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International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 14
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
An Efficient Rate Allocation Scheme with Selective
Weighted Function for Optimum Peak-to-Average
Power Ratio for Transmission of Image Streams
Over OFDM Channels Usama S. Mohammed
#1, and H. A. Hamada
*2
# Department of Electrical Engineering
- Electrical Engineering Department, Assiut University - South Valley University
Assiut 71516, Egypt , Aswan, Egypt [email protected]
Abstract— This paper proposes new scheme for efficient rate
allocation in conjunction with reducing peak-to-average power
ratio (PAPR) in orthogonal frequency-division multiplexing
(OFDM) system. Modification of the set partitioning in hierarchical trees (SPIHT) image coder is proposed to generate
four different groups of bit-stream relative to its significances.
The significant bits, the sign bits, the set bits and the
refinement bits are transmitted in four different groups. The
proposed method for reducing the PAPR utilizes twice the unequal error protection (UEP) using the Read-Solomon codes
(RS) in conjunction with bit-rate allocation. The output bit-
stream from the source code (SPIHT) will be started by the
most significant types of bits (first group of bits). The optimal
unequal error protection (UEP) of the four groups is proposed. As a result, the proposed structure gives a significant
improvement in bit error rate (BER) performance. Performed
computer simulations have shown that the proposed scheme
outperform the performance of most of the recent PAPR
reduction techniques in most cases. Moreover, the simulation results indicate that the proposed scheme provides significantly
better PSNR performance in comparison to well-known robust
coding schemes.
Index Term— SPIHT coding, unequal error protection
(UEP), rate allocation, RS codes, OFDM, PAPR.
I. INTRODUCTION
Orthogonal frequency-division multip lexing (OFDM)
scheme [1], [2] is used in most recent wireless
communicat ions systems due to its high spectrum efficiency
and robustness in multi-path propagation. OFDM is a
special form of multi-carrier modulation and mit igate inter
symbol interference (ISI) by mult iplexing the data on
orthogonal property. Moreover, it is, spectrally, more
sufficient technique
than a conventional signal carrier modulat ion technique.
However, one of major drawbacks of OFDM is the high
peak-to-average power ratio (PAPR) of the transmitted
signal [3].
The high PAPR of the transmitted signal significantly
reduces the average power at the output of the high power
amplifier (HPA) used at the transmitter. Indeed, the input
signal must lie in the linear region of the HPA, which is well
below the saturation power and the increased linear dynamic
range requirements impose the use of very expensive HPAs.
It is therefore preferable if possible to reduce the PAPR of
the signal to avoid the use of back-off. Several methods
have been proposed to reduce the PAPR. These methods can
be categorized into signal distortion methods and signal
scrambling methods [4-8]. The signal distortion methods
reduce high peaks directly by distorting the signal prior to
amplification. Clipping the signal before amplification is a
simple method to limit PAPR. However, the out-of-band-
and in-band interference due to use these methods will
increase the degradation of the system performance. Signal
scrambling methods are all variat ions on how to scramble
the codes to decrease the PAPR. Coding techniques can be
used for signal scrambling. However, searching for the best
code and the overhead associated will be exponentially
increased with the increase in the number of carriers. There
are three practical solutions of the signal scrambling
methods [5]: block coding, selective mapping and partial
transmit sequences. The signal scrambling techniques can be
classified into schemes with explicit side information and
schemes without side information. The scheme of signal
scrambling with side information introduces redundancy, so
the effective throughput is reduced. At this point it is worth
mentioning that increasing redundancy affects on the total
transmission rate. So, the maximum redundancy for each
data packet must be estimated relative to the packet data
significance. As an illustrative method, the jo int source and
block coding scheme with bit-rate optimizat ion. In this
paper, the proposed method for reducing the PAPR utilizes
twice the unequal erro r protection (UEP) using the Read-
Solomon codes (RS) [19] in conjunction using selective
weighted function with bit-rate allocation. In the fo llowing
Section, the PAPR problem in conjunction with the
optimum UEP will be described.
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Fig. 1. Block description of the OFDM system
In OFDM system, a block of N complex symbols is fo rmed
with each symbol modulation one of N subcarriers with
frequency for The N-subcarrier is chosen as orthogonal.
The complex envelope of the transmitted OFDM signal is
represented by [2]:
1N
0n
tn
fj2πe
nS
N
1x(t)
( (1)
Where is the data symbol, N is number of subcarriers and
represents frequency of n-th subcarriers, the OFDM system
shown in Fig. 1. In this work, a new scheme combines
simply modification of the set partitioning in hierarchical
trees (SPIHT) image coding technique followed by an
optimum UEP technique is proposed. The modified SPIHT
coder will generate four groups of bit-stream. The
significant bits, the sign b its, the set bits, and the refinement
bits are transmitted in four different groups. The main idea
behind this approach is that the output of the SPIHT image
coding (source code) will be sent relative to its significant
informat ion. The idea of the proposed algorithm can be used
with any scalable image coding technique.
The paper is organized as follows: the source code and
the PAPR problem in OFDM are d iscussed in the next
section; the proposed algorithm is introduced in Section III .
Weighted function are presented in section IV. Selective
weighted function are presented in section V.
Implementations and computer results are presented in
section VI. Finally, conclusions are given in Section VII.
II. SOURCE CODE PEAK-TO-AVERAGE POWER RATIO
PROPLEM
A. Peak-to-Average Power Ratio proplem
OFDM consist of many modulated subcarriers. As
mentioned in the previous section, this leads to a problem
with the peak to average power ratio. If N subcarriers are
added up
coherently, the peak power is N times the average power in
the case of the baseband signal. The PAPR is defined [8], [9]
as follows:
2
txE
2txmax
PAPR (2)
It is clear, from Equation (2), that the PAPR reduction
techniques are concerned with reducing max . However,
since most systems employ discrete-time signals, the
amplitude of samples of x(t) is dealt with in many of the
PAPR reduction techniques. Since symbol spaced sampling
of Equation (1) sometimes misses some of the signal peaks
and results in optimistic results for the PAPR, signal
samples are obtained by oversampling (1) by a factor of L to
approximate the true PAPR better. The L-t imes oversampled
time-domain samples are obtained by an LN-point inverse
discrete Fourier t ransform (IDFT) of the data block with (L -
1) N zero-padding. It was shown in [10] that L=4 is
sufficient to capture the peaks.
A large number of OFDM PAPR reduction techniques
have appeared in the literature, all having the purpose of
reducing the required HPA back-off and the effects of its
nonlinearity. Fig. 2 shows a typical AM/AM response for an
HPA, with the associated input and output back-off regions
(IBO and OBO), respectively.
Fig. 2. A typical power amplifier response.
The various approaches are quite different from each
other and impose different constraints. First, coding in [11]
relies on using several bits or b it sequences which would
carry a properly chosen code (sometimes with erro r
Data
Source
ECODE
R
S/P
M A P P E
R
IFF
T
M O D U L A T O R
P/S
D E C O D E R
P/S
D E M A P P E R
F F
T
S/P
Data
Sink
D E M O D U L A T O R
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correcting capabilities) that minimizes the PAPR of the
resulting transmitted signal. The PAPR is reduced, but so is
the data rate. Other methods use phase manipulations (e.g.
Selective Mapping (SLM), Partial Transmit Sequences
(PTS), Random Phasor [12-14]). A lthough these methods
are very effective, it has a high complexity and also requires
side information coded to be transmitted. This fact raises
problems in terms of compliance to standards. Other
methods such as Tone Reservation [15] propose inserting
anti-peak signals in unused or reserved subcarriers. The
method does not cause any in-band distortion, but it reduces
the useful data rate. Although suited in some
implementations (IEEE 802.16e for example), it is not
always standard compliant (the bandwidth sacrifice required
by this method is not acceptable in IEEE 802.16d).Another
methods proposes altering the QAM constellation in order to
reduce high signal peaks. The first method relying on the
principle of constellation expansion was Tone Injection [15].
It involves a complex optimizat ion process that makes it
scarcely attractive for systems with a high number o f
carriers. Simpler constellation extension methods were
recently developed. Active constellation extension (ACE)
[16] allows the corner QAM constellation points to be
moved within the quarter p lanes outside their nominal
values. The other border points are allowed to be d isplaced
along rays pointing towards the exterior of the constellation.
The interior points are not modified, in order to p reserve the
minimum d istance between the constellation symbols.
Recently, a simple non-iterative PAPR reduction method
relying on metric -based symbol pre-distortion (MBSP) was
proposed in [17]. From all of the algorithms described above,
only the last two are suited for a pract ical implementation in
a system compliant to the IEEE 802.16d standard. In this
work we use The HighPower Amplifier (HPA) is Rapp’s
solid state power amplifier model (SSPA) [34, 35] with the
characteristic
(3)
where vin, vout are the complex input and output signals,
respectively. vsat is the output saturation level. The
parameter p , often called “knee factor”, controls the
smoothness of the characteristic.
The input back-off (IBO) with respect to the saturation
values can be defined as,
(4)
In this paper, a rapp model HPA is assumed with knee factor
p = 2, IBO = 3.5 dB.
B. Source code (SPIHT) and the UEP process
The SPIHT method is consider the best image coding
technique in terms of decoded image quality, progressive
rate control and transmission, and the simplicity of the
coding process [18].
In the SPIHT coding algorithm, after the wavelet transform
using 9/7 tap wavelets from Antonini et al. [20] is applied to
an image, the main algorithm works by partitioning the
wavelet decomposed image into significant and insignificant
partitions based upon the following function
otherwise0,
2n}j)b(i,{Tj)(i,
max1,(T)
nS
( (5)
where Sn(T) is the significance of the set of coordinates T,
and b(i,j) is the coefficient value at coordinate (i,j). There
are two passes to the algorithm, the sorting pass and the
refinement pass. The sorting pass is performed on the list of
insignificant sets (LIS), list of insignificant pixels (LIP) and
the list of significant pixels (LSP). The LIP and LSP consist
of nodes that contain single pixels while the LIS contains
nodes that have descendants. The maximum number of b its
required to represent the largest coefficients in the spatial
orientation tree is obtained and designed as nmax and is
given by
}j)b(i,{max
j)(i,log 2nmax (6)
During the sorting pass, those coordinates of the pixels
which remain in the LIP are tested for significance by using
equation (5). The result Sn(T) is sent to the output. Those
that are significant will be transferred to the LSP as well as
have their sign bit output. Sets in the LIS will also have their
significance tested and if found to be significant, will
removed and partitioned into subsets. Subsets with a single
coefficient and found to be significant will be added to the
LSP, or else they will be added to the LIP. During the
refinement pass, the n-th most significant bit of the
coefficients in the LSP is output. The value of n is decreased
by 1 and the sorting and refinement passes occur again. This
continues until either the desired rate is reached or until n=0
and all nodes in the LSP have all their bits output.
In this work, modificat ion of the output bit-stream of the
SPIHT coder is done. The modificat ion process is based on
the type of bits and their contribution in the PSNR of the
reconstructed image. The bit erro r sensitivity (BES) study is
performed by first coding the original image using the
SPIHT coder. One bit in the coded image is corrupted,
starting from the first bit to the last bit. Each time a bit is
corrupted, the coded image is decoded and the resultant
MSE is obtained. The corrupted bit is corrected before
proceeding on to the next b it. On analysis, there are 4 major
types of bit sensitivities within the SPIHT coded bits. Their
description is summarized as follows: (1) the significance
bit in the b it stream. It decides whether nodes in the LIP are
significant, (2) the sign bit of a significant node that is
transmitted after the significance b it, (3) the set bit that
decided the set is significant or not, (4) the refinement b its
that are transmitted during the refinement passes.
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 17
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
0 1 2 3 4 5 6 7 8 9 100
500
1000
1500
2000
2500
3000
3500
4000
4500
Packet Number
MS
E
Error in Significance bit
Error in Sign bit
Error in Set bit
Error in Refinement bit
Fig. 3. Error bit sensitivities within the SPIHT coded bit stream
In Fig.3, the order of significance from the most significant
types of bits to the least significant is: significance b its >
sign bits > set bits > refinement bits. In the first step of the
proposed schame, Spiht coder will be modified to generate
four groups of bit stream related to the order significance i.e .;
the output bit stream will be started by the most significant
types of bit (first group of bits).
The optimum bit rate for each group of bits is computed
using the optimization algorithm. The inputs to the
optimization algorithm are the packet length, the bit erro r
rate (BER), and the expected decrease in the distortion of
packets. The output rate allocation vectors are used with RS
codes to generate the transmitted bit-stream.
III. PROPOSED OPTIMUM DOUBLE CODING TECHNIQUE FOR
OVER ALL DISTORTION REDUCTION
OFDM system use RS (Reed-Solomon) coder as channel
coder it protect data transmit only on one direct ion column
or row. In this work we modified the system making RS
coder protect the data transmit on two way column and row,
protection data on two way will make b it rate increase. A
comprehensive review of the great variety of erro r control
and concealment techniques has been presented in the paper
by Wang and Zhu [21]. Unequal error protection (UEP)[22]
can significantly incrtease the robustness of the transmission
and provide graceful degradation of the picture quality in
case of a deteriorating channel. UEP was adapted to packet
networks by Albanese et al. in their priority encoding
transmission (PET) scheme. Optimization of the rate
allocation in such a scheme was addressed by [23]-[24] ].
Wireless image transmission using turbo codes and optimal
unequal error protection is proposed by Thomos et al. [25].
They proposed a novel scheme based on the SPIHT source
coder applied in conjunction with the application of the
turbo codes [26]. Their methodology, termed turbo-coded
SPIHT (TCS), was implemented and tested in conjunction
with two protection strategies, one using equal error
protection (EEP) and the other using (UEP). The TCS with
successive decoding (terms TCSD) was also implemented
and evaluated in this work.
In this work, the proplem of UEP will be studied from
different view. The source code (SPIHT for image) is
modified to generate four different bitstreams. The
contribution of each one in the overall peak signal – to –
noise ratio PSNR in the received image is estimated and the
protection of each one is based on this estimation.
A. Problem formulation
In this work, the problem of FEC using RS codes will be
introduced. We assume that the image source is encoded by
the SPIHT coder. The generated bitstream is partitioned into
a sequence of packets.
Let denote the expected decrease in distortion if the ith
packet is decoded. The overall distortion can be written as
follows:
l
1i
ii0 ΔDPDD(l)
(7)
Where D0 is the expected distortion when the rate is zero, Pi
is the probability that the ith
packet and its preceding
packets are received correctly, and l is the number of source
packets that the transmitter chose to send. The probability Pi
can be written in the form:
i
1j
jji )(rQP
(8)
Where )(rQ jj is the probability that the j
th layer of source
packet is received correctly when sending by a rate of .
Substituting from equation (8) in equation (7) yields to:
i
i
1j
jj
l
1i
0 ΔD))(rQ(DD(l)D(r)
(9)
With the distortion expression in equation (9), for any rate
allocation vector . we can min imize the expected
distortion subject to a transmission rate constraint. The
problem can be formulated as follows:
l
1j
Rj
rtosubjectD(r)minr (10)
Where R is the total transmission rate.
B. Forward Error Correction with RS Codes
Assuming that, the stream is partitioned into coding blocks.
Each coding block has k source packet. For each block of k
source packets, we assume that parity packets are produced
using a systematic style erasure correction code. is the
maximum amount of redundancy that will needed by the
transmitter to protect the source. . In this work, we study the
signal transmition over BSC and AWGN channel. First Let
the packet transmitted through binary symmetric channel
with bit error rate . Then, the packet loss probability is
given by:
(11)
Assuming independent bits and is the number of bits in
the packet. For AW GN channel packet is transmitted
symbol by symbol through the channel, where each MQAM
symbol has b bits in it, modulated using fixed power
MQAM. Thus, each packet corresponds to
MQAM symbols. We assume additive white Gaussian noise
at the receiver frontend, and no interference from
other signals. The channel is narrowband, so the power
spectra of both the received signal and the noise have no
frequency dependence, i.e., the channel is characterized by a
single path gain variable. For
(12)
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 18
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
Where is the per symbol, is the symbol error
rate where of MQAM in channels is
(approximately) given by [27].
(13)
It is shown in [28] that the output of a linear minimum
mean-square error detector is approximated by a
Gaussian distribution. After channel decoding with a
RS code for source layer , the probability that the layer
of source packet is received correctly can be written as
follows [29]:
(14)
Where is the expected number of source
packets that can be recovered and it can be written as
follows:
k(P))S(1(P)Sv
r
r
v(P))S(1(P)S
v
r(P)Sk,,EP(r
v
j
vr
j
r
kv
j
1-k
1v j
v
j
vr
j
j
jj
j
j
j
(15)
Hence, with the expected distortion expression in equations
(9), (13) and (14), for any rate allocation vector , we can
optimize the rate vector to min imize the expected distortion
subject to a transmission rate constraint.
C. The Optimization Technique.
Equation (10) can be solved by finding the rate allocation
vector r that minimizes the Lagrangian equation.
OR
l
1i
irλD(r)λ)J(r,
(15)
l
1i
i
1j
iijj0 ]λrΔD))(rQ[(Dλ)J(r,
(16)
The solution of this problem is characterized by the set of
distortion increment iD , and )r(Q jj
with which the
layer source packet is recovered correctly. In this work, the
problem is solved by using an iterative approach that is
based on the method of alternating variab les [30]. The
objective function J(r1,…….,rl) in equation (16) is
minimized one variab le at a time, keeping the other
variables constant, until convergence. To be specific, let r(0)
be any initial rate allocation vector and let r( t)
=(r1(t)
,……,
rl(t)
) be determined for t=1,2,… as follows: select one
component x {r1,……,rl} to optimize at step t. this can be
done in a round-robin style. Then, for x = ri we can perform
the following rate optimization:
l
iv
v
1j
ivjjri
(t)
l
(t)
1ri
(t)
i
λrΔD))(rQ(minarg
)r,......,J(rminargr
(17)
For fixed λ the minimizat ion problem can be solved using
standard non-linear optimization procedures, such as
gradient-descent type algorithm [30]. In our simulation
results, we always start with the init ial rate allocation vector
r= (1, 1,……,1).
D. The proposed scheme
In the beginning as shown in Fig. 4, the SPIHT coder output
bitstream modificat ion has done. The modification process
is based on the type of bits and their contribution in the
PSNR of the reconstructed image. The bit error sensitivity
(BES) study is performed by first coding the original image
using the SPIHT coder. One b it in the coded image is then
corrupted, starting from the first bit to the last bit. Each time
a bit is corrupted, the coded image is decoded and the
resultant MSE is calculated. The corrupted bit is corrected
before proceeding on to the next bit. On analysis, the
resultant BES study is carried out on a 256*256*8 image of
Lena coded at source code rate of 0.5 bpp using the SPIHT
algorithm. On analysis, there are 4 major types of bit
sensitivities within the SPIHT coded bits, as shown in Fig.3.
the output bitstream will be started by the most significant
types of bits (first group of bits). The proposed scheme can
be summarized as follows: (1) the SPIHT image coding
technique is modified to generate 4 groups of bitstream
related to the order of significance , (2) the output data is
partitioned into a sequence of packets, (3) the changing in
MSE is calculated and the expected decrease in distortion
iΔD is then approximately estimated, (4) the optimization
algorithm is applied to generate the optimum bit rate for
each group of bits. The inputs to the optimization algorithm
are the packet length, the bit error rate , and expected
distortion iΔD , (5) the output are the rate allocation vectors
used with RS codes to generate the transmitted bitstream,
(6) the receiver will decode the receiving bitstream by using
RS decoder and the modified SPIHT decoder.
E. Image Transmission over OFDM system with RS
channel coding (FEC)
0.01 and 0.001, for gray-scale Lena image.
Firstly the wavelet transform using 9-tap low pass filter and
7-tap high-pass filter are applied to the original image to
decompose it into sub-images. Only 6-layer is used in our
test. The modified SPIHT coder is then applied to the
wavelet coefficients to generate the source bitstream with a
bit rate of 0.5 bpp. The source bitstram is divided into
packets of lenght
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Colu
mn
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
Fig. 4. modified OFDM system
2000 bits and each packet is div ided into 25 b locks of length
80 bits. Th is means that each block has 10 symbols of one
byte for each. In the simulation results, the total bitstream of
the Lena image is divided into 17 packets. These 17 packets
are div ided into 4 groups of packets as follows: (1) 2
packets for the significant informat ion, (2) 5 packets for the
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 19
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
S/P
MA
PPE
R
P/S
DEMA
PPE
R
FF
T
S/P
De
modulat
or
IFFT
2RSDE
CODE
RA
4G SPI
HT Deco
der
Data
e
2RS
Coder
4G SPIH
T Enco
der
Optimization
technique
M
odulat
or
P/S
RCPC
& INTERLEVER
RCPC &
DE INTERLEVER
BER
Data
sign bit, (3) 8 packets for the set bit, (4) 2 packets for the
refinement bits.
Fig. 5. Channel rates for the protection of “ Lena” as determined using the algorithm
In the beginning, we tried to put the results of the
method in a comparison form with the result of the equal
error protection method. In the case of , the
number o f RS symbols is selected to be 8-symbol for each
row of packet that make the total symbols per packet are
450 symbol ber packet. In the case of , the total
symbols per packet ( in Eq.9) is selected to be no more
than 450 symbol ber packet and the optimization algorithm
is used to determine the number of RS symbols for each
column and row of packets. The result of this step is shown
in Fig.5. It is clear from Fig. 5 that the significance and sign
packets are protected by 8-symbol for column and row, the
set packets are protected by 2-symbol for column and row,
and the refinement packets are protected by 8-symbol fo r
row and zero for column.
Fig . 6 depicts the average PSNR of the decoded Lena image
as a function of the transmission rate for the EEP and the
UEP coding method. In particular, our proposed scheme for
UEP outperforms the system of EEP by 4.2 dB.
1 2 3 4 5 6 7 8 9 10
x 10-3
10
15
20
25
30
35
Bit Error Rate
PS
NR
(dB
)
EEP
UEP
Fig. 6. the average PSNR of the decoded Lena image as a function of the
channel BER for the RS (EEP & UEP) channel coding.
IV. WEIGHTING FUNCTION This method addresses the PAPR reduction of OFDM by
combination of both signal scrambling and signal distortion
techniques [31]. The PAPR is to be reduced by both
amplitude weighting and random phase updating. The
OFDM signal for one symbol interval 0 ≤t ≤T is written
as
t
T
mj
mm ewbts2
)(
( (18)
Where M is number of subcarriers, mb is modulation data
of the subcarriers, T is the OFDM symbol period, and
is a complex factor defined as
( (19)
Where m a positive real value and m is the phase of m-th
subcarriers. The block diagram of an OFDM modulator with
complex weighting factors is shown in Fig . 7. To calculate
PAPR, first we obtain the instantaneous power of OFDM
signal from Eq(18).
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Fig. 7. Block diagram of complex-weighted OFDM modulator.
( (20) Which can be written as
( (21)
The average power P(t) over a symbol period of T, we
obtain
( (22)
We can say
( (23)
Where The symbols on different carriers are assumed to be
independent )(* nmbbE nm Therefore, the second
term in Eq.(22) is zero. The variation of the instantaneous
power of OFDM signal from the average is.
( (24)
The variance is obtained by averaging of 2))(( tP
over a symbol period of T
( (25)
Where )(iRcc is the autocorrelation function of the
complex sequence
(26)
The parameter ρ is the power variance of the OFDM
signal and it has been shown that is a good measure of the
. now we consider different weighting functions in
this work. In order to be able to compare them with each
other we assume the power of all weighting factors be
constant,
11
0
2
M
m
mW
(27)
the PAPR of OFDM signal can be written as
( (28)
Weighting function :
1. Barlett: Th is weighting function has triangular
shape and expressed by
( (29)
2. Rectangular: This weighting function has a
rectangular shape
(30)
3. Raised cosine: this weighting function is exp lained
by
(31)
4. Half-sine the shape of this weighting function is
described by
( (32)
5. Shannon: the shape of these weighting factors is the
sinc function defined by
(33)
6. Gaussian: these factor are generated based on the
Gaussian function
(34)
7. Chebyshev: the shape of this weighting function is
exponentially increasing,
( (35)
The modulated signal will have distortion due to in band and
out of band distortion and PAPR reduction using weighted
function make system more sensitive for noise of channel.
V. SELECTIVE WEIGHTING FUNCTION
The weighted function method for PAPR has high distortion
due to channel noise that will effect on signal recover. In
this work, we don’t added weighted function to all
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 21
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
S/P
M
AP
PE
R
P/S
DE
MAPP
ER
FF
T
S/P
D
em
od
ulat
or
IFFT
2RSD
ECOD
ERA
4G SPI
HT Dec
oder
Data
e
2RS
Coder
4G
SPIHT
Encoder
Optimization
technique
Mod
ulat
or
P/S
RCPC &
INTERLEVE
R
RCPC
& DE
INTERLEVER
BER
Data
PAPR
reductio
n
if necessary side information
Fig. 8. modified OFDM system with selective weighted function method for PAPR reduction
The weighted function method for PAPR has high
distortion due to channel noise that will effect on signal
recover. In this work, we don’t added weighted function to
all t ransmit ion frame. As shown in Fig.8, the frame pass
through PAPR reduction block test.
The PAPR reduction block test flowshart shown in Fig .9
If the PAPR larger than PAPRo (peak-to-average power
ratio threshold) we make fram pass through multip le
weighted function then test PAPR of each fram and select
one which gave minimum PAPR and transmit side
information.
Fig. 9. Selective weighted PAPR reduction method flowshart
VI. COMPUTER RESULTS
We compare between the result of data transmit over
original and modified OFDM systems using Barlett
weighting function PAPR reduction method, Compound
method PAPR reduction
method [32], and PAPR reduction using selective weigthing
function.
A. Barlett Weighting function with original and modified
OFDM system
We use the Barlett weighting function method and compare
the simulat ion result for original and modified OFDM
system. data transmition over two type of channel, b inary
symitric channel and AWGN Chennal.
1) Binary symitric channel:
Here the data transmit over b inary symitric channel.
Table I. show simulat ion result when use this method
throw systems with and without UEP at Different
kinds of sources transmited over BSC. Fig. 10 show
receved Lena image transmit over orig inal and
modified OFDM system with channel BER=0.01, and
Fig. 11 show receved Lena image t ransmit over
original and modified OFDM system with channel
BER=0.001, Fig12 show Channel rate protection as
determined using the algorithm when use Barlett
weighting function method.
PAPR measurment
If PAPR
>PAPRo
Use weighted
function and select minimum
PAPR
Transmit the
frame
Transmit the frame and side
information
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 22
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
T ABLE 1
SIMULATION RESULT WHEN USE BARLETT WEIGHTING
METHOD THROW SYSTEMS WITH AND WITHOUT UEP,OVER BSC
Source data
type
MSE transmission
rate
Max
(PAPR)
Channel BER=0.01
Random data
source
1.08224e+004 122880 bps 10.683
dB
Image data
source over
Original OFDM
1.0364e+004 122880 bps 9.8068
dB
Image data source over
Modified
OFDM
4.9676e+003 121600 bps 10.2945 dB
Channel BER=0.001
Random data
source 1.0582e+004 122880 bps
Source data
type
MSE transmission
rate
Max
(PAPR)
Image data
source over
Original OFDM
4.017e+003 122880 bps 9.915 dB
Image data
source over
Modified
OFDM
2.0714424+003 121600 bps 9.963 dB
(a) (b)
Fig. 10. the receved Lena image transmit over original and modified OFDM system
over BSC channel with BER=0.01 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 7.975), (b) modified OFDM (PSNR= 11.1693)
(a) (b)
Fig. 11. the receved Lena image transmit over original and modified OFDM system over BSC channel with BER=0.001 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 12.09), (b) modified OFDM (PSNR= 14.968)
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Colu
mn
Fig .12. Channel rates protection as determined using the
algorithmfor Lena image for BSC with BER=0.01
2) AWGN channel: The transmited bit stream transmit over
AWGN channel, Table II show simulat ion result when use
this method throw systems with and without UEP at
different source data type transmit over AW GN channel. Fig.
13 show receved Lena image transmit over original and
modified OFDM system with channel BER=0.01, Fig. 14
show receved Lena image t ransmit over original and
modified OFDM system with channel BER=0.001. Fig15
show Channel rate protection as determined using the
algorithm when use Barlett weighting function method.
T ABLE II
SIMULATION RESULT WHEN USE BARLETT WEIGHTING METHOD THROW SYSTEMS WITH AND WITHOUT UEP,OVER
AWGN CHANNEL
Source data type MSE transmission rate
Max (PAPR)
Channel BER=0.01
Random data
source
9.8499e+003
30720 syps 10.68 dB
Image data source over Original
OFDM
9.433e+003 30720 syps 9.8 dB
Image data source over Modified
OFDM
1.353e+003 30080 syps 9.5 dB
Channel BER=0.001
Random data
source
9.559 +003 30720 syps 10.683dB
Image data source
over Original
OFDM
8.6 +003 30720 syps 9.8 dB
Image data source over Modified
OFDM
5.327e+002 30080 syps 10.13 dB
(a) (b)
Fig. 13. the receved Lena image transmit over original and modified OFDM system over AWGN channel with BER=0.01 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 8.384), (b) modified OFDM (PSNR= 15.0815)
(a) (b)
Fig. 14. the receved Lena image transmit over original and modified OFDM
system over AWGN channel with BER=0.001 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 18.785), (b) modified OFDM (PSNR= 20.865)
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 23
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Colu
mn
Fig. 15. Channel rates protection as determined using the
algorithm for AWGN channel with BER=0.01
B. compound method simulation result
We use the compound method [32] for original and
modified OFDM system the data will pass over two type of
channel BSC and AWGN.
1) BS Channel: Data transmit over BSC, Tab le 3 show
simulation result when use compound method throw
systems with and without UEP at different source data type
over BSC. Fig 16 show receved Lena image transmit over
original and modified OFDM system with channel
BER=0.01, Fig 17 show receved Lena image transmit over
original and modified OFDM system with channel
BER=0.001, Fig 18 show Channel rate protection as
determined using the algorithm when use compound
method. T ABLE III
SIMULATION RESULT WHEN USE COMPOUND METHOD THROW SYSTEMS WITH AND WITHOUT UEP,OVER BSC
Source data type MSE transmission
rate
Max
(PAPR)
Channel BER=0.01
Random data
source
1.03324e+004
122880 bps 7.739
dB
Image data source
over Original
OFDM
1.166778e+004
122880 bps 8.5378
dB
Image data source
over Modified
OFDM
4.0651e+003 121600 bps 7.5253
dB
Channel BER=0.001
Random data
source
1.006e+004 122880 7.739
dB
Image data source
over Original
OFDM
1.03695e+003 122880 bps 8.5378
dB
Image data source
over Modified
OFDM
5.47694e+002 117760 bps 8.6578
dB
(a) (b)
Fig. 16. the receved Lena image transmit over original and modified OFDM system over BSC with BER=0.01 (PSNR result is proposed in dB), (a) original
OFDM (PSNR= 7.46), (b) modified OFDM (PSNR= 12.04)
(a) (b)
Fig. 17. the receved Lena image transmit over original and modified OFDM system over BSC with BER=0.001 (PSNR result is proposed in dB), (a) original OFDM (PSNR=
17.973), (b) modified OFDM (PSNR= 20.7454)
2) AWGN channel: Here we use compound method and
AWGN channel, Table IV show simulat ion result
when use compound method throw systems with and
without UEP at different source data type over
AWGN channel. Fig 19 show receved Lena image
transmit over orig inal and modified OFDM system
with channel BER=0.01, Fig 20 show receved Lena
image transmit over original and modified OFDM
system with channel BER=0.001, Fig 21 show
Channel rate protection as determined using the
algorithm when use compound method.
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Colu
mn
Fig. 18. Channel rates protection as determined using
the algorithm for Lena image over BSC with
BER=0.01.
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 24
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
T ABLE IV
SIMULATION RESULT WHEN USE COMPOUND METHOD THROW
SYSTEMS WITH AND WITHOUT UEP,OVER AWGN CHANNEL
Source data type MSE transmission rate
Max (PAPR)
Channel BER=0.01
Random data source 9.8069e+003
30736 syps 7.739 dB
Image data source over
Original OFDM
4.3469e+003
30736 syps 7.6733 dB
Image data source over Modified OFDM
1.55262e+003 29455 syps 7.6733 dB
Channel BER=0.001
Random data source 9.45e+003 30736 syps 7.74 dB
Image data source over
Original
4.4014+002 30736 syps 8.5378 dB
Source data type MSE transmission rate
Max (PAPR)
Image data source over
Modified OFDM
1.585e002 28480 syps 7.7989 dB
(a)
(b)
Fig. 19. the receved Lena image transmit over original and modified OFDM system over AWGN BER=0.01 (PSNR result is proposed in dB), (a) original
OFDM (PSNR= 14.26), (b) modified OFDM (PSNR= 16.22)
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of R
S s
ymbo
l ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of R
S s
ymbo
l ber
Col
umn
Fig. 21. Channel rates protection as determined using the
algorithm for Lena image over AWGN channel with
BER=0.01.
C. Selective Weighting function with original and modified
OFDM system
Here we use our proposed method (selective weight ing
function) and compare the simulation result for original and
modified OFDM system, the data will pass over two type of
channel BSC and AWGN channel compare the result with result of compound method and the Barlett PAPR method.
1) BS Channel: Data transmit over BSC, Table. V show
simulation result when use this method throw systems with
and without UEP at different source data type and BSC.
Fig.22 show receved Lena image transmit over orig inal and
modified OFDM system with channel BER=0.01. Fig. 23
show receved Lena image t ransmit over original and
modified OFDM system with channel BER=0.001.Fig. 24
show Channel rate protection as determined using the
algorithm. T ABLE V
SIMULATION RESULT WHEN USE SELECTIVE WEIGHTED METHOD THROW SYSTEMS WITH AND WITHOUT UEP,OVER BSC
CHANNEL
Source data type MSE transmission rate
Max (PAPR)
Channel BER=0.01
Random data
source
1.0022e+004 122944 bps 8.738 dB
Image data source over
Original OFDM
1.87672e+003 122944 bps 8.75 dB
Image data source over
Modified OFDM
8.873685e+002 120380 bps 8.7263 dB
Channel BER=0.001
Source data type 9.8e+004 122944 bps 8.738 dB
Random data source
4.27316e+002 122944 bps 8.7263 dB
Image data
source over Original OFDM
1.3246e+002 120336 bps 8.748 dB
(a)
(b)
Fig. 22 the receved Lena image transmit over original and modified OFDM system over BSC with BER=0.01 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 18.384) , (b) modified OFDM (PSNR= 19.815)
(a) (b)
Fig. 20. The receved Lena image transmit over original and modified OFDM system over AWGN channel with BER=0.001 (PSNR result is
proposed in dB), (a) original OFDM (PSNR= 21.6948), (b) modified OFDM (PSNR= 26.13)
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 25
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
(a) (b)
Fig.23 the receved Lena image transmit over original and modified OFDM system over BSC with BER=0.001 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 21.6948), (b) modified OFDM (PSNR= 26.13)
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Colu
mn
Fig. 24. Channel rates protection as determined for
Lena image using the algorithm over BSC with
BER=0.01
3) AWGN Channel: Here data
transmit over AWGN channel, Table VI show
simulation result when use this method throw systems
with and without UEP at different source data type
and transmit over AW GN channel. Fig. 25 show
receved Lena image transmit over orig inal and
modified OFDM system with channel BER=0.01. Fig.
26 show receved Lena image transmit over original
and modified OFDM system with channel
BER=0.001. Fig. 27 show Channel rate protection as
determined using the algorithm.
4)
TABLE VI
SIMULATION RESULT WHEN USE SELECTIVE WEIGHTED METHOD THROW SYSTEMS WITH AND WITHOUT UEP,OVER
AWGN CHANNEL
Source data type MSE transmission rate
Max (PAPR)
Channel BER=0.01
Random data
source
9.6638e+003
30736 syps 8.74 dB
Image data source over Original
OFDM
1.16e+003 30736 syps 8.73 dB
Image data source
over Modified OFDM
6.793e+002 30407 syps 8.733 dB
Channel BER=0.001
Random data
source
9.006e+003 30736 syps 8.738 dB
Image data source over Original
OFDM
3.626e002 30736 syps 8.75 dB
Image data source over Modified
OFDM
0.6964e002 30403 syps 8.74 dB
(a) (b)
Fig.25 the receved Lena image transmit over original and modified OFDM system over AWGN channel with BER=0.01 (PSNR result is proposed in dB), (a) original OFDM (PSNR= 18.384), (b) modified OFDM (PSNR= 19.815)
(a) (b)
Fig. 26. The receved Lena image transmit over original and modified OFDM system over AWGN channel channel BER=0.001 (PSNR result is proposed in dB), (a) original OFDM (PSNR=22.53), (b) modified OFDM
(PSNR=29.7)
0 2 4 6 8 10 12 14 16 18 200
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
4
5
6
7
8
9
10
Packet Number
Num
ber
of
RS
sym
bol ber
Row
Fig. 27. Channel rates protection as determined using the algorithm when data
transmit over AWGN with BER=0.01.
0 2 4 6 8 10 12
10-2
10-1
100
PAPRo
pr
( P
AP
R >
PA
PR
o )
Conventional
SLM, u = 4
CLP
Huffmant
Barlett weighted
Proposed method
Compound method
Fig. 28. CCDF Comparison of the proposed algorithm with Slm u=4,Huffman coder,clipping,compound and Barlett weighting function
Fig.28 show the power Complementary Cumulative
Distribution Function (CCDF) curves provide critical
informat ion about the signal encountered in proposed
algorithm and the another PAPR reduction method .
International Journal of Video& Image Processing and Network Security IJVIPNS-IJENS Vol:09 No:10 26
95610-7474 IJVIPNS-IJENS © December 2009 IJENS I J E N S
VII. CONCLUSIONS
In this paper we have conseder the proplem of reduction
PAPR in OFDM system by an efficient rate allocation
scheme with selective weighted function efficint rate
allocation done useing Reed So lomon coder porotection
with an UEP, study result over two type of channel and
compare result by two method Barlett and compound
method, the proposed method reduce the PAPR more than ,
Conventional system, SLM (selective mapping u=4) [37],
clping method[36], Barlett weigthed function,Huffmant
method [33], and less than compound but the over all
distortion less than all, UEP make improvement in the
transmission rate.
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