PAPR Reduction in Wavelet Based SC-FDMA Using ... - IEEE Xplore

PAPR Reduction in Wavelet Based SC-FDMA Using PTS scheme for LTE Uplink Transmission Ishu, Naresh Kumar Department of Electronics and Communication Engineering University Institute of Engineering and Technology, Panjab University Chandigarh-160036, India

Abstract— Single Carrier Frequency Division Multiple Access (SCFDMA) has become a promising technique for Long Term Evolution (LTE) uplink transmission. SCFDMA is often referred as Discrete Fourier Transform (DFT) spread Orthogonal Frequency Division Multiple Access (OFDMA). The reason for using SC-FDMA for uplink transmissions is its lower Peak to Average Power Ratio (PAPR) performance. Lower PAPR makes the system power efficient, increases coverage area and allows use of small size terminal. Partial Transmit Sequence (PTS) is scheme used for reducing PAPR in different technologies. Analysis has been done using PTS scheme in OFDMA. In this paper, Wavelet based SCFDMA is proposed for analyzing Peak to Average PAPR performance using PTS scheme. Then Analysis is carried out by using different wavelets and different number of carriers. This analysis will show that the further PAPR reduction takes place in wavelet based SCFDMA using PTS scheme. Thus wavelet based SCFDMA gives better PAPR performance instead of DFT based SCFDMA. Keywords—Long term Evolution (LTE); Single carrier Frequency Division Multiple Access (SCFDMA); Orthogonal Frequency Division Multiple Access (OFDMA); Peak to Average Power Ratio (PAPR); Partial Transmit Sequence (PTS)

SC-FDMA has lower PAPR as compared to OFDMA. SCFDMA is DFT pre-coded OFDMA. It is desirable to reduce PAPR of SC-FDMA so as to increase the power efficiency. There are various schemes that are used for reducing PAPR such as block coding, cyclic coding etc. Use of these schemes is only in the specific applications like binary signalling. These cannot be used for large no of subcarriers. Other method of reducing PAPR non-linearly predistorts the signal to combat the high peaks of signal before amplification which in turn results in loss of power efficiency. We are proposing a flexible and distortion less method to reduce PAPR. Partial transmit Sequence (PTS) is one of the attractive method to reduce PAPR. In this method, the input data is optimally phase rotated. This helps in reduction of PAPR. In this paper we are going to use PTS scheme in Wavelet based SC-FDMA [2, 3]. The 1st section briefly introduced about generation of wireless Technologies. Then in following section, basic principle of OFDMA has explained. Application of PTS scheme in OFDMA has also discussed in section 2. The next section 3 describes about the SC-FDMA. The proposed method is explained in section 3. The section 4 explains the parameters which are used to carry out the analysis. The paper is concluded in last section.

I. INTRODUCTION

II. ORTHOGONAL FREQUENCY DIVISION MULTIPLE ACCESS (OFDMA)

The Wireless technologies have been getting experience of 4 or 5 generations since 1970. These technologies have been getting evolved in order to achieve main targets such as high spectral efficiency and more prone to multipath fading. Now a day, Long Term Evolution (LTE) is being used for wireless communication [1]. Single Carrier Frequency Division Multiple Access (SCFDMA) has become an attractive technology for LTE uplink, as it has low Peak to Average Power Ratio (PAPR). The use of Orthogonal Frequency Division Multiple Access (OFDMA) in transmission systems exhibit high peaks. Thus OFDMA transmission systems need large back off for power amplifiers, to keep out of band power below imposed level. Thus OFDMA is not used for uplink transmission as power efficiency is main target to be achieved [2,3].

A. Basic Principle OFDMA has become an attractive scheme in LTE downlink transmissions due to its advantages which are high spectral efficiency, protection against narrow band interference and multipath fading. But for uplink transmissions, it encounters the problem of high PAPR. In OFDMA, the input data splits into the subcarriers which are orthogonal to each other. But with the increase in number of subcarriers, envelope variations take place after IFFT operation. Here, the data is sent on parallel subcarriers which got added in phase. Thus results in higher PAPR. High PAPR value makes the system power inefficient. Power amplifiers needs large back off value for low distortion [3, 4]. The signal with high PAPR value got nonlinearly distorted by power amplifiers. This leads to adjacent channel interference and

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system performance degradation. Thus lower PAPR is desirable [3]. B. Conventional OFDMA System model There are many methods to reduce PAPR value. PTS scheme is one of them. In OFDMA, the input data is partitioned into blocks Xm (m=0, 1,2, . . . ,M-1). Block consists of M symbols. Data carrying symbols are sub carrier mapped onto a set of subcarriers fm (m=0, 1, 2, ….. M-1). Subcarriers are made orthogonal to each other by use of IDFT operation (1) such that fm= mf’, Where f’=1/MT and T is symbol period. Then PAPR is calculated from this transmit sequence. This is represented in equation (2) [5]. ‫ݔ‬௠ ൌ

σ௠ୀெିଵ ܺ௠ ݁ ௝ଶగ௠Ȁெ ௠ୀ଴

n= 0,1,2. . . . ., M-1.

(1)

In a OFDMA symbol, xn is the nth signal component. The PAPR of OFDMA is the ratio of peak to average value of the transmit signal. ܲ‫ ܴܲܣ‬ൌ

ெ௔௫௩௔௟௨௘௢௙௧௥௔௡௦௠௜௧௦௜௚௡௔௟ ஺௩௘௥௔௚௘௣௢௪௘௥௢௙௦௜௚௡௔௟

ൌ

୫ୟ୶ሾȁ௫ሺ௧ሻȁమ ሿ ாሾȁ௫ሺ௧ሻȁమ ሿ

(2)

E [.] is the expected value of average of a transmit signal. C. Partial Transmit Sequence (PTS) in OFDMA PTS is a promising method to reduce PAPR of transmit signal by keeping it distortion less. Figure 1 shows block diagram of OFDMA using PTS. In OFDMA, the input data X is partitioned into disjointed sub blocks Xm where m=0,1,2,.... M-1. These disjointed sub blocks are multiplied with phase weighing vectors. These phase weighing vectors are obtained with optimization algorithm. The minimization of PAPR occurs by optimally combining these sub bocks. This can be expressed in following expression (3) [5, 6]. ܾ௠ ܺ௠ ܺ ᇱ ൌ σ௠ୀெିଵ ௠ୀ଴

III. SINGLE CARRIER FREQUENCY DIVISION MULTIPLE ACCESS (SC-FDMA) A. Background of SCFDMA SC-FDMA has become a preferred technology for LTE uplink transmission. The reason for becoming attractive technology for uplink transmissions is that it has combined advantages of OFDMA like spectral efficiency, less sensitivity to the carrier frequency offset with lower PAPR. OFDMA suffers from the problem of high PAPR. SCFDMA is often referred as DFT spread OFDMA in which subcarriers are transmitted over the channel sequentially rather than in parallel. Thus there occur small variations in instantaneous power of transmitting signal which lowers PAPR. Lower PAPR provides advantage to mobile terminal. This will increase battery life time of mobile phones [8]. Low PAPR is a desirable factor. PAPR in SCFDMA can be improved by using PTS scheme. This scheme can utilize multi domain signal processing. In SC-FDMA, the time domain transmit signal is multiplied with the phase rotation factor as in OFDMA. B. System Model using PTS scheme

(3)

Figure 2 shows the block diagram of SC-FDMA using PTS scheme. The input data is partitioned into various Xm sub blocks where m =0, 1, 2, . . , M-1. These sub blocks are transformed into frequency domain with use of M point DFT operation. This is expressed in following expression (5) [8].

(4)

Y=FM Xm

bm are phase rotating vectors where m=0,1,2...M-1. In time domain, it can be represented as (4) [5, 6] ܾ௠ ‫ݔ‬௠ ‫ ݔ‬ᇱ ൌ σ௠ୀெିଵ ௠ୀ଴

Fig. 1: OFDMA using PTS scheme

x’ is time domain signal after IFFT operation. Values are chosen from a set of discrete values ejĳ. Values for phase rotation belong to {±1, ±j} set. With these values PAPR can be reduced to 3 dB [6, 7].

(5)

Where [FM]m,l=ej2ʌml/M and FN-1 are M point Fourier transform matrix and N point inverse Fourier transform matrix respectively. The M point Y is sub carrier mapped on to N subcarriers. These mapped subcarriers are transformed to the time domain with the use of N point IDFT matrix. The time domain set y is expressed in (6) expression [8]. y= FN-1SY

(6)

S is sub carrier transform matrix. y is time domain original SC-FDMA transmit signal (7) [8].

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y=[yo,y1,y2 ...,yN-1]T

(7)

This time domain signal is multiplied with the phase rotating factor bm to minimize PAPR. Thus the transmitting signal becomes expression (8) [8]. ܾ௠ ‫ܨ‬ேିଵ ܻܵ ‫ ݕ‬ᇱ ൌ σ௠ୀெିଵ ௠ୀ଴

(8)

For the phase recovery, receiver should have the knowledge of bm. This can lower data rate.

taken as 128 and 128000 respectively to get the results. The number of symbols used is 1000. Firstly the analysis of PAPR performance of OFDMA has been carried out. Then comparison of PAPR performance between original OFDMA and OFDMA using PTS scheme is done. Figure 3 illustrates the PAPR performance comparison. It shows that the PAPR performance improves by 3 db with the multiplication of phase rotating factor. As we have already discussed, SC-FDMA has lower PAPR than OFDMA. Figure 4 shows this result that SC-FDMA better PAPR performance than OFDMA using PTS scheme. PAPR performance of OFDMA

0

10

Orignal OFDMA using PTS

-1

CCDF

10

-2

10

Fig. 2: SC-FDMA using PTS scheme

C. Wavelet based SC-FDMA using PTS scheme

-3

10

We are proposing a method to minimize PAPR. Wavelet based SC-FDMA using PTS scheme has been proposed. In this method, DFT is replaced with DWT. Then we get approximation and detailed coefficient after M point DWT operation. These coefficients are sub carrier mapped followed by N point IDWT operation. As we know, Wavelet provides better localization property in time and frequency domain. Thus keeping peaks of transmit signal distortionless, it maintains Peak power near about average power [11, 12]. D. PAPR Calculation Calculation of PAPR in SC-FDMA is done by following Expression. This is expressed in (9) expression [8]. ܲ‫ ܴܲܣ‬ൌ

୫ୟ୶ሾȁ௬ሺ௧ሻȁమ ሿ ாሾȁ௬ሺ௧ሻȁమ ሿ

1

2

3

4

5 PAPR0

6

7

8

9

10

Fig. 3: comparison of PAPR performance of original OFDMA and OFDMA using PTS. comparison of PAPR performance of OFDMA & SC-FDMA

0

10

OFDMA SC-FDMA

-1

10

-2

10

-3

10

0

1

2

3

4

5 PAPR0

6

7

8

9

10

Fig 4: comparison of PAPR performance of original OFDMA and original SC-FDMA

PAPR Performance improvement is necessary in wireless communication. So, further improvement is done using PTS scheme in SCFDMA. This is illustrated in Figure 5. This figure shows the result that the improvement in PAPR performance takes place by 2 db [6].

(9)

IV. RESULT ®

To evaluate the performance of proposed scheme, Matlab software is used. The size of FFT/DWT and data length is

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0

CCDF

The power efficiency is needed in wireless communications. It provides the adequate coverage area, lowers power consumption and allows small size terminals. So, it is necessary to handle the power efficiency. For this, the improvement of PAPR performance is required for uplink transmissions. For this, improvement is done by using wavelet transform in SCFDMA transmission instead of using Fourier transform [9, 10].

Wavelet Transform provides better reconstruction property than Fourier transform. Wavelet provides better localization properties in both time and frequency domain. Thus provides better performance than Fourier transform. In our proposed


method, we are using DWT in SCFDMA using PTS scheme. The results are shown in Figure 6. The results shows wavelet based SC-FDMA results in low PAPR.

CCDF

The wavelet diversity is also a important property of wavelets. We are using here the different Wavelets such as Haar and Daubechies. From the Figure 7 we see that Haar shows best performance in case of PAPR. In case of Daubechies Wavelet, as the order of Wavelet decreases, performance improves.

PAPR performance using different wavelets

0

10

-1

10

PAPR performance of SCFDMA using PTS

0

10

db20 haar db10 db2 haar

Orignal SC-FDMA SC-FDMA using PTS

-2

10

-1

10

0

0.5

1

1.5

2 PAPR0

2.5

3

3.5

4

CCDF

Fig. 7: Comparison of PAPR performance of Wavelet based SC-FDMA using different wavelets PAPR performance using different number of carriers

0

-2

10

10

no of carriers=128 no. of carriers=2048 no of carriers=16384

-3

0

1

2

3 PAPR0

4

5

6

Fig. 5: Comparison of PAPR performance of original SC-FDMA and SCFDMA using PTS.

CCDF

10

-1

10

Comparison of PAPR performance using PTS

0

10

-2

CCDF

10

0

0.2

0.4

0.6

0.8

1 PAPR0

1.2

1.4

1.6

1.8

2

Fig. 8: PAPR performance of SC-FDMA using different number of carriers

-1

10

V. CONCLUSION

DFT-SCFDMA using PTS DWT-SCFDMA using PTS

-2

10

0

0.5

1

1.5

2 2.5 PAPR0

3

3.5

4

4.5

Fig. 6: Comparison of PAPR performance of DFT SC-FDMA and DWT SCFDMA using PTS

The number of carriers plays a major role in PAPR performance. As their number increases, the performance improves. This result is shown in Figure 8.

The improvement of PAPR is a desirable factor for uplink transmission at mobile terminal. A new transceiver scheme of Wavelet based SC-FDMA using PTS scheme has been proposed for reduction of PAPR. Wavelet transform provides better localization property in both time and frequency domain than Fourier transform. With this proposed method PAPR performance improves by 4 db than its original SC-FDMA. The results are also analyzed in OFDMA. In OFDMA, using PTS scheme PAPR factor is improved. PAPR performance is also analyzed by varying the number of carriers and by using different wavelets.

Acknowledgment The Authors would like to thank Prof. Renu Vig, Director of UIET, Panjab University, Chandigarh for providing lab facilities to complete this work.


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