BER Performance For OFDM Using Non-Conventional - IJETAE

International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 3, March 2012)

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BER Performance For OFDM Using Non-Conventional

Transform and Non-Conventional Mapping Schemes

Shilpi Gupta1, Dr. Upena D. Dalal 2

1,2Assistant Professor, ECE Department, SVNIT, Surat

[email protected]

[email protected]

Abstract— In this paper, the Bit Error Rate (BER),

performance of conventional Discrete Fourier Transform

(FFT) - OFDM system is compared with Non- conventional

Discrete Cosine Transform (DCT)- OFDM system in AWGN

and Rayleigh fading environment. Performance has been

given with conventional mapping schemes like BPSK, QPSK

and non- conventional mapping schemes like DQPSK and π/4

DQPSK. Simulation results show that DCT based schemes

gives better error performance in comparison of FFT based

schemes. Further DCT based technique using non-

conventional mapping schemes outperforms the conventional

mapping schemes for the same DCT based technique.

Keywords— Bit- error rate (BER), Discrete Cosine

Transform (DCT), Fast Fourier Transform (FFT),

Orthogonal Frequency Division Multiplexing (OFDM),

Multicarrier Modulation (MCM).

I. INTRODUCTION

OFDM systems are often used for digital

communications due to several different reasons, including

their inherent frequency diversity due to multicarrier

modulation. This feature is particularly attractive for

wireless communications, where multipath channels are

common [1].

Multicarrier communication systems were first

introduced in the 1960s with the first OFDM patent being

filed at Bell Labs in 1966. In 1971, the Discrete Fourier

Transform (DFT) was proposed [2], which made OFDM

implementation cost-effective. Further complexity

reductions were realized in 1980. Wireless applications of

OFDM intended to focus on broadcast systems, such as

Digital Video Broadcasting (DVB) and Digital Audio

Broadcasting (DAB), and relatively low-power systems

such as Wireless Local Area Networks (WLANs). Such

applications benefit from the low complexity of the OFDM

receiver, while not requiring a high-power transmitter in

the consumer terminals.

Multicarrier modulation (MCM) is used not only in the

physical layers of many wireless network standards, such

as IEEE 802.11a, IEEE 802.16a, and HIPERLAN/2, but in

wire-line digital communication systems, such as

asymmetric digital subscriber loop (ADSL). All of these

systems actually belong to the class of discrete Fourier

transform (DFT) - based MCM’s.

Particularly, in orthogonal frequency - division

multiplexing systems, digital modulations and

demodulations can be realized with the inverse discrete

Fourier transform (IDFT) and discrete Fourier transform,

respectively [3].

Conventionally, Fast Fourier transform (FFT) is the

basic transform scheme which is used in OFDM systems

for multicarrier modulation of the data to be transmitted;

the user information after applying the FFT transformation

follows the cyclic shift properties of the FFT matrix. Cyclic

prefix, merely involves pre-pending some numbers of the

ending data vector entries to the beginning of the OFDM

symbol to be transmitted, then the interference will

resemble a flat fading channel (as long as the maximum

delay spread of the channel is less than the length of the

cyclic prefix).

The cyclic shift properties are actually not unique to the

DFT as the basis function. In fact, cyclic shift properties

were extended to a wide variety of sinusoidal transforms in

[1] [8]. In this it has been shown that how the cyclic shift

properties can be derived for transforms such as DCT

through the use of symmetric extension.

Martcucci described how cyclic shift properties can be

extended to other sinusoidal transforms [8]. In particular he

showed how these properties can be derived for the

Discrete Cosine Transform (DCT) and Discrete Sine

Transform (DST) through the use of symmetrical

extension.



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Symmetric extension involves the replicating of a

sequence such that the resulting sequence is either

symmetric or asymmetric.

N by N DCT matrix is orthogonal to N/2 by N IDCT

matrix, which represents the transmitter inverse

transformation operation followed by the symmetric

extension and so recovers the original transmitted symbol

sequence.

II. SYSTEM MODEL

Fig 1 Simulation Diagram for OFDM System

High speed serial data to be transmitted is divided into

low speed parallel streams. These lower-data-rate signals

are sent over multiple channels so that multipath time

delays have less of an effect. An OFDM system treats the

source symbols e.g., the QPSK at the transmitter as though

they are in the frequency-domain. These symbols are the

inputs to an IFFT block to bring the signal into the time-

domain. The IFFT takes in N symbols at a time where N is

the number of subcarriers in the system. Each of these N

input symbols has a symbol period of T seconds. The basis

functions for an IFFT are N orthogonal sinusoids. Each

input symbol acts like a complex weight for the

corresponding sinusoidal basis function. Since the input

symbols are complex, the value of the symbol determines

both the amplitude and phase of the sinusoid for that

subcarrier. The IFFT output is the summation of all N

sinusoids. Thus, the IFFT block provides a simple way to

modulate data onto N orthogonal subcarriers.

Cyclic prefix to the signal in the time domain is used to

avoid inter-block interference (IBI). At the end of

transmitter parallel data is converted to serial and is

transmitted through the channel.

At the receiver, an FFT block is used to process the

received signal and bring it into the frequency-domain.

Ideally, the FFT output will be the original symbols that

were sent to the IFFT at the transmitter.

III. TRANSFORM SCHEMES

Transform is a technique that use one transformation

formula which converts signals or sequences from time

domain to another corresponding domain depending upon a

particular transform, that domain is easy and suitable for

computations and also we can extract more information in

that domain which is necessary for signal processing. An

inverse transform formula is used to again convert back

that signal into time domain.

Purpose of Transformation:

1. For extracting more information from the transformed

domain (e.g. frequency domain) for the purpose of

signal processing.

2. For the purpose of simplification of computations in

that domain.

A. Discrete Fourier Transform

Conventionally, Fast Fourier transform (FFT) is the basic

transform scheme which is used in OFDM systems for

multicarrier modulation of the data to be transmitted.

Let The sequence of N numbers x0, ..., xN−1 is transformed

into another sequence of N complex numbers. DFT/IDFT

Transforms are interesting from the OFDM perspective

because they can be viewed as mapping data onto

orthogonal subcarriers so these are good candidate.

The Discrete Fourier transform (DFT) is given by

∑

Xk can thus be viewed as coefficients of x in an orthogonal

basis. The inverse discrete Fourier transform (IDFT) is

given by

∑



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B. Discrete Cosine Transform

Orthogonal basis functions are needed to construct

baseband multicarrier signal. Only complex exponential

function is not the way to construct multicarrier but

alternatives may be there like DCT, DST and others.

DCT is Orthogonal transfer function tend to redistribute

the energy contained in the signal so that the most of

energy is contained in a small no. of components.

For a given 2-D data sequence x (i, j), 0 ≤ i, j , the

corresponding 2-D DCT coefficient sequence X (u, v), 0 ≤

u, v ≤ N-1, is defined as

X (u, v) =

( ) ( )∑ ∑ ( )

( )

( )

Where ( ) {

√

Similarly for IDCT,

( )

∑∑ ( ) ( ) ( )

( )

( )

The cyclic shift properties are actually not unique to the

DFT as the basis function. In fact, cyclic shift properties

were extended to a wide variety of sinusoidal transforms in

[1] [8]. In this it has been shown that how the cyclic shift

properties can be derived for transforms such as DCT

through the use of symmetric extension.

IV. MAPPING SCHEMES

Most OFDM systems use a fixed modulation scheme

over all carriers for simplicity. However each carrier in a

multiuser OFDM system can potentially have a different

modulation scheme depending on the channel conditions.

Any coherent or differential, phase or amplitude

modulation scheme can be used including BPSK, QPSK,

8PSK, 16 QAM, 64QAM… Each modulation scheme

provides a tradeoff between spectral efficiency and the bit

error rate [7]. The spectral efficiency can be maximized by

choosing the highest modulation scheme that will give an

acceptable Bit Error Rate.

All the standards are used for short distance

communication and so the multipath scenario occurs there.

In this environment the carrier frequency offset and

Doppler spread are very critical issue.

π/4- DQPSK OFDM system having small carrier

frequency offsets and small Doppler spreads do not have

much influence on the BER performance. However,

keeping other conditions the same carrier frequency offset

leads to worse system BER performance degradation than

the same amount of Doppler shift [5].

π /4 DQPSK is one of the differential modulation scheme

which has been firstly proposed by Baker [8] and was

extensively examined by Feher [9][10]. The π/4- shifted

differentially encoded quadrature phase shift keying is

receiving prominent attention in recent years because it is

used by TDMA- based digital cellular mobile telephone

systems such as North American IS-54 system [11], for

high efficiency of its power spectral density. It has also

been adopted in Digital Audio Broadcasting (DAB)

standard.

The performance of π/4-QPSK modem with differential

detection has been analyzed theoretically by computer

simulations [12][13]and experimentally [14][15]. The BER

performances of several differential modulation schemes,

including MDPSK and π/4-DQPSK were examined in [16]-

[19] by using Gaussian approximation methods.

The advantages associated with π/4-shifted QPSK are

cited in [20]. This modulation can be detected using a

coherent detector, a differential detector, or a discriminator

followed by an integrate-and-dump filter. The choice of

using both differential detection and discriminator

detection provides an advantage since both can be

performed by low-complexity receiver structures. While,

coherent detection requires a more complex receiver than

either differential or discriminator detection due to the

carrier recovery process.

V. SIMULATION RESULTS

Parameters for Simulation:

SNR= 20 dB and 30 dB for FFT and 20 dB for DCT; IDCT

/ IDFT bin size = 1024 No. Of Subcarriers = 210, Channel:

AWGN



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(a)

(b)

(c)

Fig 2 Constellation Diagram Using FFT (a) BPSK (b) QPSK (c) Pi/4

DQPSK

(a)

(b)

(c)

Fig 3 Constellation Diagram Using DCT (a) BPSK (b) QPSK (c) Pi/4

DQPSK

Fig. 4 illustrates the simulation results of BER vs. SNR

for different mapping schemes (conventional and non-

conventional) along with different transform schemes FFT

and DCT (conventional and non- conventional). The

system parameters used in simulation are SNR= 1:30 dB,

Data Subcarriers = 210, Symbol per carrier =50, IFFT/

IDCT bin size = 1024, Channel: AWGN

Fig 4: Comparison of BER performance of Different Modulation

Techniques with DCT and FFT Transform over AWGN Channel

VI. CONCLUSION

Constellation of mapping schemes BPSK, QPSK, and

Pi/4 DQPSK using DCT in AWGN Channel at SNR of

30dB is quiet good in comparison of using FFT transform

at same SNR. It is reflecting that DCT- OFDM can

transmit the data by using low transmission power in

comparison of FFT- OFDM.

In AWGN Channel scenario it is observed that BER

performance of DCT-OFDM with conventional and non-

conventional transform is better in comparison of FFT-

OFDM. It can also be observed that non- conventional

mapping scheme (Pi/4 DQPSK, DQPSK) gives better

performance in both the combinations (DCT and FFT). It

can be justified from the fact that it uses differential

detection so less complex circuitry is required hence cost

effective.

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Qua

drat

ure

In-Phase

Constellation at SNR= 30 dB

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Qua

drat

ure

In-Phase

Constellation at SNR= 30 dB

-1.5 -1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Quadra

ture

In-Phase

Constellation of Pi/4 DQPSK at SNR =30 dB

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Qua

drat

ure

In-Phase

constellation :scatterplot for BPSk at SNR = 20 dB

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Qua

drat

ure

In-Phase

constellation :scatterplot for QPSk at SNR = 20 dB

-1 -0.5 0 0.5 1

-1

-0.5

0

0.5

1

Qua

drat

ure

In-Phase

constellation :scatterplot of pi/4dqpsk at SNR =20 dB



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