International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 70
ISSN 2229-5518
A Comparative Study of PAPR Reduction
Techniques for OFDM Systems: An Overview
Sapna Agarwal, Pankaj Sharma, Joyti, Rahul Choudhary, Ruchi Singh
Abstract— Orthogonal Frequency Division Multiplexing (OFDM) has been adopted as a predominant access technique to meet the challenges offered by next generation broadband wireless mobile systems. OFDM has gained a lot of interest in recent years because of its robustness against multipath fading. Despite many potential advantages offered by OFDM system, it suffers from major drawback of high Peak-to-Average Power Ratio (PAPR) which leads to inefficiency of radio frequency (RF) power amplifiers. In this paper, some of the important PAPR reduction techniques are reviewed and their analysis is done on the basis of their computational complexity, BER performance, spectral efficiency etc.
Index Terms— Orthogonal Frequency Division Multiplexing (OFDM), Peak-to-Average Power Ratio (PAPR), High Power Amplifier (HPA), Complementary Cumulative Distribution Function (CCDF), Partial Transmit Sequence (PTS), Selective Mapping (SLM).
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OFDM is a multicarrier modulation technique for future mobile communication systems due to many advantages such as high spectral efficiency, low implementation complexity, robustness with respect to multipath fading and ability for high data rates [4]. Therefore, OFDM has been widely de- ployed in many wireless communication standards such as IEEE 802.11a standard for Wireless Local Area Networks (WLAN), IEEE 802.16a standard for Wireless Metropolitan Area Networks (WMAN), Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), the European HIPER- LAN/2 and high speed cellular data [7].
OFDM is a parallel multicarrier transmission scheme whose basic principle is to split a high-rate data stream into a number of lower rate streams that are transmitted simultaneously over a number of subcarriers. Because the symbol duration increas- es for lower rate parallel subcarriers, the relative amount of dispersion in time caused by multipath delay spread is de- creased. Intersymbol interference is eliminated almost com- pletely by introducing a guard time in every OFDM symbol. In the guard time, the symbol is cyclically extended to avoid intercarrier interference [5].
However, the major problem one faces while implementing OFDM system is the high peak-to-average power ratio of this system. A large PAPR increases the complexity of the analog- to-digital and digital-to-analog converter and reduces the effi- ciency of the radio-frequency (RF) power amplifier [8], which may severely impair system performance due to non-linear distortion and detection efficiency degradation [1]. The non-
linear effects on the transmitted OFDM symbols are spectral
PAs requires a back off which is approximately equal to PAPR for distortion-less transmission. This situation leads to de- crease in the efficiency of amplifiers and make them expensive [6].
At present, various PAPR reduction methods have been proposed in literature including clipping and filtering, selec- tive mapping, partial transmit sequence, coding techniques
etc. In order to utilize the technical features of the OFDM, it has been necessary to research on the characteristics of the PAPR, including its distribution and reduction. In this paper, a comprehensive review and comparison of some of the im- portant PAPR reduction methods is given based on theoretical analysis.
In this paper, firstly we describe the OFDM system model. Then we define the PAPR and give the classification of PAPR reduction methods. Then we analyse five typical techniques of PAPR reduction and finally compare them on the basis of transmission power, data rate loss, implementation complexi- ty and Bit-Error-Rate (BER) performance etc.
Let a block of N symbols X={Xk , k=0,1,2,...N-1} is formed with each symbol modulating one of a set of subcarriers {fk , k=0,1,2,...N-1} where N is the number of subcarriers. The N are chosen to be orthogonal, that is, fk =k∆f, where ∆f=1/NT and T is the original symbol period. Therefore, the complex envelope of the transmitted OFDM symbol signals can be written as:
N −1
spreading, intermodulation and changing the signal constella-
x(t) =
1 ∑ X
e j 2πf k t , 0 ≤ t ≤ NT
(1)
tion. In other words, the nonlinear distortion causes both in- band and out-of-band interference to signals. Therefore, the
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• Sapna Agarwal, EC Department, MIT, Moradabad, India.
• Dr. Pankaj Sharma, EC Department, MIT, Moradabad, India.
• Jyoti, EC Department, MIT, Moradabad, India.
• Rahul Choudhary, EC Department, MIT, Moradabad, India.
• Ruchi Singh, EC Department, MIT, Moradabad, India.
N k =0
where j=√(-1)
The equation (1) defines the OFDM signal x(t) where N
subcarriers are added together. If N is large enough, then,
based on central-limit theorem (CLT), the resulting signal x(t)
will be close to a complex Gaussian process. This means that
both of its real and imaginary parts are Gaussian distributed
and its envelope and power follows Rayleigh and exponential
distributions respectively [2].
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In general, the PAPR of OFDM signals x(t) is defined as the ratio between the maximum instantaneous power and its av- erage power:
One of the simplest approaches to reduce the PAPR of OFDM symbols is to clip the parts of the signals that are out- side the allowed region. In this method, a soft limiter is em- ployed to clip the signal envelope to a predefined threshold
max
2
x(t )
level if the signal exceeds that level; otherwise, the limiter
PAPR[ x(t )] = 0≤t ≤ NT
Pav
(2)
passes the signal without change [2,3]. The clipping function
F(x[n]) is defined as:
where Pav is the average power of x(t) and it can be com- puted in the frequency domain because Inverse Fast Fourier
x[ n]
if x[ n] ≤ A
Transform (IFFT) is a (scaled) unitary transformation [1].
To better approximate the PAPR of continuous-time OFDM
F (x[ n]) =
Ae
j∠x[n]
if x[ n] > A
(6)
signals, the OFDM signals samples are obtained by L times
oversampling. L-times oversampled time-domain samples are
LN-point IFFT of the data block with (L-1)N zero-padding. The
where x[n] is the OFDM signal, A is the clipping level and
<x[n] is the angle of x[n}. The clipping ratio γ is defined as:
PAPR computed from the L–times oversampled time domain
OFDM signal samples can be defined as:
γ = A Pavg
(7)
max
x[n] 2
where P
avg
is the average power of the signals before clip-
PAPR{x[n]} = 0≤n≤ N −1
(3)
ping.
E 
x[n]
2
where E{.} denotes the expectation operator.
The most informative metric used for evaluating the PAPR
is complementary cumulative distributive function (CCDF).
PAPR reduction capability is measured by the amount of CCDF reduction achieved. CCDF provides an indication of the probability of the OFDM signal’s envelope exceeding a speci- fied PAPR threshold within the OFDM symbol and is given
by:
Clipping is a nonlinear process and causes both in-band distortion and out-of-band radiation into OFDM signals, which degrades the system performance including BER and spectral effi- ciency. Filtering after clipping can preserve the spectral effi- ciency and hence improve the BER performance but it can gen- erate large time-domain peaks [9]. For this reason, to reduce the peak regrowth, a repeated clipping and filtering operation is used to ap- proach a desired PAPR reducti on. However, the iterative signal takes long time and it will increase the computational com- plexity of an OFDM transmitter.
CCDF {PAPR(x n (t ))}= prob{PAPR(x n (t ))> δ }
(4)
As improved clipping methods, peak windowing schemes at-
where PAPR(xn(t)) is the PAPR of the nth OFDM symbol and δ is some threshold. The probability of PAPR of the nth OFDM symbol with N subcarriers exceeding a threshold δ is ex- pressed by the CCDF as [2]:
tempt to minimize the out of band radiation by using narrowband
windows such as Gaussian window to attenuate peak signals [1].
CCDF {PAPR(x n (t ))}= 1 − (1 − e− δ )LN
where L is oversampling factor.
(5)
A large PAPR would drive PAs at the transmitter into satu- ration, producing interference among the subcarriers that de- grades the BER performance and corrupts the spectrum of the signal. To avoid driving the PA into saturation, the PAPR should be reduced and it is preferable to solve the problem of high PAPR by reducing the peak power of the signal [2]. PAPR reduction techniques are broadly classified into two categories- Signal Scrambling Techniques and Signal Distor- tion Techniques. Signal scrambling techniques scramble the input data sequence using a number of specialized scrambling sequences and the sequence which produces the lowest PAPR is used for transmission. Signal distortion techniques reduce the PAPR by distorting the transmitted OFDM signal before passing it through the PA. These techniques causes both in- band and out-of-band distortion which leads to increase in BER [13]. Fig.1 shows the classification of PAPR reduction techniques.
Fig.1. Classification of PAPR reduction techniques
In the TR scheme, a small number of unused subcarriers called peak reduction carriers (PRCs) are reserved to reduce the PAPR and the goal of the TR scheme is to find the optimal values of the PRCs that minimize the PAPR of the transmitted OFDM
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International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 72
ISSN 2229-5518
signal. Fig.2 describes the block diagram of tone reserva- tion (TR). The objective of TR method is to find the time
plication of X and b m.
x m = IFFT X e jψ m ,1 X
jψ
e m , 2 .....X
jψ
e m ,N
(12)
domain signal c to be added to the original time domain
signal x to reduce the PAPR. If the added frequency vector
is denoted as C, then the new OFDM signal is defined as
[2]:
1 2 N
The ability of PAPR reduction in SLM depends on the number of generated phase sequences M and the design of
~x = x + c = IFFT (X + C )
(8)
these phase sequences. Information about the selected phase
sequence should be transmitted to the receiver as side infor-
To achieve distortionl ess data transmission, the data symbol vec-
tor X=[X0 X0...... X N-1 ] and the reserved symbol vector C=[C0
C0...... CN-1 ] are restricted to lie in the disjoint frequency sub- spaces, i.e.,
mation so that the original symbol sequence can be recovered at the receiver which reduces the data transmission rate. The SLM needs [log2 M] bits as side information and 'M' IFFT oper- ations for each data block [15]. The phase sequences need to be
X n n n
n ∈ S
c
(9)
stores at both the transmitter and receiver. If the side infor-
mation is detected erroneously at the receiver then it causes
n
n ∈ S
the incorrect recovery of the whole OFDM symbol. Therefore,
strong protection of the side information is required resulting
where S denotes the index set of the data-bearing subcarri-
ers and Sc represents the index set of the PRCs [10]. With this
design approach, at the receiver the information symbols are
simply recovered by selecting the outputs of the FFT with in-
dices in the set, requiring no extra operation. In addition, no
side information is required to be transmitted. The Tone Res-
ervation is a simple algorithm, used at transmitter of the
OFDM system without any additional complexity at the re-
ceiver end. The reserved tones for PAPR reduction may pre-
sent a non-negligible fraction of the available bandwidth and resulting in a reduction in data rate.
in more loss of data transmission rate.
Fig. 2 Block diagram of SLM.
0
10
Fig. 2 Block diagram of Tone Reservation.
Original OFDM SLM in OFDM
In SLM, a set of different OFDM symbols xm, 0≤m≤M-1, each of length N, all representing the same information as the
original OFDM symbols are generated, and then the symbol 10-2 with the least PAPR is transmitted. Mathematically, the transmitted OFDM symbol x is represented as:
~x = argmin PAPR x m
(10) 10-3
0≤m≤ N −1
where argmin[.] represent the argument of its value is min- imized.
A block diagram of the SLM technique is depicted in Fig.3. The original data block X=[X1 , X2 .... XN] is multiplied ele- ment-by-element by M different phase sequences b m, each of length N, prior to performing IFFT. These phase sequences are represented as:
-4
10
4 5 6 7 8 9 10 11 12
PAPR (db)
Fig. 2 PAPR performance of SLM and original OFDM for N=64, L=4, M=4
b = e
jψ m,1 , e
jψ m,1 .....e
jψ m, N
, 0 ≤ m ≤ M − 1
(11)
The optimization process of selecting the best out of M
OFDM signals may become more computational if the size of
the OFDM blocks is large and if the number of phase sequenc-
where ψm,k takes value between 0 and 2π, excluding 2π, i.e.,
ψm,k є [0, 2π) for k=1,2...N. Therefore, the modified OFDM sym- bol xm, 0≤m≤M-1, is the IFFT of the element-by-element multi-
es M is increased, which is required to achieve a considerable
PAPR reduction.
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In PTS, the input data block, X=[X1 X2 ...... XN], is parti- tioned into V disjoint subblocks, which are represented by the vectors {X(m), m=0,1,...., V-1} as shown in fig. Therefore, we can get:
V −1
take W different values, b m=e[j2πk/W], where k=0,1, ..., W-1.. The first phase factor b 1 can be set to 1 without any loss of per- formance; therefore, V-1 phase factors are to be found by an exhaustive search. Hence, WV-1 sets of phase factors are searched to find the optimum one. The reduction of PAPR by PTS scheme depends on the value of V and W. On one hand,
X = ∑ X (m)
m=0
(12)
the larger is the number of sub blocksV, the greater is the re- duction in PAPR. On the other hand, the search complexity is
where
X (m) = [ X (m) X (m) .....X (m) ] , 0≤m≤V-1. In general, the
increasing exponentially with V. In general, PTS needs V IFFT
0 1 V −1
sub-block partitioning can be done in three ways: adjacent partition, interleaved partition and pseudorandom partition. Then, the IFFT for each sub-block, xm, 0≤m≤V-1, is computed
operations for each data block and number of the required
side information bits is [Vlog2W], where [x] denotes the small- est integer that does not exceed x.
and weighted by a phase factor bm
= e jψ m , where ψm=[0,2π),
0≤m≤V-1. The objective now is to select the set of phase fac-
tors, b m's that minimizes the PAPR of the combined time do- main signal x, where x is defined as:
M −1
The main feature of coding techniques is that they have an inherent capability to provide error detection and correction; therefore they serve as more proximity techniques for practical
x = ∑bm x m
m=0
(13)
OFDM system design. The fundamental idea is that of all pos-
sible code words only those which have low peak power will
Therefore, there are two important issues should be solved in PTS: high computational complexity for searching the op- timal phase factors and the overhead of the original phase fac- tors as side information needed to be transmitted to receiver for the correct decoding of the transmitted bit sequence [14].
Fig. 2 Block diagram of PTS.
0
10
original OFDM PTS in OFDM
-1
10
-2
10
-3
10
2 3 4 5 6 7 8 9 10 11
PAPR(db)
be chosen for transmission. This can be done by block coding
the data such that the 3-bit data word is mapped onto a 4-bit
codeword such that the set of permissible sequences does not
contain those that result in high PAPR. However, this ap-
proach suffers from the need to perform an exhaustive search
to find the best codes and to store large lookup tables for en-
coding and decoding, especially for a large number of subcar-
riers and also this approach does not address the problem of error correction [11].
Large PAPR reduction can be achieved if the long infor- mation sequences are divided into sub-blocks, using sub-block coding (SBC) scheme. In SBC method, an odd parity bit is added to each sub-block and position of the added parity is optimized to further reduce PAPR. Moreover instead of one coding scheme, two coding schemes can be used to encode each sub-block, and the combination of the coded sub-blocks can be optimized to lower PAPR. Both methods require the transmission of the side information to the receiver to indicate the locations of the parity bits or the coding schemes used to encode each sub-block. This means that the bandwidth effi- ciency of the system will be reduced [2].
On the other hand, it is discovered that the use of a Golay complementary sequence as codewords to control the modula- tion results in signals with a PAPR of at most 2. Golay com- plementary sequences are the sequence pairs for which the sum of autocorrelation functions is zero for all delay shifts unequal to zero [12]. The schemes that combine block coding approach and the use of GCS, can incorporate both features of error correction and control over PAPR. However such schemes are useful for OFDM systems with large number of subcarriers. For OFDM systems with large number of subcar- riers, this approach results in transmission rate loss and in- creased computational complexity due to the exhaustive search requires to find good codes [2].
Fig. 2 PAPR performance of PTS and original OFDM for N=64, L=4, V=4, W =4
Assume there are W phase angles to be allowed, thus b m can
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TABLE 1
COMPARISON OF PAPR REDUCTION TECHNIQUES
OFDM is an attractive multicarrier modulation technique for wired as well as wireless applications due to its robustness against multipath fading, high data rates and spectral efficiency. The major drawback of OFDM system is its high PAPR due to which PA drives into saturation region and causes non-linear distortion and spectral spreading. There are several techniques in literature to reduce PAPR which decrease the PAPR substantially at the expense of increased BER, increased transmitted power, reduced bit rate, or increased complexity. In this paper, five typi- cal PAPR reduction techniques are analysed and their comparison is done on the basis of BER performance, bit rate loss, implemen- tation complexity and transmit signal power increase.
We analyse that all the techniques can reduce PAPR signifi-
cantly but no single technique can provide best results under all circumstances. Therefore, a proper technique should be selected on the basis of system requirements and available resources.
We would like to thank our Director General Prof. (Dr.) S. Mukherjee and the HOD, ECE Department and all other facul- ty members for extending their help and support in giving technical ideas about the paper and motivating to complete the work effectively and successfully.
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Sapna Agarwal is currently pursuing her B.Tech in Elec- tronics and Communication Engineering from Moradabad Institute of Technology affiliated to UPTU, India. Her re- search interests include Wireless communication systems, especially OFDM systems with emphasis on PAPR problem. E-mail: sapnaagarwal09314@gmail.com
Dr. Pankaj Kumar Sharma received his B.E. degree in E&T.C. Engineering from North Maharashtra University, Jalgaon (M.S), India, M. Tech. and Ph.D. degree from MNNIT, Allahabad, India. He is currently with M.I.T, Mo- radabad (U.P.), India, where he is working as an Associate Professor in the Department of Electronics and Communica- tion Engineering. He is a member of IEEE, Institution of Engineers (India), Institution of Electronics and Telecom-
munication Engineers (IETE), Computer Society of India (CSI), Indian Society for Technical Education (ISTE) and International Association of Engineers (IAEN), Hongkong. He has authored or co-authored more than 30 technical
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International Journal of Scientific & Engineering Research, Volume 5, Issue 5, May-2014 75
ISSN 2229-5518
papers in major national and international conferences and journals. His current research interests are in the area of wireless communication systems, especially OFDM systems with emphasis on PAPR problem.
E-mail: pankaj354518@yahoo.com
Jyoti is currently pursuing her B.Tech in Electronics and Communication Engineering from Moradabad Institute of Technology affiliated to UPTU, India.
E-mail: jyotipalxx2@gmail.com
Rahul Choudhary is currently pursuing her B.Tech in Electronics and Communication Engineering from Morada- bad Institute of Technology affiliated to UPTU, India.
E-mail: rahulchoudhary1079@gmail.com
Ruchi Singh is currently pursuing her B.Tech in Electron- ics and Communication Engineering from Moradabad Insti- tute of Technology affiliated to UPTU, India.
E-mail: ruchisingh2424@gmail.com
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