Simulation of OFDM modulation

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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ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 3, May – June, 2013, pp. 162-176
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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 e π 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
1 nmN j
N
m n
n
C a e
N
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
channelNoise
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
L
j f t
m
m
h t e t
L
θ π
δ 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
N
j k
N
j
X k x j w − −
=
= ∑ (5)
( ) ( ) ( )( )1 1
1
1 N
j k
N
k
x j X k w
N
− − −
=
= ∑ 6)
With
2 i
N
Nw 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 modiance of the ulated signal
linear SNR
σ = (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 outputIFFT
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 y
M 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 if
RMSP s
τ
τ
−
≥
= 


(9)
• Root Mean square Power at the output of transmission channel (RMSPo), define by:
( )
2
2
2
1
0
2
0 other
s
o
e siRMSP s
τ τ
τ
π
−
−

 ≥= 


(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
2
dBBER 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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176
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Simulation of OFDM modulation

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