Simulation of ofdm modulation adapted to the transmission of a fixed image

International Journal of Electronics and Communication Engineering & Technology (IJECET),

ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 3, May – June (2013), © IAEME

162

SIMULATION OF OFDM MODULATION ADAPTED TO THE

TRANSMISSION OF A FIXED IMAGE ON DISTURBED CHANNEL

Louis Paul Ofamo Babaga, Ntsama Eloundou Pascal

Physics Department, Faculty of Sciences/ University of Ngaoundere, P. O; Box 454

Ngaoundere, Cameroon

ABSTRACT

In recent years, the speed in the transmission of audio and video data is a major

concern. Thus, in this paper we present the results of the modulated OFDM (Orthogonal

Frequency Division Multiplexing) still images that is based on the fast Fourier transform

(FFT: Fast Fourier Transform) digital transmission. These results are obtained from a chain

of communication developed in MATLAB. We evaluate the performance of the transmission

system in terms of visual quality of the image reception (98% of the original image). We also

obtain the different values of SNR, TEB, and other important parameters relying on the

classic OFDM with a guard interval of time corresponding to 25% of the useful symbol

period, and the modified OFDM, by just reducing that interval. The results are presented

according to three patterns of M-PSK modulation frequency used in simulation. Namely:

BPSK, QPSK and 16PSK and by extension, 256PSK modulation. It should be noted that

convolutional coding is used to improve transmission quality.

Keywords: Digital transmission, Orthogonal Frequency Division Multiplexing (OFDM),

FFT, cyclic time guard.

I. INTRODUCTION

Future mobile radio communication systems that can provide diverse transmission

services such as video, voice, image and other data, with high transmission rate and low

power transmission, are of great interest. The problem of transmitting high data rates on the

frequency of a fading channel is inter-symbol interference (ISI), which severely degrades

system performance. OFDM digital subcarriers in multiple form by the orthogonal frequency

division transmission, is a solution that can effectively combat ISI [1,2]. OFDM scheme, a bit

stream is converted to high-speed trains with parallel low bit rate. Parallel streams are

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163

modulated on orthogonal subcarriers. Spectrum of these subcarriers are closely spaced and

covered with a high efficiency of bandwidth. The bandwidth of these subcarriers is small

compared to the coherence bandwidth of the channel that is the sub-carriers are not subject to

flat fading. OFDM also uses a time guard duty at the beginning of each symbol to remove

any shorter than its length [3] ISI. In this paper, a study on combined use of convolutional

coding and OFDM technique for the transmission of fixed images, simulated with Matlab is

presented in four modulation formats (BPSK, QPSK, 16PSK and 256PSK). Thus, we propose

a new division of time Guard in OFDM system (below 25% of a useful symbol period). This

system will provide better picture quality reception. The paper is organized as follows:

Section 2 provides background information on the OFDM modeling classic system, Section 3

presents the OFDM implemented modulator, Section 4 presents the disturbed channel, the

overview of the demodulation is given in Section 5, and the results are given in Section 6.

II. OFDM MODELING

OFDM is a combination of modulation and multiplexing. We use DPSK modulation.

In OFDM, the sub-carrier frequencies are chosen so that the sub-carriers are orthogonal to

each other, meaning that cross-talk between the sub-channels is eliminated and inter-carrier

guard bands are not required. According [4], in an OFDM system, the carrier spacing 1/NT is

f, where N is the number of carriers, and 1/T is the symbol rate [5]. With this carrier

spacing, sub-channels can maintain orthogonality, although they overlap. Therefore, there is

no inter-carrier interference (ICI) with ideal OFDM systems. The transmitted signal through

the system for an OFDM symbol period is of following form:

2( ) ( ) nj f t

e n

n

s t R a h t eπ φ+

= ∑ (1)

Where an is the data symbol transmitted on the n-th subcarrier, h(t) is the pulse

shaping filter response.

fn is the n-th subcarrier frequency fn = f + N∆f.

As the number of OFDM subcarriers increases, the complexity of the modulator and

demodulator is increased accordingly. However, the OFDM modulator and the demodulator

can be implemented easily by use of inverse discrete Fourier transform (IDFT) and discrete

Fourier transform (DFT), respectively. In practice, the couple IFFT/FFT (fast Fourier

transforms inverse and direct) is used for its efficiency and speed.

The time-domain coefficients Cm can be calculated by:

21

0

1nmN j

Nm n

n

C a eN

π− −

=

= ∑ (2)

Where an is the input to the IDFT block which is the data symbol for n-th subcarrier.

Cm is the m-th output of IDFT block. After this operation, the parallel output of IDFT

block Cm (m = 1, …, N - 1) is converted into a serial data stream. Figure 1 shows a block

diagram of the OFDM transmitter. In equation (2), the data symbols of the frequency domain

are converted to a series of samples in the time domain.



164

Figure 1. OFDM transmission and reception scheme

* Preservation of orthogonality (Guard Interval) Following the same symbol arriving at a receiver by two paths will add causing two

types of defects:

• The intra symbol interference: addition of a symbol with itself slightly out of phase.

• The inter symbol interference: adding a symbol with the following over the preceding

slightly out of phase.

Between each transmitted symbol, inserting a guard interval called "dead zone". In

addition, the useful symbol duration is greater than the spread echoes. These two precautions

will limit the inter-symbol interference. The time you issue differs from the information

symbol period because it must take into account relevant periods between a "call time",

which aims to eliminate the ISI continues despite the carrier orthogonality. Between the

symbol periods (Ts), the useful (Tu) and the guard interval (Tg), therefore establish the

relationship:

s u gT T T= + (3)

Figure. 2. Time guard interval (cyclic prefix)

Figure 2 shows the addition of a guard interval. The symbol period is extended so as

to be greater than the integration period Tu. All carriers are cyclical inside you; it is the same

for the entire modulated signal. The length of the interval is selected to match the expected

level of multipath. It should not be too much of you, not to sacrifice too much data capacity

(and spectral efficiency). For DAB (Digital Audio Broadcasting), a guard about you Tu/4 is

Binary input

data (image)

Serial

to

Parallel

DPSK

Modulation

(1, 2, 4 or 8

bits)

Cyclic

extension

addition

Parallel

to

Serial

Communication

channel

Noise

Binary

output data

(image)

DPSK

Demodulation

(1, 2, 4 or 8 bits)

FFT

(DFT)

Cyclic

extension

removal

Convolutional

encoder

Convolutional

decoder

OFDM modulator

OFDM demodulator

Serial

to

Parallel

Parallel

to

Serial

IFFT

(IDFT)

Guard period IFFT output

Tg Tu

Ts



165

used; DVB (Digital Video Broadcasting) has more options, the largest being Tu/4 where

OFDM modified guard interval ≤ Tu/4; we also simulated and compared with the results for

Tg=Tu/4.

At the receiver, the signal is converted to base band and sampled at the symbol rate

1/T. Then, N serial samples are converted to parallel data and passed to a DFT which

converts the signal from time domain to frequency domain. To decrease the SNR required to

achieve the required quality of the received image, a convolutional coding [5, 6, 7] is applied

to the OFDM system. OFDM coding is the concatenation of the OFDM system with

convolutional encoding. As seen, the convolutional coding is integrated into the OFDM

system to improve the performance in noisy channels [5, 8]. The binary input information are

first encoded using any encoding of convolutional code rate, then, they are modulated and

transmitted through a channel with additive noise. In this model consider frequency selective

time varying fading channel with additive noise, where the channel impulse response can be

represented by the formula:

( ) ( )2

1

1( ) m Dm

Lj f t

m

m

h t e tL

θ πδ τ

+

=

= −∑ (4)

Where L is the number of reflected multipaths, τm is the delay, θm is the phase rotation

and fDm is the Doppler frequency offset of the mth

path.

III. OFDM MODULATION

Conventional OFDM can be modified by adjusting certain sensitive parameters and/or

adding new elements that can improve the system. Thus, conventional time guard 25% of

symbol period can be reduced to a reasonable value to avoid inter-symbol interference. In the

classic OFDM, we could associate a convolutional coding to improve the visual quality of the

image reception (See figure 1)

3.1 Convolutional coding

According [4], simulation studies have been performed using convolutional coding

with OFDM systems considered in figure 1. The parameters of the convolution coding are

code rate (r) equal 1/2 and 1/3 with constraint lengths (K) equal 3 and 7 for each of them. For

rate 1/2 the function generators are [6,7] for constraint length 3 and [133,171] for the

constraint length 7, while for rate 1/3 are [6,7,7] for the constraint length 3, and

[133,145,175] for the constraint length 7. All these generator vectors are represented in octal

form.

3.2 Type of OFDM modulation implemented The flow of serial input data to be converted in parallel, the modulator has to add a

number of zeros at the end of the data stream in order to adapt the data flow to enter a 2-D

matrix [9]. Suppose a frame of data with 11530 symbols is being transmitted by 400 carriers

with a capacity of 30 symbols/carrier, 470 zeros are padded at the end in order for the data

stream to form a 30-by-400 matrix, as shown in Figure 3. Each column in the 2-D matrix

represents a carrier while each row represents one symbol period over all carriers.



166

Figure 3. Data transmission matrix

3.2.1 Differential Phase Shift Keying (DPSK) modulation

The DPSK Baseband Modulator block modulates the signal using the differential

phase shift keying method. The output is a baseband representation of the modulated signal.

Before, differential encoding can be operated on each carrier (column of the matrix),

an extra row of reference data must be added on top of the matrix [10]. The modulator creates

a row of uniformly random numbers within an interval defined by the symbol size (order of

PSK chosen) and patches it on the top of the matrix. Figure 4 shows a 31 by 400 resulted

matrix.

Figure 4. Differentiated matrix

For each column, starting from the second row (the first actual data symbol), the value

is changed to the remainder of the sum of its previous row and itself over the symbol size

(power 2 of the PSK order).

Figure 5 show the signal modulated on a carrier; modulated in a symbol period. The

DPSK modulator generates a matrix filled with complex number whose phases are translated

into small amplitudes [11]. These complex numbers are then converted into a rectangular

shape for further processing. The BPSK (symbol size is 2), 16PSK (symbol size is 24) and

256PSK (28) just follow the same principle.

Figure 5. OFDM time signal (one symbol period in one carrier)

30

400

Data

31

400

Data

Reference Row



167

3.2.2 Bloc of Inverse Fast Fourier Transform

For a vector of length N, direct and inverse Fast Fourier transforms are given by

formulas (5) and (6):

( ) ( ) ( )( )1 1

1

Nj k

N

j

X k x j w− −

=

=∑ (5)

( ) ( ) ( )( )1 1

1

1 Nj k

N

k

x j X k wN

− − −

=

= ∑ 6)

With

2 i

NN

w e

π−

=

Figure 6, shows an enlarged to a certain size of the IFFT matrix (e.g. size of the IFFT

= 1024) and becomes a matrix 31×1024. Since each column of the matrix represents a DPSK

support, their values are stored in the columns of the matrix where the IFFT their

corresponding carriers should reside. Their combined values are stored in the columns

corresponding to the locations of carriers combined.

Figure 6. IFFT matrix

All other columns in the IFFT matrix are set to zero. The matrix for signal

transmission, Inverse Fast Fourier Transform (IFFT), and only the real part of the result is

valuable, so that the imaginary part is eliminated [12].

3.2.3 Insert periodic time guard

An exact copy of the last portion of 25% of each symbol period (row of the matrix) is

inserted at the beginning of the classic OFDM [13, 14]. The time of periodic care, is

synchronization to the receiver for each symbol period demodulation signal reception [7].

The guard time is changed during the simulation. Modified OFDM has a guard interval of

20% of symbol period;

Figure 7 shows a time domain representation of an OFDM Signal. Figure (7.a) shows

a time domain representation of the conventional OFMD signal, where the guard period is

fixes during all the frame of the data file of the image. Figure (7.b) shows a time domain

representation of the new guard period where, g gmT T≥ et u umT T≥

31

400

Data

400

1024

Data

conjugate



168

Figure.7. Integration of the signal with guard interval

The matrix becomes a matrix of modulation when converted to serial. A time-

modulated in a data frame signal is generated.

IV. COMMUNICATION CHANNEL

Two properties of a typical communication channel are modelled. First, a variable

clipping (off peak power) to MATLAB program is set by the user. The root mean square

powers of the transmitted (RMSP) before and after the channel signal are indicated.

Secondly, the channel noise is modeled by adding white Gaussian noise (AWGN) defines by:

var mod

iance of the ulated signal

linear SNRσ = (7)

With 10 10

dBSNR

linear SNR =

It has a mean of zero and a standard deviation equaling the square root of the quotient

of the variance of the signal over the linear Signal-to-Noise Ratio, the dB value of which is

set by the user as well.

Guard Period

Symbol N

Copy

Tg

IFFT output

Guard Period

IFFT

Tu

Ts

Symbol

N-1

Symbol

N+1

Guard

Period

Symbol N

Copy

Tgm

IFFT output

IFFT

Tuu

TS

Symbol

N-1

Symbol

N+1

Guard

Period b)

IFFT

a)



169

V. OFDM DEMODULATION

The DPSK Baseband Demodulator block demodulates a signal that was modulated

using the differential phase shift keying method. The input is a baseband representation of the

modulated signal. The input must be a discrete-time complex signal. The input can be either a

scalar or a frame-based column vector.

As any type of modulation/demodulation, the OFDM demodulation process is

essentially an inverse of the OFDM modulation. And as the modulator, the OFDM

demodulator demodulates the received data frame with respect to the transmitted image

unless the data have a length less than the total number of symbols per frame designed [15].

For remove a periodic time guard, the previous example used in section 3.2 should

continue to be used for illustrative purposes. Figure 8 shows that after converting a frame of

discrete time signal from serial to parallel, a length of 25% of a symbol period is discarded

from all rows. Thus the remaining is then a number of discrete signals with the length of one

symbol period lined up in parallel.

Figure 8. Time Guard Removal

VI. SIMULATION RESULTS

The performance evaluation is done by measuring the quality of the received image.

There are two ways to measure quality image: subjective based and objective based. The root

mean square error (RMSE) and SNR are the most commonly objective based measure used

due to their simplicity and ease of calculation.

Root mean square error between the original and reconstructed image frame defined

by:

( )1 1

2

0 0

1( , ) ( , )

M N

x y

RMSE g x y f x yM N

− −

= =

= −×∑∑ (8)

Where f(x,y) is the original image frame

g(x,y) is the reconstructed image frame after the decompression process.

M x N is dimensions of image frame

In this paper objective and subjective criteria are used.

The different values of BER (Bit Error Rate) and other parameters are presented in

terms of four modulation formats used in the simulation. Namely: BPSK, QPSK, 16-PSK and

256-PSK. The performances of conventional OFDM system are evaluated by the following

parameters:

• Root Mean Square Power at the input of transmission channel (RMSPi), define by:

30

400

Data

31

1280

Data 30

400

Data

31

1024

Data



170

1 0

0 other

s

i

e ifRMSP s

τ

τ−

≥=

(9)

• Root Mean square Power at the output of transmission channel (RMSPo), define by:

( )2

221

02

0 other

s

oe siRMSP s

τ τ

τπ

−−

≥=

(10)

Where s is the RMS delay (root mean square) transmission.

τ is the average delay introduced by the noisy channel and τ is the delay in the

entrance channel.

• Bit Error Rate define by:

( )BPSK, QPSK

1

2dB

BER erfc SNR= (11)

The simulation is performed for two cases: the classical OFDM and modified OFDM.

Simulation results are presented through the measurement of the quality of picture. The

simulation parameters chosen are shown in Table 1.

Table1. Parameters of simulation

Parameters Values

Source Image

Size

256x256

IFFT size 2048

Number of

Carriers

1009

Modulation

Method

BPSK, QPSK, 16PSK or

256PSK

Peak Power

Clipping

10 dB

Signal-to-Noise

Ratio

[0….25] dB

Information in table 1 can be modified depending on the configuration of OFDM

system desired. The size of IFFT is 2048 and offers a channel bandwidth wide (20 MHz).

Table 2 shows input images for four modulation formats and guard interval of 25% of

useful symbol period. We observe that, for a SNR of 25 dB, reconstructed images are almost

identical to the original image for BPSK and QPSK. For 16PSK and 256PSK modulations,

the reconstructed images are noisy.

A table 3, 4 and 5 shows the variation of different parameters. We find that the values

of RMSPo are less than the RMSPi. For BPSK modulation, the BER is much reduced.

For BPSK modulation with a SNR 25 dB, the quality of reconstructed image is

95.8%.



171

Table 6 shows the results of the modified OFDM. For OFDM modified, the image

quality improves with SNR smaller and guard intervals of 20% of a useful symbol period.

With a convolutional code rate of 1/3, a guard interval of 20% and a SNR of 16dB, received

image are identical to the original image.

Table 2. OFDM simulated classic transmission, original and received images with a guard

time of 25% of the useful symbol period (without convolutional coding)

Original

image

Received

image

SNR = 0dB

Received

image

SNR = 5dB

Received

image

SNR = 10dB

Received

image

SNR = 25dB

BPSK

modulation

with guard

time

interval

25%

QPSK

modulation

with guard

time

interval

25%

16PSK

modulation

with guard

time

interval

25%

256PSK

modulation

with guard

time

interval 25%



172

Table 3. Numerical results for a BPSK

SNR

(dB)

RMSPi

(dB)

RMSPo

(dB)

BER

(%)

Image quality

(%)

0 15.32 13.34 17.31 23.00

5 14.75 11.86 2.03 84.91

10 15.11 10.95 0.16 91.50

25 17.30 9.10 0.00001 95.80

Table 4. Numerical results for a QPSK

SNR

(dB)

RMSPi

(dB)

RMSPo

(dB)

BER

(%)

Image quality

(%)

0 14.02 13.02 46.31 8.38

5 14.61 11.91 18.85 43.91

10 14.35 10.09 2.28 91.22

25 14.61 7.16 0.0001 93.80

Table 5. Numerical results for a 16PSK

SNR

(dB)

RMSPi

(dB)

RMSPo

(dB)

BER

(%)

Image quality

(%)

0 15.18 13.33 84.86 2.32

5 16 12.74 72.61 7.56

10 14.03 10.3 56.39 19.16

25 15.18 7.53 9.59 81.75

Table 6 clearly shows that changing the guard interval keeps below 25% of the

symbol period; we get sharper images with SNR lower than those used by conventional

OFDM.



173

Table 6. Modified OFDM: performances of image transmission with guard time intervals

equal to 20% and a convolutional coding

Original Image

SNR

(dB)

guard

Interval

modified (%)

image

Quality

(%)

Image received

Uncoded

OFDM

(QPSK)

19.00

20.00

97.05

Coded

OFDM

r=1/2

(QPSK)

17.00

20.00

97.90

Coded

OFDM

r=1/3

(QPSK)

16.00

20.00

98.90

Table 7 shows a comparison between conventional OFDM and modified OFDM. For

a QPSK modulation format, comparisons show that the addition of a convolutional coding,

and the modified of time guard of 25% to 20% of useful symbol period, we obtains

reconstructed images identical to the original image. This shows the improvement of our

system; hence the advantage of our modified OFDM system. The choice of QPSK format for

the comparison is interesting. Table 7 shows the best image quality of modified OFDM for

different values of SNR, to be compared with the results obtained from convolution OFDM.

Compared to the work of [3, 4], obtained results are satisfactory and improved



174

Table 7. Comparison of results between conventional OFDM and OFDM modified

conventional OFDM Modified OFDM

Received

image

SNR 25 dB 25 dB

Type of

modulation

QPSK Without

convolutional coding

QPSK Without


Guard

interval

25% 20%

Image quality 94,80% 96.82%

Received

image

SNR 20 dB 20 dB

Type of

modulation

QPSK Without


QPSK With convolutional

coding r =1/2

Guard

interval

25% 20%

Image quality 93.50% 97.90%

Received

image

SNR 17 dB 17 dB

Type of

modulation

QPSK Without


QPSK With convolutional

coding r =1/3

Guard

interval

25% 20%

Image quality 92.2% 98.90%



175

VII. CONCLUSIONS

In this study, we developed a simulation model of the transmission of fixed images in

a noisy modified by the OFDM channel, using four modulation formats in Matlab. We have

shown the interest of a guard interval time modification below 25% of the useful symbol

period in order to recover a high quality signal transmitted. The addition of convolutional

coding further improves the quality reception. The results obtained using three modulation

formats (BPSK, QPSK, 16PSK) are acceptable, we get very close to 10-5 % for BPSK bit

error rate. The simulation consisted in comparing the conventional OFDM transmission

system (guard time of 25% of useful symbol period), and the modified OFDM with DPSK

modulation (guard time of 20% of useful symbol period). The modified OFDM provides a

better quality image than the classic reception system. Here the choice of the QPSK format

for comparison is very important.

However, in our future researches, we would to implement this OFDM modulation

technique with QAM modulation format, and short guard time interval, so as to further clarify

the received image.

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