OFDM: Modulation Technique for Wireless Communication

International Journal of Innovative Research in Advanced Engineering (IJIRAE)
Volume 1 Issue 1 (March 2014)
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ISSN: 2278-2311 IJIRAE | http://ijirae.com
© 2014, IJIRAE - All Rights Reserved Page - 1
OFDM: Modulation Technique for Wireless
Communication
Rashmi.R Sarala.S.M
Department of Electronics and Communication Department of Electronics and Communication
M.S.Ramaiah Institute of Technology, Bangalore, India M.S.Ramaiah Institute of Technology, Bangalore, India
rashmirmohan@gmail.com saralasm@msrit.edu
Abstract— Orthogonal Frequency Division Multiplexing (OFDM) has become the modulation technique for many wireless
communication standards. In a wireless system, a signal transmitted into channel bounces off from various surfaces resulting
in multiple delayed versions of the transmitted signal arriving at the receiver. The multiple signals are received due to the
reflections from large objects, diffraction of electromagnetic waves around objects .This causes the received signal to be
distorted. OFDM provides tolerance to such frequency selective channels and provides high data rates. In this paper we
propose to analyze the theory of OFDM, simulate the OFDM transceiver using MATLAB and perform BER analysis.
Keywords— OFDM, FFT, IFFT, ISI, BPSK, QPSK, AWGN, RAYLEIGH CHANNEL
I. INTRODUCTION
The progress in the semiconductor technology has made radio transmission without any physical connection possible
throughout the world. The goal of future wireless communication is to provide communication with high data rates. The
most popular technique in wireless communication is Orthogonal Frequency Division Multiplexing (OFDM). When the
data is transmitted at high data rates over wireless radio channels, the symbols may overlap over each other which can
lead to inter symbol interference (ISI). OFDM can combat the effect the ISI.OFDM is increasingly used in high mobility
wireless communication systems, e.g. mobile WiMAX (IEEE 802.16e) and 3GPP’s UMTS Long-Term Evolution (LTE).
The developments of OFDM systems can be divided into three parts .They are Frequency Division Multiple Access
(FDMA), Multicarrier Communication and Orthogonal Frequency Division Multiplexing.
In FDMA, the available bandwidth is divided into multiple channels and then allocated to the users.
In Multicarrier Communication the signal is divided into a number of signals over a frequency range, whereas OFDM
spaces the channels much closer by placing the carriers orthogonal to each other, thus using the spectrum efficiently as
shown in Fig.1.
Fig.1 a.)Multicarrier Technique (FDM) b.)Orthogonal Frequency Division Multiplexing.
In 1960’s, the concept of using parallel data transmission by multicarrier modulation was published. However it was not
practical to implement until the discovery of using the Discrete Fourier Transform (DFT).DFT is implemented using the
computationally efficient Fast Fourier Transform (FFT).
II. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
A. Theory of OFDM
OFDM is a multicarrier transmission technique in which the high rate single data stream is transmitted over a number of
low rate parallel subcarriers. Because of the low rate parallel subcarriers, the symbol duration increases which will

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reduce the effect of multipath delay spread on the signal. Fig.2 shows the orthogonal subcarriers in frequency and time
domain.
In a single carrier system, a single fade or interference can cause the entire link to fail, but in a multicarrier system, only a
small percentage of the subcarriers will be affected.
The term orthogonal in OFDM refers to the fact that the center frequencies of the sub channel are separated by the
reciprocal of the OFDM block time T. Suppose the symbol length is T, sinusoidal signals differing in frequency by
1/T,will be orthogonal over the period T.
The bandwidth upon which the channel response can be assumed to be flat is known as coherence bandwidth of the
channel.
Fig.2: a) Spectrum of Orthogonal subcarriers b.)Time domain representation of orthogonal subcarriers.
If the data is transmitted at high rate, the bandwidth of the channel becomes wide and may exceed the coherence
bandwidth of the channel. This distorts the signal and causes Inter Symbol Interference (ISI).
A guard interval is introduced in every OFDM symbol to eliminate ISI. Two approaches are followed in OFDM to insert
guard interval. The first one is known as zero padding, where zeros are inserted between OFDM symbols .The second
one is known as cyclic prefix, where a part of the end of the OFDM symbol is copied and inserted in the beginning of the
next OFDM symbol in time domain.
The length of the guard interval must be at least equal to the length of the channel response to avoid the ISI.
Usage of cyclic prefix is preferred than zero padding when FFT is used. Because FFT algorithms require the signal to be
periodic to produce accurate results and cyclic prefix makes the signal periodic. Fig. 3 shows the OFDM symbol with
cyclic prefix.
Fig. 3: OFDM symbol with cyclic prefix in time domain.
Fig. 4: Block diagram of the OFDM system
B. System Description

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The block diagram of an OFDM system is represented in Fig.4.
OFDM symbols are generated as follows .The transmitter section converts the digital data to be transmitted into a
mapping of the sub carrier’s amplitude and phase using modulation techniques.
The modulation technique such as the BPSK, QPSK or QAM can be used. The modulated data is converted into parallel
stream for faster and optimum utilization of the bandwidth.
Time domain representation of the data is created by using an Inverse Fast Fourier Transform (IFFT) which is an
efficient method to implement DFT.
OFDM symbol time domain representation is extended by addition of cyclic prefix to each symbol that solves both ISI
and inter carrier interference (ICI).
The time domain signal is passed through the channel.
At the receiver side, the cyclic prefix is removed and converted to frequency domain by using FFT. Finally the parallel
data is converted back to serial data.
Mathematically, each subcarrier can be formulated as follows:
(1)
where Ac (t) is amplitude and
 c (t) is phase.
An OFDM symbol consists of many subcarriers. It is represented by:
)(
1
)(
1
0
tA
N
tS
N
n
ns 



)]([ ttj nne  
(2)
where   nn 0
Ac (t) and  c (t) get different values in different symbols, but they are constant in every symbol and only depend on
frequency of carriers.
In every symbol, we have,
nn t  )( , nn AtA )( (3)
If the signal is sampled with 1/T where T is the duration of a symbol and substituting (3) in (2) we get,




1
0
1
)(
N
n
ns A
N
kTS
])
0
[( nkTnj
e
 
(4)
When 0 =0, (3) is converted to an IDFT transform.
By adding cyclic prefix in time domain, ISI can be prevented.
)(nsT (5)
where Ncp is the length of the cyclic prefix.
III. SIMULATION
In this paper, we have simulated the OFDM transceiver using the model shown in Fig.4.We have used two modulation
schemes, namely BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying).The ofdm symbols created
after taking ifft is passed through the Gaussian channel which adds additive white Gaussian noise (AWGN).Cyclic prefix
does not hold any significance in AWGN channel. The demodulation is performed at the receiver.
Multipath Rayleigh fading channel is also considered for simulation. It is generated by considering sum of two random
variables .Each path in the multipath scenario can be modelled as circularly symmetric Gaussian random variables with
respect to time when central limit theorem is applied ,the envelope of the random variables will follow Rayleigh
distribution .Hence it is known as Rayleigh fading channel.
|)(|)()( tctcjetcAtcS  

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We have plotted the Bit error rate (BER) by considering the signal-to-noise ratio for the modulation techniques specified.
An OFDM symbol is created after taking the 64 point ifft of the modulated data .An OFDM containing 64 subcarriers
generated using BPSK modulation is as shown in Fig .5.
Fig. 5: An OFDM symbol of containing 64 subcarriers using BPSK modulation.
Simulated BER curves for BPSK, and QPSK in AWGN channel is as shown in Fig. 6.
Fig. 6: BER vs. SNR plot for OFDM using BPSK, QPSK modulation techniques in AWGN channel.
Simulated BER curves for BPSK, and QPSK in Rayleigh channel is as shown in Fig. 7. A 10 tap Rayleigh channel has
been considered with a cyclic prefix of length 16.Cyclic prefix is used to minimize the effect of ISI. AWGN will also
have an influence in the BER value in the Rayleigh fading channel.

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Fig.7: BER vs. SNR plot for OFDM using BPSK, QPSK modulation techniques in Rayleigh channel.
TABLE I
SIMULATION PARAMETERS
Parameters Specification
FFT size 64
No of subcarriers 64
Channel Model AWGN& Rayleigh
Signal constellation BPSK&QPSK
No of symbols 10000
Cyclic Prefix length 16
It is observed that for a particular value of SNR, the BER for BPSK and QPSK is almost equal in AWGN channel and in
Rayleigh channel. The advantage of using QPSK modulated data is that it can be transmitted as twice the data rate when
compared to BPSK modulated data. However, QPSK transmitters and receivers are complicated and expensive when
compared to BPSK.
IV.CONCLUSIONS
OFDM provides high data rates and is robust in frequency selective channels .It minimizes the effect of ISI. Hence it is
suitable for wireless communication .Simulation was performed for OFDM using BPSK and QPSK modulation in
AWGN and in Rayleigh channels. The BER performance is similar for both, but QPSK is expensive in terms of
bandwidth when compared to BPSK.
REFERENCES
[1] Ramjee Prasad,” Basics of OFDM and Synchronization “in OFDM for Wireless Communications systems, Artech, House, Inc, 2004, pp.117-122.
[2] J.J.van de Beek, P.Odling, S.K.Wilson and P.O.Borjesson,”Orthogonal Frequency-Division Multiplexing (OFDM)”, International Union of Radio
Science (URSI), Oxford University Press, 1999.
[3] Bernard Sklar,”Rayleigh Fading Channels in Mobile Digital Communication Systems Part II: Mitigation, IEEE Communications Magazine, July
1997.
[4] Ghassan M.T.Abdalla,”Orthogonal Frequency Division Multiplexing Theory and Challenges “, University of Khartoum Engineering Journal, Vol.1
Issue 2pp.1-8, October 2011.
[5] Dusan Matic,”Mathematical description of OFDM”, JPL’s Wireless Communication Reference Website, Analog and Digital Transmission Chapter.

OFDM: Modulation Technique for Wireless Communication

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OFDM: Modulation Technique for Wireless Communication