- Email: [email protected]
PAPR Reduction in SC-FDMA Using NCT Technique
Available online at www.sciencedirect.com
ScienceDirect Procedia Technology 10 (2013) 927 – 934
International Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 2013
PAPR Reduction in SC-FDMA Using NCT Technique Sandeep Shuklaa,*, Saurabh Shuklaa, Neetesh Purohita a
IIIT- Allahabad, India
Abstract Orthogonal Frequency Division Multiplexing (OFDM) technology is undoubtedly the best available option for supporting high data rate in both wired and wireless communication systems. But, the feature of high peak-to-average power ratio (PAPR) restricts its usage in some applications for which single carrier frequency division multiple access (SC-FDMA) technique is usually adopted. In this work, a new scheme using Nonlinear Companding Transform (NCT) technique is proposed for further reducing the peak-to-average power ratio (PAPR) of SC-FDMA. It transforms the SC-FDMA signal by properly choosing the transform parameters for achieving a favorable tradeoff between PAPR reduction and bit error rate (BER) performances. The simulation results show better performance of the proposed scheme as compared to competitive alternatives. © 2013 © 2013 The The Authors. Authors.Published PublishedbybyElsevier ElsevierLtd. Ltd. Selection and thethe University of of Kalyani, Department of Computer Science & Engineering. Selection andpeer-review peer-reviewunder underresponsibility responsibilityofof University Kalyani, Department of Computer Science & Engineering Keywords: Orthogonal Frequency Division Multiplexing (OFDM); Single carrier frequency division multiple access (SC-FDMA); Nonlinear Companding Transform (NCT); peak-to-average power ratio (PAPR).
1. Introduction New Technologies and thereby new applications are emerging to provide better services over the wireless network. The success of second generation cellular system has accelerated the demand of multimedia applications availability over wireless communication systems. To achieve the goals, the next generation mobile systems are designed such that a minimum data rate of 10-20 Mbps (at least 2 Mbps in the moving vehicles) can be achieved in 4G. OFDM [1] technique is suitable for multipath environment and possesses high spectral efficiency,
* Sandeep Shukla. Tel.: +91-8574740457. E-mail address:[email protected]
2212-0173 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering doi:10.1016/j.protcy.2013.12.439
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Sandeep Shukla et al. / Procedia Technology 10 (2013) 927 – 934
thus it is recommended for the fourth generation cellular network. OFDM is known since a long time but it is the advancements in digital signal processing techniques which enable it to be implemented in modern wireless systems. OFDM is a multicarrier modulation technique possessing several favourable properties like better spectral efficiency, robustness against frequency selective fading channels, higher immunity to inter symbol interference, low implementation complexity, uniform average power spectral density, very much capable to handle strong echoes and less occurrence of non-linear distortion. The PAPR of the signal ݔሺݐሻ is given as the ratio between the peak instantaneous power and the average power occur in OFDM symbol transmission. It can be written as: ܲ ܴܲܣൌ ୭ஸ୲ஸ
ȁ௫ሺ௧ሻȁమ ாሾȁ௫ሺሺ௧ሻȁమ ሿ
(1)
Where E[.] denotes the expectation operator. For reduction of the high PAPR in OFDM transmission system, instantaneous peak power of the OFDM signal should be minimized. Since OFDM signal is the sum of the N signals then for the analysis of highest PAPR, if each signal is considered to have maximum amplitude of 1 volt and all of these signals are added up at the same time at these maximum amplitude which is unlikely but possible, making the OFDM signal amplitude of N volts which leads to N times higher PAPR than the PAPR of single carrier transmission system. If there is very high Peak-toAverage Power Ratio (PAPR) in OFDM based transmission systems then it requires the use of sophisticated and costly radio transmitters which have High Power Amplifiers (HPA) which can operate in a very large linear range. Otherwise non-linear signal distortion occurs, which may lead to high adjacent channel interference and performance degradation. These demands result in complex and costly hardware systems. Hence to minimize the problem of complex hardware design it is better to employ efficient PAPR reduction techniques. There are different PAPR reduction techniques and their selection criteria which are given in the literature [2, 3]. Single carrier frequency division multiple access (SC-FDMA) is the technique which basically uses the single carrier modulation, which is an extension of the OFDMA system having similar overall complexity and performance. It has a major advantage over OFDMA system that it has lower PAPR because of its integral single carrier structure [4] and due to its high transmission power efficiency. It is widely used in uplink multiple access transmission of 3G LTE of 3GPP [5]. In OFDM system to reduce the PAPR, another type of companding technique is used, known as Non Linear Companding Transform. This technique converts the OFDM signals into a specific statistics form, which can be given by a piecewise probability density function with an inflexion point. Theoretical analysis shows that, this scheme may drastically decrease the impact of companding distortion on the BER performance to achieve a given PAPR level, while simultaneously achieving a favourable trade-off between the PAPR reduction and BER performance. This work proposes a technique for further reducing the PAPR by introducing the Nonlinear Companding Transform (NCT) [6, 7] techniques with the single carrier frequency division multiple access (SC-FDMA) [8, 9]. Section II introduces the proposed scheme, Section III contains the result and finally the conclusion is given in section IV. 2. Proposed PAPR reduction scheme The below figure 1 shows the block diagram of the proposed PAPR reduction technique of the SC-FDMA and nonlinear companding technique. SC-FDMA is a discrete Fourier transform-spread version of OFDMA, where time domain data symbols are converted to frequency domain by DFT before applying OFDMA modulation. By applying the DFT before passing it through the IDFT it ensures that the subcarriers are orthogonal to each other which results the overall transmit signal as the single carrier signal leading to the single carrier frequency division multiple access (SC-FDMA). To decrease the computational complexity of the system, FFT is used in place of DFT operation and IFFT in place of IDFT operation. In the subcarrier mapping scheme there are N subcarriers, among which M subcarriers are placed by the input data where M
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I/P
Subcarrier Mapping
M pt FFT
S/P
P/S & NCT
N pt IFFT
Add CP
D A C Channel + Noise
O/P
Equalizer & Subcarrier Demapping
M Pt IFFT
P/S
N Pt FFT
S/P
Remove CP
A D C
Fig. 1 Block diagram of a proposed SC-OFDM Transceiver
There are two modes to choose the subcarriers for transmission in SC-FDMA. In first mode the localized FDMA (LFDMA), FFT outputs of the input data are placed on the consecutive subcarriers in the form of chunk. While in the second mode of subcarrier mapping the distributed FDMA (DFDMA), the FFT outputs of the input data are placed on the entire subcarriers with zeros occupying in unused subcarriers. There is another case of distributed FDMA where FFT outputs of the input data are placed over the entire subcarriers having the equal distance in between each subcarrier, known as interleaved FDMA (IFDMA) [10]. These two subcarrier mapping schemes have advantages over each other as distributed FDMA has simpler scheduling and higher frequency diversity while localized FDMA has higher frequency selective gain. ݔ
ܺ
ܺ ݎ݁݅ݎݎܾܽܿݑݏ ݉ܽ݃݊݅
ܶܨܨ ݐ݊݅ ܯ ܯ
ܯ
ݔ ܰ ܶܨܨܫ ݐ݊݅
ܰ
ܰ
Fig. 2 Generation of SC-FDMA transmits symbols.
Let ݔ be the data symbols which is to be modulated,on doing the FFT of ݔ the frequency domain samples are ܺ . Let ܺ be the frequency domain samples after the subcarrier mapping of the frequency domain samples ܺ and the time domain samples after taking the IFFT of the ܺ be ݔ . For IFDMA the frequency domain samples ܺ can be given as following, ܺୀொǤ ൌ ቄ
ܺ ǡ Ͳ
Ͳ݉ ܯെͳ ݁ݏ݅ݓݎ݄݁ݐ
(2)
For LFDMA the frequency domain samples ܺ can be given as following, ܺୀொǤ ൌ ቄ
ܺ ǡ Ͳ
Ͳ݊ ܯെͳ ܯ ݊ ܰെͳ
(3)
Where N =Total number of subcarriers, M=Data block size, Q=Bandwidth spreading factor. Taking the IFFT of the frequency domain subcarrier mapped signal ܺ will get the time domain samples as ݔ . Now the signal ݔ will be transformed according to the companding transform function ݂ሺǤ ሻ. The transformed signal can be given as following, ݕୀ ݂ሺݔ ሻ,
݊ ൌ Ͳǡͳǡʹǡ ǥ ǥ ǥ ǥ ܰ െ ͳ
(4)
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And the transfer function is given as following, భ శభ ȁೣȁమ ۓ ቆି൬ ൰ቇ ۖ ݊݃ݏሺݔሻ ቌାଵ ൭ͳ െ ݁ మ ൱ቍ ǡ ȁݔȁ ߙ ۖ
݂ሺݔሻ ൌ
(5)
మ
ȁೣȁ ۔ ൭షቆ మ ቇ൱ ۖ݊݃ݏሺݔሻ ൮ଵି ൲ǡȁݔȁ ߙ ሺሻ ାଵ ۖ ە
The transform parameters such as k and p are variables which are used to obtain ultimate companding form so as to achive favourble tradeoff between reduced PAPR and bit error rate (BER) performance. Where ݇ ൌ
ାଵ శభ ሺାଵିሻ
, ܣൌ
ାଷ ሺଵିሻାଵ ͵ߪ ଶ Ǥ ାଵ ሺଵି య ሻାଷ
, ߙ ൌ ߪ ቀെ ቀͳ െ
ሺሻశభ ାଵ
భ మ
ቁቁ .
The transfer curves of equation (5) is shown in Figure.3. It can be seen from Fig. that this scheme compresses the large signals while partially expands the small ones simultaneously. This transform has some other advantages such as it can maintain a constant average power level in the transformed signal. As a result, it not only reduces the PAPR more effectively, but also the small signals become more immune from the channel noise. 1.4
1.2
Output |y|
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1 Input |x|
1.2
1.4
1.6
1.8
2
Fig. 3 Transfer curve of the nonlinear companding transform
3. Result and Discussion The performance of the proposed scheme is evaluated in terms of the reduction of the PAPR and BER performance through numerical simulations. PAPR statics are shown in terms of CCDF (Complementary Cumulative Distribution Function) which gives the probability that PAPR is greater than a certain PAPR value PAPR0 (Pr{PAPR>PAPR0}). Comparison of the performance of OFDMA, SC-FDMA and the proposed scheme has been done. In this simulation model the total number of subcarriers has been taken as 512, input data block size to 16 and bandwidth spreading factor to 32. To acquire the CCDF of PAPR to be ten thousand times, a uniformly random data points were generated. Transmission bandwidth of 5 MHz and symbol constellations as QPSK and 16-QAM was considered.
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In this simulation model the raised-cosine (RC) pulse and squared-root raised-cosine (RRC) pulse [11] have been applied which are widely used for pulse shaping in wireless communications. So these are used in SC-FDMA signals which suffer from the higher instantaneous out of band radiation. The effect of out of band radiation is more in case of IFDMA since out of band radiation increases by increasing the roll of factor over the range 0 to 1 but at the same time PAPR also decreased. Thus a trade-off between PAPR performance and out of band radiation can be seen. In figure 5.a and figure 5.b, plots of CCDF of PAPR for the OFDMA, SC-FDMA and proposed scheme for QPSK and 16QAM modulation formats are shown respectively. Comparison of the PAPR values which exceeded with probability less than 0.01% (Pr{PAPR>PAPR0} = 10-4), or 99.99-percentile PAPR, has been done. From these results it can be seen that in all the cases SC-FDMA has lower PAPR compared to OFDMA, IFDMA has the lowest PAPR, and LFDMA and DFDMA have very similar PAPR performances. 0.06
0.04
0.02
0
-0.02
-0.04
-0.06
0
200
400
600
800
1000
1200
Fig. 4 OFDM signal containing sinusoidal high peaks
In the result from figure 5.a it is clearly seen that IFDMA has lower PAPR in comparison to OFDMA, DFDMA and LFDMA. It has got 3.7 dB, 1.1 dB and 0.7 dB lower PAPR in comparison to OFDMA, DFDMA and LFDMA respectively. But the proposed scheme has achieved more improvement of 1.0 dB, 1.6 dB and 1.3 dB reduced PAPR of IFDMA, DFDMA and LFDMA respectively over the existing techniques and overall of 4.7 dB reduced PAPR for IFDMA in comparison to OFDMA system. The detailed analysis of the 99.99-percentile PAPR for SC-FDMA and proposed technique is given in Table.1. Table.1 99.99-percentile PAPR for SC-FDMA and proposed technique Modulation
Pulse shaping
IFDMA
DFDMA
LFDMA
OFDMA
0 dB
7.5 dB
7.5 dB
10.4 dB
SC-FDMA
6.7 dB
7.8 dB
7.4 dB
N/A
PROPOSED
5.7 dB
6.2 dB
6.1 dB
SC-FDMA
6.6 dB
7.8 dB
7.6 dB
PROPOSED
5.7 dB
6.2 dB
6.1 dB
None RC QPSK RRC
None RC 16-QAM RRC
N/A
5.1 dB
8.9 dB
8.9 dB
10.1 dB
SC-FDMA
7.9 dB
8.8 dB
8.4 dB
N/A
PROPOSED
6.2 dB
6.6 dB
6.5 dB
SC-FDMA
7.7 dB
8.6 dB
8.4 dB
PROPOSED
6.2 dB
6.7 dB
6.6 dB
N/A
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Fig. 5.a The CCDF statistics of PAPR for the OFDMA, SC-FDMA with N= 512, QPSK modulation, and the without pulse shaping
Fig. 5.b The CCDF statistics of PAPR for the OFDMA, SC-FDMA and Proposed scheme with N= 512, QPSK modulation, and Raised cosine pulse shaping
Fig. 6.a The CCDF statistics of PAPR for the OFDMA, SC-FDMA with N= 512, 16-QAM modulation, and without pulse shaping
Sandeep Shukla et al. / Procedia Technology 10 (2013) 927 – 934
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Fig. 6.b The CCDF statistics of PAPR for the OFDMA, SC-FDMA and Proposed scheme with N= 512, 16-QAM modulation, and Raised cosine pulse shaping
Fig. 7 BER performance for the proposed OFDM system with ideal channel estimation and linear MMSE equalization
As it is known that companding operation causes certain signal attenuation that leads to all curves related to the companding transformed signals to be located at the right side of the ‘original SC-FDMA signal’ curve. It can be seen from the figure. 7, that the proposed scheme has relatively low BER performance such as to reach a BER of a ͳͲିଷ ,the required SNR for proposed IFDMA is 13.2 dB which is roughly 2.7dB higher to SC-FDMA but it has certainly very good PAPR performance as 4.7 dB reduced PAPR is achieved by proposed technique compared to OFDM system. 4. Conclusions A technique is proposed for PAPR reduction using nonlinear companding technique over the SC-FDMA technique. The results show that the proposed technique has better PAPR reduction compared to OFDMA and SC-FDMA signals with overall same BER performance. The main idea of the proposed combination is to reduce
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PAPR, improve the BER performance and spectrum efficiency over the conventional PAPR reduction technique of the OFDM system. Two different modes of subcarrier mapping methods, distributed and localized, give the system designer more flexibility to adapt the different radio environments. References [1] [2]
Nee, R.V. and R. Prasad, OFDM for Wireless Multimedia Communications, Artech House Publishers, Norwood, MA, January 2000. S. H. Han and J. H. Lee, “An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission,” IEEE Wireless Commun., vol. 12, no. 2, April 2005, pp. 56–65. [3] V. Vijayarangan, Dr. (Mrs) R. Sukanesh , “An Overview Of Techniques For Reducing Peak to Average Power Ratio And Its Selection Criteria For Orthogonal Frequency Division multiplexing Radio Systems” Journal Of Theoretical And Applied Information Technology, Year 2009 ,Vol-5, No-5, E-Issn- 1817-3195/Issn-1992-8645 [4] D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar and B. Eidson, “Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems,” IEEE Commun. Mag., vol. 40, no.4, April 2002, pp. 58–66. [5] 3rd Generation Partnership Project (3GPP); Technical Specification Group Radio Access Network; Physical Layer Aspects for Evolved UTRA, http://www.3gpp.org/ftp/Specs/html-info/25814.htm, date of site access 24/08/2013. [6] Yong Wang · Jianhua Ge · Lihua Wang · Jing Li (2012) “Reduction of PAPR of OFDM Signals Using Nonlinear Companding Transform” Wireless Pers Communication DOI10.1007/s11277-012-0820-2 [7] Hou, J., Ge, J., Zhai, D., & Li, J. (2010). Peak-to-average power ratio reduction of OFDM signals with nonlinear companding scheme. IEEE Transactions on Broadcasting, 56(2), 258–262. [8] H. G. Myung, J. Lim, and D. J. Goodman, "Peak-to-Average Power Ratio of Single Carrier FDMA Signals with Pulse Shaping," The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC ’06), Helsinki, Finland, Sep. 2006 [9] H.G. Myung and D.J. Goodman, “Single carrier FDMA: a new air interface for long term evolution,” Wireless Communications and Mobile Computing, 2008, p. 198. [10] U. Sorger, I. De Broeck and M. Schnell, “Interleaved FDMA - A New Spread-Spectrum Multiple-Access Scheme,” Proc. IEEE ICC ’98, pp. 1013–1017, Atlanta, GA, June 1998. [11] T. S. Rappaport, Wireless Communications: Principles and Practice, Second Edition. Prentice Hall, 2002
ScienceDirect Procedia Technology 10 (2013) 927 – 934
International Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 2013
PAPR Reduction in SC-FDMA Using NCT Technique Sandeep Shuklaa,*, Saurabh Shuklaa, Neetesh Purohita a
IIIT- Allahabad, India
Abstract Orthogonal Frequency Division Multiplexing (OFDM) technology is undoubtedly the best available option for supporting high data rate in both wired and wireless communication systems. But, the feature of high peak-to-average power ratio (PAPR) restricts its usage in some applications for which single carrier frequency division multiple access (SC-FDMA) technique is usually adopted. In this work, a new scheme using Nonlinear Companding Transform (NCT) technique is proposed for further reducing the peak-to-average power ratio (PAPR) of SC-FDMA. It transforms the SC-FDMA signal by properly choosing the transform parameters for achieving a favorable tradeoff between PAPR reduction and bit error rate (BER) performances. The simulation results show better performance of the proposed scheme as compared to competitive alternatives. © 2013 © 2013 The The Authors. Authors.Published PublishedbybyElsevier ElsevierLtd. Ltd. Selection and thethe University of of Kalyani, Department of Computer Science & Engineering. Selection andpeer-review peer-reviewunder underresponsibility responsibilityofof University Kalyani, Department of Computer Science & Engineering Keywords: Orthogonal Frequency Division Multiplexing (OFDM); Single carrier frequency division multiple access (SC-FDMA); Nonlinear Companding Transform (NCT); peak-to-average power ratio (PAPR).
1. Introduction New Technologies and thereby new applications are emerging to provide better services over the wireless network. The success of second generation cellular system has accelerated the demand of multimedia applications availability over wireless communication systems. To achieve the goals, the next generation mobile systems are designed such that a minimum data rate of 10-20 Mbps (at least 2 Mbps in the moving vehicles) can be achieved in 4G. OFDM [1] technique is suitable for multipath environment and possesses high spectral efficiency,
* Sandeep Shukla. Tel.: +91-8574740457. E-mail address:[email protected]
2212-0173 © 2013 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the University of Kalyani, Department of Computer Science & Engineering doi:10.1016/j.protcy.2013.12.439
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Sandeep Shukla et al. / Procedia Technology 10 (2013) 927 – 934
thus it is recommended for the fourth generation cellular network. OFDM is known since a long time but it is the advancements in digital signal processing techniques which enable it to be implemented in modern wireless systems. OFDM is a multicarrier modulation technique possessing several favourable properties like better spectral efficiency, robustness against frequency selective fading channels, higher immunity to inter symbol interference, low implementation complexity, uniform average power spectral density, very much capable to handle strong echoes and less occurrence of non-linear distortion. The PAPR of the signal ݔሺݐሻ is given as the ratio between the peak instantaneous power and the average power occur in OFDM symbol transmission. It can be written as: ܲ ܴܲܣൌ ୭ஸ୲ஸ
ȁ௫ሺ௧ሻȁమ ாሾȁ௫ሺሺ௧ሻȁమ ሿ
(1)
Where E[.] denotes the expectation operator. For reduction of the high PAPR in OFDM transmission system, instantaneous peak power of the OFDM signal should be minimized. Since OFDM signal is the sum of the N signals then for the analysis of highest PAPR, if each signal is considered to have maximum amplitude of 1 volt and all of these signals are added up at the same time at these maximum amplitude which is unlikely but possible, making the OFDM signal amplitude of N volts which leads to N times higher PAPR than the PAPR of single carrier transmission system. If there is very high Peak-toAverage Power Ratio (PAPR) in OFDM based transmission systems then it requires the use of sophisticated and costly radio transmitters which have High Power Amplifiers (HPA) which can operate in a very large linear range. Otherwise non-linear signal distortion occurs, which may lead to high adjacent channel interference and performance degradation. These demands result in complex and costly hardware systems. Hence to minimize the problem of complex hardware design it is better to employ efficient PAPR reduction techniques. There are different PAPR reduction techniques and their selection criteria which are given in the literature [2, 3]. Single carrier frequency division multiple access (SC-FDMA) is the technique which basically uses the single carrier modulation, which is an extension of the OFDMA system having similar overall complexity and performance. It has a major advantage over OFDMA system that it has lower PAPR because of its integral single carrier structure [4] and due to its high transmission power efficiency. It is widely used in uplink multiple access transmission of 3G LTE of 3GPP [5]. In OFDM system to reduce the PAPR, another type of companding technique is used, known as Non Linear Companding Transform. This technique converts the OFDM signals into a specific statistics form, which can be given by a piecewise probability density function with an inflexion point. Theoretical analysis shows that, this scheme may drastically decrease the impact of companding distortion on the BER performance to achieve a given PAPR level, while simultaneously achieving a favourable trade-off between the PAPR reduction and BER performance. This work proposes a technique for further reducing the PAPR by introducing the Nonlinear Companding Transform (NCT) [6, 7] techniques with the single carrier frequency division multiple access (SC-FDMA) [8, 9]. Section II introduces the proposed scheme, Section III contains the result and finally the conclusion is given in section IV. 2. Proposed PAPR reduction scheme The below figure 1 shows the block diagram of the proposed PAPR reduction technique of the SC-FDMA and nonlinear companding technique. SC-FDMA is a discrete Fourier transform-spread version of OFDMA, where time domain data symbols are converted to frequency domain by DFT before applying OFDMA modulation. By applying the DFT before passing it through the IDFT it ensures that the subcarriers are orthogonal to each other which results the overall transmit signal as the single carrier signal leading to the single carrier frequency division multiple access (SC-FDMA). To decrease the computational complexity of the system, FFT is used in place of DFT operation and IFFT in place of IDFT operation. In the subcarrier mapping scheme there are N subcarriers, among which M subcarriers are placed by the input data where M
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I/P
Subcarrier Mapping
M pt FFT
S/P
P/S & NCT
N pt IFFT
Add CP
D A C Channel + Noise
O/P
Equalizer & Subcarrier Demapping
M Pt IFFT
P/S
N Pt FFT
S/P
Remove CP
A D C
Fig. 1 Block diagram of a proposed SC-OFDM Transceiver
There are two modes to choose the subcarriers for transmission in SC-FDMA. In first mode the localized FDMA (LFDMA), FFT outputs of the input data are placed on the consecutive subcarriers in the form of chunk. While in the second mode of subcarrier mapping the distributed FDMA (DFDMA), the FFT outputs of the input data are placed on the entire subcarriers with zeros occupying in unused subcarriers. There is another case of distributed FDMA where FFT outputs of the input data are placed over the entire subcarriers having the equal distance in between each subcarrier, known as interleaved FDMA (IFDMA) [10]. These two subcarrier mapping schemes have advantages over each other as distributed FDMA has simpler scheduling and higher frequency diversity while localized FDMA has higher frequency selective gain. ݔ
ܺ
ܺ ݎ݁݅ݎݎܾܽܿݑݏ ݉ܽ݃݊݅
ܶܨܨ ݐ݊݅ ܯ ܯ
ܯ
ݔ ܰ ܶܨܨܫ ݐ݊݅
ܰ
ܰ
Fig. 2 Generation of SC-FDMA transmits symbols.
Let ݔ be the data symbols which is to be modulated,on doing the FFT of ݔ the frequency domain samples are ܺ . Let ܺ be the frequency domain samples after the subcarrier mapping of the frequency domain samples ܺ and the time domain samples after taking the IFFT of the ܺ be ݔ . For IFDMA the frequency domain samples ܺ can be given as following, ܺୀொǤ ൌ ቄ
ܺ ǡ Ͳ
Ͳ݉ ܯെͳ ݁ݏ݅ݓݎ݄݁ݐ
(2)
For LFDMA the frequency domain samples ܺ can be given as following, ܺୀொǤ ൌ ቄ
ܺ ǡ Ͳ
Ͳ݊ ܯെͳ ܯ ݊ ܰെͳ
(3)
Where N =Total number of subcarriers, M=Data block size, Q=Bandwidth spreading factor. Taking the IFFT of the frequency domain subcarrier mapped signal ܺ will get the time domain samples as ݔ . Now the signal ݔ will be transformed according to the companding transform function ݂ሺǤ ሻ. The transformed signal can be given as following, ݕୀ ݂ሺݔ ሻ,
݊ ൌ Ͳǡͳǡʹǡ ǥ ǥ ǥ ǥ ܰ െ ͳ
(4)
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Sandeep Shukla et al. / Procedia Technology 10 (2013) 927 – 934
And the transfer function is given as following, భ శభ ȁೣȁమ ۓ ቆି൬ ൰ቇ ۖ ݊݃ݏሺݔሻ ቌାଵ ൭ͳ െ ݁ మ ൱ቍ ǡ ȁݔȁ ߙ ۖ
݂ሺݔሻ ൌ
(5)
మ
ȁೣȁ ۔ ൭షቆ మ ቇ൱ ۖ݊݃ݏሺݔሻ ൮ଵି ൲ǡȁݔȁ ߙ ሺሻ ାଵ ۖ ە
The transform parameters such as k and p are variables which are used to obtain ultimate companding form so as to achive favourble tradeoff between reduced PAPR and bit error rate (BER) performance. Where ݇ ൌ
ାଵ శభ ሺାଵିሻ
, ܣൌ
ାଷ ሺଵିሻାଵ ͵ߪ ଶ Ǥ ାଵ ሺଵି య ሻାଷ
, ߙ ൌ ߪ ቀെ ቀͳ െ
ሺሻశభ ାଵ
భ మ
ቁቁ .
The transfer curves of equation (5) is shown in Figure.3. It can be seen from Fig. that this scheme compresses the large signals while partially expands the small ones simultaneously. This transform has some other advantages such as it can maintain a constant average power level in the transformed signal. As a result, it not only reduces the PAPR more effectively, but also the small signals become more immune from the channel noise. 1.4
1.2
Output |y|
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1 Input |x|
1.2
1.4
1.6
1.8
2
Fig. 3 Transfer curve of the nonlinear companding transform
3. Result and Discussion The performance of the proposed scheme is evaluated in terms of the reduction of the PAPR and BER performance through numerical simulations. PAPR statics are shown in terms of CCDF (Complementary Cumulative Distribution Function) which gives the probability that PAPR is greater than a certain PAPR value PAPR0 (Pr{PAPR>PAPR0}). Comparison of the performance of OFDMA, SC-FDMA and the proposed scheme has been done. In this simulation model the total number of subcarriers has been taken as 512, input data block size to 16 and bandwidth spreading factor to 32. To acquire the CCDF of PAPR to be ten thousand times, a uniformly random data points were generated. Transmission bandwidth of 5 MHz and symbol constellations as QPSK and 16-QAM was considered.
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In this simulation model the raised-cosine (RC) pulse and squared-root raised-cosine (RRC) pulse [11] have been applied which are widely used for pulse shaping in wireless communications. So these are used in SC-FDMA signals which suffer from the higher instantaneous out of band radiation. The effect of out of band radiation is more in case of IFDMA since out of band radiation increases by increasing the roll of factor over the range 0 to 1 but at the same time PAPR also decreased. Thus a trade-off between PAPR performance and out of band radiation can be seen. In figure 5.a and figure 5.b, plots of CCDF of PAPR for the OFDMA, SC-FDMA and proposed scheme for QPSK and 16QAM modulation formats are shown respectively. Comparison of the PAPR values which exceeded with probability less than 0.01% (Pr{PAPR>PAPR0} = 10-4), or 99.99-percentile PAPR, has been done. From these results it can be seen that in all the cases SC-FDMA has lower PAPR compared to OFDMA, IFDMA has the lowest PAPR, and LFDMA and DFDMA have very similar PAPR performances. 0.06
0.04
0.02
0
-0.02
-0.04
-0.06
0
200
400
600
800
1000
1200
Fig. 4 OFDM signal containing sinusoidal high peaks
In the result from figure 5.a it is clearly seen that IFDMA has lower PAPR in comparison to OFDMA, DFDMA and LFDMA. It has got 3.7 dB, 1.1 dB and 0.7 dB lower PAPR in comparison to OFDMA, DFDMA and LFDMA respectively. But the proposed scheme has achieved more improvement of 1.0 dB, 1.6 dB and 1.3 dB reduced PAPR of IFDMA, DFDMA and LFDMA respectively over the existing techniques and overall of 4.7 dB reduced PAPR for IFDMA in comparison to OFDMA system. The detailed analysis of the 99.99-percentile PAPR for SC-FDMA and proposed technique is given in Table.1. Table.1 99.99-percentile PAPR for SC-FDMA and proposed technique Modulation
Pulse shaping
IFDMA
DFDMA
LFDMA
OFDMA
0 dB
7.5 dB
7.5 dB
10.4 dB
SC-FDMA
6.7 dB
7.8 dB
7.4 dB
N/A
PROPOSED
5.7 dB
6.2 dB
6.1 dB
SC-FDMA
6.6 dB
7.8 dB
7.6 dB
PROPOSED
5.7 dB
6.2 dB
6.1 dB
None RC QPSK RRC
None RC 16-QAM RRC
N/A
5.1 dB
8.9 dB
8.9 dB
10.1 dB
SC-FDMA
7.9 dB
8.8 dB
8.4 dB
N/A
PROPOSED
6.2 dB
6.6 dB
6.5 dB
SC-FDMA
7.7 dB
8.6 dB
8.4 dB
PROPOSED
6.2 dB
6.7 dB
6.6 dB
N/A
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Fig. 5.a The CCDF statistics of PAPR for the OFDMA, SC-FDMA with N= 512, QPSK modulation, and the without pulse shaping
Fig. 5.b The CCDF statistics of PAPR for the OFDMA, SC-FDMA and Proposed scheme with N= 512, QPSK modulation, and Raised cosine pulse shaping
Fig. 6.a The CCDF statistics of PAPR for the OFDMA, SC-FDMA with N= 512, 16-QAM modulation, and without pulse shaping
Sandeep Shukla et al. / Procedia Technology 10 (2013) 927 – 934
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Fig. 6.b The CCDF statistics of PAPR for the OFDMA, SC-FDMA and Proposed scheme with N= 512, 16-QAM modulation, and Raised cosine pulse shaping
Fig. 7 BER performance for the proposed OFDM system with ideal channel estimation and linear MMSE equalization
As it is known that companding operation causes certain signal attenuation that leads to all curves related to the companding transformed signals to be located at the right side of the ‘original SC-FDMA signal’ curve. It can be seen from the figure. 7, that the proposed scheme has relatively low BER performance such as to reach a BER of a ͳͲିଷ ,the required SNR for proposed IFDMA is 13.2 dB which is roughly 2.7dB higher to SC-FDMA but it has certainly very good PAPR performance as 4.7 dB reduced PAPR is achieved by proposed technique compared to OFDM system. 4. Conclusions A technique is proposed for PAPR reduction using nonlinear companding technique over the SC-FDMA technique. The results show that the proposed technique has better PAPR reduction compared to OFDMA and SC-FDMA signals with overall same BER performance. The main idea of the proposed combination is to reduce
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PAPR, improve the BER performance and spectrum efficiency over the conventional PAPR reduction technique of the OFDM system. Two different modes of subcarrier mapping methods, distributed and localized, give the system designer more flexibility to adapt the different radio environments. References [1] [2]
Nee, R.V. and R. Prasad, OFDM for Wireless Multimedia Communications, Artech House Publishers, Norwood, MA, January 2000. S. H. Han and J. H. Lee, “An Overview of Peak-to-Average Power Ratio Reduction Techniques for Multicarrier Transmission,” IEEE Wireless Commun., vol. 12, no. 2, April 2005, pp. 56–65. [3] V. Vijayarangan, Dr. (Mrs) R. Sukanesh , “An Overview Of Techniques For Reducing Peak to Average Power Ratio And Its Selection Criteria For Orthogonal Frequency Division multiplexing Radio Systems” Journal Of Theoretical And Applied Information Technology, Year 2009 ,Vol-5, No-5, E-Issn- 1817-3195/Issn-1992-8645 [4] D. Falconer, S. L. Ariyavisitakul, A. Benyamin-Seeyar and B. Eidson, “Frequency Domain Equalization for Single-Carrier Broadband Wireless Systems,” IEEE Commun. Mag., vol. 40, no.4, April 2002, pp. 58–66. [5] 3rd Generation Partnership Project (3GPP); Technical Specification Group Radio Access Network; Physical Layer Aspects for Evolved UTRA, http://www.3gpp.org/ftp/Specs/html-info/25814.htm, date of site access 24/08/2013. [6] Yong Wang · Jianhua Ge · Lihua Wang · Jing Li (2012) “Reduction of PAPR of OFDM Signals Using Nonlinear Companding Transform” Wireless Pers Communication DOI10.1007/s11277-012-0820-2 [7] Hou, J., Ge, J., Zhai, D., & Li, J. (2010). Peak-to-average power ratio reduction of OFDM signals with nonlinear companding scheme. IEEE Transactions on Broadcasting, 56(2), 258–262. [8] H. G. Myung, J. Lim, and D. J. Goodman, "Peak-to-Average Power Ratio of Single Carrier FDMA Signals with Pulse Shaping," The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC ’06), Helsinki, Finland, Sep. 2006 [9] H.G. Myung and D.J. Goodman, “Single carrier FDMA: a new air interface for long term evolution,” Wireless Communications and Mobile Computing, 2008, p. 198. [10] U. Sorger, I. De Broeck and M. Schnell, “Interleaved FDMA - A New Spread-Spectrum Multiple-Access Scheme,” Proc. IEEE ICC ’98, pp. 1013–1017, Atlanta, GA, June 1998. [11] T. S. Rappaport, Wireless Communications: Principles and Practice, Second Edition. Prentice Hall, 2002