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International Journal of Electrical & Computer Sciences IJECS Vol: 9 No: 9 - 431 -

1944091 IJECS-IJENS @ International Journals of Engineering and Sciences IJENS

AbstractOrthogonal Frequency Division Multiplexing(OFDM) suffers from high side lobes in transmitted signal whichenhance its sensitivity to inter-carrier interference (ICI) andnarrowband interference (NBI). In literature, Wavelet PacketModulation (WPM) has been proposed as an alternative toOFDM. WPM offers much lower side lobes in transmitted signal,which reduce its sensitivity to ICI and NBI. This paper presents aperformance comparison of OFDM and WPM over multipath

wireless channel with NBI. WPM utilizes a time domainminimum mean square error (MMSE) equalizer for theequalization of multipath wireless channel. It is shown that WPMemploying a time domain MMSE equalizer exhibits higherimmunity to NBI compared to an OFDM system, over multipathwireless channel.

Index TermsWavelet Packet Modulation, narrowbandinterference (NBI ), MMSE equalization.

I. INTRODUCTION

FDM is a Discrete Fourier Transform (DFT) based multi-

carrier modulation (MCM) scheme. It is robust againstfrequency selective fading as the subcarriers in anOFDM system transform a frequency selective channel intonumerous flat fading channels [1]. OFDM is alsocomputationally efficient due to Fast Fourier Transform (FFT)implementation [1]. However, it suffers from high side lobesin transmitted signal, due to rectangular pulse shape ofsinusoidal carriers [1]. However, it suffers from high sidelobes in transmitted signal, due to rectangular pulse shape ofsinusoidal carriers [1]. High side lobes enhance the sensitivityof OFDM systems to ICI and NBI [1], [2]. Various types ofwindows can be applied to improve the pulse shape of OFDMsymbol. Raised cosine filtering has also been considered for

this purpose, however it increases the computationalcomplexity of the OFDM system [3], [4]. Therefore, WPM, aDiscrete Wavelet Packet Transform (DWPT) based MCMscheme, is proposed as an alternative to OFDM system [5].WPM offers improved spectral shaping as compared to DFT-based MCM schemes, with comparable computationalcomplexity [4]. I t offers lower magnitude side lobes in

Manuscript received September 18, 2009.The authors are with the Faculty of Electronic Engineering, Ghulam Ishaq

Khan Institute of Engineering Sciences and Technology, Topi - 23640,District Swabi, Pakistan (e-mails: [email protected],[email protected], [email protected]).

transmitted signal, which in turn reduce ICI and NBI [5]. Inliterature, some comparisons of bit error rate (BER)performance have been made between OFDM and WPM inNBI [6], [2]. It has been shown that BER performance of boththe schemes is highly dependent on NBI, however, WPMexhibits higher immunity to NBI as compared to an OFDMsystem [6], [2]. However, these comparisons analyzed theperformance of both schemes merely over additive white

gaussian noise (AWGN) link and did not evaluate theirperformance over a multipath wireless channel [6], [2].

Therefore, in order to accurately determine the sensitivity ofboth schemes to NBI in wireless communications, the effectof multipath wireless channel must be included. This paperpresents a comparison of BER performance of WPM andOFDM based communication systems over multipath wirelesschannel in the presence of NBI. WPM utilizes a time domainMMSE equalizer for the equalization of multipath wirelesschannel. The OFDM system, utilizes cyclic prefix (CP) inguard band interval to cancel inter symbol interference (ISI).A frequency-domain zero-forcing equalizer in OFDM systemcompensates for channel distortion suffered by each

subcarrier.Section II discusses the system model and section III

focuses on the channel equalization in WPM. NBI is described

in section IV while section V presents the simulation results of

the BER comparison of the two schemes in NBI. Finally

conclusions are presented in section VI.

II. SYSTEM MODEL

System model of the DWPT based MCM system studied in

this paper is shown in Fig.1. The transmitted symbol ( )s t in a

MCM scheme is the sum of amplitude modulated M

waveforms ( )m t as follows,

( ) ( )1

0

M

m mm

s t d t

=

= (1)

where md is a constellation encodedmthdata symbol

modulating themthwaveform ( )m t [6]. The waveforms are

mutually orthogonal and are expressed mathematically as,

( ) ( ) ( )m nt t m n = (2)

( )1 for 0

0 otherwise

kk

==

Performance Comparison of Wavelet PacketModulation and OFDM over Multipath Wireless

Channel with Narrowband Interference

Usman Khan, Sobia Baig and M. Junaid Mughal

O

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SerialtoParallelConverter

ConstellationEncoding

.

.

.

.

.

.

.

.

M

M

M

M

.

.

.

.

h0[n]

h1[n]

hM-2[n]

hM-1[n]

Channel + +Data In

ParalleltoSerialConverter

ConstellationDecoding

.

.

.

.

.

.

.

.

M

M

M

M

.

.

.

.

h0[-n]

h1[-n]

hM-2[-n]

hM-1[-n]

Time DomainMMSE Equalizer

Data Out

AWGN NBI

Fig. 1. Block diagram of WPM

where represents a convolution operation.OFDM, a DFT based MCM scheme, utilizes M complex

exponentials ( ) ( )2 /j mt Mw t e as the MCM basis functions ( )m t .

These basis functions are limited in time-domain by the

window function ( )w t which corresponds to a sinc-shaped

waveform in the frequency domain. WPM utilizes waveletpackets as the MCM basis functions. Wavelet packets arederived through the DWPT [6]. DWPT is implemented usingmultistage tree-structured quadrature mirror filter (QMF) bank[7]. DWPT decomposes the signal into wavelet packets usinganalysis side of multistage tree-structured QMF bank. Theinverse DWPT (IDWPT) reconstructs the signal as the sum ofthe wavelet packets using synthesis side of the multistage tree-structured QMF bank.

In this paper, we have utilized a multistage tree-structured

Daubechies QMF bank, which is implemented by Mallets fast

algorithm [8]. The synthesis bank constructs a signal as the

sum of 2JM = wavelet packets. These wavelet packets arebuilt by successive iterations each consisting of filtering and

upsampling operations. The wavelet packets are given by the

convolution equation

[ ] [ ] [ ],2 1, /2j i low j ih n h n h n= (3)

[ ] [ ] [ ],2 1 1, /2j i hi j ih n h n h n+ = , (4)

where j is the iteration index, 1 j J and i is the wavelet

x[n]

hhi[-n]

hlow

[-n] 2

2

xp[n]

hhi[n]

hlow

[n]2

2

+

Analysis Synthesis

Fig. 2. Wavelet Packet Elementary Block Decomposition andReconstruction

packet index, ( )0 /2 1i M [7]. The sequences [ ]lowh n and

[ ]hih n are the discrete impulse responses of the low pass and

high pass filters of the QMF bank with perfect reconstruction.

While, [ ], /2j ih n is the upsampled version of [ ],j ih n . The high

pass filter can be found from low pass filter using relationship

[ ] ( ) [ ]1 1n

hi lowh n h L n= , (5)

whereL is the length of the sequence. The impulse responsesof the decomposition filters are the time reversed versions of

the synthesis filters as shown in Fig. 1 and 2. Therefore, the

decomposition filters act as matched filters to detect the

original transmitted waveform.

III. CHANNEL EQUALIZATION FOR WPM IN MULTIPATHWIRELESSCHANNEL

A. Channel ModelWe have considered a multipath wireless channel for the

performance evaluation of WPM and OFDM systems. The

received signal in a multipath wireless channel consists of aseries of attenuated, time delayed and phase shifted replicas ofthe transmitted signal [9]. Therefore, the baseband impulseresponse of a multipath wireless channel can be expressed as,

( ) ( ) ( )( )1

2

0

,m

c k

Nf t

im k kk

c a t e t t

=

= (6)

where ( ),ka t and ( )i t are the amplitudes and propagation

delays, respectively, of thekth multipath component at time t

[9]. The exponent ( )2 c kf t represents the phase shift

encountered due to free space propagation of thekthmultipath

component. mN is the number of multipaths of the channel and

( )t is the Dirac delta pulse.The mathematical model of a time-varying multipath

channel is represented by (6). The gain ( )0 ,a t at any time t

corresponds to the shortest path and is Rician distributed if

there is a line of sight, and Rayleigh distributed if there is no

line of sight [9].

B. Time Domain Equalization for WPMA time domain linear equalizer is employed to compensate

for the signal distortion caused by the multipath wirelesschannel. MMSE algorithm is utilized to train the equalizercoefficients. It provides a more robust solution than zero

forcing equalizer as it considers the channel noise into account[10]. Ifx is the transmitted signal matrix andc is the channel

impulse response vector, then the received signal y is given

by,

0Ty =c x+n (7)

where 0n is the channel noise andTc is the transpose ofc[10].

The MMSE approach finds the optimum weights eqw for the

MMSE equalizer using channel correlation matrixR andchannel impulse response vectorP , as given below

-1eqw =R P (8)

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HR =E yy (9)

*P =E yx , (10)

whereE denotes the expected value, Hy is the conjugate

transpose ofyand *x is the conjugate ofx [10]. Then the

equalizer output eqy is given by

Heq eqy =w y . (11)

We have evaluated the performance of WPM and OFDM

over multipath wireless channel in the presence of NBI.

Therefore, NBI is briefly discussed here.

IV. NARROWBAND INTERFERENCE

The NBI usually arises in wireless communication due to

interference of different signals at the receiver. It can be

modeled by a sinusoidal wave which interferes with the signal

of interest at the receiver [2]. The interfering signal I[n] is a

sinusoid having frequency fi and power2

i iP A= , where Ai is

the amplitude of the sinusoid. Then the received signal r[n] isthe sum of the transmitted signal t[n] with the interfering

signal I[n] [2].

[ ] [ ] [ ]r n t n I n= + (12)

[ ] 2 ij f niI n Ae= (13)

The level of interference depends upon the power of

interfering signal iP and its frequency if.

OFDM and WPM are both MCM schemes. The energy of

an individual symbol in MCM system is concentrated in its

respective modulated subcarrier. Therefore, if the interfering

frequency fi matches the centre frequency of a sub-carrier then

BER increases for that sub-carrier, but it decreases

when ifmoves away from the centre frequency. In case, the

sub-carriers waveforms have null out-of-band energy, the

interference will be limited to the subcarrier whose band

includes the frequency if. But in actual systems, sub-carriers

waveforms do not have a null out-of-band energy, therefore,

interference is caused by the side lobes of the adjacent

subcarriers [6]. DWPT based MCM scheme, offers lower

magnitude side lobes in transmitted signal as compared to

DFT based MCM scheme, and therefore, it may prove to be

more robust against NBI. Henceforth, a performance

comparison is made between the two schemes in the presence

of NBI over multipath wireless channel.

V. PERFORMANCE COMPARISON OF WPM AND OFDM OVERMULTIPATHWIRELESSCHANNEL

In this section, simulation results are presented which showthe performance comparison of WPM and OFDM in terms ofBER in the presence of NBI over multipath wireless channelwith AWGN. The channel is modeled as a six-ray Rayleighfading channel. WPM system utilizes a time domain MMSEequalizer for the channel equalization, while, OFDM utilizes a

TABLE ISIMULATION PARAMETERS

Parameter WPM OFDM

Data Rate 2-Mbps 2-Mbps

Sampling frequency 4- MHz 4-MHz

Modulation 2-ary QAM 2-ary QAM

Wavelet Daubechies-2 -

DWPT Decomposition level 2 -

No of sub-carriers - 8

frequency domain zero-forcing equalizer composed of a singletap per subcarriers for channel cancellation. Matlab is used as

a simulation tool. Simulation parameters are specified in TableI.

We have compared the BER performance for both theschemes as a function of the normalized interfering frequency.Moreover, BER performance is also compared for both theschemes as a function of the power of NBI signal. Signal tonoise ratio (SNR) for both the schemes is 20 dB. Resultsobtained through simulation are shown in Fig. 3 and 4respectively.The simulation results for both the modulation schemes

show that the level of interference is dependent on the

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-4

10-3

10-2

10-1

100

Interfering Frequency

BER

OFDM

WPM

Fig. 3. BER performance comparison of OFDM and WPM as afunction of normalized frequency of NBI signal at power 0 dB

-20 -15 -10 -5 0 510

-3

10-2

10-1

NBI power in dB

BE

R

OFDM

WPM

Fig. 4. BER performance comparison of OFDM and WPM as afunction of power of NBI signal at normalized frequency of 0.5

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frequency and power of NBI signal. The simulation results inFig. 3 present the BER performance as a function ofnormalized interfering frequency at the NBI power level of 0dB. The results obtained have shown that BER performance ofboth modulation schemes is highly dependent on thefrequency of NBI signal. However, OFDM system has shownhigher BER when the interfering frequency corresponds to thecenter frequency of a sub-carrier. The WPM system shows the

same behavior but with a smoother BER curve. Thesimulation results in Fig. 4 present the BER performance as afunction of power of NBI signal while the normalizedinterference frequency is arbitrarily chosen to be 0.5. Theresults obtained have shown that as the power of the NBIsignal is increased the BER increases for both the modulationschemes. However, WPM shows more robustness to thepower of NBI signal as it provides better BER performancethan OFDM.

Hence, WPM employing a time domain MMSE equalizerhas a better BER performance than OFDM in the presence ofNBI over multipath wireless channel. In general, resultsobtained have shown that WPM system utilizing a time

domain MMSE equalizer is capable of high immunity to NBIover multipath wireless channel as compared to an OFDMsystem.

VI. CONCLUSION

Performance comparison is made between WPM employing

a time domain MMSE equalizer and OFDM in the presence of

NBI over multipath wireless channel. It has been established

that WPM systems employing a time domain MMSE equalizer

exhibits higher immunity to NBI as compared to OFDM

systems. NBI usually arises in wireless communication due to

interference of different signals at the receiver. Therefore,

future modulation techniques have to cope not only with

channel distortion, but also with NBI originating from other

sources as well. In this scenario, WPM with high immunity to

NBI can emerge as a strong contender for modulation

techniques in transceivers, for wireless communication.

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[1] J . A. C. Bingham, ADSL, VDSL, Multicarrier Modulation, Wiley-Interscience, 2000.

[2] M. Gautier, M. Arndt and J. Lienard, Efficient wavelet packetmodulation for wireless communication, in Proc. AICT 2007,Mauritius, May 2007.

[3] J . Armstrong, Analysis of new and existing methods of reducingintercarrier interference due to carrier frequency offset in OFDM, IEEE

Trans. Commun., vol.47, pp. 365-369, Mar. 1999.[4] H. Murakami, Implementation and Perfect Reconstruction of a

Maximally Decimated FIR Filter Bank Using Parallel ModuleDecomposition, IEEE Trans. Signal Processing,vol.45, no. 2, February1997.

[5] B. G. Negash and H. Nikookar, "Wavelet-based multicarriertransmission over multipath wireless channels," Electronics Letters, vol.36, no. 21, pp. 1787--1788, Oct. 2000.

[6] A. Jamin and P.Mahonen. "Wavelet packet modulation for wirelesscommunication," Wireless Communication and Mobile Computing

Journal, vol. 5, no. 2, pp 123--137, Mar. 2005.[7] M. Vetterli, J . Kocacevic, Wavelets and Subband Coding, Prentice Hall,

1995.[8] S. Mallat, A Wavelet Tour of Signal Processing, Published, 1999, ISBN

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