E[ xn ] not require any complex optimization technique. In [13] authors proposed Zero PAPR Zadoff-Chu where E [.] denotes expectation and the precoder based technique for Single Carrier Complementary Cumulative Distribution Function Frequency Division Multiple Access (SCFDMA). (CCDF) for an OFDM signal can be written as This technique is efficient, signal independent, P ( PAPR  PAPR0 )  1  (1  e  PAPR0 ) N  (3) distortion less, it does not require any optimization algorithm and PAPR is completely eliminated. This paper analyses PAPR of the DHT- where PAPR 0 is the clipping level. This equation Precoding based OFDM system for PAPR can be read as the probability that the PAPR of a reduction. It is organized as follows: Section II symbol block exceeds some clip level PAPR 0 . describes the basics of the OFDM system and PAPR reduction, In Section III we present the proposed system model for PAPR reduction, and III. PROPOSED MODEL A. The Precoding Based OFDM system Section IV presents computer simulation results and section V concludes the paper. II. OFDM SYSTEM & PAPR REDUCTION The OFDM system splits the high speed data stream into a number of parallel low data rate streams and these low rates data streams are transmitted simultaneously over a number of orthogonal subcarriers. Fig.2 Block diagram of pre IFFTbased OFDM system. Fig. 2 shows the block diagram of Precoding Based OFDM System. We implemented the Precoding matrix P of dimension N ×N before the IFFT to reduce the PAPR. The Precoding matrix P can be written as Fig.1 Block diagram of OFDM System. Fig. 1 illustrates the block diagram of an OFDM system. Baseband modulated symbols are passed where P is a Precoding Matrix of size N ×N is through serial to parallel converter which generates shown in equation (4). The complex baseband complex vector of size N. We can write the OFDM signal with N subcarriers can be written as complex vector of size N as N 1 1 X  [ X 0 , X 1 , X 2 .......... .. X N 1 ] T x(t )  N  P. X k 0 k .e j 2  kft ,0  t  NT    (5) X is then passed through the IFFT block. The We can express modulated OFDM vector signal complex baseband OFDM signal with N with N subcarriers as. subcarriers can be written as xN  IFFT {P. X N }              (6) n 1 N _! j *2* * k  X k .e N , n  0,1,2,3,....N  1.  (1) The PAPR of OFDM signal in (5) can be written asxn  2 N k 0 max xn PAPR                 (7 )Here j=  1 and the PAPR of OFDM signal in (1) can 2 E[ xn ] be written as B. The Discrete Fourier Transform (DFT) Precoding 528 | P a g e
  3. 3. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532The DFT of a sequence of length N can be defined IV. SIMULATION RESULTS as We performed extensive simulations in N 1 MATLAB® in order to evaluate the performanceX (k )   x(n).e  j 2  nk , K  0,1,2,...... N  1    (8) of DHT-Precoder based OFDM System , DFT- n 0 Precoder based OFDM System , SLM based The IDFT can be written as OFDM System and Conventional based OFDM N 1 1x ( n)  N  X (k ).e n 0 j 2  nk , K  0,1,2,...... N  1  (9) System. To show the PAPR analysis of DHT- Precoded OFDM system, data is generated  j 2  mn randomly then modulated by M-QAM (where M=16, 32, 64, 256). We compared our simulationwhere pmn  e N ,m and n are integers from results with DFT-Precoded OFDM system on one 0 to _-1 and P is precoding matrix of size N×N hand and also we compared our simulation results shown in equation(4). with WHT-Precoder OFDM system, SLM-OFDM system and OFDM-Original system. To show theC. The Discrete Hartley Transform (DHT) overall performance of the DHT-Precoder basedPrecoding OFDM system for PAPR reduction in MATLAB® The DHT is a linear transform. In DHT N we considered M-QAM for N=64. It is to be notedreal numbers that M-QAM has itself PAPR. x0 , x1 , x2 ,...... xN 1 are transformed in to N real numbers H 0 , H1 , H 2 ,...... H N 1 . According to [15] the N-point DHT can be defined as N 1 2  nk 2  nk H k   xn .[cos( )  sin( )] n 0 N N N 1 2  nk  x(n).cas( )              (10 ) n 0 N where casθ=cosθ+sinθ, and K=0,1,2,...N-1 2  mnpmn  cas( )            (11) N P is precoding matrix of size NXN shown in equation (4), m and n are integers from 0 to N-1.The DHT is also invertible transform which allows us to recover the x n from H k and inversecan be obtained by simply multiplying DHT of H k 1 by . N Fig.3 CCDF comparison of DHT-PrecoderD. Walsh Hardmard Transform Predocing Based OFDM System with DFT-Precoder Based The Hadamard transform (also known as OFDM system, WHT-Precoder Based OFDMthe Walsh–Hadamard transform, Hadamard– System,SLM-OFDM (V=2) System and OFDMRademacher–Walsh transform, Walsh transform, or Original System for 16-QAMWalsh–Fourier transform) is an example of a Figure.3 shows the CCDF comparisons ofgeneralized class of Fourier transforms. It performs DHT-Precoder Based OFDM system with DFT-an orthogonal, symmetric, involutional, linear Precoder Based OFDM system, WHT-Precoderoperation on real numbers (or complex Based OFDM system, SLM-OFDM (with V=2)numbers, although the Hadamard matrices system and OFDM-Original system for N=256. Atthemselves are purely real). 2 clip rate of 10 , the PAPR gain of 3dB, 2.5dB and The Hadamard transform can be regarded 2dB is achieved when we compare DHT-Precoderas being built out of size-2 discrete Fourier Based OFDM system with OFDM-Original system,transforms (DFTs), and is in fact equivalent to a WHT-Precoder Based OFDM system and SLM-multidimensional DFT of size OFDM (with V=2) system respectively for 16- . It decomposes an QAM. However, DHT-Precoding basedarbitrary input vector into a superposition of Walsh OFDM system does not perform as well as DFT-functions. Precoding based OFDM system, which is better than DHT-Precoding based OFDM system by 3dB at same clip rate. 529 | P a g e
  4. 4. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532 Fig.5. CCDF comparison of DHT-Precoder Based OFDM System with DFT-Precoder Based OFDM system, WHT-Precoder Based OFDM System,SLM-OFDM (V=2) System and OFDM Original System for 32-QAM Figure.5 shows the CCDF comparisons of DHT-Precoder Based OFDM system with DFT- Precoder Based OFDM system, WHT-Precoder Based OFDM system, SLM-OFDM (with V=2) system and OFDM-Original system for N=32 At 2 clip rate of 10 , the PAPR gain of 3.5dB, 2.7dB and 2.3dB is achieved when we compare DHT- Precoder Based OFDM system with OFDM- Original system, WHT-Precoder Based OFDM system and SLM-OFDM (with V=2) system respectively for 32-QAM. However, DHT- Precoding based OFDM system does not perform as well as DFT-Precoding based OFDM system,Fig.4. CCDF comparison of DHT-Precoder which is better than DHT-Precoding based OFDMBased OFDM System with DFT-Precoder Based system by 2.7dB. DFT-Precoding based OFDMOFDM system, WHT-Precoder Based OFDM system given rise to nearly same, where theoreticalSystem,SLM-OFDM (V=2) System and OFDM PAPR of 64-QAM is 2.30dB.Original System for 16-QAM Figure.4 shows the CCDF comparisons ofDHT-Precoder Based OFDM system with DFT-Precoder Based OFDM system, WHT-PrecoderBased OFDM system, and OFDM-Original system 2for N=16. At clip rate of 10 , the PAPR gain of3.5dB, 3.3dB and 1dB is achieved when wecompare DHT-Precoder Based OFDM system withOFDM-Original system, WHT-Precoder BasedOFDM system and Original-OFDM (with V=2)system respectively for 16-QAM.. Fig.6. CCDF comparison of DHT-Precoder Based OFDM System with DFT-Precoder Based OFDM system, WHT-Precoder Based OFDM System,SLM-OFDM (V=2) System and OFDM Original System for 64-QAM with N=32 Figure.6 shows the CCDF comparisons of DHT-Precoder Based OFDM system with DFT- Precoder Based OFDM system, WHT-Precoder Based OFDM system, SLM-OFDM (with V=2) system and OFDM-Original system for N=32 At 2 clip rate of 10 , the PAPR gain of 5.2dB, 5dB and 3dB is achieved when we compare DHT-Precoder 530 | P a g e
  5. 5. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532Based OFDM system with OFDM-Original system,WHT-Precoder Based OFDM system and SLM-OFDM (with V=2) system respectively for 64-QAM. However, DHT-Precoding based OFDMsystem perform as well as DFT-Precoding basedOFDM system. DFT-Precoding based OFDMsystem given rise to nearly same, where theoreticalPAPR of 64-QAM is 2.30dB. Fig.8. CCDF comparison of DHT-Precoder Based OFDM System with DFT-Precoder Based OFDM system, WHT-Precoder Based OFDM System,SLM-OFDM (V=2) System and OFDM Original System for 256-QAM with N=256.Fig.7. CCDF comparison of DHT-Precoder Figure.8 shows the CCDF comparisons ofBased OFDM System with DFT-Precoder Based DHT-Precoder Based OFDM system with DFT-OFDM system, WHT-Precoder Based OFDM Precoder Based OFDM system, WHT-PrecoderSystem,SLM-OFDM (V=2) System and OFDM Based OFDM system, SLM-OFDM (with V=2)Original System for 64-QAM with N=64. system and OFDM-Original system for N=256. At Figure.7 shows the CCDF comparisons of 2DHT-Precoder Based OFDM system with DFT- clip rate of 10 , the PAPR gain of 2.4dB, 1.7dBPrecoder Based OFDM system, WHT-Precoder and 1.8dB is achieved when we compare DHT-Based OFDM system, SLM-OFDM (with V=2) Precoder Based OFDM system with OFDM-system and OFDM-Original system for N=32 At Original system, WHT-Precoder Based OFDM 2 system and SLM-OFDM (with V=2) systemclip rate of 10 , the PAPR gain of 3.8dB, 3.6dB respectively for 256-QAM. However, DHT-and 1dB is achieved when we compare DHT- Precoding based OFDM system does not performPrecoder Based OFDM system with OFDM- as well as DFT-Precoding based OFDM system,Original system, WHT-Precoder Based OFDM which is better than DHT-Precoding based OFDMsystem and SLM-OFDM (with V=2) system system by 0.2dB at same clip rate. If comparison torespectively for 64-QAM. However, DHT- table 1, DFT-Precoding based OFDM system givenPrecoding based OFDM system perform as well as rise to nearly same, theoretical PAPR of 256-QAMDFT-Precoding based OFDM system. DFT- is 4.23dB.Precoding based OFDM system given rise to nearly Thus, it can be concluded that DHT-same, where theoretical PAPR of 64-QAM is Precoding based OFDM system performs better2.30dB. than most of the popular PAPR reduction schemes for OFDM system, except DFTPrecoding based OFDM system. V. CONCLUSION In this paper, we made a comparative study PAPR of DHT-Precoded OFDM system with DFT & WHT(where M=16, 32, 64, 256). Matlab simulation shows that DHT-Precoded OFDM 531 | P a g e
  6. 6. BhanuPavanKumar.M/ International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 1, January -February 2013, pp.527-532System shows better PAPR gain as compared to Modulation”, PhD thesis, University ofOFDM-Original system, WHT-Precoder Based Stanford, 1999.OFDM system and Precoder based OFDM system [9] Seungsoo Yoo, Seokho Yoon, S.Yongrespectively. Thus, it is concluded that DHT Kim, and Iickho Song, “A novel PAPRPrecoder Based OFDM System shows better PAPR reduction scheme for OFDM systems:reduction then WHT-Precoder Based OFDM Selective mapping of partial tonesSystem, Precoder based-OFDM System and (SMOPT)”, IEEE Trans. ConsumerOFDM-Original system for MQAM and the PAPR Electronics, vol. 52, no. 1, pp.40–43, Feb.can also be reduced with the decrease of the no.of 2006.sub carriers used in the specified modulation [10] Luqing Wang and Chintha Tellambura ,”Arechnique. Additionally, the DHT-Precoded OFDM Simplified Clipping and Filteringsystem does not require any power increase, Technique for PAR Reduction in OFDMcomplex optimization and side information to be Systems”, Signal Processing Letters, IEEEsent for the receiver. , vol.12, no.6, pp. 453-456, June 2005. [11] S.Hee Han and J.Hong Lee, "PAPRREFERENCES Reduction of OFDM Signals Using a [1] Yiyan Wu and Zou Y. William, Reduced Complexity PTS Technique", “Orthogonal frequency division Signal Processing Letters, IEEE, Vol.11, multiplexing: A multi-carrier modulation Iss.11, Nov. 2004, Pages: 887- 890. scheme”, IEEE Trans. Consumer [12] Varun Jeoti and Imran Baig, “A Novel Electronics, vol. 41, no. 3, pp. 392–399, Zadoff-Chu Precoder Based SLM Aug. 1995. Technique for PAPR Reduction in OFDM [2] R.van Nee and A. de Wild, “Reducing the Systems”, invited paper, Proceedings of Peak-To-Average Power Ratio of 2009 IEEE International Conference on OFDM”, Vehicular Technology Antennas, Propagation and Systems (I_AS Conference, 1998. VTC98. 48th IEEE, 2009), 3-5 Dec. 2009, Johor, Malaysia. Volume.3, 18-21 May 1998, pages: 2072- [13] Varun Jeoti and Imran Baig, “Zero PAPR 2076. Zadoff-Chu Precoder Based Technique for [3] Yajun Kou, Wu-Sheng Lu and Andreas SC-FDMA”, invited paper, Proceedings of Antoniou, “A new peak-toaverage power- 2009 IEEE International Conference on ratio reduction algorithm for OFDM Antennas, Propagation and Systems (I_AS systems via constellation extension”, 2009), 3-5 Dec. 2009, Johor, Malaysia. IEEE Trans. Wireless Communications, [14] Robert Bäuml, Robert F. H. Fischer and vol. 6, no. 5, pp. 1823–1832, May 2007. Johannes B. Huber, “Reducing the Peak- [4] Tao Jiang and Guangxi Zhu, to-Average Power Ratio of Multicarrier “Complement block coding for reduction Modulation by Selected Mapping,” Elect. in peak-to-average power ratio of OFDM Letters. vol. 32, no. 22, Oct. 1996. signals” , IEEE Communications [15] R.N. Bracewell, “Discrete Hartley Magazine, vol. 43, no. 9, pp. S17–S22, transform”, J. Opt. Soc. Am., vol.73, no. Sept. 2005. 12, pp. 1832–1835, Dec. 1983. [5] S.Ben Slimane, “Reducing the peak-to- average power ratio of OFDM signals through precoding”, IEEE Trans. Vehicular Technology, vol. 56, no. 2, pp. 686–695, Mar. 2007. [6] Homayoun Nikookar and K.Sverre Lidsheim, “Random phase updating algorithm for OFDM transmission with low PAPR”, IEEE Trans. Broadcasting, vol. 48, no. 2, pp. 123–128, Jun. 2002. [7] Tao Jiang, Wenbing Yao, Peng Guo, Yonghua Song and Daiming Qu, “Two novel nonlinear Companding schemes with iterative receiver to reduce PAPR in multicarrier modulation systems”, IEEE Trans. Broadcasting , vol. 52, no. 2, pp. 268–273, Mar. 2006. [8] J.Tellado-Mourelo, “Peak to Average Power Ratio Reduction for Multicarrier 532 | P a g e

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