A NEW PULSE SHAPE USED TO REDUCE THE ICI POWER IN

OFDM SYSTEMS

Alexandra Ligia Balan

and Nicolae Dumitru Alexandru

Department of Computer, Electronics and Automation, “Ştefan cel Mare” University of Suceava

Str. Universitatii, no.13, 720229, Suceava, Romania

Department of Telecommunications, “Gh. Asachi” Technical University of Iaşi, Bd. Carol, I no 11, 700506, Iaşi, Romania

Keywords: Orthogonal Frequency Division Multiplexing (OFDM), Inter-symbol Interference (ISI), Inter-carrier

Interference (ICI), Frequency Offset, Bit Error Rate (BER).

Abstract: In this paper we analyze a new pulse shape in order to reduce ICI power in a N-subcarrier OFDM system.

The aim is to obtain a small average ICI power and a convenient bit error rate (BER). We focused our paper

on three aspects of the analysis, average ICI power, the ratio of average signal power to average ICI power,

which is denoted as SIR, and the BER performance for OFDM systems.

1 INTRODUCTION

Orthogonal Frequency Division Multiplexing is a

modulation technique used in communication

systems. However, a well-known problem in OFDM

is its sensitivity to frequency offset errors that

destroy the sub-carriers orthogonality, causing a

degradation of system performance in terms of inter-

carrier interference (ICI).

The OFDM technique uses the principle of

multi-carrier transmission to convert a serial high-

rate data stream into multiple parallel low-rate sub-

streams. Each sub-carrier is modulated by another

sub-stream. The symbol rate on each subcarrier is

much less than the initial serial data symbol rate and

the effects of inter-symbol interference (ISI)

decrease significantly.

In order to minimize ICI in OFDM systems, a

number of methods have been developed recently.

Some of these methods are using new pulse shaping

techniques (Tan and Beaulieu, 2004); (Mourad,

2006); (Kumbasar and Kucur, 2007); (Alexandru

and Alexandru, 2010).

In the sequel, our paper proposes a new pulse

shape used in OFDM systems and investigates its

properties exploring inter-carrier interference (ICI)

and bit error rate (BER) performance for OFDM

systems.

2 PROBLEM STATEMENT

In this section we will briefly review some basic

notions used to describe the inter-carrier interference

analysis. The OFDM system model and ICI analysis

followed the same technique as in the work of Tan

and Beaulieu (2004).

The average ICI power, (Tan and Beaulieu,

2004); (Kumbasar and Kucur, 2007), averaged

across different sequences is:



























ICI



(1)

The average ICI power depends not only on the

desired symbol location,

m , and the transmitted

symbol sequence, but also on the pulse-shaping

function at the frequencies



,/ fTmk 

,mk



1,...,1,0  Nk

and the number of

subcarriers.

The ratio of average signal power to average ICI

power is denoted as signal-to-interference ratio SIR,

(Tan and Beaulieu, 2004; Kumbasar and Kucur,

2007) and is expressed as

 











fTmkPfPSIR

(2)

Besides the ICI power (P

ICI

), BER also has an

important role in evaluating the performance of an

308

Balan A. and Alexandru N..

A NEW PULSE SHAPE USED TO REDUCE THE ICI POWER IN OFDM SYSTEMS.

DOI: 10.5220/0003814503080311

In Proceedings of the 2nd International Conference on Pervasive Embedded Computing and Communication Systems (PECCS-2012), pages 308-311

ISBN: 978-989-8565-00-6

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

OFDM communications system. It is desirable to

obtain a balance between a small P

ICI

and also a

satisfactory BER, having as a result an efficient

pulse.

A detailed analysis of the BER performance for

OFDM systems is presented by Khoa (2008). The

expressions of the bit error rate (BER) are derived

using a BPSK transmission and an OFDM system

with BPSK modulation over the AWGN channel.

Based on the analysis performed in the work of

Khoa (2008), the BER of an OFDM system can be

obtained as a function of frequency offset,



0 ff , phase error



, average ICI power and



fP . The OFDM system model is proposed by Tan

and Beaulieu (2004) employing BPSK modulation

over the AWGN channel.

Kumbasar and Kucur (2007) have proposed a

new pulse shaping function to reduce ICI in OFDM

systems and denoted as improved sinc power pulse

(ISP). Numerical and simulation results show that

the ISP pulse shape, which is a modification of SP

pulse (Mourad, 2006), provides a good improvement

regarding ICI power, as compared to previously

reported pulse shapes.

Recently we have proposed (Alexandru and

Onofrei, 2010) a new type of pulse that is a

generalization of ISP pulse defined by Kumbasar

and Kucur, (2007). Its Fourier transform can be used

to decrease ICI in OFDM systems. To define the

new shape a generalized formula for



fP was used

() ( )

{}

()()()

()()

sin sin

exp

sin

fb cfT

Pf afT

fb cfT

ìü

ïï

íý

ïï

îþ

(3)

Figure 1: Comparison of ISP pulse shape and the new

pulse shape.

3 PULSE CHARACTERISTICS

Based on our earlier studies and analysis we propose

a new pulse shape used to obtain improved

performance with respect to the reduction of average

ICI power of a N-subcarrier OFDM systems.

To construct the new pulse we started from the

pulse shape proposed by Jayasimha and Singh,

(2000). The new pulse shape is defined in the

frequency domain as:



















2sinc

)(



(4)

The new proposed pulse is plotted in Figure 1

together with the ISP pulse for different values of

the parameters. A closer look reveals that the tails of

the new pulse are smaller. Therefore we expect to

obtain improved performance in term of ICI

analysis.

4 SIMULATION RESULTS AND

DISCUSSIONS

In this section we illustrate the performance of the

new proposed pulse and compare it with results

recently reported in literature. Using the recently

proposed techniques for ICI and BER analysis (Tan

and Beaulieu, 2004); (Kumbasar and Kucur, 2007);

(Khoa, 2008), we study the performance of the new

pulses in a 64-subcarrier OFDM-BPSK

communication system.

4.1 ICI Analysis

In the sequel we followed the same model presented

by Tan and Beaulieu (2004), to evaluate the average

ICI power and the average signal power to average

ICI power ratio (SIR). The simulations results are

obtained for a 64-subcarrier OFDM system.

4.1.1 The Average ICI Power

In order to observe the improvements achieved for

the new pulse, in term of average ICI power, we

study its behavior compared with ISP pulses taken

as a reference.

The results obtained from average ICI power

analysis are presented in Figure 2. We observe that

performance of the proposed pulses is superior to

ISP pulse (Kumbasar and Kucur, 2007).

Figure 2 shows that the proposed pulse

outperforms reference pulses in terms of average ICI

power, for all the selected values of the parameters.

From Figure 2 we observe the decrease in ICI power

due to the increase of the sinc function degree.

A NEW PULSE SHAPE USED TO REDUCE THE ICI POWER IN OFDM SYSTEMS

309

Figure 2: Comparison of average ICI power for the new

pulse shape and ISP pulse, in a 64-subcarrier OFDM

system.

The variations of average ICI power with sample

location m are presented in Figure 3. The normalized

frequency offset is

05.0fT .

Studying the results plotted in this figure we

observe the decrease in ICI power due to the

increase of the sinc function degree. The best results

were obtained for n=4.

For comparison purposes, we have represented in

Figure 3, the ICI power for the new pulse (n=2 and

n=4) together with the rectangular pulse (RP), raised

cosine (RC), BTRC (Beaulieu, Tan and Damen,

2001) and ISP (Kumbasar and Kucur, 2007) pulses.

For new pulse (n=2), the ICI power is -67.20dB,

which is by 46.26 dB better than RP, 34.9 dB better

than RC, 27.26 dB better than BTRC, 9.76dB better

than ISP (a=1, n=2).

With respect to the new pulse, with n=4, we

observed good improvements and the ICI power is -

135.98 dB, which is by 115.04 dB better than RP,

103.68 dB better than RC, 96.04 dB better than

BTRC, 26.84dB better than ISP (a=1, n=4).

Figure 3: ICI power for different sample locations in a 64-

subcarrier OFDM system; (

05.0



fT ).

As expected, the ICI drops for the samples

located near sample locations 0 and N-1, because

these samples have fewer interfering samples.

Figure 4: SIR for different pulse shapes in a 64-subcarrier

OFDM system.

4.1.2 The Signal-to-interference Ratio SIR

The comparative performances of these pulses in a

64-subcarrier OFDM system in terms of the average

signal power to average ICI power ratio, denoted as

SIR, are illustrated in Figure 4. Looking at Figure 4,

we observe that the results obtained for the SIR ratio

show better performance for the new pulse as

compared with those obtained for the ISP pulse,

which is taken as a reference.

4.2 BER Analysis

Further, this section investigates the bit error rate

(BER) as a function of the signal to noise ratio per

bit (

SNR







) value.

In Figure 5 it is plotted the BER versus SNR

(signal-to-noise ratio) for different values of the

parameters a, and n that are involved in the pulse

shape equations. We compared the known ISP pulse

and RP pulse with the new pulse shape proposed in

this paper.

The effect of the carrier phase noise,



, in a

BPSK-OFDM system with

1.0fT is evident.

From the results illustrate in the Figure 6, it can be

noticed that a smaller carrier phase noise,



determines an improvement of BER.

From the figures 5a and 5b it can be seen that the

proposed pulse exhibits better performance than the

reference pulses, when the design parameters are

1,5.0



and

1,1 



for ISP pulse and



n for the new pulse. We observe that the

improvements are visible in the first case presented

(Figure 5a). In Figure 5a it is represented with

dashed line the results obtained for the new pulse.

The results are better for both cases

30



and

10



(thicker line). In Figure 5b we observe that

PECCS 2012 - International Conference on Pervasive and Embedded Computing and Communication Systems

310

(a) (b)

Figure 5: BER performance of an OFDM-BPSK system using the new proposed pulse, ISP pulse and RP pulse with

1.0fT , N = 256.

the results obtained for the new pulse are also better

than the results obtained for the ISP pulse even if

improvements are not as obvious as in Figure 6a.

One can notice that the results obtained for the

BER versus SNR of an OFDM BPSK system are

better or comparable with the results obtained for all

reference pulses.

Even if in some cases the obtained results are

comparable or slightly worse than those known in

the literature we can say that the proposed pulse has

theoretical and practical importance because it is

characterized by low-complexity and a smaller

number of parameters that are involved in pulse

shape design.

5 CONCLUSIONS

In this paper we studied the performance of a N-

subcarrier OFDM systems in the presence of

frequency offset, in terms of ICI and BER

performance.

We have investigated a new pulse shape, which

according to the analysis performed above presents

significant improvements in the reduction of inter-

carrier interference (ICI) power caused by the

frequency offset. The SIR performance increase with

the new pulse shape, as compared to the ISP pulse

shape and conventional pulse shapes.

We studied the effects of the carrier phase noise

and pulse shaping on BER of an N-subcarrier

OFDM-BPSK system as a function of the carrier

frequency offset

f

, the carrier phase noise



average ICI power and P( f ).

It should be pointed out that in this paper we

investigated a new pulse characterized by low

complexity and a smaller number of parameters that

are involved in pulse shape design.

Numerical and simulation results show that the

proposed pulse presents theoretical and practical

importance.

ACKNOWLEDGEMENTS

This paper was supported by CNCSIS-UEFISCSU

Project number RU-107/2010.

REFERENCES

Tan P., Beaulieu N. C., 2004. Reduced ICI in OFDM

Systems Using the Better Than Raised-Cosine Pulse

IEEE Communications Letters, 8(3), pp.135-137.

Mourad, H. M., 2006. Reducing ICI in OFDM systems

using a proposed pulse shape, Wireless Personal

Communications, 40, pp 41–48.

Kumbasar V., Kucur O., 2007. ICI reduction in OFDM

systems by using improved sinc power pulse, Digital

Signal Processing, 17, pp. 997–1006.

Khoa N. L., 2008. Insight on ICI and its effects on

performance of OFDM systems”, Digital Signal

Processing, 18, pp. 876–884.

Beaulieu N. C, Tan C. C., Damen M. O., 2001. A better

than Nyquist pulse, IEEE Communications Letters, 5,

pp.367–368.

Alexandru N. D, Onofrei A. L., 2010. ICI Reduction in

OFDM Systems Using Phase Modified Sinc Pulse,

Wireless Personal Communications, 53, pp. 141–151.

S. Jayasimha, P. K. Singh., 2000. Design of Nyquist and

Near-Nyquist Pulses with Spectral Constraints,

http://www.signion.com.

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