OFDM Using Different Modulations 2

International Journal of Advanced Engineering Technology E-ISSN 0976-3945

IJAET/Vol.II/ Issue I/January-March 2011/47-52

Research Article

PERFORMANCE OF OFDM MULTIPLEXING

TRANSMISSION USING DIFFERENT DIGITAL

MODULATION SCHEMES R Bhagya

1 , Dr. A G Ananth

2

Address for Correspondence 1Lecturer, Department of Telecommunication Eng., RVCE. 2Professor Department of Telecommunication Eng., RVCE.

E Mail [email protected], [email protected]

ABSTRACT:

A detail analysis of the performance of an orthogonal frequency division multiplexing (OFDM) transmission with

different digital modulation techniques such as BPSK, QPSK and QAM has been carried out. BER performance has

been determined for Additive white Gaussian Noise (AWGN) channel. The simulation results for the performance

of OFDM using different digital modulation schemes BPSK, QPSK and QAM are determined for comparing their

performances. It is observed that the OFDM multiplexing shows 4dB improvement in BER performance for QAM

modulation compared to that of QPSK modulation. Similarly QPSK modulation techniques exhibits 2dB

improvement in the performance compared to BPSK modulation. It is observed that OFDM multiplexing indicates a

gradual improvement in BER performance with higher digital modulation techniques. The simulation results are

presented and discussed in the paper.

KEYWORDS: Phase Shift Keying (PSK), Quadrature Amplitude modulation (QAM), Orthogonal frequency division multiplexing (OFDM).

INTRODUCTION:

The key challenge faced by future wireless

communication systems is to provide high-data-

rate wireless access at high quality of service

(QoS). Combined with the facts that spectrum is

a scarce resource and propagation conditions are

hostile due to fading and interference from other

users. This requirement calls for means to

radically increase spectral efficiency and to

improve link reliability. The wireless channel is

distinct and much more unpredictable than the

wire-line channel because of factors such as

multipath and shadow fading, doppler spread,

and delay spread or time dispersion.

OFDM is expected to be used in future

broadcasting and wireless LAN (WLAN)

systems. IEEE 802.11a is the technology that

used OFDM concept [1]. Since wireless

technologies become a very high demand

nowadays, OFDM has been chosen to be a

subject study for different digital modulation

schemes [2].

The present study involves four procedures

namely modeling, simulations of the OFDM

transmission system, digital transmission system

and computation and comparison of BER.

1. ORTHOGONAL FREQUENCY DIVI-SION

MULTIPLEXING (OFDM)

OFDM (Orthogonal Frequency Division

Multiplexing) is a Multi-Carrier Modulation

technique in which a single high rate data-stream

is divided into multiple low rate data-streams

and is modulated using sub-carriers which are

orthogonal to each other and can be thought of

as a large number of low bit rate carriers

transmitting in parallel. All these carriers

transmitted using synchronized time and

frequency, forming a single block of spectrum,

to ensure that the orthogonal nature of the

structure is maintained.

Consider a quadrature modulated data sequence

of the N channels (d0, d1, d2, dN-1) and {1,

3} in 16-QAM. These modulated data are fed

into an inverse fast fourier transform (IFFT)



circuit and an OFDM signal is generated. The

transmitted data is given by,

)()))(2(cos

)())(2(sin

)(()(

)))(2(sin)(

))(2(cos)(()(

kTstfkTstfi

kdQikTstfi

kdIijkTstf

kTstfikdQi

kTstfikdIits

+

=

pipi

pipi

(1)

where Ts is the symbol duration of the OFDM

signal and

if ( i=0, 1, 2 ) is the frequency of the ith

subcarrier given by,

Tsifif /0+=

(2)

Here, )(tf is the pulse waveform of each of the

symbols and it is defined as,

=)(0

)0(1)(

otherwise

Tsttf

(3)

The OFDM signal includes many carrier signals

with their own frequencies which is then fed into

a guard time insertion circuit to reduce ISI.

Since the duration of each symbol is long, it can

be affordable to insert a guard interval between

the OFDM symbols and thus the inter-symbols

interference [ISI] can be eliminated.

The total symbol duration:

nT

gT

totalT +=

(4)

where, gT

= guard time interval

After the insertion of a guard interval, the

OFDM signal is given by,

)('))(2(exp)()('total

kTtftotal

kTtfikdits = pi

(5)

where f (t) is the modified pulse waveform of

each symbol defined as

>=

),(0

)(1)(

TstTgt

TstTgtf

(6)

At the receiver, the received signal is given by,

)()(),()( tndtsthtr += (7)

where ),( th is the impulse response of the

radio channel at time t , )(tn is the complex

AWGN.

At the receiver, received signal )(tr is filtered

by a band pass filter. An orthogonal detector is

then applied to the signal where the signal is

down converted to IF band. Then, an FFT circuit

is applied to the signal to obtain Fourier

coefficients of the signal in observation periods

].,[ Tsii totalTtotalT + The output, )(' kdi of the FFT circuit of the

thi OFDM sub channel is given by,

dttotal

kTtfijtrTskdi ))(2(exp)(/1)(' = pi (8)

The characteristics of delayed wave, )(kih in a multipath fading environment can be

estimated, therefore the received data also can

be equalized as follows:

))('()))(*')('/))(*'()(" kdikhikhikhikdi = (9) Where * indicates the complex conjugate.

By comparing )(' kdi and )(" kdi the BER

performance can be calculated. The BER

depends on the level of the receivers noise.

Thus in OFDM transmission, the orthogonal is

preserved and the BER performance depends on

the modulation scheme in each sub-channel [3,

6].

2. DIGITAL MODULATION TECHNIQUES

2.1 BPSK

BPSK (Binary Phase Shift Keying) is the

simplest form of PSK which uses two phases



which are separated by 180. The constellation

points are positioned, they are shown on the real

axis, at 0 and 180 in Figure 1. It is unsuitable

for high data-rate applications as it is only be

able to modulate 1 bit/symbol.

Figure 1 BPSK Constellation Diagram

The BPSK modulated signal is given by,

)10(0

};];)2(cos/2)(1

[

),2(cos/2)(1

{[

bTt

tcf

bT

bEts

tcf

bT

bEts

BPSKs

=

==

pi

pi

where bE

= Energy per bit, bT

=Bit period

}])(1

[],)(1

[{

0;2(cos/2)(1

tEbtEbBPSKS

bTttfc

bTt

pi

=

=

The Average probability of bit error of the

BPSK signaling is:

)0/(2/1 NEberfceP = (11) BPSK is considered bandwidth efficient and

its bandwidth efficiency increases with the

increase in the number of bits per symbol. The

channel bandwidth required to pass BPSK

signals is given by,

TB /2= where T is the symbol duration, which is

related to bit duration, bT

and is given by,

M

bTT

2log=

where M is the no. of levels.

M

bRB

2log/2=

where, bTb

R /1=

The BPSK bandwidth efficiency given by,

2/

2log M

B=

2.2 QPSK

QPSK (Quadrature Phase Shift Keying) is a

4-ary PSK signal. The phase of the carrier in the

QPSK takes 1 of 4 equally spaced shifts, such as

0, pi/2, pi, 3pi/2, where each value of phase

corresponds to a unique pair of message bits.

This method yields the signal constellation in

Figure 2.

Figure 2 QPSK Constellation Diagram

Table 1: The Binary Di-bit and corresponding phase



The QPSK transmitted signal is defined by,

)(22

)(11

sin/2]4/)12[(sin

cos/2]4/)12[(cos

sin]4/)12[(sin/2

cos]4/)12[(cos/2)(1

tist

is

tcwTiE

tcwTiE

tcwiTE

tcwiTEts

pi

pi

pi

pi

+=

=

=

where 4,3,2,1=i The QPSK modulated wave can be expressed

as,

tcwTEt

evend

tcwTEt

oddd

tcwt

evendTE

tcwt

odddTE

tcwTt

evendE

tcwTt

odddEts

sin}/2)({

cos}/2)({

sin)(/2

cos)(/2

sin/2)(

cos/2)()(

+

+=

+=

(12)

The bandwidth efficiency of QPSK is twice that

of PSK since we are transmitting two bits per

signal. The Average probability of bit error of

the QPSK signaling is:

)0/(2/1 NEberfceP = (13) 2.3 QAM

QAM (Quadrature Amplitude Modulation) is a

modulation scheme which is carried out by

changing (modulating) the amplitude of two

carrier waves. The carrier waves are out of phase

by 90, and are called Quadrature carriers in

Figure 3.

Figure 3 16-QAM constellation diagram

The first stage in the modulation block needs to

be a serial to parallel conversion to change the

bit stream into log2M streams, where M is

number of symbols in the constellation. The bit

rate of each of the new streams is only 1 /

log2M.

In the case of 16-QAM there are then 4 input

streams which index a lookup table. One of the

signals then modulates the quadrature, Q carrier

and the other modulates the in-phase, I carrier.

The signal stage of the modulation is simply the

addition of the Q and I signals to form M-QAM

modulated signal.

RESULTS AND DISCUSSION:

The simulation results for the performance of

OFDM for different digital modulation

techniques BPSK, QPSK and QAM for AWGN

channel are obtained using MATLAB. The

BER values as function of SNR are determined

for each modulation scheme for the purpose of

comparing their relative performances. The

Figure 4, 5, 6 shows the bit-error-rate

performances for OFDM as a function of SNR

for three the different digital modulation

schemes



Figure 4: BER Vs SNR for BPSK modulation

technique.

Figure 4 shows that for OFDM transmission

using BPSK modulation, the BER decreases

exponentially with SNR. The Figure indicates

that for BER values ~10^-4 the SNR ~ 8 dB.

Similarly Figure 5 shows that for OFDM

transmission using QPSK modulation, the BER

decreases exponentially with SNR. The figure

indicates that for BER values ^~10-4 the SNR ~

9.5 dB

Figure 5: BER Vs SNR for QPSK modulation

technique.

Further Figure 6 shows that for OFDM

transmission using QAM modulation, the BER

decreases exponentially with SNR. The figure

indicates that for BER values ~10^-4 the SNR ~

13 dB. These observations clearly exhibit a

gradual improvement for different modulation

schemes from BPSK to QAM modulation.

Figure 6: BER Vs SNR for QAM modulation

technique.

It is evident from the Figures that considerable

improvement in SNR performance can be

achieved for QAM modulation compared to

BPSK modulation. Also it is seen that for BER

values of 10^-4, there is considerable

improvement in BER performance for QPSK

modulation ~1.5 dB when compared to BPSK

modulation for OFDM transmission systems.

Similarly there is an improvement of ~3.5 dB

improvement from QPSK to QAM modulation.

These observations clearly indicate significant

increase in the BER performance ~5 dB from

BPSK to QAM modulation schemes

Hence it may be concluded that for OFDM

transmission schemes it is possible to achieve

significant improvement in BER performance



for higher version of digital modulation

techniques

We have extrapolated the BER value to 10^-5

and derived the SNR values for the three

modulation schemes based on the simulation

results. The SNR values for QAM modulation is

SNR ~15 dB, for QPSK Modulation SNR ~11

dB and BPSK modulation SNR ~9 dB. These

measurements also indicate that for lower BER

values the SNR performance further increases

from BPSK to QPSK by ~ 2 dB and for QPSK

to QAM ~ 4 dB and BPSK to QAM ~ 6 dB.

It can be concluded from the results that there is

a considerable improvement in the SNR values

as we go from lower to higher digital

modulation schemes for OFDM transmission.

These observations are important for

applications relating to implementation of

MIMO (Multi Input Multi Output) [4,5]

transmission techniques.

CONCLUSIONS:

It can be concluded form the above observations

that,

1. The OFDM multiplexing techniques gives

better SNR performances for digital

transmission.

2. The SNR performance for BER values of

10^-4 improves with different modulation

schemes from BPSK to QPSK (~1.5 dB) and

QPSK to QAM (~3.5 dB) and BPSK to

QAM (~5 dB)

3. The extrapolated SNR performance for BER

values of 10^-5 improves with different

modulation schemes from BPSK to QPSK

(~2 dB) and QPSK to QAM (~ 4 dB) and

BPSK to QAM (~ 6 dB)

ACKNOWLEDGEMENT:

We wish to acknowledge the support given by

Principal, RV College of Engineering,

Bangalore for carrying out the present research

work and HOD department of

telecommunication for constant encouragement.

We also wish to thank Syed A Malik and Seema

M Magi for software support.

REFERENCES

1. Allert van Zelst, and Tim C. W. Schenk,

Implementation of a MIMO OFDM-Based

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on Signal Processing, VOL.52, No. 2, Feb

2004, Pages 483-494.

2. Orlandos Grigoriadis, H. Srikanth Kamath,

Iaeng, BER Calculation Using Matlab

Simulation For OFDM Transmission,

Proceedings of the International Multi-

Conference of Engineers and Computer

Scientists 2008 Vol II IMECS, Mar 2008,

Pages 19-21.

3. DM Wireless Systems: Basics, Perspectives,

and Challenges, IEEE Wireless

Communications, Aug 2006, Pages 31 37.

4. A. J. Paulraj, D. Gore, R. U. Nabar, and H.

Bolcskei, An Overview of MIMO

Communications - A Key to Gigabit

Wireless, Nov 2003.

5. Dr.Jacob Sharony, Introduction to Wireless

MIMOTheory and Applications, IEEE LI,

November 15, 2006.

6. Ryszard Struzak, Channel & Modulation:

Basics, The Abdus Salam International

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(Italy), 5 to 24 February 2007.

Documents

OFDM Using Different Modulations 2