# Two novel low complexity schemes for PAPR reduction in OFDM systems using cyclically shifted time domain sequences.

IntroductionOFDM is a widely preferred multiplexing scheme for several broadband wireless data transmission systems including Digital Video Broadcasting--Terrestrial (DVB-T), Digital Audio Broadcasting (DAB), Wireless Local Area Networks (WLANs), Wireless Microwave Access (WiMAX), Wireless Metropolitan Area Networks (WMANs) and 4G Wireless Systems (Jiang and Wu, 2008). However the envelope variations of an OFDM signal results in large PAPR and demands an expensive High Power Amplifier (HPA) with large dynamic range in order to perform linear amplification of an OFDM signal. Hence PAPR reduction ahead of being fed into the amplifier is desired in OFDM systems to employ efficient HPA such that the overall modulation process is effective. Several solutions were suggested by researchers to minimize the probability of occurrence of large PAPR in OFDM signals including Clipping and filtering method (Armstrong 2002), SLM (Bauml et al., 1996), PTS (Muller and Huber, 1997), Companding Scheme (Huang et al., 2004) and certain time domain methods.

2. Ofdm System and Papr Problem:

A vector of complex valued signals X = [[X.sub.0], [X.sub.1],...,[X.sub.n-1]] is created by mapping the information bit stream to the symbols based on modulation constellation like M-ary Phase Shift Keying (MPSK) or M-ary Quadrature Amplitude Modulation (MQAM). OFDM signal is generated by super positioning the N complex symbols modulated N orthogonal subcarriers each of which consumes equal bandwidth and have a fixed frequency spacing of [delta]f = 1/(NT), where NT refers to useful data period. The time domain OFDM signal is mathematically expressed as

x(t) = 1/[square root of N] [N-1.summation over (m=0)][X.sub.m][e.sup.j2[pi][delta]fmt]

Where m = 0, 1,...,(N - 1).

While the OFDM signal in discrete time domain which will be used in the rest of the paper is given as

x(t) = 1/[square root of N] [N-1.summation over (m=0)][X.sub.m][e.sup.j2[pi]km/LM]

Where k = 0, 1,...,(N - 1) and L is oversampling factor.

PAPR of an OFDM signal is written as

PAPR = Max[[absolute value of[x.sub.m]].sup.2]/E{[[absolute value of[x.sub.m]].sup.2]}

Where E{[[absolute value of[x.sub.m]].sup.2]} is the average power of the OFDM symbol x.

3. Related Work:

PAPR reduction is performed by employing some properties or methods in time domain to the original OFDM signal so that the alternate candidate signals are generated and the candidate with lowest PAPR is selected for transmission.

Generation of candidates in time domain includes computing the product of circular convolution of the OFDM data and IFFT of optimized cyclically shifted phase sequences (OCSPS) (Lu et al., 2007). While Low Complexity PAPR reduction schemes namely linear symbol combining technique needs one IFFT block per OFDM symbol (Alsusa and Yang, 2008) and Time Domain Sequence Superposition (TDSS) demands two IFFT blocks were introduced (Yang et al., 2008). A scrambling technique, namely selective time domain filtering generates candidates by employing filter banks but data recovery at the receiver requires pilot tone channel estimation and demodulation techniques (Du et al., 2009).

In this paper, a time domain based PAPR reduction technique is proposed to generate multiple candidates each with different PAPR values by employing cyclically shifted sequences. Finally the candidate with minimum PAPR is selected for transmission. The rest of the paper is organized as follows. Section 4 proposes the two LC schemes based on cyclically shifted sequences for PAPR minimization in OFDM system. Section 5 elaborates on the simulation result of the proposed schemes. Section 6, specifies the computational complexity involved in the proposed methods while conclusion is reported in Section 7.

4. Proposed LC Schemes for Papr Reduction Using Cyclically Shifted Sequences:

The proposed method employs a basic signal processing operation in time domain, which involves linear combination of one OFDM sequence with cyclically shifted and scaled version of other OFDM sequence. The first method employs CSS with varied delays and fixed phase rotation vector defined by the scaling factor while the second method employs fixed delay and calculates the optimum phase factor such that candidate with minimum PAPR is produced.

4.1. Linear combination of CSS with different delays (LCCSS-D):

Let [x.sup.k] denote the time domain OFDM signal produced by using conventional SLM scheme. In the proposed LC method one time domain sequence [x.sup.1] is fixed and the other sequence [x.sup.2] is cyclically to generate new sequence [x.sup.2.sub.m,cs] is given by

[x.sup.2.sub.m,cs] = shift [[x.sup.2](m x CS)]

Where CS denotes the cyclically shifting number defined as CS [member of] (1,2,...,LN) and m [member of] (1,2,... (LN - 1/cs)).

[FIGURE 1 OMITTED]

Equivalent candidates of an OFDM signal generated by linear superpositioning [x.sup.1] with [x.sup.2.sub.m,cs] is given as [[??].sub.m] = [x.sup.1] + [[alpha].sup.m] [x.sup.2.sub.m,cs]

Where [alpha] is a linear scaling factor defined between 0 and 1. The number of candidates generated can be adjusted by varying the parameters k and CS.

The candidate with minimum PAPR is transmitted along with the scaling factor and cyclic shifting number to the receiver.

4.2. Linear combination of CSS with optimal phase factors (LCCSS-OPF):

Assume a random phase sequence of length L given as [c.sub.k] = [[c.sub.0], [c.sub.v],...,[c.sub.L-1]] where [c.sub.k] = [e.sup.j[]]k and [[].sub.k] is uniformly distributed in the interval [0,2[pi]]. The periodic extension of [c.sub.k] is given by

c((k))L = [i=[infinity].summation over (i=-[infinity])][c.sub.k+iL]

Where c[((k)).sub.L] is k mod L. The first N elements of c[((k)).sub.L] are chosen using a rectangular window to form a N length phase sequence in the following manner

[b.sub.k] = c[((k)).sub.L].[r.sub.k]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Since N = ML the phase sequence [b.sub.k] is of length N and contains M periods of c[((k)).sub.L]. L different Cyclically shifted phase sequence, [b.sup.(l).sub.k] with L samples are generated in the following manner

[b.sup.(l).sub.k] = [i=[infinity].summation over (i=-[infinity])][c.sub.k+iL].[r.sub.k], 1 = 0,1,...,(L - 1) and k = 0,1,...,(N - 1)

and are employed in the proposed method for PAPR reduction in OFDM systems.

[FIGURE 2 OMITTED]

The candidates generated based on Cyclically Shifted Sequences (CSS) with optimal phase factors [b.sup.(l).sub.k] is given by

[[??].sub.m] = x + [D.summation over (k=l)][x.sup.2.sub.m,cs].[b.sup.(l).sub.k]

The steps involved in LCCSS-OPF is given below

(i) Compute the time domain sequence [x.sub.n] using one N point IFFT, i.e., [x.sub.n] = IFFT{[X.sub.K]}.

(ii) Generate the cyclically shifted sequence.

(iii) Calculate the optimal phase sequence [b.sup.(l).sub.k] using eqn. (8)

(iv) Compute the candidates using eqn (9).

(v) Select the candidate [[??].sub.m] with minimum PAPR.

6. Simulation Result and Numerical Analysis:

The proposed CSS assisted PAPR reduction schemes are evaluated by performing several simulations on [10.sup.5] OFDM symbols that are modulated using randomly generated orthogonal subcarriers and compared with the conventional SLM and PTS scheme with number of subblocks, M = 2 and M = 4.

6.1. CCDF vs. PAPR:

MATLAB is used for calculating the Complementary Cumulative Distributive Function (CCDF) of an OFDM signal (CCDF = PAPR > PAPR0), which is considered as a comprehensive parameter to estimate the PAPR reduction performance of any method. The plot for CCDF vs. PAPR is given in Fig. 1. The PAPR reduction performance of the proposed LCCSS-D is better than SLM scheme and PTS (M = 2) by 1.08 dB and 0.49 dB respectively. While LCCSS-OPF outperforms LCCSS-D, SLM and PTS schemes. The LCCSS-OPF's PAPR reduction performance is better than SLM, PTS (M = 2 and M = 4) and LCCSS-D by 2.28 dB, 1.69 dB, 0.15 dB and 1.2 dB respectively.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

6.2. BER vs. SNR:

BER performance of the proposed schemes are compared with that of conventional SLM and PTS scheme in Additive White Gaussian Noise (AWGN) channel and is given in Fig. 2. Since the phase rotation vectors have different magnitude, the signal X yields different gains on different sub carriers which leads to degradation in BER performance for large M. The BER performance of LCCSS-OPF is better than PTS scheme (M = 4) and slightly degraded compared to PTS scheme (m = 2). While LCCSS-D's BER performance is better than PTS (M = 4 and M = 2) and LCCSS-OPF.

6. Computational Complexity:

The number of IFFT operation in PTS and SLM scheme is equal to that of statistically independent random sequence and the product of number of sub blocks and N respectively whereas the proposed method requires just one IFFT operation. While the number of complex additions and multiplications involved in the proposed methods are compared with that of SLM and PTS Schemes and tabulated in the Table 1.

Where M refers to number of sub blocks and D refers to number of shift.

7. Conclusion:

Two LC distortion less schemes for PAPR reduction is proposed in this paper which employs CSS in time domain to compute the candidate signal with reduced PAPR. The BER and PAPR reduction performance of both the proposed methods are compared with that of conventional PTS and SLM schemes. LCCSS-D scheme achieves a PAPR reduction performance of 2.7 dB while LCCSS-OPF scheme achieves a PAPR reduction performance of 4.07 dB compared with that of the original OFDM signal.

References

Alsusa, E. and L. Yang, 2008. A Low-Complexity Time-Domain Linear Symbol Combining Technique for PAPR Reduction in OFDM Systems, IEEE transactions on Signal Processing, 56(10): 4844-4855.

Armstrong, J., 2002. Peak-to-average power ratio for OFDM by repeated clipping and frequency domain filtering, Electronics Letters, 38(8): 246-247.

Bauml, R.W., R.F.H. Fischer and J.B. Huber, 1996. Reducing the peak-to-average power ratio of multicarrier modulation by selected mapping, IEEE Electronics Letters, 32(22): 2056-2057.

Du, Z., N.C. Beaulieu and J. Zhu, 2009. Selective Time-Domain Filtering for Reduced-Complexity PAPR Reduction in OFDM, IEEE transactions on Vehicular Technology, 58(3): 1170-1176.

Jiang, T. and Y. Wu, 2008. "An overview: Peak-to average power ratio reduction techniques for OFDM signals," IEEE transactions on Broadcasting, 54(2): 257-268.

Huang, X., J. Lu, J. Zheng, K.B. Letaif and J. Gu, 2004. "Companding Transform for reduction in peak-to-average power ratio of OFDM signals," IEEE transactions on Wireless Communications, 3(4): 2030-2039.

Lu, G., P. Wu and D. Aronsson, 2007. Peak-to-average power ratio reduction in OFDM using cyclically shifted phase sequences, IET Communications, 1(6): 1146-1151.

Muller, S.H. and J.B. Huber, 1997. "OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences," Electronics Letters, 33(5): 368-369.

Yang, L., K.K. Soo, Y.M. Siu and S.Q. Li, 2008. A low complexity selected mapping scheme by use of time domain sequence superposition technique for PAPR reduction in OFDM systems, IEEE transactions on Broadcasting, 54(4): 821-824.

(1) Arvind Chakrapani and (2) Dr. V. Palanisamy

(1) Assistant Professor, Department of ECE, Tamilnadu College of Engineering, Coimbatore, Tamilnadu, India (2) Principal, Info Institute of Engineering, Coimbatore, Tamilnadu, India

Corresponding Author: Arvind Chakrapani, Assistant Professor, Department of ECE, Tamilnadu College of Engineering, Coimbatore, Tamilnadu, India

Corresponding Author: Arvind Chakrapani, Assistant Professor, Department of ECE, Tamilnadu College of Engineering, Coimbatore, Tamilnadu, India

Table 1: Computational complexity comparison between PTS, SLM and proposed schemes. Schemes No. of Complex No. of Complex Additions Multiplications PTS MN[log.sub.2]N 1/2MN[log.sub.2]N SLM N[log.sub.2]N 1/2mog2N LCCSS-D N[log.sub.2]N + 1/2N[log.sub.2]N (M - 1)N LCCSS-OPF N[log.sub.2]N + 1/2N[log.sub.2]N (M - 1)DN

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Title Annotation: | Original Article |
---|---|

Author: | Chakrapani, Arvind; Palanisamy, V. |

Publication: | Advances in Natural and Applied Sciences |

Date: | Oct 1, 2012 |

Words: | 2011 |

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