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  1. 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – INTERNATIONAL JOURNAL OF ELECTRONICS AND 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October, 2013, pp. 207-213 © IAEME: www.iaeme.com/ijecet.asp Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com IJECET ©IAEME A NEW APPROACH IN DISTORTIONLESS TECHNIQUES FOR PAPR REDUCTION IN MULTICARRIER TRANSMISSION SYSTEMS Ms. Shraddha R. Waghmare Electronics and Communication Engineering Department, Dr. Babasaheb Ambedkar College of Engineering and Research, Nagpur (India) Prof. Dr. Shripad P. Mohani Electronics and Telecommunication Engineering Department, College of Engineering, Pune (India) ABSTRACT Orthogonal frequency division multiplexing (OFDM) is a robust and effective multicarrier transmission technique for high speed communication in wireless mobile environment and applications. A major challenging issue in application of OFDM is its high peak to average power ratio (PAPR). Selective mapping (SLM) is one of the promising techniques which offer distortionless PAPR reduction at the cost of bandwidth efficiency and computational complexity. In this work, SLM is modified by using new phase sequences, which are combinations of Centering matrix along with Hadamard and Riemann matrices. Simulation results show that the proposed phase sequences offer improved PAPR reduction and thus outperform some of the previously proposed techniques. Keywords: Centering operation, Multicarrier Systems, Orthogonal Frequency Division Multiplexing (OFDM), Peak to average power ratio (PAPR), Selected Mapping (SLM) I. INTRODUCTION Orthogonal Frequency Division Multiplexing is extensively implemented in various high speed wireless communication standards because of its favorable properties such as high spectral efficiency, robustness to channel fading, capability of handling multipath fading and immunity to impulse interference. Interestingly, OFDM is a combination of modulation and multiplexing. ne major limitation is its large Peak to Average Power Ratio (PAPR). These large peaks cause saturation in power amplifiers at the transmitting end, leading to inter-modulation among the subcarriers, which causes an increase in the out of band (OOB) energy of the spectrum. Hence, to design a cost effective and robust system, it is highly desirable to reduce the PAPR. Reduction of PAPR is a major challenge for which many techniques are proposed in the literature. 207
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME Advancement to the existing Selected Mapping technique for PAPR reduction is done by introducing new set of phase sequences. The proposed phase sequences show enhanced performance with respect to PAPR reduction. II. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING (OFDM) The multicarrier modulation techniques employ several carriers, within the allocated bandwidth, to convey the information from source to destination. Each carrier may utilize one of the several available digital modulation techniques (BPSK, QPSK or QAM) [1]. Generally, an OFDM signal can be represented as: cሺtሻ = ∑୒ିଵ ୬ୀ଴ s୬ ሺtሻ sinሺ2πf୬ tሻ Where: c(t) s୬ ሺtሻ (1) : OFDM signal representation in Time Domain : Symbols mapped to chosen constellation (BPSK/QPSK/QAM) f୬ : Represents the orthogonal frequencies Equation (1) can be thought of as an Inverse Fast Fourier Transform (IFFT) where ‘N’ is the size of IFFT. The Fourier transform breaks a signal into different frequency bins by multiplying the signal with a series of sinusoids. Since the OFDM signal is in time domain (refer (1)), IFFT is the appropriate choice to use at the transmitter. To acquire the original transmitted signal, FFT is performed at the receiver side [2]. III. PEAK TO AVERAGE POWER RATIO (PAPR) The mathematical representation of PAPR of an OFDM signal can be given as – PAPRሼcሺtሻሽ ൌ మ ౣ౗౮ ౥ರ౤ರొషభ│ୡሺ୲ሻ│ మ (2) ୉ቂ│ୡሺ୲ሻ│ ቃ ଶ Where E ቄ│cሺtሻ│ ቅ denotes the expectation of c (t). PAPR can be expressed in ‘dB’ as follows. PAPR (dB) = 10logଵ଴ PAPR ୡሺ୲ሻ (3) Some of the distortion based techniques for PAPR reduction include clipping and filtering, commanding, coding. Selective mapping (SLM), partial transmit sequence (PTS), tone reservation, tone injection, constellation extension are Distortion less Techniques for PAPR reduction. SLM technique improves PAPR statistics of an OFDM signal significantly without any in-band distortion and out-of-band radiation. The selection of proper phase sequences to achieve good PAPR reduction is very important in the SLM technique [3]. IV. SELECTED MAPPING TECHNIQUE (SLM) SLM method is a distortion less probabilistic technique for PAPR reduction. This technique is called distortion less because the quantity with which the actual signal is altered is sent as side information [4] In this method, the original modulated OFDM data block is multiplied element by element with phase sequences; 208
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME Bሺ୳ሻ ൌ ሾb୳,଴ , b୳,ଵ , … … b୳,୒ିଵ ሿ୘ u=1, 0, 2…..U To make the U phase rotated OFDM data blocks X ሺ୳ሻ ൌ ሾX ୳,଴ , X୳,ଵ , … … X୳,୒ିଵ ሿ୘ The classical definition of SLM refers to a random sequence to be used as phase altering sequence [3][4]. Where X୳,୫= X୫ . b୳,୫ , m=0, 1 … N െ 1 All phase rotated OFDM data blocks represent the same information as that of the unmodified OFDM. PAPR is calculated for phase rotated OFDM data blocks by using (2) and (3). Among the modified data blocks, one with the lowest PAPR is selected and transmitted. The information about the selected phase sequence should be transmitted to the receiver as side information. Reverse operation should be performed at the receiver to obtain the original data block [3], [4]. Fig. 1 Block diagram of the SLM scheme in OFDM V. EXISTING PHASE SEQUENCE FOR SLM The Matrices like Hadamard and Riemann are very popular phase sequence generating matrices for SLM techniques [5][6]. A newly introduced matrix called Centering matrix has given so far the best performance as compared to the conventional matrices. [7] 5.1 Centering matrix The centering matrix is a symmetric and idempotent matrix, which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component [7]. The structure of centering matrix (C୬ ) is given by C୬ ൌ I୬ െ 1 O n ୬ Where, I୬ - is the n-by-n identity matrix O୬ - is an n-by-n matrix of all 1's 209
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME VI. PROPOSED PHASE SEQUENCE In this experimentation, combinations of the Centering matrix with the special matrices like Hadamard and Riemann has been explored. The formulation of the new phase sequence generating Matrices is explained below. 6.1 Centering of Hadamard and Riemann Matrices Centering operation on a data matrix is done by multiplying the particular matrix with the Centering matrix. The values of the newly formed data matrices get close to their respective mean values after the centering operation [8]. Centered Hadamard matrix: Centered Riemann matrix: Where, H୬ - Hadamard matrix (n-by-n) C୬ - Centering matrix (n-by-n) C୦ = C୬ * H୬ C୰ = C୬ * R ୬ 6.2 New Phase Matrix In the quest of finding new phase sequences, another combination of centering matrix with the special matrices is formed. The proposed phase sequences are generated by performing elementby-element multiplication of Centering matrix with Hadamard and Riemann matrices. This combination delivers a new set of phase sequences, which offers better results than the other matrices considered in this experimentation. As there is element-by-element multiplication between the two matrices, it has fewer computations than the Centered matrices explained earlier. Instead of using any random sequence as phase sequence, a combination of two standard matrices is being used in this work. This matrix combination can also be generated at the receiver, leading to a reduction in side information, as only the row index number can be sent as side information. Modifications in the existing SLM scheme are introduced by the newly proposed phase sequences. New Hadamard Cୡ୦ሺ୬ୣ୵ሻ = C୬ .* H୬ New Riemann Cୡ୰ሺ୬ୣ୵ሻ = C୬ .* R ୬ VII. SIDE INFORMATION The side information is the most important aspect of the SLM technique. Thus, it is highly essential to save the side information from getting corrupted while it travels through the channel. In this experimentation, the side information is sent in the form of row index or row number of the phase sequence generator matrix, which provides the least PAPR for a particular OFDM symbol [7] [9]. BCH coding is done on the set of side information collected for all the corresponding OFDM symbols. The Bose, Chaudhuri and Hocquenghem (BCH) codes form a large class of powerful random error-correcting cyclic codes. For any positive integers mሺm ൒ 3ሻ and tሺt ൏ 2୫ିଵ ሻ, there exists a binary BCH code with the following parameters: Block Length: n ൌ 2୫ െ 1 Number of parity-check digits: n െ k ൑ mt Minimum distance: d୫୧୬ ൒ 2t ൅ 1 This code is capable of correcting any combination of ‘ ’ or fewer errors in a block of n ൌ 2୫ െ 1 digits. BCH code of size (7, 4) is used in this experimentation. 210
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME VIII. RESULTS Following are the system specifications used commonly for both unmodified OFDM, conventional SLM and modified SLM scheme [12]. The simulation is performed using MATLAB. TABLE I System Specifications Number of input bits Modulation IFFT/FFT size for OFDM s (N) Oversampling Rate Phase altering matrix (U) 20,000 16 QAM 64 4 16-by-16 Side information generated is of 4 bits (log ଶ Uሻ for every OFDM symbol. The CCDF plot in Fig.2 shows the PAPR reduction for each individual phase matrix. It can be observed that the proposed new Riemann matrix performs exceedingly well than other matrices considered in this experimentation. The proposed new Hadamard matrix offers PAPR reduction nearly same as that of the Centering matrix. CCDF plots of PAPR(dB) values 0 Basic OFDM Hadamard Riemann Centering Cent. Hadamard Cent. Riemann New Hadamard New Riemann -1 10 Unmodified Hadamard Riemann Circulant Circulant. Hadamard Circulant Riemann New. Hadamard New. Riemann -1 10 B it E rror Rate P ro b a b ility ,P (P A P R (d B )) > = P A P R o Bit Error Probability curve 0 10 10 -2 10 -3 10 -2 10 -4 1 2 3 4 5 6 7 PAPRo dB 8 9 10 11 10 12 Fig 2. CCDF plots for Different phase matrices 10 20 30 40 Eb/No, dB 50 60 70 Fig 3. BER plots for different phase matrices The Centered Hadamard performs better than original Hadamard and Centered Riemann provides more PAPR reduction than the original Riemann matrix. The proposed New Riemann matrix shows near elimination of peaks from the OFDM signal. PAPR reduction of around 8 dB to 8.5 dB is obtained. Centering matrix shows PAPR reduction more than Riemann (refer Fig. 2) [7]. From this work, it can be stated that the proposed new Riemann matrix performs even better than the Centering matrix. The proposed new Riemann matrix was tested for its PAPR performance on a fixed input bit stream taking different M-QAM constellations and IFFT sizes. Four times oversampling of the modulated symbols is performed before taking IFFT. Following table demonstrates the results. An OFDM symbol is generated using the combinations of M-QAM and IFFT and minimum PAPR (dB) is found. 211
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME IFFT 64 128 256 TABLE II M-QAM 16QAM 32QAM 16QAM 32QAM 16QAM 32QAM Min. PAPR(dB) 0.1643 0.2000 0.0629 0.0613 0.0250 0.0212 It can be observed from Table. II, as the IFFT size increases, the PAPR of the OFDM signal reduces by a significant value. For the same IFFT size, if M-QAM constellation is changed, PAPR of the particular signal does not undergo any major change. The OFDM symbols are transmitted through AWGN channel i.e. AWGN noise is added to the transmitted signal. The robustness of a communication system is determined by the performance of the receiver. The BER vs SNR performance for various phase matrices is compared to that of the unmodified OFDM in Fig. 3. The unmodified original OFDM and SLM with Hadamard and Centering matrix present almost the same performance. BER of the system with proposed new Riemann matrix can be reduced by applying high SNR. As trade-off is usually experienced in communication, here also a trade-off between BER and PAPR performance in the proposed scheme is seen. IX. CONCLUSION In this paper, a modification in the phase sequence for conventional SLM scheme is proposed. The proposed new Riemann phase sequence shows PAPR reduction to a greater extent as compared to that obtained by using other phase altering matrices. It indeed outperforms the already proposed Centering, Riemann and Hadamard matrices, in terms of amount of PAPR reduction in OFDM. The side in formation sent along with the individual OFDM data blocks is the row index number of the selected phase sequence instead of sending the whole of the phase sequence. Thus the bandwidth efficiency and the power consumption of the system is enhanced. However, the proposed phase sequences cause an increase in bit error rate (BER). To reduce the BER, highly powerful error control codes (have the effect of increase in bandwidth) can be used. Use of higher transmit power can be another alternative for BER reduction. So, either of the two resources, signal-to-noise ratio (SNR) or bandwidth, can be used to reduce the BER. REFERENCES Books: [1] Richard Van Nee, Ramjee Prasad, “OFDM for Wireless Multimedia Communication,” Artech House universal personal communication library, Boston, London, pp. 33–37. [2] Charan Langton, “Intuitive guide to principles of communication, Orthogonal Frequency Division Multiplexing Tutorial,” Copyright 2004. Wadsworth, 1993, pp. 123–135. Proceedings Papers: [3] Tao Jiang, and Yiyan Wu “An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals,” IEEE Trans.on Broadcasting. vol.54, No.2, June 2008. [4] D. S. Jayalath and C. Tellambura, “SLM and PTS Peak-Power Reduction of OFDM Signals without Side Information,” IEEE Trans. on Wireless Communications. vol 4, No.5, September 2005. 212
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 5, September – October (2013), © IAEME [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] N.V. Irukulapati, V.K. Chakka and A. Jain, “SLM based PAPR reduction of OFDM signal using new phase sequence,” Electronics Letters, 19th November 2009, vol.45, No. 24 M.Palanivelan, Dr. Sheila Anand and M.Gunasekaran, “Matrix based low Complexity PAPR Reduction in OFDM Systems,” IJECT, vol. 2, Issue 2, June 2011. Thitapha Chanpokapaiboon, Potchara Puttawanchai, and Prapun Suksompong , “Enhancing PAPR Performance of MIMO-OFDM Systems Using SLM Technique with Centering Phase Sequence Matrix,” ECTI Association of Thailand-Conference 2011. Communication Systems Wireless/ Mobile Communications & Technologies, Paper ID 1481. William Revelle, “Matrix Algebra,” Northwestern University January 24, 2007. Marco Breiling, Stefan H. Müller-Weinfurtner, and Johannes B. Huber, “SLM Peak-Power Reduction without Explicit Side Information,” IEEE Communications, vol. 5, No. 6, June2001. Lajos Hanzo, Raymond Steete and,Peter-Marc Fortune, “A subband coding, BCH coding, and 16QAM system for mobile radio speech communication,” IEEE Trans. on Vehicular Technology, vol 39, No. 4, November 1990. Hank Wallace, “Error Detection & Correction using the BCH code,” Copyright (C) 2001. “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications High-speed Physical Layer in the 5 GHz Band,” IEEE STD 802.11a- 1999(R2003) (Supplement to IEEE Std 802.11-1999). Vinay BK, and Sunil MP, “FPGA Based Design & Implementation of Orthogonal Frequency Division Multiplexing Transciever Module Using VHDL”, International Journal of Advanced Research in Engineering & Technology (IJARET), Volume 4, Issue 6, 2013, pp. 70 - 83, ISSN Print: 0976-6480, ISSN Online: 0976-6499, Published by IAEME. K.Muralibabu, Dr.K.Ramanaidu, Dr.S.Padmanabhan and Dr.T.K.Shanthi, “A Novel PAPR Reduction Scheme using Discrete Cosine Transform Based on Subcarrier Grouping in OFDM System”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 3, Issue 3, 2012, pp. 251 - 257, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472, Published by IAEME. Bharti Rani and Garima Saini, “Cooperative Partial Transmit Sequence for PAPR Reduction in Space Frequency Block Code MIMO-OFDM Signal”, International Journal of Electronics and Communication Engineering & Technology (IJECET), Volume 3, Issue 2, 2012, pp. 321 - 327, ISSN Print: 0976- 6464, ISSN Online: 0976 –6472, Published by IAEME. 213