An Efficient Rate Allocation Scheme with Selective ... IJVIPNS-IJENS.pdf · An Efficient Rate...

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]

[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.



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



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.



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)



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



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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).



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



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& 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



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


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)



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


BER=0.01, Fig 17 show receved Lena image transmit over


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.



T ABLE IV

SIMULATION RESULT WHEN USE COMPOUND METHOD THROW

SYSTEMS WITH AND WITHOUT UEP,OVER AWGN CHANNEL


Max (PAPR)

Channel BER=0.01

Random data source 9.8069e+003

30736 syps 7.739 dB


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


Original

4.4014+002 30736 syps 8.5378 dB


Max (PAPR)


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


Max (PAPR)

Channel BER=0.01

Random data

source

1.0022e+004 122944 bps 8.738 dB


Original OFDM

1.87672e+003 122944 bps 8.75 dB


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)



(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


Max (PAPR)

Channel BER=0.01

Random data

source

9.6638e+003

30736 syps 8.74 dB


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


OFDM

3.626e002 30736 syps 8.75 dB


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 .



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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