PAPR reduction performance analysis of Optimized Matrix based Phase Sequences in OFDM systems

PAPR reduction performance analysis of Optimized Matrix based Phase Sequences in OFDM systems T.V.Deepan 1, S. Diwaar 2, M. Palanivelan 3,Dr. Sheila Anand 4, [1][2] Student, Dept of ECE, [3] Associate Professor, [4] Dean(Research) Computer Studies, Rajalashmi Engineering College, Chennai, India. [1] deepan.tv@gmail.com [2] appu.diwaar@yahoo.in [3] velan.research@gmail.com [4] sheila.anand@gmail.com ABSTRACT:- Orthogonal Frequency Division Multiplexing (OFDM) is the digital multicarrier modulation scheme for high speed communication systems. One of the major problems in OFDM is the occurrence of high Pea to Average Power Ratio (PAPR). Due to high PAPR the signal leads to out-of-band (OBO) distortion and increase in Bit Error Rate (BER). The reduction in PAPR is desirable in order to obtain the power efficiency of the amplifier at the transmitter. This paper proposes a Matrix based Phase Sequences (MPS) using special matrices for reducing PAPR of the OFDM signals, in addition to greater reduction in computational complexity. This technique does not require the transmission of Side Information (SI) to the receiver for original phase recovery. OFDM system is implemented in several broadband communication systems lie Wireless Local Area Networ (WLAN), Worldwide interoperability for Microwave Access (WiMax), Digital Video Broadcasting (DVB) and Digital Audio Broadcasting (DAB). The results show that the proposed scheme offers better PAPR reduction with less computational complexity. Power Saving gain analysis also performed for the proposed scheme. Key Words:- OFDM, PAPR, MPS, CCDF, OBO 1 INTRODUCTION High speed data communication for wireless system uses OFDM as a promising technique, due to its typical robust performance on frequency selective fading channels and for digital multi-carrier modulations. The multipath fading effects is mitigated by dividing the data into large number of relatively narrowband channels. Digital signal processing has made a greater impact in the development of this scheme. International standards maing use of OFDM for wireless communications [1]-[4] are already established by IEEE 802.11, IEEE 802.16, IEEE 802.20, European Telecommunication Standard Institute (ETSI) and Broadcast Radio Access Networ (BRAN) committees. Pea-to-Average Power Ratio (PAPR) [2] is one of the main drawbacs in OFDM systems. The occurrence of PAPR will mae the power amplifier to drive it to non-linearity which causes in-band & out-of-band (OBO) distortions and affects Bit Error Rate (BER) performance. Various methods for PAPR reduction in OFDM systems have been presented to avoid the occurrence of large PAPR. Partial Transmit Sequences (PTS) and Selective Mapping (SLM) [3] are the most effective schemes to reduce large PAPR. Finding the optimum phase sequence requires the exhaustive search over all combinations of the allowed phase factors and the search complexity increases exponentially with the number of sub blocs. In this paper we propose Matrix based Phase Sequences (MPS) to reduce search complexity of the phase sequence. Further PAPR reduction performance of the proposed scheme is compared with existing probabilistic schemes. 1.1 OFDM OFDM consist of a bloc of N data streams X() (=0, 1,, N-1), of vector X, which will be transmitted in parallel. The complex baseband representation of a multicarrier signal consisting of N subcarriers is given by, x( t) 1 N N 1 0 x ( t), 0 t NT Each baseband subcarrier is given as[4]-[6] (t) e j2f t (2) where ƒ is the th subcarrier frequency. The subcarrier frequencies ƒ are equally spaced as given by f NT (3) Equation (3) helps us to define the parallel disjoint subcarrier to follow Orthogonality. 1.2 PAPR (1) International Academic and Industrial Research Solutions (IAIRS) Page 59

The main problem of OFDM signal is that, it has high Pea to Average Power Ratio (PAPR) due to its nature of multicarrier modulation [6]-[11]. This high PAPR causes an increase in bit error rate and out-of-band (OBO) distortion. PAPR is defined as in equation (4) max 0, T S( t) PAPR S( t) t 2 2 (4) In general, most of the signals wor in discrete time domain signals, therefore we need to oversample the continuous signal x(t) by a factor L, to approximate the value of PAPR [11]-[16]. The L-time oversampled signal and PAPR can be expressed as x 1 1 N n0 N x ( ) where = 0,1,,LN-1 ( ) e n n n j2 n / LN max[ x PAPR ( x 2 2 ) (5) ; = 0,1,,L N-1 (6) ] (7) where ε(.) denotes the average value over the time duration of OFDM symbol. The Cumulative Distribution Function (CDF) and Complimentary CDF (CCDF) of PAPR are commonly used performance measures for PAPR reduction. The probability that the PAPR given by equation (8) exceeds a threshold P 0 nown as CCDF, can then be defined by P (PAPR > P 0 ) = 1- (1-exp (-P 0 )) N (8) This equation (8) assumes that the N time domain signal samples are mutually independent and uncorrelated. The rest of the paper is organized as follows. In section 2, we discuss the existing techniques for PAPR reduction. In section 3, the proposed system is discussed and section 4 shows the simulation results supporting the ideas presented. Finally, the results are summarized in section 5. 2 RELATED WORK 2.1 Partial Transmit Sequence (PTS) PTS is one of the techniques to reduce the PAPR of the OFDM signal. PTS requires M number of IDFT operations for each data bloc which leads to higher computational complexity. The side information required in this scheme is M 1 log 2 W ; m=1, 2, 3.M. (9) resulting in poor bandwidth efficiency. In PTS technique [7],[9] data bloc of N symbols is partitioned into V number of disjoint sub blocs X m =[X m,0, X m,1, X m,v-1 ] T, where m=1,2,3.m, such that X m m X 1 and the sub blocs are combined to minimize the PAPR in time domain. The L-times oversampled time domain signal X m ; m=1,2,3 M,[17] is obtained by taing an IFFT of length VL on X m concatenated with (L-1)V zeros. These are called Partial Transmit Sequences. The time domain signal after combining is given by x'( b) M b m x m m1 (10) The selection of phase factors is limited to a set with a finite number of elements to reduce the search complexity. The set of allowed phase factor is given as, l=0,1,2 W-1 and W is the number of allowed phase factors. Therefore exhaustive phase search is required The time domain signal x can be shown in matrix form as in (11) M (11) The phase sequences are given in matrix form as in (12) International Academic and Industrial Research Solutions (IAIRS) Page 60

(12) It is noted that all the elements of each row of the matrix A are of the same values. To have exact PAPR calculation at least four times oversampling is necessary as the oversampling of x add zeros to the vector, the number of phase sequence to multiply the matrix X will remain the same. 2.2 Selected Mapping (SLM) In SLM technique, the transmitter generates a set of sufficiently different candidate [18] data blocs, all representing the same information as the original data bloc and selects the most favourable one for transmission. In the bloc diagram of SLM as given in figure 1. Each data bloc [3] is multiplied by B number of different phase sequences, each of length N, resulting in B number of modified data blocs. Figure 1: SLM Bloc Diagram Among the modified data blocs, the one with the lowest PAPR is selected for transmission. Information about the selected phase sequence should be transmitted to the receiver as Side Information (SI). At the receiver, the inverse operation is performed to recover the original data. The conventional SLM technique requires B number of IDFT blocs and number of SI bits [1, 9]. This approach is applicable for all types of modulation and any number of subcarriers. PAPR reduction performance is based on the number of phase sequences and the design of the phase sequences 3 PROPOSED SYSTEM The bloc diagram of the proposed OFDM system with Matrix based Phase Sequences (MPS) technique for PAPR reduction is shown in figure 2. MPS is formed based on Riemann and Hilbert matrix [5], [6]. The input data stream is generated from random source. Data is mapped on to Quadrature Amplitude Modulation (QAM) [6]-[8] constellation. These serially mapped symbols are converted into parallel, then symbols are partitioned into sub blocs based on PTS [9]. Each sub-bloc is multiplied with phase sequence generated using MPS technique. Figure 2: Proposed OFDM system with MPS International Academic and Industrial Research Solutions (IAIRS) Page 61

After phase sequence multiplication, the sequence which yields minimum PAPR will be selected and transmitted. In this model, channel noise is assumed to be Gaussian. At the Receiver, phase sequence recovery is done and signals are passed through FFT. DeMapping of symbols is carried out to recover the original data. Receiver can able to recover the data without any side information with the help of special structure of phase sequence matrix. It is seen that, this method greatly reduces the PAPR, phase search complexity and comparable computational complexity [4]. The proposed MPS technique for reduction of PAPR is described as a flow diagram given in figure 3. 3.1 Matrix based Phase Sequence (MPS) Method In Conventional PTS(C-PTS), oversampling will add zeros to the vector, the only section that counts in the phase sequence multiplication will be N elements. The proposed MPS, still has N rows and the oversampling factor does not have any effect on the proposed matrices given in equation (13) b= N/S N/S Dimension of the matrices is S*NL, where S=D, D=1,2,3 D N (14) If the number of allowed phase factor is constant then the value of S [5] depends on the number of sub-bloc V.If the system requires more number of subcarriers essentially we need to go for more number of sub-blocs for better PAPR reduction. (13) Figure 3: Flow diagram of MPS based OFDM System Increase in sub-blocs simultaneously increases the number of phase sequences to optimize. This will lead to greater phase search complexity. In our proposed MPS method, there are N number of phase factors which are formed from International Academic and Industrial Research Solutions (IAIRS) Page 62

Riemann and Hilbert matrix. In this system, even if the number of sub-blocs increases the phase search complexity is reduced with good PAPR reduction. Most of the PAPR reduction techniques use random phase sequences for optimization. This forces transmitter to send Side Information to the receiver. The optimum phase sequence requires N 8 iterations if the N different random phase factors are used, which is not practical. In MPS, we apply the same iteration as applied in C-PTS. If the number of sub-carriers is high for example IEEE 802.16, LTE the number of used sub carries are large, therefore the phase search complexity for such systems are very high. MPS matrix based on Riemann and Hilbert are discussed below. 3.2 MPS based on Riemann Matrix Riemann matrix is formed from the equation, A (n,m) = n-1 if n divides m = -1 otherwise (15) Riemann matrix of order 8x8 is generated from equation (15) as given in (16) R= Riemann matrix in MPS form R= (16) (17) 3.3 MPS based on Hilbert Matrix Hilbert matrix is special ind of Cauchy matrix [8] Cauchy matrix of dimension m x n is of the form as in a ij 1 ; x y i j 1 i m, 1 j n; (18) where x i and y j are elements of field F and Hilbert matrix is calculated from the Cauchy matrix using Hilbert matrix (HL) with order (8 x 8) is generated using equation (18) as given in equation (19) HL= (19) Hilbert matrix in MPS form A= (20) Table 1 compares the obtained original PAPR values with MPS based Riemann and Hilbert matrices. We have considered some random data bloc as input and obtained values show that MPS based Riemann matrix offers better reduction than the MPS based Hilbert matrix. However that MPS based Hilbert matrix method greatly reduces the complexity as compared to the conventional schemes. However this scheme is effective for all types of data blocs. International Academic and Industrial Research Solutions (IAIRS) Page 63

Table 1: Comparison of PAPR Values for various MPS with Original values SAMPLE DATA BLOCK 1 1-1 -1 1 1-1 1-1 -1 1 1 1-1 -1 1-1 1 1-1 1-1 -1 1 ORIGINAL PAPR (db) RIEMANN (db) MPS HILBERT (db) 5.9264 3.0103 5.9001 5.8521 3.1003 5.1435 4.4817 3.001 4.113 4 SIMULATION RESULTS To compare and evaluate the PAPR reduction performance, extensive simulations have been performed based on Matrix based Phase Sequences (MPS) technique using MATLAB. In simulations, an OFDM system has been considered with N=8 and 16, oversampling factor L=4 and Quadrature Amplitude Modulation (QAM) is implemented. The simulation parameters used are given in Table 2. It is seen that, highest PAPR results when all the bits in a data bloc are same and orthogonal. It can be seen from the results that OFDM with MPS wors effectively gives reduced PAPR for all types of data blocs. In the simulation we used 16-QAM baseband modulation scheme. Each modulated symbol is transmitted through N=16 sub carriers by 64-point IFFT and L=4 oversampling is employed to estimate PAPR precisely. To analyze PAPR reduction and power amplifier efficiency, we consider class A power amplifier which is the most linear with power efficiency. Table 2: Simulation Parameters Parameter Specifications Modulation QAM Number of data subcarriers M 8,16 Number of FFT/IFFT points(n) 64 Number of data symbols 16 Over sampling factor L=4 Bandwidth, BW Sampling Frequency, (BW x L) 1MHz 4 MHz Number of Guard Interval Samples 32 Channel Model Gaussian Figure 4: CCDF of PAPR in MPS & PTS with N=8 Figure 4 shows the CCDF of PAPR in the MPS technique with QAM Modulation scheme. It is easy to observe that at 0.001% of CCDF the PAPR value for the C-PTS offers 2 db reduction when compared with actual value of original data International Academic and Industrial Research Solutions (IAIRS) Page 64

blocs. Our proposed MPS with Spectial Matrices performed better in reduction compared to other schemes, as it shows 3 db reduction from the original values. Figure 5:CCDF of PAPR in MPS & PTS with N=16 Figure 5 shows the CCDF of PAPR in the MPS technique with N=16 and QAM Mapping scheme. It is observed that at 0.001% of CCDF the PAPR value for the proposed MPS with Riemann matrix offers 2.7 db reduction when compared with original data blocs. Figure 6 shows the CCDF of PAPR in MPS technique with QAM Mapping scheme. It is observed that, at 0.0001% of CCDF the PAPR value for the conventional SLM offers 1 db reduction when compared with actual value of original data blocs. Our proposed MPS with Spectial Matrices, we found that Riemann Matrix performed better in reduction compared to other schemes also it offers 3 db reduction from the original values. Figure 7 shows the CCDF of PAPR in the MPS technique with N=16 and QAM Mapping scheme. It is seen that at 0.001% of CCDF the PAPR value for the proposed MPS with special matrix offers 2.2dB reduction when compared with actual value of original data blocs. Figure 6:CCDF of PAPR in MPS & SLM with N=8 Figure 8 shows the BER performance under AWGN channel obtained for the proposed MPS and other existing schemes. Figure 7:CCDF of PAPR in MPS & SLM with N=16 We conclude that BER performance of MPS is comparable with conventional schemes at BER = 10-4. International Academic and Industrial Research Solutions (IAIRS) Page 65

Figure 8: BER performance for MPS Table 3 shows the Comparitive study of MPS- Riemann when N=8 and N=16 for various clipping probabilities. Table 3 : Clipping probabilities of MPS-Riemann with N=8 & 16. MPS-Riemann[PAPR in db] Probability N=8 N=16 7.2 7.6 8 8.5 9 9.6 Table 4 : Clipping probabilities of MPS-Hilbert with N=8 & 16. MPS-Hilbert Probability N=8 N=16 7.9 8 8.2 8.6 9.2 9.7 From Table 3 & 4, it is shown that even if the number of subcarriers increases PAPR will not increase in the proposed scheme. The gain saving analysis is one of the important parameter that helps us to study the difference in PAPR reduction. Figure 9 and 10 compares saving gain values for MPS with PTS & SLM. Figure 9: Saving Gain MPS Vs PTS International Academic and Industrial Research Solutions (IAIRS) Page 66

5 4 3 2 1 0 Saving Gain MPS vs SLM Figure 10: Saving Gain MPS Vs PTS 5 CONCLUSION & FUTURE WORK In this paper, the performance of OFDM transmission systems in relation to PAPR, BER and Power saving analysis is evaluated using Matrix based Phase Sequences using special matrices such as Riemann and Hilbert matrix. From the simulation results, it is seen that the proposed technique offers better PAPR reduction with reduced computational and phase search complexity. Also from the analysis of gain saving it is proved that efficiency of power amplifier increases. Side Information is not required to be transmitted to the receiver for recovery. In addition, it is shown that BER performance of the proposed technique offers similar performance with conventional schemes. Further the effect of Out of Band (OBO) distortion can be obtained for the proposed scheme to ensure its required BER performance for OFDM Systems. REFERENCES [ 1] Seung Hee Han, Jae Hong Lee, An Overview Of Pea-To-Average Power Ratio Reduction Techniques For Multicarrier Transmission IEEE Wireless Communications April 2005. [ 2] L.J.Cimini, Jr, and N.R.Sollenberger, Pea-to- Average power ratio reduction of an OFDM signal using PTS, IEEE Communication Letters.. vol. 4, no. 3, pp.86-88.mar. 2000. [ 3] Chih-pengli, Novel low complexity SLM schemes for PAPR reduction in OFDM systems, IEEE Transaction on signal processing, vol 58,5 may 2005. [ 4] L. Yang, R. S. Chen, Y. M. Siu, and K. K. Soo, PAPR reduction of an OFDM signal by use of PTS with low computational complexity, IEEE Trans. Broadcast., vol. 52, no. 1, pp. 83-86, March 2006. [ 5] Pooria Varahram, Borhanuddin Mohd Ali Partial Transmit Sequence Scheme With New Phase Sequence for PAPR Reduction in OFDM Systems IEEE Transactions on Consumer Electronics, Vol 57,No 2,May2011. [ 6] M.Palanivelan, Dr.Sheila Anand, M.Gunasearan, Matrix Based Low Complexity PAPR Reduction In OFDM Systems IJECT Volume 2,Issue 2,Pg no 158-162 June 2011. [ 7] Jun Hou,Jienhua Gc, and Jing Li Pea-to-Average Power Ratio Reduction Of OFDM Signals Using PTS Scheme With Low Computational Complexity IEEE Transactions Broadcasting,VOL.57.N0 1,MARCH 2011. [ 8] Cauchy matrix, Cauchy determinants, Generalization. Available: http://en.wiipedia.org/wii/cauchy_matrix. [ 9] R. J. Baxley and T Zhou., Comparing slected mapping and partial transmit sequence for PAPR reduction, IEEE Trans.Broadcast., vol. 53, no. 4, pp.797-803, December 2007. [ 10] Seran Dursun, Artyom M. Grigoryan, Nonlinear L2-by-3 transform for PAPR reduction in OFDM. [ 11] C. Tellambura, Computation of continuous time PAR of an OFDM signal with BPSK sub carriers, IEEE Communication letters, vol.5, no.5.pp 185-187,may2001. [ 12] D. L. Jones, Pea power reduction in OFDM and DMT via active channel modification, in Proc. Asilomar Conference on Signals, Systems, and Computers, vol. 2, 1999, pp. 1076 1079. [ 13] Hee HS, Hong LJ, An overview of pea-to-average power ratio reduction techniques for multicarrier International Academic and Industrial Research Solutions (IAIRS) Page 67

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