Technique. Navneet Kaur, Lavish Kansal. Department of Electronics and Communication Engineering. Lovely Professional University, Phagwara. Punjab, India.
(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013
PAPR Reduction of OFDM Signal by Using Walsh Hadamard Transform with -Law Companding Technique Navneet Kaur, Lavish Kansal Department of Electronics and Communication Engineering Lovely Professional University, Phagwara Punjab, India
Abstract—Orthogonal Frequency Division Multiplexing (OFDM) is an emerging field of research in wireless communication and telecommunication. OFDM finds its application where high data rate is required at low latency and better spectral efficiency as it provides enhanced spectral efficiency than Frequency division multiplexing (FDM). Peak to Average Power Ratio (PAPR) is the limiting factor for an OFDM system as it degrades the system performance. There are many techniques to overcome the problem of PAPR. Precoding is a new method which is having less complexity compared to the other power reduction techniques and also it can reduce PAPR considerably and results in no distortion. In this paper, a joint -Law companding technique and Walsh Hadamard Transform (WHT) method is proposed to reduce peak-to-average of OFDM signal in Additive White Gaussian Noise (AWGN). The performance of the techniques was evaluated by using computer simulations. Simulation results shows that the proposed scheme may obtain significant PAPR reduction while maintaining good performance as compared to ordinary precoding method. Keywords— OFDM, FFT, PAPR, AWGN, CCDF, WHT
I. INTRODUCTION The Orthogonal Frequency Division Multiplexing (OFDM) has drawn major attention over last decade for its usefulness in broad band wireless communication. Due to its numerous benefits like high data transmission rate, high bandwidth efficiency, robustness against multi-path fading and less complex equalizer. OFDM is a multi-carrier modulation technique where data symbols modulate a subcarrier which is taken from orthogonally separated subcarriers with a separation of within each sub-carrier [1]. Here, the spectra of sub-carrier are overlapping; but the sub-carrier signals are mutually orthogonal, which is utilizing the bandwidth very efficiently. To maintain the orthogonality, the minimum separation between the sub-carriers should be to avoid Inter Carrier Interference (ICI) and Inter Symbol Interference (ISI). By choosing the sub-carrier spacing properly in relation to the channel coherence bandwidth, OFDM can be used to convert a frequency selective channel into a parallel collection of frequency flat sub-channels.
OFDM uses a large quantity of closely roomed orthogonal sub-carriers fig. 1 shows the generation of the OFDM signal through the block diagram. The Basic Principle is to split a high Data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers. N input bits are sending for channel coding and interleaving. Coding and interleaving are added in the system to obtain the robustness needed to protect against burst errors. Using conventional modulation scheme each sub-carrier is modulated such as PSK, QAM etc. at a low symbol rate, maintaining data rates related to conventional distinct carrier modulation systems in the equivalent bandwidth. Then N such symbols are transferred by the serial-to-parallel converter where single steam is divided into similar streams .Therefore the high bit rates seen early on a single carrier is condensed to lower bit rates on the subcarrier These complex parallel data symbols are then fed to the IFFT block for a normal OFDM system. . As a result, the OFDM symbol generated for an N-subcarrier system translates into N samples, with the sample being: =∑
exp{
} ; 0≤ i≤ N-1
(1)
The most effective guard period i.e cyclic prefix is used for extension of the symbol. This allows time for multipath signals from the previous symbol to die away before the information from the current symbol is gathered thus reduces ISI and ICI. OFDM transmission scheme is an attractive technology but has one major drawback of high PAPR. Peak-to-average power ratio (PAPR) is proportional to the number of subcarriers used for OFDM systems. An OFDM system with large number of subcarriers will thus have a very large PAPR when the subcarriers add up coherently. Large PAPR of a system makes the implementation of digital-to-analog converter (DAC) and analog-to-digital converter (ADC) extremely difficult. The design of RF amplifier also becomes increasingly difficult as the PAPR increases.
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(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013
Fig 1: Block Diagram of OFDM system
To reduce the PAPR, many techniques have been proposed. Such as clipping, coding, partial transmit sequence (PTS), selected mapping (SLM), interleaving [2] [3], nonlinear companding transforms[4] [5], hadamard transforms [6] and other techniques etc. these schemes can mainly be categorized into signal scrambling techniques, such as PTS, and signal distortion techniques such as clipping, companding techniques. -Law companding shows better performance than other existing nonlinear techniques because it reduces the distortion of signal. Walsh hadamard transform may reduce PAPR of OFDM signal without increasing while the error probability of the system [6]. In this paper, an efficient reducing PAPR technique based on joint -Law companding and walsh hadamard transform method is proposed. This scheme will be compared with the walsh hadamard precoding technique. The organization of this paper is as follow. Section II presents the PAPR problem in OFDM systems. -Law companding technique is introduced in section III .Walsh Hadamard Transform is explained in section IV. In section V, a PAPR reduction scheme by combing -Law companding technique with walsh hadamard transform precoding technique is proposed. Simulation results are reported in section VI and conclusions are presented in VII. II. PAPR IN OFDM SYSTEM A multicarrier signal is the sum of many independent signals modulated onto sub channels of equal bandwidth. An OFDM symbol consists of N subcarriers by the frequency spacing of f. Thus, the total bandwidth B will be divided into N equally spaced subcarriers and all the subcarriers are orthogonal to each other within a time interval of length T= ⁄ . Each subcarrier can be modulated independently with the complex modulation symbol , where m is a time index and n is a subcarrier index. Then within the time interval T the following signal of the m-th OFDM block period can be described as: = where,
∑
The total continuous time signal x (t) consisting of all the OFDM block is given as: =
{
∑
∑
=
(5)
If the bandwidth of the OFDM signal is B = N x f and the signal x (t) is sampled by the sampling time of t = , then the OFDM signal is in discrete time form and can be written as shown in: =
⁄
∑
⁄
X(t) = ∑
where, (t) is a rectangular pulse applied to each subcarrier [7].
(6)
(7)
PAPR is defined as:
PAPR =
(8)
The mean envelope power of the baseband expression defined as: |
|
(9)
The average power is defined as: = E [P] =E[|
(3)
, k=0, 1,…, N-1
where, n denotes the index in frequency domain and X is the complex symbol in frequency domain. Due to the presence of large number of independently modulated sub-carriers in an OFDM system the peak value of the system can be very high as compared to the average of the whole system. This ratio of the peak to average power value is termed as Peak-to-Average Power Ratio (PAPR). The PAPR is the relation between the maximum powers of a sample in a given OFDM transmit symbol divided by the average power of that OFDM symbol. The mean envelope power of the baseband expression:
P= ∑ (2)
(4)
For a single OFDM symbol consider (m=0) without loss of generality. This can be shown because there is no overlap between different OFDM symbols. Since m = 0, can be replaced by .Then, the OFDM signal can be described as follows:
(t) is defined as: (t)
∑
| ]
(10)
Complementary Cumulative Distribution Function (CCDF) curves present vital information regarding the OFDM signal to be transmitted. It is used to measure the
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(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013 effectiveness of PAPR reduction technique, which is the probability that PAPR exceeds some threshold.
III. -LAW COMPANDING TRANSFORM The Orthogonal Frequency Division Multiplexing (OFDM) signal is similar to the speech signal, in the sense that large signals occur very infrequently, the same companding technique can be used to improve the OFDM transmission performance .The key idea of the Mu Companding Transform is to effectively reduce the Peak-toAverage Power Ratio (PAPR) of the transmitted or the companded OFDM signals by transforming the statistics of the amplitudes of these signals into uniform distribution. The uniform distribution of the signals can be obtained by compressing the peak signals and expanding the small signals. The process of companding enlarges the amplitudes of the small signals, while the peaks remain unchanged. Therefore, the average power is increased and thus the Peakto-Average Power Ratio (PAPR) can be reduced. This technique also eliminates the Out-of-Band Interference (OBI), which is a type of distortion caused by clipping the original OFDM signals. The other advantage of the companding transform is that, it can maintain a constant average power level. The companded signal obtained by using the -Law Companding Transform is given by the equation as: =
| |
(7)
transform is to reduce the autocorrelation of the input sequence to reduce the peak to average power problem and it requires no side information to be transmitted to the receiver. H is assumed as the hadamard transform matrix of N orders, and hadamard matrix is standard orthogonal matrix. The hadamard matrix of 2 orders is stated by: =
]
[
(8)
Every element of hadamard matrix only is 1 or -.1.
PROPOSED SCHEME The goal of precoding techniques is to obtain a signal with lower PAPR than in the case of OFDM without precoding techniques and to reduce the interference produced by multiple users. The -Law Companding Transform also causes less spectrum side-lobes as compared to other reduction techniques. In proposed scheme -Law companding was combined with precoding technique called Discrete Cosine TransformII. An OFDM transmitter combines precoding approach in frequency domain with -Law companding scheme in time domain is shown in fig. 2. ] is modulating Let C, denoted C =[ symbols on K data subcarriers after the process of signal constellation mapping. The vector D is obtained by precoder process and mapping to N -points IFFT with N -L points zero padding is express as: V.
]
D=[ where, =original OFDM signal; =255 and is called as -Law parameter of the compander , that controls the amount of compression; =sign function: = Companded Signal obtained by -Law Companding Transform. The original OFDM signal is converted into the companded signal by using the -Law Companding Transform.
IV. WALSH HADAMARD TRANSFORM The paper, by Park et. al. [8] proposes a scheme for PAPR reduction in OFDM transmission using walsh hadamard transform. The proposed hadamard transform scheme may reduce the occurrence of the high peaks comparing the original OFDM system.The idea to use the hadamard
(9)
After the IFFT process, the complex signal in the time domain can be written as: =
⁄
∑
, k=0, 1,…, N-1
(10)
After applying the DCT-II on OFDM signal the signal get compressed decreasing the PAPR value. -Law companding is performed on the I and Q outputs of the IFFT after precoding. A --Law companding technique utilizes --Law algorithm companding transform by compressing the peak signals and enlarging the small signals for reducing PAPR. By using -Law companding techniques, the new signal of proposed scheme is express as: =
|
Fig. 2 Block scheme of DCT-II Precoding technique with-law companding in OFDM system
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|
(11)
(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013
PAPR Reduction for PSK Modulation
0
VI. SIMULATION RESULTS Computer simulations are used to evaluate the peak-toaverage ratio reduction capability with proposed scheme in this section.. In simulation, an OFDM system is considered where data is randomly generated with subcarriers N=2400, then the signal is modulated by M-PSK and M-QAM respectively. The channel modeled is an additive white Gaussian noise (AWGN). The PAPR reduction capability is measured by the complementary cumulative distribution (CCDF = Prob (PAPR>PAPR0), which indicates the probability that PAPR is above a certain threshold. We compared the simulation results of proposed system with DCT-II precoded OFDM signal and precoded clipped signal. The results are presented in following figures and then the reduction in PAPR value was observed for precoded signal and for clipped precoded signal.
10
CCDF
(WHT OFDM) (Companded)
-1
10
-2
10
5
5.5
6
6.5
7
7.5 PAPR0
8
8.5
9
9.5
10
Fig. 4: CCDF of -Law companding with proposed WHT technique for 32 PSK PAPR Reduction for PSK Modulation
0
10
Fig. 4 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=32 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
CCDF
(WHT OFDM) (Companded)
-1
10
PAPR Reduction for PSK Modulation -0.1
10
-2
10
5.5
6
6.5
7
7.5 PAPR0
8
8.5
9
(WHT OFDM) (Companded)
9.5
Fig. 3: CCDF of -Law companding with proposed WHT technique for 16 PSK CCDF
Fig. 3 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=16 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
-0.3
10
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10
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10
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7 PAPR0
7.5
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9
Fig. 5: CCDF of -Law companding with proposed WHT technique for 64 PSK
Fig. 5 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=64 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
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(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013
PAPR Reduction for PSK Modulation
PAPR Reduction for PSK Modulation -0.1
-0.1
10
10
(WHT OFDM) (Companded)
(WHT OFDM) (Companded)
-0.2
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CCDF
CCDF
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6.4
6.6 6.8 PAPR0
7
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7.4
7.6
Fig. 6: CCDF of -Law companding with proposed WHT technique for 128 PSK
Fig. 8: CCDF of -Law companding with proposed WHT technique for 512 PSK
Fig. 6 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=128 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
Fig. 8 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=512 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
PAPR Reduction for PSK Modulation
PAPR Reduction for PSK Modulation -0.1
10
-0.1
10
(WHT OFDM) (Companded)
(WHT OFDM) (Companded)
-0.2
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CCDF
CCDF
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8
6
PAPR0
6.2
6.4
6.6
6.8 7 PAPR0
7.2
7.4
7.6
7.8
Fig. 7: CCDF of -Law companding with proposed WHT technique for 256 PSK
Fig. 9: CCDF of -Law companding with proposed WHT technique for 1024 PSK
Fig. 7 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=256 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
Fig. 9 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=1024 using PSK modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
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(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013
PAPR Reduction for QAM Modulation
PAPR Reduction for QAM Modulation
0
10
-0.1
(WHT OFDM) (Companded)
(WHT OFDM) (Companded)
10
-0.2
CCDF
CCDF
10
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7.5
8
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8.5
5
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7
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8.5
Fig. 10: CCDF of -Law companding with proposed WHT technique for 16 QAM
Fig. 12: CCDF of -Law companding with proposed WHT technique for 512 QAM
Fig. 10 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=16 using QAM modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
Fig. 12 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=512 using QAM modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
PAPR Reduction for QAM Modulation PAPR Reduction for QAM Modulation
-0.1
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(WHT OFDM) (Companded)
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(WHT OFDM) (Companded)
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Fig. 11: CCDF of -Law companding with proposed WHT technique for 64 QAM
Fig. 11 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=64 using QAM modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
5
5.5
6
6.5 PAPR0
7
7.5
8
8.5
Fig. 13: CCDF of --Law companding with proposed WHT technique for 1024 QAM
Fig. 13 shows the CCDF performance of proposed scheme about the PAPR reduction. In simulation, at CCDF=10-3, for M=1024 using QAM modulation the PAPR of proposed scheme is almost 1 dB smaller than that of companding technique. We can see that when walsh hadamard matrix and -Law companding are combined, this technique provides better performance than that of the simple precoding walsh hadamard transform.
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(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 13 Issue: 02, April, 2013 VII. CONCLUSIONS In this paper, a PAPR reduction scheme based on joint hadamard transform and -Law companding technique is proposed. The PAPR reduction performance and BER performance are evaluated by computer simulation. Simulation results shows that the proposed approach has significant results in PAPR reduction.. On the other hand, the BER of system using proposed PAPR reduction scheme is not degraded. ACKNOWLEDGMENT Foremost, I would like to express my sincere gratitude to Mr. Lavish Kansal who gave his full support in the compilation of this report with his stimulating suggestions and encouragement to go ahead in all the time of the thesis. At last but not the least my gratitude towards my parents, I would also like to thank God for the strength that keep me standing and for the hope that keep me believing that this report would be possible. REFERENCES [1]
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area includes Communication.
Navneet Kaur was born in Kapurthala .She has done her B.Tech degree in Electronics and Communication Engineering from Lovely Professional University, Phagwara, India. She is currently pursuing her M.Tech degree from Lovely Professional University, Phagwara, India. Her research Digital Communication & Wireless
Lavish Kansal was born in Bathinda. He received his B.Tech degree in Electronics and Communication Engineering from PTU, Jalandhar in 2009 and M.E. degree in Electronics and Communication Engineering from Thapar University, Patiala in 2011. He is working as Assistant Professor in the department of Electronics and communication Engineering, Lovely Professional University, Phagwara, India. He has published 15 papers in International journals. His research area includes Digital Signal Processing, Digital Communication & Wireless Communication.
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