 Open Access
 Total Downloads : 210
 Authors : Raghavendra B K, Dr. D. Seshachalam, Suma M. N
 Paper ID : IJERTV3IS061472
 Volume & Issue : Volume 03, Issue 06 (June 2014)
 Published (First Online): 02072014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Comparison of PAPR Reduction by Coding in OFDM System
Raghavendra B K*, Suma M.N**, Dr. D. Seshachalam***
*M.Tech. Dept of Electronics & Communication, B.M.S.C.E, Bangalore, India
**Associate Professor, Dept of Electronics & Communication, B.M.S.C.E, Bangalore, India
***Professor and H.O.D, Dept of Electronics & Communication, B.M.S.C.E, Bangalore, India
Abstract – Orthogonal Frequency Division Multiplexing (OFDM) is an efficient modulation technique in both broadband wired and wireless communication. It has many advantages such as eliminating Inter symbol Interference (ISI), efficient use of spectrum and dividing the channel into narrowband flat fading sub channels and many more. One of the major disadvantages of OFDM is that the time domain OFDM signal which is a sum of several sinusoids leads to high peak to average power ratio (PAPR). This paper investigates three methods for PAPR reduction such as combined Rotated Hadamard transform, combined Riemann transform and ZadoffChu Matrix Transform to achieve more novel PAPR reduction. The performance of these PAPR reduction techniques are analyzed by plotting the complementary cumulative distribution function (CCDF) plot and calculating BER and a comparison is made between all the above methods. The simulation results shows that the ZadoffChu Matrix Transform reduces PAPR much better than the Rotated Hadamard transform, Riemann matrix transform and Conventional OFDM.
Keywords OFDM, PAPR, Hadamard transform, Riemann, ZCT, companding, CCDF, BER,

INTRODUCTION
In todays world, wireless communications has become an essential part of everyday life. Orthogonal frequency division multiplexing (OFDM) has become popular in wireless applications. OFDM provides greater immunity to multipath fading and also reduces the complexity of equalizers [1]. OFDM is widely adopted in various communication standards like Digital Audio Broadcasting (DAB), Digital video
Broadcasting (DVB), Wireless Local Area Networks (WLAN), Wireless Metropolitan Area Networks (WMAN),
all variations on how to scramble the codes to decrease the PAPR. Coding techniques can be used for signal scrambling [4]. Comparatively signal distortion techniques are straight forward techniques. Signal distortion methods distort the high peak valued portion of OFDM signals using different techniques for PAPR reduction. The precoding based techniques are simple linear techniques to implement without the need of any side information. This paper compares the three precoding methods for PAPR reduction such as combined Rotated Hadamard transform (RHT), combined Riemann matrix Transform (RMT) and ZadoffChu Matrix Transform (ZCT) to achieve more novel PAPR reduction.
The rest of the paper is organized as follows: section II describes the PAPR problem in OFDM system. Section III compares the different transforms. Section IV reports steps involved in the scheme. Section V reports the simulation results and conclusion is presented in section VI.

SYSTEM MODEL
This section illustrates the basic OFDM system and the PAPR definition. Figure 1 gives the block diagram of an OFDM system consisting of N subcarriers. Baseband modulated symbols are passed through serial to parallel converter which generates complex vector of size N. We can write the complex vector of size N
as X = X0 X1 . . XN 1 T. X is then passed through the IFFT block. The complex baseband OFDM signal with N subcarriers can be written as
1 N1
IEEE 802.11 and IEEE 802.16 wireless broadband access systems, etc.
Large PAPR could cause poor power efficiency or serious
x n X(k)ej2nk / N
N k0
n=0, 1, 2 N1 (1)
performance degradation to transmit power amplifier [2]. Therefore, nonlinearities may get overloaded by high signal peaks, causing inter modulation among subcarriers and, more critical, undesired outofband radiation. If RF power amplifiers are operated without large power backoffs, it is
The PAPR is the ratio of peak power to the average power of OFDM signal. For discrete time domain OFDM signal, it can be calculated as.
max{ xn2 }
impossible to keep the outofband power below specified
PAPR dB 10 log
(2)
limits. This leads to very inefficient amplification and expensive transmitters so that it is highly desirable to reduce the PAPR [3].
Several schemes have been proposed to reduce the PAPR. These techniques can mainly be categorized into three types namely Signal scrambling techniques, Signal distortion techniques and block coding. Signal scrambling techniques are
10
E{ xn2 }
Data
QAM/ PSK
Mapping
S/P
Add CP
and IFFT
P/S
directly translated into a better BER performance in OFDM system of rotated Hadamard over Hadamard.

Riemann matrix transform
The Riemann matrix [6] is defined by
A = B (2: n+1, 2: n+1)
AWGN
Channel
Where,
1 otherwise
Bi, j i 1 if i divides j
The Riemann matrix has these properties:
(6)
Data
QAM/ PSK
Demapping
P/S
Remove CP and FFT
A/D

Each Eigen value e (i) satisfies e i m 1 , where
m
m = n+1.

i ei i 1 With at most m m exceptions.
Fig 1 . Block diagram of OFDM system
Where E [.] denotes expectation and the CCDF for an OFDM

All integers in the interval [m/3, m/2] are Eigen values.
Using Equation (6), Riemann Matrix (A) of order 4 can be written as:
signal can be written as.
1 1 1 1
1 2 1 1
(7)
P PAPR PAPR
1 exp PAPR
N
(3)
A
0 0 1 1 3 1
1 1 1 4
Where PAPR0 is the clipping level
Equation (2) predicts that the PAPR can be defined by the amplitude of output signal. So when output signal exceed a certain value then obviously PAPR also take a higher value.



COMPARISION OF THE DIFFERENT TRANSFORMS

Companding transforms
A companding transform [7] [8] performs compression at the transmit end after the IFFT process and expansion at the receiver end prior to FFT process. After companding, the signal now becomes.
A. Rotated Hadamard Transform
The rotated Hadamard matrix [5] is a Hadamard matrix with the rotation described in Equation 4 below.
s n C x n
vx n
ln 1 u x n
ln 1 u
v
x n
(8)
U 1 H
j m
(4)
Where v is the average amplitude of signal and u is the
N M M diag exp C
Where C is the rotation value from which the modulation is rotated back on to itself. H is the Hadamard matrix and M is the size of the matrix. The Hadamard matrix of order 2 is
companding parameter. This transform reduces the PAPR of OFDM signal by amplifying the small signal and shortening the big signal. In receiver end, the receiver signal is to be expanded by the inverse companding transform before it is sent to the FFT process unit. The expanding equation is
given by
vr n r n ln 1 u
y n C1 r n
exp 1
(9)
H 1 1 1
(5)
u r n v
2 2 1
1
The fig 2 shows the system block. The modulation data is multiplied by U and the rotation takes place produing a higher modulation scheme. The rotated Hadamard is capable of achieving 16QAM. So this rotated Hadamard produces a higher order scheme than the traditional Hadamard. This is
D. ZadoffChu Matrix Transform
ZadoffChu sequences [9] are class of poly phase sequences having optimum correlation properties. ZadoffChu sequences have an ideal periodic autocorrelation and constant magnitude. The ZadoffChu sequences of length L can be defined as:
j 2 r k 2
The expression in (18) suggests that xn are IFFT of
L 2
qk
constellation data X1 pre multiplied with quadratic phase and
z k e
j 2 r k k 1qk
for L even
(10)
IFFT precoded, and then alternated with Â±1. The PAPR of ZCTOFDM signal in (16) can be written as
L 2
e for L odd
max{ xn2 }
Where k = 0, 1, 2 L1, q is any integer, r is any integer relatively prime to L and j= 1 .
PAPR dB
2
xn }
(17)
In this technique the baseband modulated data is passed through serial to parallel converter which generates a complex


STEPS INVOLVED
vector of size N that can be written as X X0 X1 ..X
N 1
T .
The PAPR of OFDM signal is reduced by using the above
techniques with companding transform. The input data is
0 1 N 1
Later ZadoffChu Transform (ZCT) is applied to this complex vector which transforms this complex vector into new vector of length N that can be written as Y=RX= Y Y ..Y T
Where R is a ZCT based rowwise precoding matrix of size L = NÃ—N. With the use of reordering as given in equation (11)
k mN l (11)
Matrix R with row wise reshaping can be written as
transformed by Rotated Hadamard Transform or Riemann Matrix transform or by using ZCT, The transformed data stream is given as input to IFFT signal processing unit. The block diagram of the system is as shown in fig 2.
The signal processing step is as below:
Step 1: The sequence X is transformed by RHT or RMT or ZCT i.e. Y=KX.
Step 2: y=IFFT(Y), where y=[y (1) y (2) y (N)] T
Step 3: Do companding transform to y, i.e. s (n) =C{y (n)}.
r00
r01
r( N1)0
Step 4: Transmit the signal through an AWGN channel
r r r
Step 5: Do inverse companding transform to the received
R
10 11 ( N1)1
(12)
signal r (n) i.e.
C1 r n
y n
r( N1)0 r( N1)1
rN1( N1)
Step 6: Do FFT transform to signal
y n i.e.
Y FFT(y)
By letting q = 1 and r = 1 the ZCT for Even L can be written
Step 7: Do inverse RHT or RMT or ZCT to the signal
Y, i.e.
as rk= exp [(j*pi*k2) / L2]. Accordingly, precoding X gives
rise to Y as follows:
Y RX
(13)
X KT Y . Then the signal X is demapped to bit stream.

SIMULATION RESULTS
N1
Ym rm,l Xl
l0
m 0, 1,..N 1
(14)
The simulation of the above OFDM system for PAPR reduction is performed using MATLAB. The channel is
Here rm,l means mth row and lth column of precoder matrix. The complex baseband OFDM signal with N subcarriers without precoding is given by
modelled as AWGN channel. In simulation, an OFDM system with subcarrier N=64 is considered and for mapping MQAM (Where M=16, 64) modulations are used. The simulation results show the comparison between RHT, RMT, ZCT and conventional OFDM.
1
N1
j2nm/ N
N
xn Xm e
m0
n=0, 1, 2.. , N1 (15)
Fig 3 and Fig 4 shows the CCDF comparisons of ZCT with
RHT, RMT and OFDM conventional without and with companding (u=1) respectively for N=64. At clip rate of 101,
However, expanding (15) while using q = 1 and r = 1 in (10), gives complex baseband ZCT precoding based OFDM signal with N subcarriers as
the PAPR gain of 5.3dB, 4.8dB and 4.4dB is achieved without companding and it is 5.7dB, 3dB and 2.7dB with companding.
N1
L1
jl2
2ml
xn
1 e
N
j2nm/ N e
jm2
Yl e L e L
2
j
(16)
m0
l0
Data
QAM/PSK
Mapping
S/P RHT or RMT
or ZCT
IFFT
Companding Transform
P/S
Channel
AWGN
Data QAM/PSK Demapping
P/S
Inverse RHT or RMT
or ZCT
FFT
Companding Transform Inverse
S/P
Fig 2 . General block diagram for the above Techniques
When ZCT OFDM system is compared with conventional OFDM, RMT and RHT for 16QAM modulation
Fig 3 . CCDF plot without companding for N=64 and M=16 QAM
Fig 4 CCDF plot with companding for N=64 and M=16 QAM
Fig 5 CCDF plot with companding for N=64 and M=16 QAM
Fig 6 . CCDF plot without companding for N=64 and M=64 QAM
Similarly Fig.5 and Fig.6 shows that at clip rate of 101 the PAPR gain of 4.3dB, 3.8dB and 3.3dB is achieved without companding and it is 5.5dB, 2.6dB and 2.2dB with companding when ZCT OFDM system is compared with conventional OFDM, RMT and RHT for 64QAM modulation.
Fig 7 and fig 8 shows the BER performance of above mentioned techniques in AWGN channel for 16 QAM modulations without and with companding. Similarly fig 9 and fig 10 shows the BER performance of above techniques in AWGN channel for 64 QAM modulations without and with companding.
Fig 7 . BER plot without companding for N=64 and M=16 QAM
Fig 8 . BER plot with companding for N=64 and M=16 QAM
From fig 7 it is observed that to achieve BER of 101 the ZCT OFDM requires 5.5 dB SNR whereas conventional OFDM requires 6.8dB and RHT requires 9dB SNR hence ZCT based OFDM system shows better BER reduction compared to all the other transforms.
Fig 9 . BER plot without companding for N=64 and M=64 QAM
Fig 10 . BER plot with companding for N=64 and M=64 QAM
Table 1 and table 2 summarize the PAPR comparison for the above mentioned schemes without and with companding technique. It is observed that the companding technique greatly reduces PAPR in RMT and RHT compared to ZCT and conventional OFDM for both 16QAM and 64QAM modulation.
WITHOUT COMPANDING (CLIP RATE 101)
Type of Modulation (M QAM)
PAPR of OFDM (dB)
PAPR of RMT
( dB )
PAPR of RHT
( dB )
PAPR of ZCT (dB)
16
8.3
7.8
7.4
3
64
8.5
8
7.5
4.2
TABLE I. PAPR COMPARISON WITHOUT COMPANDING
TABLE II. PAPR COMPARISON WITH COMPANDING
WITH COMPANDING (CLIP RATE 101)
Type of Modulation (M QAM)
PAPR of OFDM (dB)
PAPR of RMT
( dB )
PAPR of RHT
( dB )
PAPR of ZCT (dB)
16
8.3
5.4
5.1
2.4
64
8.5
5.6
5.2
3

CONCLUSION
In this paper Comparison of three different transforms for PAPR reduction in companding technique for OFDM system is performed. The BER and CCDF plots for these three transforms are obtained for 16QAM and 64QAM modulation techniques.
It is clear from tables 1 and table 2 that ZCT based OFDM system reduces PAPR much better than te Rotated Hadamard matrix transform, Riemann matrix transform and Conventional OFDM and it also reduces BER much better than all the other mentioned schemes. In addition ZCT OFDM systems dont require any side information to be sent for the receiver. Thus it is concluded that ZCT based OFDM system are more favourable than Rotated Hadamard Transform, Riemann matrix transform and Conventional OFDM.
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