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Ber Calculation Using Matlab Simulation For

Ofdm Transmission

Orlandos Grigoriadis, H. Srikanth Kamath, Member, IAENG

Abstract—Orthogonal frequency division multiplex

(OFDM) modulation is being used more and more in

telecommunication, wired and wireless. DVB and DAB

already use this modulation technique and ADSL is based

on it. The advantages of this modulation are the reason for

its increasing usage. OFDM can be implemented easily, it is

Spectraly efficient and can provide high data rates with

sufficient robustness to channel imperfections.

The purpose of this paper is to use a Matlab simulation

of OFDM to see how the Bit Error Ratio (BER) of a

transmission varies when Signal to Noise Ratio (S/N Ratio)

and Multipropagation effects are changed on transmission

channel.

Index Terms— BER, FFT, ISI, OFDM, S/N

I. INTRODUCTION

In an OFDM [4] scheme a large number of sub-

channels or sub-carriers are used to transmit digital data.

Each sub-channel is orthogonal to every other. They are

closely spaced and narrow band. The separation of the

sub-channels is as minimal as possible to obtain high

spectral efficiency. OFDM is being used because of its

capability to handle with multipath interference at the

receiver.

These two are the main effects of multipropagation [3].

Frequency selective fading

Interfierence (ISI) [5]. In OFDM the large number of

narrow band sub-carriers provides sufficiently “flat”

channels. Therefore the fading can be handled by simple

equalizing techniques for each channel. Furthermore the

large amount of carriers can provide same data rates of a

single carrier modulation at a lower symbol rate.

The symbol rate of each channel can be dropped to a

point that makes each symbol longer than the channel’s

impulse response. This eliminates ISI.

The two main drawbacks of OFDM are the large

dynamic range of the signals being transmitted and the

sensitivity to frequency errors.

Using a Matlab simulation we can implement an

OFDM transmission. Using the simulation we can easily

change the values of S/N ratio [2] and change the

multipropagation effects on the transmission. Then we

can analyze the results of each transmission and see how

the BER [1] is changed.

and Inter Symbolic

II. OFDM SIMULATION

A. The Matlab source code

The Matlab code used in this paper was developed by

Alan C. Brooks and Stephan Hoelzer [8]. This

implementation is used to transmit a computer file in

binary data form modulated by OFDM and 16- QAM

modulation. A scheme

implementation can be seen in Fig 1. As it can be seen in

the figure channel imperfections are modeled in this

implementation. In the end of the transmission, when the

receiver receives the data, a comparison of the

transmitted and the received messages is done in order to

calculate the Bit Error Ratio (BER).

This paper does not explain in detail the simulation

code. It uses it to create results and see the behavior of

OFDM under different channel properties. Nevertheless

some of the main variables of the code are described,

because the choice of them has a critical effect on the

results.

of every part of the

Figure 1. Matlab Flow Chart

B. General Options in the Simulation

The general options of each transmission are in the

setup.m file of the simulation. Two of the most important

variables are analyzed.

One of the main characteristics of every simulation

model of OFDM is the size of the fast Fourier

transformation (FFT) used to generate the signal. In the

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol II

IMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3IMECS 2008

Page 2

simulation it is equal to the number of samples for the

transmission signal. In the code this variable is named

fft_size. The more the size of the FFT is increased the

more samples there are for each signal. The more samples

there are the smoother and more accurate the signal is.

Another very important variable is the number of the

carriers (or the sub – channels) being used in every

simulation. This variable is named num_carriers.

According to the number of sub – carriers the data is cut

into pieces, which are called chunks. Each carrier

transmits 2 data bits. The first is coded in the real part of

the Fourier transformation of signal and the second in the

imaginary.

C. Variables which have an effect on S/N ratio

In this implementation noise is added to the

transmission signal. In the setup.m file there is the

variable called noise_level. This variable changes the

level of the noise of the channel. The level of the noise is

given by the following equation:

levelnoiseAA

sn

_

⋅=

Where An is the level of the noise

As is the level of the signal

We know that the S/N ratio is given by the following

equation [2]

2

/

noise

A

n

⎠

⎝

The noise produced is uniformly distributed in the

closed space:

[

s

noiseA level noise

⋅−

,_

The noise after being generated is added to the signal.

This is done in the ch_noise.m file.

(1)

2

_

1

level

A

NS

s

=

⎟⎟

⎞

⎜⎜

⎛

=

(2)

]

s

A level

⋅

_

D. Variables which have an effect on multipropagation

Adding two delayed and attenuated copies of the signal

to itself simulates multipath propagation. The copies are

named echoes. The first echo is delayed less and has a

higher level than the second.

The time of the delay of the two echoes are changed by

the variables d1 and d2. But it is also a function of the

number of carriers. Actually the time of the delay for both

echoes is analog to the number of carriers. So each time

the number of carriers changed in the tests, to keep the

time of delay stable, d1 and d2 variables were divided by

the change. This is done in order to make the tests

equivalents.

The level of the echoes is changed by the variables a1

and a2 and it is given by the following equation.

AaA

11

=

Where Aecho1 is the level of the first echo

Aecho2 is the level of the second echo

s echo

s echo

AaA

22

=

(3)

III. PLOTS OF BER AS A FUNCTION OF S/N RATIO

AND MULTIPROPAGATION

A. BER and S/N ratio

To make the plots of the BER as a function of the S/N

ratio a file was transmitted for many S/N ratios. As

mention before the S/N ratio can be changed by the

noise_level variable, which changes the S/N ratio

according to the equation (2).

Each time a transmission took place the noise_level

variable changed. The lowest S/N ratio was decided to

have the value 0.1 and the highest 10. Therefore, by

solving the equation (2), the noise_level variable varies

from 0.3162 to 3.162.

The transmission was simulated for 5 sets of carriers.

32, 64, 128, 256 and 512 carriers. For each set of carriers

a BER curve as a function of S/N ratio was plotted.

There are two plots. In the first the echoes have high

level and in the second low levels. To be exact, in the first

plot the two echoes have a level of 0.50 and 0.40 times

and in the second 0.10 and 0.05 times the level of the

signal. The results can be seen in Fig 2. and Fig 3.

Figure 2. BER as a function of S/N ratio.

Multipropagation effects are high

Figure 3. BER as a function of S/N ratio.

Multipropagation effects are low

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol II

IMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3 IMECS 2008

Page 3

B. BER as a function of Multipropagation

In these plots the behavior of the BER of OFDM can be

seen as a function of the level of the signals.

As before, a file was transmitted, each time with a

different level for the echoes. The level of the echoes has

a start value of 0.05 for the first and 0 for the second

times the level of the signal. They have a final value of

0.50 and 0.40 times the level of the signal.

Again the transmission was simulated for 5 sets of

carriers. 32, 64, 128, 256 and 512 carriers. For each set of

carriers a BER curve was plotted. The x – axis of the

plots represents the factor by which the level of the signal

is to be multiplied to equal the first echo.

There are two plots. In the first the transmission takes

place with a low S/N ratio - 0.1 - and in the second with a

high – 10.

The results of the BER as a function of

multipropagation for each set of carriers can be seen in

the Fig 4. and Fig 5.

Figure 4. BER as a function of Multipropagation. S/N

Ratio is 0.1

Figure 5. BER as a function of Multipropagation. S/N

Ratio is 10

IV. CONCLUSION

The first and obvious thing we can notice from all the

Plots is that the more we increase the number of carriers

for certain S/N Ratio and Multipropagation effect the

more the BER increases. This is to be expected, because

the more we increase the number of carriers the more we

increase the symbol rate and therefore the data rate.

From the plots of the BER as a function of the S/N ratio

we can see that when the S/N ratio is very low (0.1)

multipropagation does not have any impact on the BER.

Furthermore, it has an impact when the S/N ratio has high

values, for example 512 carriers have 15% BER when

Multipropagation is low and the S/N ratio is 10 but it

drops to 8% BER when Multipropagation is high and the

S/N ratio is again 10.

This can be seen from the plot of BER as a function of

Multipropagation when we have the S/N ratio is equal to

0.1. The BER by every set of carriers stays constant

though the multipropagation effects are increased.

From the Plot of BER

Multipropagation with a high S/N ratio we can notice that

the less the number of carriers, the more immunity the

transmission to the Multipropagation effects.

as a function of

ACKNOWLEDGMENT

This work was done in the VSLI design / DSP lab of

MIT and it was supported by all the staff working in the

lab and by the Senior Lecturer Mr. Srikanth Kamath.

REFERENCES

[1]Wikipedia, free encyclopedia, article on bit error rate

http://en.wikipedia.org/wiki/Bit_error_rate

[2] Wikipedia, free encyclopedia, article on signal to

noise ratio http://en.wikipedia.org/wiki/S/n_ratio

[3] Wikipedia, free encyclopedia, article on

multipropagation propagation of a telecommunication

signal http://en.wikipedia.org/wiki/Multipath

[4] Wikipedia, free encyclopedia, article on COFDM

http://en.wikipedia.org/wiki/COFDM

[5] Wikipedia, free encyclopedia, article on intersymbol

interference

http://en.wikipedia.org/wiki/Intersymbol_interference

[6] Thesis of Eric Lawrey on OFDM modulation

technique for wireless radio applications, submitted on

October 1997

http://www.skydsp.com/publications/4thyrthesis/index.ht

m

[7] Paper of Guillermo Acosta on OFDM Simulation

Using Matlab

http://www.ece.gatech.edu/research/labs/sarl/tutorials/OF

DM/Tutorial_web.pdf

[8] A study by Alan C. Brooks and Stephen J. Hoelzer on

OFDM Simulation using Matlab

http://cegt201.bradley.edu/projects/proj2001/ofdmabsh/

[9] Wireless Digital Communications by Molisch

Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol II

IMECS 2008, 19-21 March, 2008, Hong Kong

ISBN: 978-988-17012-1-3IMECS 2008