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ADAPTIVE WIENER FILTERING APPROACH FOR SPEECH
ENHANCEMENT
M. A. Abd El-Fattah*, M. I. Dessouky , S. M. Diab and F. E. Abd El-samie#
Department of Electronics and Electrical communications, Faculty of Electronic EngineeringMenoufia University, Menouf, Egypt
E-mails: * [email protected] , # [email protected]
ABSTRACT
This paper proposes the application of the Wiener filter in an adaptive manner inspeech enhancement. The proposed adaptive Wiener filter depends on the adaptation of the
filter transfer function from sample to sample based on the speech signal statistics(mean
and variance). The adaptive Wiener filter is implemented in time domain rather than in
frequency domain to accommodate for the varying nature of the speech signal. The proposed method is compared to the traditional Wiener filter and spectral subtraction
methods and the results reveal its superiority.
Keywords:Speech Enhancement, Spectral Subtraction, Adaptive Wiener Filter
1 INTRODUCTIONSpeech enhancement is one of the most
important topics in speech signal processing.
Several techniques have been proposed for this
purpose like the spectral subtraction approach, the
signal subspace approach, adaptive noise canceling
and the iterative Wiener filter[1-5] . The performances of these techniques depend on
quality and intelligibility of the processed speech
signal. The improvement of the speech signal-to-noise ratio (SNR) is the target of most techniques.
Spectral subtraction is the earliest method forenhancing speech degraded by additive noise[1].
This technique estimates the spectrum of the clean
(noise-free) signal by the subtraction of the
estimated noise magnitude spectrum from the noisysignal magnitude spectrum while keeping the phase
spectrum of the noisy signal. The drawback of this
technique is the residual noise.
Another technique is a signal subspace
approach [3]. It is used for enhancing a speech
signal degraded by uncorrelated additive noise orcolored noise [6,7]. The idea of this algorithm is
based on the fact that the vector space of the noisy
signal can be decomposed into a signal plus noise
subspace and an orthogonal noise subspace.
Processing is performed on the vectors in the signalplus noise subspace only, while the noise subspace
is removed first. Decomposition of the vector space
of the noisy signal is performed by applying an
eigenvalue or singular value decomposition or by
applying the Karhunen-Loeve transform (KLT)[8].
Mi. et. al. have proposed the signal / noise KLT
based approach for colored noise removal[9]. Theidea of this approach is that noisy speech frames
are classified into speech-dominated frames and
noise-dominated frames. In the speech-dominatedframes, the signal KLT matrix is used and in the
noise-dominated frames, the noise KLT matrix is
used.In this paper, we present a new technique to
improve the signal-to-noise ratio in the enhanced
speech signal by using an adaptive implementation
of the Wiener filter. This implementation isperformed in time domain to accommodate for the
varying nature of the signal.
The paper is organized as follows: in sectionII, a review of the spectral subtraction technique is
presented. In section III, the traditional Wiener
filter in frequency domain is revisited. Section IV,proposes the adaptive Wiener filtering approach for
speech enhancement. In section V, a comparative
study between the proposed adaptive Wiener filter,
the Wiener filter in frequency domain and the
spectral subtraction approach is presented.
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2 SPECTRAL SUBTRACTIONSpectral subtraction can be categorized as a
non-parametric approach, which simply needs an
estimate of the noise spectrum. It is assume that
there is an estimate of the noise spectrum that istypically estimated during periods of speaker
silence. Letx(n) be a noisy speech signal :
)()()( nvnsnx += (1)
wheres(n) is the clean (the noise-free) signal, and
v(n) is the white gaussian noise. Assume that the
noise and the clean signals are uncorrelated. Byapplying the spectral subtraction approach that
estimates the short term magnitude spectrum of the
noise-free signal )(S by subtraction of the
estimated noise magnitude spectrum )( V from
the noisy signal magnitude spectrum )(X . It is
sufficient to use the noisy signal phase spectrum asan estimate of the clean speech phase
spectrum,[10]:
))(exp())()(()( XjNXS = (2)
The estimated time-domain speech signal isobtained as the inverse Fourier transform of
)( S .
Another way to recover a clean signal s(n)from the noisy signal x(n) using the spectral
subtraction approach is performed by assumingthat there is an the estimate of the power spectrum
of the noise )(vP , that is obtained by averaging
over multiple frames of a known noise segment.
An estimate of the clean signal short-time squaredmagnitude spectrum can be obtained as follow [8]:
otherwise0,
0(2
)(if,(2
)(2
)(
))=
vPXvPX
S(3)
It is possible combine this magnitude spectrum
estimate with the measured phase and then get theShort Time Fourier Transform (STFT) estimate as
follows:
)()()(
XjeSS
= (4)
A noise-free signal estimate can then be obtainedwith the inverse Fourier transform. This noise
reduction method is a specific case of the general
technique given by Weiss, et al. and extended by
Berouti , et al.[2,12].The spectral subtraction approach can be
viewed as a filtering operation where high SNR
regions of the measured spectrum are attenuated
less than low SNR regions. This formulation can begiven in terms of the SNR defined as:
)(
2)(
vP
XSNR = (5)
Thus, equation (3) can be rewritten as:
11
12
)(
(
2
)(
2
)(
+
)=
SNRX
vPXS
(6)
An important property of noise suppression
using spectral subtraction is that the attenuation
characteristics change with the length of theanalysis window. A common problem for using
spectral subtraction is the musicality that results
from the rapid coming and going of waves oversuccessive frames [13].
3 WIENER FILTER IN FREQUNCYDOMAIN
The Wiener filter is a popular technique that
has been used in many signal enhancement
methods. The basic principle of the Wiener filter is
to obtain a clean signal from that corrupted byadditive noise. It is required estimate an optimal
filter for the noisy input speech by minimizing theMean Square Error (MSE) between the desired
signal s(n) and the estimated signal )( ns . The
frequency domain solution to this optimization
problem is given by[13]:
)()(
)()(
PvPs
PsH
+= (7)
where )(Ps and )(Pv are the power spectral
densities of the clean and the noise signals,
respectively. This formula can be derivedconsidering the signal s and the noise signal v as
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uncorrelated and stationary signals. The signal-to-
noise ratio is defined by[13]:
)(
)(
vP
PsSNR = (8)
This definition can be incorporated to the Wiener
filter equation as follows:
11
1(
+=)
SNRH (9)
The drawback of the Wiener filter is the fixed
frequency response at all frequencies and the
requirement to estimate the power spectral densityof the clean signal and noise prior to filtering.
4 THE PROPOSED ADAPTIVE WIENERFILTER
This section presents and adaptive
implementation of the Wiener filter which benefitsfrom the varying local statistics of the speech
signal. A block diagram of the proposed approach
is illustrated in Fig. (1). In this approach, the
estimated speech signal mean xm and variance2
x are exploited.
A priori knowledge
Degraded speech Enhancedx(n) speech
signal )( ns
A priori
knowledge
Figure 1: Typical adaptive speech enhancement systemfor additive noise reduction
It is assumed that the additive noise v(n) is
of zero mean and has a white nature with variance
of v2.Thus, the power spectrum )(vP can be
approximated by:
vPv 2=)((10)
Consider a small segment of the speech
signal in which the signal x(n) is assumed to be
stationary, The signal x(n) can be modeled by:
)()( nwmnx xx += (11)where xm and x are the local mean and standarddeviation ofx(n). w(n) is a unit variance noise.
Within this small segment of speech, theWiener filter transfer function can be approximated
by:
)()(
)()(
PvPs
PsH
+=
vs
s
22
2
+=
(12)
From Eq.(12), because )(H is constant over thesmall segment of speech, the impulse response of
the Wiener filter can be obtained by:
))(22
2
nnhvs
s (=+
(13)
From Eq.(13), the enhanced speech )( ns within
this local segment can be expressed as:
))-)(()(22
2
nmnxmnsvs
sxx (+=
+
))((22
2
x
vs
sx mnxm +=
+
(14)
If it is assumed that xm and s are updated ateach sample, we can say:
))()(()(
)()()(
22
2
nmnxn
nnmns x
vs
sx +=
+
(15)
In Eq.(15), the local mean )(nmx and
))()(( nmnx x are modified separately fromsegment to segment and then the results are
combined. If s2
is much larger than v2
the
output signal )( ns is assumed to be primarily due
tox(n) and the input signal x(n) is not attenuated. If
s2
is smaller than v2
, the filtering effect is
performed.
Space-variant
h(n)
Measure of
Local speech
statistics
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Notice that xm is identical to sm when
vm is zero. So, we can estimate xm (n) in Eq.(15)fromx(n) by:
+
=+==
Mn
Mnk
xs kxM
nmnm )()12(
1)()(
(16)
where )12( +M is the number of samples in theshort segment used in the estimation.
To measure the local signal statistics in
the system of Figure 1, the algorithm developed
uses the signal variance s2
. The specific method
used to designing the space-variant h(n) is given by
(17.b).Since
222vsx += may be estimated
fromx(n) by:
>
=otherwise,0
)(if)()(
2222
2, vxvx
s
nnn
(17.a)
Where
+
=
+
=Mn
Mnk
xx nmkxM
n 2))()(()12(
1)( 2
(17.b)
By this proposed method, we guarantee thatthe filter transfer function is adapted from sample
to sample based on the speech signal statistics.
5 EXPERIMENTAL RESULTSFor evaluation purposes, we use different
speech signals like the handel, laughter and gong
signals. White Gaussian noise is added to each
speech signal with different SNRs. The differentspeech enhancement algorithms such as the
spectral subtraction method, the Weiner filter infrequency domain and the proposed adaptive
Wiener filter are carried out on the noisy speech
signals. The peak signal to noise ratio (PSNR)
results for each enhancement algorithm are
compared.
In the first experiment , all the above-
mentioned algorithms are carried out on the Handlesignal with different SNRs and the output PSNR
results are shown in Fig. (2). The same experiment
is repeated for the Laughter and Gong signals and
the results are shown in Figs.(3) and (4),respectively.
From these figures, it is clear that the proposed
adaptive Wiener filter approach has the best
performance for different SNRs. The adaptiveWiener filter approach gives about 3-5 dB
improvement at different values of SNR. The non-
linearity between input SNR and output PSNR isdue to the adaptive nature of the filter.
-10 -5 0 5 10 15 20 25 30 350
10
20
30
40
50
60
70
80
Input SNR (dB)
O
utpu
t
P
S
N
R
(d
B
)
Spectral Subtraction
Wiener Filter
Adaptive Wiener Filter
Figure 2:PSNR results for white noisecase at-10 dB to +35 dB SNR levels for Handle signal
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-10 -5 0 5 10 15 20 25 30 350
10
20
30
40
50
60
Input SNR (dB)
O
u
tp
u
t
P
S
N
R
(d
B
)
Spectral Subtraction
Wiener Filter
Adaptive Wiener Filter
Figure 3:PSNR results for white noise case at -10 dBto +35 dB SNR levels for Laughter signal
-10 -5 0 5 10 15 20 25 30 350
10
20
30
40
50
60
70
80
Input SNR (dB)
O
u
tp
u
t
P
S
N
R
(
d
B
)
Spectral Subtraction
Wiener Filter
Adaptive Wiener Filter
Figure 4: PSNR results for white noise case at -10 dBto +35 dB SNR levels for Gong signal
The results of the different enhancement
algorithms for the handle signal with SNRs of 5,10,15 and 20 dB in the both time and frequency
domain are given in Figs. (5) to (12). These results
reveal that the best performance is that of the
proposed adaptive Wiener filter.
0 2000 4000 6000 8000-1
0
1
(a)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(b)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(c)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(d)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(e) Time(msec)
A
m
plitude
Figure 5: Time domain results of the Handel sig. atSNR = +5dB (a) original sig. (b) noisy sig. (c) spectral
subtraction. (d) Wiener filtering. (e) adaptive Wienerfiltering.
0 1000 2000 3000 4000
-40
-20
0
(a)
Am
plitude(dB)
0 1000 2000 3000 4000-40
-20
0
(b)
Am
plitude(dB)
0 1000 2000 3000 4000-40
-20
0
(c)
Amplitude(dB)
0 1000 2000 3000 4000-40
-20
0
(d)
Amplitude(dB)
0 1000 2000 3000 4000
-40
-20
0
(e) Freq.(Hz)
Am
plitude(dB)
Figure 6:The spectrum of the Handel sig. in Fig.(5) (a)original sig. (b) noisy sig. (c) spectral subtraction. (d)
Wiener filtering. (e) adaptive Wiener filtering.
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0 2000 4000 6000 8000-1
0
1
(a)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(b)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(c)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(d)
A
m
plitude
0 2000 4000 6000 8000-1
0
1
(e) Time(msec)
A
m
plitude
Figure 11: Time domain results of the Handel sig. atSNR = 20 dB (a) original sig. (b) noisy sig. (c) spectralsubtraction. (d) Wiener filtering. (e) adaptive Wienerfiltering.
0 1000 2000 3000 4000
-40
-20
0
(a)Amplitude(dB)
0 1000 2000 3000 4000-40
-20
0
(b)Amplitude(dB)
0 1000 2000 3000 4000-40
-20
0
(c)Amplitude(d
B)
0 1000 2000 3000 4000-40
-200
(d)Amplitude(dB)
0 1000 2000 3000 4000-40
-20
0
(e) Freq. (Hz)Amplitude(dB)
Figure 12: The spectrum of the Handel sig. in Fig.(11)(a) original sig. (b) noisy sig. (c) spectral subtraction. (d)Wiener filtering. (e) adaptive Wiener filtering.
6 CONCLUSIONAn adaptive Wiener filter approach for
speech enhancement is proposed in this papaper.
This approach depends on the adaptation of thefilter transfer function from sample to sample
based on the speech signal statistics(mean and
variance). This results indicates that the proposedapproach provides the best SNR improvement
among the spectral subtraction approach and the
traditional Wiener filter approach in frequencydomain. The results also indicate that the proposed
approach can treat musical noise better than the
spectral subtraction approach and it can avoid the
drawbacks of Wiener filter in frequency domain .
REFERENCES
[1] S. F. Boll: Suppression of acoustic noise inspeech using spectral subtraction, IEEE Trans.
Acoust., Speech, Signal Processing, vol. ASSP-27,.pp. 113-120 (1979).
[2] M. Berouti, R. Schwartz, and J. Makhoul:Enhancement of speech corrupted by acoustic
noise, Proc. IEEE Int. Conf. Acoust., Speech
Signal Processing, pp. 208-211 (1979).
[3] Y. Ephriam and H. L. Van Trees: A signal
subspace approach for speech enhancement, inProc. International Conference on Acoustic,
Speech and Signal Processing, vol. II, Detroit,
MI, U.S.A., pp. 355-358, May (1993).[4] Simon Haykin: Adaptive Filter Theory,
Prentice-Hall, ISBN 0-13-322760-X, (1996).
[5] J. S. Lim and A. V. Oppenheim.: All-poleModelling of Degraded Speech, IEEE Trans.
Acoust., Speech, Signal Processing, ASSP-26,
June (1978).
[6] Y. Ephraim and H. L. Van Trees, A spectrally-
based signal subspace approach for speechenhancement, in IEEE ICASSP, pp. 804-807
(1995).
[7] Y. Hu and P. Loizou: A subspace approachfor enhancing speech corrupted by colored noise,
in Proc. International Conference on
Acoustics, Speech and Signal Processing, vol. I,
Orlando, FL, U.S.A., pp. 573-576, May (2002).
[8] A. Rezayee and S. Gazor: An adaptive KLTapproach for speech enhancement, IEEE Trans.
Speech Audio Processing, vol. 9, pp. 87-95
Feb. (2001).
[9] U. Mittal and N. Phamdo: Signal/noise KLTbased approach for enhancing speech degraded by
colored noise, IEEE Trans. Speech AudioProcessing, vol. 8, NO. 2, pp. 159-167,(2000).
[10] John R. Deller, John G. Proakis, and John H.
L. Hansen. Discrete- Time Processing of Speech
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FREQUENCY SELECTIVITY PARAMETERS ONMULTI-CARRIER WIDEBAND WIRELESS SIGNALS
Vctor M Hinostroza, Jos Mireles and Humberto OchoaInstitute of Engineering and Technology, University of Ciudad Jurez
Valle del tigris # 3247,Ciudad Jurez Chihuahua Mxico C. P. 32306
[email protected],[email protected], [email protected]
ABSTRACT.This work is a study of the effects of frequency selectivity on multi-carrier wideband signals in three differentenvironments; indoors, outdoor to indoor and outdoors. The investigation was made using measurements carriedout with a sounder with a 300 MHz bandwidth. The main part of this work is related to evaluate the contributionof several parameters; frequency selective fading, coherence bandwidth and delay spread on the frequency
selectivity of the channel. A description of the sounder parameters and the sounded environments are given. The300 MHz bandwidth is divided in segments of 60 kHz to perform the evaluation of frequency selective fading.Sub channels of 20 MHz for OFDM systems and 5 MHz for WCDMA were evaluated. Figures are provided fora number of bands, parameters and locations in the three environments. It is also shown the variation of thesignal level due to frequency selective fading. The practical assumptions about the coherence bandwidth anddelay spread are reviewed and a comparison is made with actual measurements. Statistical analysis was
performed over some of the results.
Keywords. Coherence bandwidth, frequency correlation, frequency selective fading and multi-carriermodulation.
I. INTRODUCTION.
To simulate and evaluate the performance of awireless mobile system a good channel model isneeded. Mobile communication systems are usinglarger bandwidths and higher frequencies and these
characteristics impose new challenges on channelestimation. The channel models that have been
developed for the mobile systems in use may not beapplicable anymore. To validate that the oldmodels can be used for future systems or to designnew models, it is necessary to answer the question
about how the same parameters performs at higherbandwidths? Also, we have to be able to measure
and validate some parameters and compare them towell known practical assumptions. Measurementsfor analysis of the fading statistics at commonfrequencies have been performed before, but theyhave been performed at small bandwidths, it isnecessary to update the models with higher
bandwidths.
As the data rate (the bandwidth) increases the
communication limitations come from the InterSymbol Interference (ISI) due to the dispersive
characteristics of the wireless communications
channel. The dispersive channel characteristicsarise from the different propagation paths, i.e.
multipath, between the receiver and the transmitter.This dispersion could be measured, if we couldmeasure the channel impulse response (CIR). As ageneral rule the effects of ISI on the transmission
errors is negligible if the delay spread issignificantly shorter than the duration of the
transmitted symbol. Due to the expected increase indemand of higher data rates, wideband multi-carrier systems such as; OFDM and WCDMA areexpected to be technologies of choice [1], [12] and
[14]. This is because these two technologies can provide both; high data rates and an acceptable
level of quality of service. However, these systemsneed first to address better the problem regardingchannel prediction or estimation, because thiscondition is the main boundary for higher datarates. The study of correlation of the mobile radiochannel in frequency and time domains has helped
to understand the problem of channel estimation.One of this work objectives is to evaluatefrequency selective fading (FSF) in several
environments. This work begins with the results of
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measurements made with a sounder that uses thechirp technique for sounding.
Multipath fading channels are usually classifiedinto flat fading and frequency selective fadingaccording to their coherence bandwidth relative to
the one of the transmitted signal. Coherence bandwidth is defined as the range of frequenciesover which two frequency components remain in a
strong amplitude correlation. Physically, it definesthe range of frequencies over which the channelcan be considered flat. The analytic issue ofcoherence bandwidth was first studied by Jakes [1]where by assuming homogeneous scattering, hiswork revealed that the coherence bandwidth of a
wireless channel is inversely proportional to itsroot-mean-square (rms) delay spread. The same
issue was subsequently studied by various authors[4], [8], [9], [10]. Since many practical channel
environments can significantly deviate from thehomogeneous assumption, various measurements
were conducted to determine multipath delayprofiles and coherence bandwidths[19], [20], [21],
[22], aiming to obtain a more general formula forcoherence bandwidth. In this work the variations ofthis formula are reviewed and compared withactual results and a comparison is provided.
The rest of this document is structured as follow; in
part II the theoretical foundations of the channelimpulse response frequency selective fading andcoherence bandwidth are reviewed. Also in this
part, the characteristics of the three environmentssounded are described. In part III, the frequency
selective fading evaluation and analysis arepresented. Plots of the dependency of fading deepand frequency separation of two specific points inthe response are studied. At part IV, data about therelationship between delay spread and coherence bandwidth are provided. At the end in part V,
conclusions and future work are mentioned.
II. MATHEMATICAL BACKGROUND
2.1 The wideband channel model.
The radio propagation channel is normallyrepresented in terms of a time-varying linear filter,with complex low-pass impulse response, h(t, ). Itstime-varying low-pass transfer function is [4] [6][8] [10]:
= dethftH fj2);(),(
(1)Where represents delay, using (1) the frequency
correlation function for the channel can be writtenas:
{ }
{ } 2122
2211
2211
2211);(*);(
);(*);(
ddeeththE
ftHftHE
fjf +
=
(2)
By considering the channel to have uncorrelatedscattering (US) and to be wide sense stationary(WSS), the subscript for is eliminated andf1andf2 can be replaced by f + fand t1 and t2 replacedby t + t, then:
= detRftR fjhH2);();(
(3)In (3) RH and Rh represents the correlation ofrandom variations in the channels transfer functionand its impulse response respectively. If there areUS, then tis 0 then:
{ } { }22 )();0();0( hEhERh == (4)
substituting into (3) gives:
{ }
= dehEfR fjH22)()(
(5)
where
2)(hE
is the average Power DelayProfile PDP of the channel. So, under the aboveconditions, RH is the Fourier transform of the
average PDP.
2.2 Coherence bandwidth.The multipath effect of the channel, the arrival ofdifferent signals in different time delays causes thestatistical properties of two signals of differentfrequencies to become independent if the frequency
separation is large enough. The maximumfrequency separation for which the signals are stillstrongly correlated is called coherence bandwidth
(Bc). Besides to contribute to the understanding ofthe channel, the coherence bandwidth is useful inevaluating the performance and limitations of
different modulations and diversity models.
The coherence bandwidth of a fading channel is probed by sending two sinusoids, separated infrequency by f = f1- f2 Hz, through the channel.The coherence bandwidth is defined as f, over
which the cross correlation coefficient between r1and r2 is greater than a preset threshold, say, 0=0.9. Namely:
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02,1)2var()1var(
)2,1(==
rr
rrCovC rr
(6)
Then, using (2)
==0
21
0
)2,1(2121),( drdrrrprrrrsR
(7)Wherep(r1,r2) is
=
2
0
2121
2
0
),,2,1()2,1( ddrrprrp
(8)
+
=
202
2221
221
21)1(2
exp)1(
21
rrIrrrr
WhereI0(x) is the modified Bessel function of zeroorder. Then, substituting (8) in (7) and integrating
);1;2
1,
2
1(
2),( 20
= FbsR
(9)
this may also be expressed as
+=
41
2),(
2
0
bsR (10)
[ ][ ]222221 2121),(
),(rrrr
rrsRs
=
++=
1
2)1(),( 0 EbsR (11)
Where E(x) is the complete elliptic integral of thesecond kind. The expansion of the hyper geometricfunction gives a good approximation to (9). After
several reductions and considerations, thecorrelation coefficient becomes
22
21
2)1(
),(
++
=
E
s
22
202
1
)(
s
J m
+==
(12)
It is possible to see in this expression that the
correlation decreases with frequency separation.This formula has been substituted by several practical expressions some of them are thefollowing [4], [8], [9], [10].
rms
CB50
19.0 == (13)
rms
CB5
15.0 == (14)
mean
CB8
19.0 == (15)
rms
CB2
1= (16)
In general
rms
C
kB
= (17)
It will be shown, comparing with practicalmeasurements that none of these expressions are
accurate and it is difficult to obtain a
comprehensive expression for all environments.
2.3 Sounder systems characteristics andenvironment description.
The sounder system used to make themeasurements of this work was developed atUMIST in Manchester UK and is described in [2]and [3]. This sounder uses the FMCW or chirp
technique. The generated chirp consists of alinearly frequency modulated signal with a
bandwidth of 300 MHz and a carrier frequency of2.35 GHz. The chirp repetition frequency is 100
Hertz, which allows having 50-Hertz Dopplerrange measurements. The receiver has the samearchitecture than the transmitter. But in the
receiver, the generated chirp is not transmitted butmixed with the incoming signal from the antenna,which are the multi-path components of thetransmitted chirp. This mixing allows having themulti-path components at low frequencies, theselow frequencies can be sampled, digitized and
stored in a computer to perform the requiredanalysis.
The three environments where the measurements
took place were the following: 1) Indoors, in
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Another way to look at the statistics of the fading isto calculate the CDF of this parameter. To makethe calculations of these CDFs figures, the mean
of all locations in the involved environment wereused. Figure 4 shows the CDF of the building-to-building environment for both, the 20 and 5 MHz
bandwidths, this figure shows that the fading deepfor a 20 MHz sub channel is below 7 dB for 90%of the time. On the other hand, for the 5 MHz sub
channel, the fades are below 5 dB for 90% of thetime.
Figure 2 Indoor to outdoor fading Characteristicsfor a 20 MHz sub channel
Figure 3. Outdoor to indoor fading Characteristic
. COHERENCE BANDWIDTH
igure 5 shows the frequency correlation of all
sFor a 5 MHz sub channel
IVEVALUATION.
F
locations in the indoors environment. To make thisfigure the following was done; first the PDP of all
locations was calculated. Then a Fourier transformwas performed on the PDP, which gave us thefrequency correlation for all locations. Then thefrequency correlation for each location was plottedin figure 5. On this figure, the thick and dashed lineis the line for the maximum coherence bandwidth,
when the transmitter and receiver are connected
directly. In figure 5, one can see that at 0.9
correlation coefficient, the coherence bandwidth(Bc) is lower than 10 MHz most of the locations.This is corroborated in figure 6, this figure shows
the average Bc for all locations in the indoorsenvironment. Figure 7, shows the RMS delayspread for all locations for the same environment.
Quick calculations comparing figure 11 results andexpression (13) show that, few calculated values ofthe versions of expression (13) match with the
measured values of figure 7.
igure 4. Fading CDF for indoor to outdoorFfor a 5 MHz sub channel
Figure 5. Coherence bandwidth for indoors
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Figure 6. Average of coherence bandwidth forindoors
Figure 8 shows the frequency correlation for theoutdoor to indoor environment, this figure shows
that in this environment the Bc at frequencycorrelation of 0.9 is higher than the indoorenvironment, although the delay spread is not
different is both environments. Figure 9, shows theaverage Bc for the outdoors to indoorsenvironment, one can see in this figure, that thecoherence bandwidth is higher than the indoo
expected result, but th
the other hand, in the outdoor to indoor,
reenvironment, which was an
difference is higher than expected. In indoors the
coherence bandwidth is not bigger than 20 MHz inverage. Ina
the average is about 100 MHz, here is relation of 5to 1. The difference in RMS delay spread is 100 nS
versus 200 nS, there is a relation of 2 to 1.
Figure 7. RMS delay spread for indoors
Figure 11 shows the frequency correlation for theoutdoors environment. Figure 12, shows the Bc atfrequency correlation of 0.9. In this case the Bc can
not be compared to the Bc for the other twoenvironments, since in this environment a lower
bandwidth is evaluated, 120 MHz instead of 300MHz. Despite this difference and observing
figures 11 and 12, Bc is not significantly lowereven when we have higher distances and higherdelay spread. In outdoors the Bc is not bigger than 2MHz in average. In the other hand, the RMS delay
spread is 1.5 S in average.
Figure 8. Coherence bandwidth for outdoor toindoor
Figure 9. Average of coherence bandwidth forindoor to outdoor
Table 1, shows the comparisons of B for thes of
and measured results. Thisble shows that the values of the expressions arelways lower than the measured results, which
a e
c
three environments with the different version
expressions 13 -16taainduce to conclude that the expressions wereunderestimated, at least in these environments.Moreover, it is possible to conclude th t thes
expressions were deduced with not enough
measured results. Also, table 1 show that therelationship between delay spread and coherencebandwidth, not necessarily is a single constant.
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Figure 10. RMS delay spread for outdoors toindoors
V. CONCLUSIONS.
In this work the results of analysis of frequency
selective fading on two indoor and one outdoorenvironment have been presented. The threeenvironments analyzed demonstrate that the fadingis within specific limits, these results could help tothe designers of adaptive receivers to estimate thechannel more accurately. The division of the
channel impulse bandwidth in segments of 20 and5 MHz bandwidths, allow the calculation of fadingin the bandwidth of interest for OFDM andWCDMA transmission. Plots of the frequency
selective fading will help for this assessment. Theanalysis of coherence bandwidth show that the
expressions accepted in the literature for itscalculation are not accurate and the accepted directrelationship between delay spread and coherence bandwidth is not simple. Also, additional work isrequire on try to determine how much thecombined effect of Doppler spread, time variability
and frequency offsets affects the transmission onmulti-carrier signals as the ones on OFDM y
CDMA
Figure 11. Coherence bandwidth for outdoors
Figure 12. Average of coherence bandwidth for
outdoors
Table 1. Coherence bandwidth calculations
Value from Indoors Outdoorsto indoors
Outdoors
(13) 400 kHz 200 kHz 30 kHz
(14) 4 MHz 2 MHz 300 kHz
(15) 3.3 MHz 2.5 MHz 250 kHz
(16) 3.2 MHz 1.6 MHz 212 kHz
Measured0.9 5.3 MHz 12 MHz 300 kHz
Measured0.5 19 MHz 72 MHz 5.6 MHz
Figure 13. RMS delay spread for outdoors
References.
1. Jakes W. C., Microwave mobilecommunications, (Wiley, 1974).
2. Aurelian B, Gessler F, Queseth O, StridhR, Unbehaun M, Wu J, Zander J, Flament
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M. 4th-Generation Wireless Infrastructures: Scenarios and ResearchChallenges, IEEE Personal
Communications Magazine, 8(6), 25-31,Dec 2001.
3. Salous S, Hinostroza V, Bi-dynamicindoor measurements with high resolutionsounder, 5th. International Symposiumon wireless multimedia Communications,
Honolulu Hawaii USA, October 2002.4. Golkap H., Characterization of UMTS
FDD channels ,PhD Thesis, Departmentof Electrical Engineering and Electronics,UMIST, UK 2002
5. Lee W. C. Y., Mobile CommunicationEngineering, (McGraw-Hill, 1998).
6. Bello P.A., Characterization of randomlytime-variant linear channels, IEEE
Transactions on Communications Systems,
December 1963, pp. 360-393.7. Hehn T., Schober R.m and Gerstacker W.,
Optimized Delay Diversity for FrequencySelective Fading Channels, IEEETransaction on Wireless communications,September 2005, Vol. 4, No. 5, pp. 2289-2298.
8. Hashemi H., The indoor radiopropagation channel,IEEE Proceedings,
Vol. 81, No. 81, July 1993, pp. 943-967.9. Lee W. C. Y., Mobile Communication
Engineering, (McGraw-Hill, 1999)
10. Rappaport T. S., Wirelesscommunications, (Prentice-Hall, 2002, 2nd
ed.)11. Parsons J. D., The mobile radio
propagation channel, (Wiley, 2000).12. Morelli M., Sanguinetti L. and Mengali
U., Channel Estimation for AdaptiveFrequency Domain Equalization , IEEETransaction on Wireless communication,September 2005, Vol. 4, No. 5, pp. 2508-2518.
13. Salous S., and Hinostroza V., Bi-dynamic UHF channel sounder for Indoor
environments ,IEE ICAP 2001, pp. 583-587
14. Biglieri E., Proakis J. and Shamai S.,Fading Channels: Information Theoreticand Communications Aspects, IEEETransactions on Information Theory,October 1998, Vol. 44 , No. 6, pp. 2619-
2692.15. Al-Dhahir N., Single Carrier Frequency
Domain Equalization for Space-TimeBlok-Coded Transmission over FrequencySelective Fading Channels, IEEECommunications Letters, July 2001, Vol.
5, No. 7, pp. 304-306.
16. Namgoong N, and Lehnert J., Performance of DS/SSMA Systems inFrequency Selective Fading, IEEETransaction on Wireless communication,April 2002, Vol. 1, No. 2, pp. 236-244.
17. TA0 X., et. al., Channel Modeling ofLayeredSpace-Time Code Under FrequencySelective fading Channel, Proceedings
of ICCT2003, May 2003, Berlin Germany.18. Shayevitz O. and Feder M., Universal
Decoding for Frequency SelectiveFading, IEEE Transactions onInformation Theory, August 2005, Vol.51 , N0. 8, pp. 2770-2790.
19. Snchez M and Garca M, RMS Delay andCoherence Bandwidth Measurements in
Indoor Radio Channels in the UHF Band,IEEE Transactions on Vehicular
Technology, vol. 50, no. 2, march 200120. Jia-Chin Lin, Frequency Offset
Acquisition Based on SubcarrierDifferential Detection for OFDM
Communications on Doubly-SelectiveFading Channels,
21. Yoo D.and Stark W. E., Characterizationof WSSUS Channels: Normalized Mean
Square Covariance,IEEE Transactionson Wireless Communications, vol. 4, no.
4, july 2005.
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Continuous Reverse Nearest Neighbor Search
Lien-Fa Lin*, Chao-Chun ChenDepartment of Computer Science and Information
Engineering National Cheng-Kung University, Tainan, Taiwan, R.O.C.
Department of Information Communication Southern Taiwan
University of Technology, Tainan, Taiwan, R.O.C.
[email protected],[email protected]
ABSTRACTThe query service for the location of an object is called Location Based Services
(LBSs), and Reverse Nearest Neighbor (RNN) queries are one of them. RNN queries
have diversified applications, such as decision support system, market decision,
query of database document, and biological information. Studies of RNN in the past,
however, focused on inquirers in immobile status without consideration of
continuous demand for RNN queries in moving conditions. In the environment of
wireless network, users often remain in moving conditions, and sending a query
command while moving is a natural behavior. Availability of such service therefore
becomes very important; we refer to this type of issue as Continuous Reverse
Nearest Neighbor (CRNN) queries. Because an inquirers location changes
according to time, RNN queries will return different results according to different
locations. For a CRNN query, executing RNN search for every point of time during a
continuous query period will require a tremendously large price to pay. In this work,
an efficient algorithm is designed to provide precise results of a CRNN query in just
one execution. In addition, a large amount of experiments were conducted to verify
the above-mentioned method, of which results of the experiments showed significant
enhancement in efficiency.
Keywords: Location Based Services, Location-Dependent Query, Continuous
Query, Reverse Nearest Neighbor Query, Continuous Reverse Nearest Neighbor
Query
1 INTRODUCTIONAs wireless network communications and mobile
device technology develop vigorously and
positioning technology matures gradually, LBS is
becoming a key development in the industrial as well
as academic circles [2, 5, 13, 21, 26, 27]. According
to the report of IT Roadmap to a Geospatial Future
[6], LBSs will embrace pervasive computing and
transform mass advertising media, marketing, and
different societal facets in the upcoming decade.
Despite the fact that LBSs have been existing in the
traditional calculation environment (such as Yahoo!
Local), its greatest development potential lies in the
domain of mobile computing that provides freedom
of mobility and access to information anywhere
possible.
LBSs shall become an indispensable applicationin mobile network as its required technology has
matured and 3G wireless communicationinfrastructure is expected to be deployed everywhere.
The query that answers to LBSs is referred to as
Location-Dependent Query (LDQ), of whichapplications include Range Query, Nearest Neighbor
(NN) query, K-Nearest Neighbor (KNN) query, and
Reverse Nearest Neighbor (RNN) query.
There are plenty of studies about NN [14, 22, 26],
KNN [4, 9, 14, 23, 25], CNN [17, 3, 12, 20], and
CKNN [17, 20] queries, and issues pertaining to
Reverse Nearest Neighbor (RNN) Query [10, 11, 16,
18, 19, 22, 24] have been receiving attention in recent
years. RNN query means finding a collection of
nearest neighbor objects for S, a given collection of
objects, with q, a given query object. Practical
examples of RNN query are provided in [10]. If a
bank is planning to open a new branch, and its clients
prefer a branch on a nearest possible location, then
such new branch should be established on a location
where the distance to the majority of its clients is
shorter than that of other banks. Taxi cabs selecting
passengers is another good example. If a taxi cab uses
wireless devices to find out the location of itscustomer, then RNN queries will be far more
advantageous than NN queries from the aspect of
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competition. Figure 1 illustrates that Customer c is
the nearest neighbor for Taxi a, but that does not
necessarily mean Taxi a can capture Customer c
because Taxi b is even closer to Customer c. On the
contrary, the best option for Taxi a should be
Customer d because Taxi a is the nearest neighbor for
Customer d. That is, d is the RNN for a, and a mayreach d faster than any other taxi. This is an example
of CRNN query for that the query object, the taxi,
changes location according to time. Mobile users willbe mobile in a wireless environment, and that is why
the continuous query is an important issue in the
wireless environment.
As far as the knowledge available to the
researchers is concerned, there is not yet any
researcher working on this issue. Because an inquirer
changes location constantly according to time,
changes of location will cause RNN queries to return
different results. For a CRNN query, executing RNN
search for every point of time during a continuousquery period will require a tremendously large price
to pay. The larger the number of query objects and
the shorter the time segment are, the longer the
calculation time will be.
In addition, due to the continuance nature of
time, defining the appropriate time segment for RNN
search will be a concern; if the interval between RNNsearches is too short, then more CRNN queries need
to be executed to complete the query, and vice versa.
If a RNN search is repeated over a longer period of
time to reduce the number of execution, the RNN
query result for the whole time segment will lose
accuracy due to insufficient frequency of sampling.In this paper, a more efficient algorithm is
designed to replace processing of each and everypoint of time for RNN search; just one execution of
CRNN query is all it takes to properly define the
segment for the query time that a user is interested in,
and find out the segments that share the same answer
and the RNN for each of the intervals.
Other than that, an index is also used to filter out
unnecessary objects to reduce search space and
improve CRNN search efficiency. The experiment
result suggests that using index provides efficiency
20 times better than not using index when the numberof objects is 1000.
This Study provides major contribution in three
ways:
This Study pioneers into continuous queryprocessing methods opposite to static
query regarding RNN issues. A CRNN search algorithm is proposed;
just one execution will return all CRNN
results.
The proposed method allows the indexwhich was only applicable to finding RNN
for a single query point to support CRNN
query to improve CRNN search efficiency.The structure of the other sections in this work:
Related works about RNN search are introduced in
Section 2. Concerned issues are defined and
assumptions made are described in Section 3. The
proposed CRNN search algorithm is introduced inSection 4 The experiment environment and
evaluation parameters for experimental efficacy are
described in Section 5. In the end, a conclusion andfuture study directions are provided in Section 6.
Figure 1: Example of RNN query.
2 RELATED WORKRNN search concerns about finding q, a query
that is the NN for some objects. Related works of
study about RNN search are introduced and
summarized in this section:
Index methods that support RNN searchThe number of objects can be infinite; if one mustfirst find out the distance from query q to each object
for identifying the RNN for query q, then the
efficiency may be unacceptably low due to
overwhelmingly large computation cost. To
accelerate processing speed, most of studies adopt theindex methods. Major index methods are introduced
in this section.
RNN search of different typesRNN searches in different scenarios are described
and categorized according to static and moving
situations of query q and the objects.
2.1
Index Methods for RNN Query
RNN search concerns about finding q, a query
that is the NN for some objects, and it is necessary to
find out the distance between query q and each object,
or the distance from the coordinate of query q to the
coordinate of an object. For a given q, not every
object is its RNN, and these objects which can not be
RNN may be practically left out of consideration to
reduce the number of objects to be taken into
consideration and accelerate processing speed for
RNN search. Many studies were dedicated to the
designing of an effective indexing structure for
coordinates of an object. The most famous ones areR-Tree proposed by [8] and Rdnn-Tree proposed by
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[10]. These two index methods are described below.
2.1.1R-Tree
R-Tree is an index structure developed in early
years for spatial database and was used by [10] to
accelerate RNN search processing. All objects aregrouped and then placed on leaf nodes according to
the closeness of their coordinates. That is, objects at
similar coordinates are put in one group. Next, eachgroup of objects is contained in a smallest possible
rectangle, which is called Minimum Bounding
Rectangle (MBR). Next, MBRs are grouped in
clusters, which are contained inside a larger MBR
until all objects are contained in the same MBR.
What is stored on an internal node of a R-Tree is an
MBR, in which all nodes underneath are contained,
and the root of the R-Tree contains all objects. Thesize and range of an MBR is defined by its lower left
coordinate (Ml
Md) and upper right coordinate (Mr
Mu). Figure 2 is an example of R-Tree. From a to l,
there are total 12 objects; (abcd) belong to
MBR b1, and (efg) belong to MBR b2. MBR b1
and b2 belong to MBR B1, and MBR R contains all
objects..
Figure 2: Example of R-tree Indexing
2.1.2 Rdnn-Tree
Rdnn-tree (R-tree containing Distance of NearestNeighbors) [22] improves the method of [10]. The
author proposes a single index structure (Rdnn-tree)
to provide solutions for NN queries and RNN queries
at the same time. Rdnn-tree differs from standard R-tree structure by storing extra information about
nearest neighbor of the points in each node.
Information of (ptiddnn) is stored on the leaf node
of Rdnn-tree, as shown in Figure 3. ptid means an
object of which the data concentrate on the dimension,
denoted as d, and dnn means the distance from such
object to its NN. Information of (ptrRect
MaxDnn) is stored on a non-leaf node, where ptr
points to the address of a child node, Rect contains
the MBR of all child nodes subordinate to this node,
and MaxDnn means the maximum value of dnn of all
objects in the child trees subordinate to this node. Themaximum distance from any object contained in
these child trees to its NN will not exceed MaxDnn.
Figure 3. Data structure of Rdnn-tree
2.2 Categories of Rnn queriesDepending on the static or moving status ofquery q and the query objects, related studies can be
summarized into 4 categories.
1. If query q and the query objects are both static,
then this category is called static query vs. static
objects.
2. If query q is moving and the query objects are
static, then this category is called moving query vs.static objects.
3. If query q is static and the query objects are
moving, then this category is called static query vs.
moving objects.
4. If both query q and the query objects are moving,
then this category is called moving query vs. movingobjects.
2.2.1 Static query vs. static objects
The scenario that both query q and query objects
are static is first discussed because the query and
query objects are immobile and are therefore easier
for processing than other scenarios. The method
proposed in [10] is now introduced. For static
database, the author adopts a special R-tree, called
RNN-tree, for answering RNN queries. For static
database that requires being frequently updated, the
author proposes a combined use of NN-tree andRNN-tree. NN of every object is stored in the RNN-
tree, and what are stored in the NN-tree are the
objects themselves and their respective collections of
NN. The author uses every object as the center of a
circle, of which the radius is the distance from the
object to its NN, to make a circle, and then examines
every circle that contains query q to find out the
answers of RNN queries. Such method, however, is
very inefficient for dynamic database because the
structures of NN-tree and RNN-tree must be changed
whenever the database is updated. In [22], the method
proposed by [10] is therefore improved. The author
proposes a single index structure, Rdnn-tree, foranswering NN queries and RNN queries at the same
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algorithm is divided into two steps.
Step 1: Finding segment points of CRNNqPoints of time that produce different RNN
results are identified. Based on these points of time,CRNN query is divided into several time segments
that require execution of RNN search. The RNN
result for any given point of time within one segmentwill remain constant, and different segments have
different RNN results.
Step 2: Calculating RNN result of each segmentSeparately calculate the RNN results for each of
the segments that have been divided in the previousstep.
The entire procedure for processing CRNN
Search is illustrated in Figure 5. On top of the
necessary query objects and continuous query (query
path), it is divided into two steps: finding segment
points of CRNNq and calculating RNN result of each
segment; each of the steps is described below:
Figure 5: Flow chart of CRNN query
processing
4.1 Finding segment points of CRNNWhat CRNN query pursues is a period of
continuous time; the moving distance of query
objects is very short among some adjacent points of
time for the query, thus possibly resulting in the same
RNN result. That is, the entire period of continuous
query is divided into several segments, and the RNNresults in each segment are the same. If these points
of time share the same RNN result, then it is not
necessary to execute RNN search for each of the
points of time; one-time calculation is enough.
Therefore, CRNN query does not require executing
RNN search for all points of time. Instead, points of
time that share the same RNN result are grouped into
time segments, and one-time RNN search is executed
for each of the segments. RNN of query q is a
collection of the objects of which the NN is query q.
If the distance, or N, is realized in advance, then
these objects are the RNN for query q when the
distances from query q to the objects are shorter thanthe distances from the objects to their respective NN.
As illustrated in Figure 6, if the NN of object a
is b, and a circle is made using ab as the radius witha as the center point, then the distance from query q
to a must be shorter than the distance from a to its
NN, or object b, as long as query q falls within this
circle. Therefore, during the period of time when
query q remains within this circle, RNNs of object amust include a, unless query q moves out of this
circle. Because the moving direction of query q is
assumed to be fixed, CRNN query will form a query
line (qline) from its beginning to its end. The point to
which this CRNN query begins to leave this circle is
the intersection S of this circle and the query line
formed by CRNN query. Before intersection S, the
result of RNN query must include object a; beyond
intersection S, the result of RNN query will not
include object a; the RNN results will be different.
This intersection is referred to as a segment point.
This explains why the intersection of the circle
with NN as its radius and the query line is the point
of time where RNN query produces different results.
Making a circle by using an object itself as the center
and the distance to its NN as the radius will enable all
of the intersections of the circle and the query line of
CRNN query to cut CRNN query into several time
segments that have different results of RNN query.
Figure 6. Finding segment point of CRNN search
Figure 7 illustrates the time segmentation
process described above. For object a, b, and c, their
respective NNs are identified first: NN(a)=b,
NN(b)=a, and NN(c)=b. Next, use each object as thecenter of a circle, and the distance to its respective
NN as the radius to make circles ofa, b, and c. Then,
intersections of the circles and qlines, Ps, P1, P2, P3,
P4, and Pe , are sorted according to time, and every
two intersection points define a time segment. The
entire CRNN query is cut into five time segments, [Ps
P1] , [ P1 P2] , [P2P3] , [P3P4] , and [P4Pe].
Every segment has a unique RNN query result.
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Figure 7: Segmenting of the CRNN query
4.2 Calculating RNN result of each segment
In the previous section, intersections of qlines
and the circles with the distances between the objects
and their respective NNs as the radiuses are defined.
With these intersections, CRNN query is cut into
several time segments. The next step is to find RNNs
for each of the time segments. Because the distances
from query objects to their respective NNs are used
as the radiuses to make circles which are coded by
the objects numbers, if a segment falls within a
certain circle, then the resulting RNN of this time
segment for the CRNN query is the object collection
represented by such circle. This is illustrated in
Figure 8. First, intersections of qlines that represent
the CRNN query and the circles of the objects are
sorted by time; every two intersection points define a
time segment, and there are five segments, [PsP1] ,
[ P1 P2] , [P2P3] , [P3P4] , and [P4Pe].
Segment [PsP1] is contained only by circle a,
therefore: RNN(q[PsP1]) ={a}. Next, examine
segment [PsP1]; this segment is contained by circle
a and circle b. Therefore: RNN(q [PsP1]) = {a
b}. If this process is repeated, then the obtained
results will be RNN(q[P2P3]) = {abc},
RNN(q[P3P4]) ={bc}, and RNN(q[P4P5])
={c}.
Figure 8: Calculating RNN result of each segment.
1. CRNN Algorithm with IndexNot every object will be an answer in the
processing of CRNN query. To improve RNN query
efficiency, it is preferred that the objects that can not
be answers are filtered out in advance to greatlyreduce search space for CRNN query, size of data
that requires CRNN query, and consequently,
computation cost. The process that further improvesCRNN query efficiency dramatically is referred to as
pruning process. Figure 9 illustrates the flowchart of
CRNN query processing with a pruning process
added.
Figure 9. Flow chart of CRNN query with index
Step 2 and 3 are identical to Step 1 and 2 in
CRNN search algorithm, which have been described
in the previous sections, and they will not be
reiterated again here. For step 1, the pruning process,
an index structure for Rdnn-tree is designed to
effectively execute the pruning process. The three
steps of CRNN query with index are illustrated in
Figure 9. The pruning process is described below. For
every internal node of Rdnn-tree, the distance from
query q to its node will be computed for every
separation, and the distance is denoted as D(qRect).
If D(qRect) of a node is larger than MaxDnn of the
node, then all the objects beneath it will not be
considered because the distance from query q toRectNode will be equal to or larger than the distances
from query q to all the objects underneathRectnode.
When the distance from query q to Rect node is
longer than MaxDnn, it is impossible that query q is
closer to its NN than any other object underneath
Rectnode, and no object underneath can be the RNN
result for query q. On the contrary, if D(qRect)
equals the MaxDnn of such node, then the distances
from some objects underneath Rect node to their
respective NNs are shorter than the distance from
query q to Rect. That is, some objects are the RNNresults for query q. The examination continues along
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the branch all the way to the lead node. All entries
underneath such leaf node are recorded as the
candidate objects for RNN query result. The
collection of these candidate objects is referred to as
RNNCanSet, which means the possible results for
RNN query must exist within this collection, and the
objects outside of RNNCanSet can not possibly beRNN query results. All that are needed to be
considered when finding segment point of CRNNq of
CRNN search algorithm are the objects insideRNNCanSet. This will greatly reduce the quantity of
objects needed to be handled and enhance CRNN
search algorithm efficiency.
Figure 3 explains the pruning process. It begins
with root node R. Because D(qR)MaxDnn of R,
child nodes of B1 and B2 must be examined. Because
theMaxDnn ofMBR B1 D( qB1), all child nodes
underneath B1 can be pruned. Next, D(q
B2)MaxDnn ofB2, so child nodes b3 and b4 of B2
must be examined. D(qb3) is equal to or smaller
than the MaxDnn of b3, which is also a leaf node;
therefore, h and i are placed inside RNNCanSet. Next,
b4 is examined.MaxDnn of b4 is equal to or smaller
than D(qb4); therefore, b4 can be pruned. The
entire pruning process then ends.
However, the CRNN query to be processed is
not a RNN query of a single query point; therefore,
the pruning process in [22] can not be directly used.To ensure that no possible RNN result is deleted, the
criteria of pruning is changed from the condition that
D(qRect), the distance from query point to Rect,
must be longer than MaxDnn to the condition that
MinD(qRect)>MaxDnn, where MinD(qlineRect)
represents the minimum distance from qline to Rect
node. The reason why the shortest distance is selected
is that if the minimum distance from the entire qline
toRectnode is larger thanMaxDnn, then the distance
from any given point of time on the qline to Rect
node must be longer than MaxDnn. Therefore, all the
objects underneath Rect node can not be RNN for
qline, and pruning is out of consideration. Details ofthe pruning algorithm are exhibited in Algorithm 1:
Algorithm 1: Pruning Algorithm.
5. Performance Study
To evaluate the improvement which the method
proposed in this Study has made in CRNN query
efficiency, some experiments are designed, and this
section provides descriptions of experimentenvironments, experimental parameters and settings,
and comparison of experiment results.
5.1 Experiment Settings
The coordinates of the objects disperse in an
experiment environment of [01][01] plane.
Because distribution density of the objects mayinfluence efficiency, it should be taken into
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consideration in the experiment. In the experiment,
three different types of distribution are used in the
generation of objects coordinates. The three different
types of distribution are Uniform distribution,
Gaussian distribution, and Zipf distribution. In
uniform distribution, the objects are evenly
distributed on the plane, as shown in Figure 10(a). InGaussian distribution, most of the objects concentrate
on the center of the plane, as shown in Figure 10(b).
In Zipf distribution, most of the objects will distributeat the extreme left and extreme bottom of the plane.
In the experiment, skew factor is set at 0.8, as shown
in Figure 10(c). In addition, 30 queries are generated
randomly in a [0.4 0.6][0.4 0.6] plane by
referring to [15], and the velocity vector of each
query falls between [-0.01 0.01]. Because the
influence of different types of object distribution on
efficiency is concerned in this experiment, the queries
are generated as close to the center of the plane as
possible. Having executed 30 queries, the average
cost of executing one CRNN search is used indetermining which method is more favorable. As to
the program coding of Rdnn-tree in the CRNN search
algorithm, R*-tree code of GIST[7] is used in
perfecting Rdnn-tree to make it match with the
requirement of this experiment.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Ya
xis
X axis
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Ya
xis
X axis
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Ya
xis
X axis
Figure 10 Data sets of experiment evaluation
In addition to the object distribution described
above, the influences that the amount of query time
(qline) and the number of objects may impose on
efficiency are also considered. Three data sets ofUniform, Gaussian, and Zipf are considered in object
distribution. The amount of query time (qline)
changes from query length 1 to query length 10. The
number of objects changes from 1K to 10K.
Parameters and settings used in the experiment are
listed in Table 1.
Table 1: Parameter settings of experiment
Parameter Description Settings
distribution Data distribution Uniform,
Gaussian, Zipf
interval Time interval of
Query
1, 2, 5, 8, 10
object-no Number of Data
Objects
1, 10. 30, 50 ,
100(k)
5.2 Compared Algorithms and Performance
Metrics
The most intuitive method for finding RNN is
looking for the NN of every object. If the number of
query objects is N, then time Complexity is O(n2).
Next, determine which objects NNs are query points.
If the NNs are the query points, then the objects will
be the RNNs for the query points. The required time
complexity for the RNN algorithm is O(n3).However, the most intuitive method for finding
CRNN query is executing RNN algorithm for every
point of time which is continuous, and it is
impossible to calculate the required count of
execution. Therefore, the CRNN query time must besegmented before the total execution time required
for CRNN query may be calculated. The more the
time is segmented, the more executions of RNN are
required. If a period of time is segmented into m
segments, then time complexity will be O(mn3), and
if time is not adequately segmented, then the RNN
result may be erroneous. These make it an inefficient
CRNN search algorithm, and it will not be comparedin this experiment. Efficiency of two methods is
compared in this experiment: one uses Rdnn-tree as
the index, and the other uses no index. To evaluate
these two methods, comparison of the time required
for one CRNN search execution can be used, and thiscomparison is referred to as total cost in this Study.
5.4 Performance Results and Discussion
Based on the changes of metrics (distribution,
interval, and object-no), different types of
experiments have been conducted. Results are
summarized by object-no and query interval in the
next section.
5.4.1 The effect of object-no parameter
First, the fixed query interval is set at 5. Theinfluence imposed on efficiency by object-no
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through broadcast is an effective solution for
scalability. The future goal of this Study is extending
the issues of CRNN search to the wireless
broadcasting environment.
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[18] Stanoi,I.,Riedewald, M.,Agrawal,D., and
Abbadi,A.E. (2001) Discovery of influence sets
in frequently updated databases. Proceedings of
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108.[18] Tao,Y., Papadias,D., and Lian,X. (2004) Reverse
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[20]Tao,Y., Papadias, D., and Shen,Q. (2002)Continuous nearest neighbor search.
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Energy efficient index for energy query
location-dependent data in mobile
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[23] Yiu,M.L., Papadias,D., Manoulis,N., and Tao,Y.(2005) Reverse nearest neighbors in large
graphs. Proceedings of 21st IEEE International
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[24] Yu,C.,Ooi,B.C., Tan,K.-L., and Jagadish,H.V.
(2001) Indexing the distance: An efficient
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Search k nearest neighbors on air. Proceedings
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REDUCTION OF INTERCARRIER INTERFERENCE IN OFDM
SYSTEMSR.Kumar Dr. S.Malarvizhi
* Dept. of Electronics and Comm. Engg., SRM University, Chennai, India-603203
ABSTRACT
Orthogonal Frequency Division Multiplexing
(OFDM) is a promising technique for the broadband wireless
communication system. However, a special problem in OFDM
is its vulnerability to frequency offset errors due to which the
orthogonality is destroyed that result in Intercarrier
Interference (ICI). ICI causes power leakage among
subcarriers thus degrading the system performance. This
paper will investigate the effectiveness of Maximum-
Likelihood Estimation (MLE), Extended Kalman Filtering
(EKF) and Self-Cancellation (SC) technique for mitigation of
ICI in OFDM systems. Numerical simulations of the ICI
mitigation schemes will be performed and their performance
will be evaluated and compared in terms of bit error rate
(BER), bandwidth efficiency and computational complexity.Keywords: Orthogonal Frequency Division Multiplexing(OFDM), Intercarrier Interference (ICI), Carrier Frequency
Offset (CFO), Carrier to Interference Ratio (CIR), MaximumLikelihood (ML), Extended Kalman Filtering (EKF).
1. IntroductionOrthogonal frequency division multiplexing (OFDM),
because of its resistance to multipath fading, has attracted
increasing interest in recent years as a suitable modulationscheme for commercial high-speed broadband wireless
communication systems. OFDM can provide large data rates
with sufficient robustness to radio channel impairments. It is
very easy to implement with the help of Fast FourierTransform and Inverse Fast Fourier Transform for
demodulation and modulation respectively [1].It is a special case of multi-carrier modulation in
which a large number of orthogonal, overlapping, narrow band
sub-channels or subcarriers, transmitted in parallel, divide theavailable transmission bandwidth [2]. The separation of the
subcarriers is theoretically minimal such that there is a very
compact spectral utilization. These subcarriers have different
frequencies and they are orthogonal to each other [3]. Since
the bandwidth is narrower, each sub channel requires a longersymbol period. Due to the increased symbol duration, the ISI
over each channel is reduced.
However, a major problem in OFDM is its
vulnerability to frequency offset errors between thetransmitted and received signals, which may be caused byDoppler shift in the channel or by the difference between the
transmitter and receiver local oscillator frequencies [4]. In
such situations, the orthogonality of the carriers is no longermaintained, which results in Intercarrier Interference (ICI). ICI
results from the other sub-channels in the same data block ofthe same user. ICI problem would become more complicated
when the multipath fading is present [5]. If ICI is not properly
compensated it results in power leakage among the
subcarriers, thus degrading the system performance.
In [6], ICI self-cancellation of the data-conversion
method was proposed to cancel the ICI caused by frequency
offset in the OFDM system. In [7], ICI self-cancellation of thedata-conjugate method was proposed to minimize the ICIcaused by frequency offset and it could reduce the peak
average to power ratio (PAPR) than the data-conversion
method. In [8], self ICI cancellation method which maps the
data to be transmitted onto adjacent pairs of subcarriers hasbeen described. But this method is less bandwidth efficient. In
[9], the joint Maximum Likelihood symbol-time and carrier
frequency offset (CFO) estimator in OFDM systems has been
developed. In this paper, only carrier frequency offset (CFO)
is estimated and is cancelled at the receiver. In addition,statistical approaches have also been explored to estimate and
cancel ICI [10].
Organization: This paper is organized as follows: Insection 2, the standard OFDM system has been described. In
section 3, the ICI mitigation schemes such as Self-
Cancellation (SC), Maximum Likelihood Estimation (MLE)
and Extended Kalman Filtering (EKF) methods have been
described. In section 4, simulations and results for the threemethods has been shown and are compared in terms of
bandwidth efficiency, bit error rate (BER) performance.
Section 5 concludes the paper and inference has been given.
2. System Description
The block diagram of standard OFDM system is given
in figure 1. In an OFDM system, the input data stream is
converted into N parallel data streams each with symbolperiod Ts through a serial-to-parallel Port. When the parallel
symbol streams are generated, each stream would be
modulated and carried over at different center frequencies.
The sub-carriers are spaced by 1/NTs in frequency, thus theyare orthogonal over the interval (0, Ts). Then, the N symbols
are mapped to bins of an inverse fast Fourier transform
(IFFT). These IFFT [11] bins correspond to the orthogonalsub-carriers in the OFDM symbol. Therefore, the OFDM
symbol can be expressed as
NnmjN
m
meXN
nx /21
0
1)(
=
= (1)
where the Xms are the base band symbols on each
sub-carrier. The digital-to-analog (D/A) converter then createsan analog time-domain signal which is transmitted through the
channel.
At the receiver, the signal is converted back to adiscrete N point sequence y(n), corresponding to each sub-carrier. This discrete signal is demodulated using an N-point
Fast Fourier Transform (FFT) operation at the receiver.
n
S/P IFFT P/S
Channel
D/A
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Figure 1: OFDM System Model
The demodulated symbol stream is given by:
)()()(/2
1
0
mwenymY NnmjN
n
+=
= (2)
N-1where w (m) corresponds to the FFT of the samples of w
(n), which is the Additive White Gaussian Noise (AWGN)introduced in the channel.
3. ICI Mitigation Schemes
3.1 Self-Cancellation (SC) SchemeIn this scheme, data is mapped onto group of
subcarriers with predefined coefficients. This results in
cancellation of the component of ICI within that group due tothe linear variation in weighting coefficients, hence the name
self- cancellation. The complex ICI coefficients S (l-k) are
given by
)))(/11(exp()/)((
))(()( klNj
NklNSin
klSinklSin +
+
+=
(3)
3.1.1 ICI Canceling ModulationThe ICI self-cancellation scheme requires that the
transmitted signals be constrained such that X (1) = - X (0), X
(3) = - X (2) X (N-1) = - X (N-2).The received signal on
subcarriers kand k+ 1 to be written as
[ ]
=
++=2
,..6,4,2,0
)1()()()('N
l
knklSklSlXkY (4)
[ ]
=
++=+2
,..6,4,2,0
1)()1()()1('N
l
knklSklSlXkY
(5)
where nk and nk+1 isthe noise added to it.
And the ICI coefficient S ' (l-k) is denoted as
S '(l-k) = S (l-k) S (l+1-k) (6)
Figure 2: Comparison between |S ' ' (l-k)|,|S ' (l-k)| and |S (l-k)|
It is seen from figure 2 that |S ' (l-k)|
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phases of each of the subcarriers between the successive
symbols.
When an OFDM symbol of sequence length N isreplicated, the receiver receives, in the absence of noise, the
2N point sequence i.e., {r (n)} given by
=
+=K
Kk
NknjekHkXN
nr /)(2)()(1
)( (10)
where {X(k)} are the 2K+1 complex modulationvalues used to modulate 2K+1 subcarriers,
The first set of N symbols are demodulated using an
N-point FFT to yield the sequence R1(k), and the second set is
demodulated using another N-point FFT to yield the sequenceR2(k). The frequency offset is the phase difference between R1
(k) and R2 (k), that is
R2 (k) = R1 (k) ej2 (11)
Adding the AWGN yieldsY1 (k) = R1 (k) + W1 (k) (12)
Y2 (k) = R1 (k) ej2+ W2 (k)
k = 0, 1 ...N 1
The maximum likelihood estimate of the normalizedfrequency offset is given by:
=
= =
K
Kk
K
Kk
kYkY
kYkY
)(*)(Re
)(*)(Im1
tan2
1
12
12
(13)
This maximum likelihood estimate is a conditionally
unbiased estimate of the frequency offset and was computed
using the received data. Once the frequency offset is known,
the ICI distortion in the data symbols is reduced bymultiplying the received symbols with a complex conjugate of
the frequency shift and applying the FFT,
X (n) = FFT {y (n) e-j2 n / N} (14)
3.3 Extended Kalman Filtering
Astate space model of the discrete Kalman filter isdefined as
z(n) = a(n) d(n) + v(n) (15)
In this model, the observation z(n) has a linearrelationship with the desired value d(n). By using the discrete
Kalman filter, d(n) can be recursively estimated based on the
observation of z(n) and the updated estimation in each
recursion is optimum in the minimum mean square sense.
The received symbols in OFDM System arey(n) = x(n) ej 2 n (n) / N + w(n) (16)
where y(n) the received symbol and x(n) is the FFT
of transmitted symbol. It is obvious that the observation y(n) is
in a nonlinear relationship with the desired value (n), i.ey(n) = f((n)) + w(n) (17)
where f((n)) = x(n) ej 2 n (n) / N (18)
In order to estimate
(n) efficiently in computation,we build an approximate linear relationship using the first-
order Taylors expansion:
y(n)f((n-1))+f'((n-1))[(n)-(n-1)]+w(n) (19)
where (n-1) is the estimate of(n-1).
To Define
z(n) = y(n) f((n-1) (20)
d(n) = (n) - (n-1) (21)and the following relationship
z(n) = f'((n-1)) d(n) + w(n) (22)
z(n) is linearly related to d(n). Hence the normalized
frequency offset (n) can be estimated in a recursive
procedure similar to the discrete Kalman filter. As linearapproximation is involved in the derivation, the filter is called
the extended Kalman filter (EKF). The EKF provides a
trajectory of estimation for (n). The error in each update
decreases and the estimate becomes closer to the ideal valueduring iterations.
4.2ICI CancellationThere are two stages in the EKF scheme to mitigate
the ICI effect: the offset estimation scheme and the offset
correction scheme.
4.2.1 Offset Estimation SchemeTo estimate the quantity (n) using an EKF in each
OFDM frame, the state equation is built as
(n) = (n-1) (23)i.e., in this case we are estimating an unknown constant . This
constant is distorted by a non-stationary process x(n), an
observation of which is the preamble symbols preceding the
data symbols in the frame. The observation equation is
y(n) = x(n) ej2 n (n) / N + w(n) (24)
where y(n) denotes the received preamble symbolsdistorted in the channel, w(n) the AWGN, and x(n) the IFFT
of the preambles X(k) that are transmitted, which are known at
the receiver. Assume there are Np
preambles preceding the
data symbols in each frame are used as a training sequenceand the variance 2 of the AWGN w(n) is stationary.
4.2.2 Offset Correction SchemeThe ICI distortion in the data symbols x(n) that
follow the training sequence can then be mitigated by
multiplying the received data symbols y(n) with a complex
conjugate of the estimated frequency offset and applying FFT,
i.e.x(n) = FFT{ y(n)e -j 2 n (n) / N} (25)
As the estimation of the frequency offset by the EKF
scheme is pretty efficient and accurate, it is expected that the
performance will be mainly influenced by the variation of theAWGN.
4.3Algorithm1. Initialize the estimate (0) and corresponding state
error P(0)
2. Compute the H(n), the derivative of y(n) with respect to(n) at (n-1) the estimate obtained in the previousiteration.
3. Compute the time-varying Kalman gain K(n) using theerror variance p (n-1), H(n), and 2
4. Compute the estimate y(n) using x(n) and (n-1) i.e. based on the observations up to time n-1, compute the
error between the true observation y(n) and y(n)5. Update the estimate (n) by adding the K(n)-weighted
error between the observation y(n) and y(n) to theprevious estimate (n-1)
6. Compute the state error P(n) with the Kalman gain K(n),H(n), and the previous error P(n-1).
7. If n is less than Np, increment n by 1 and go to step 2;
otherwise stop.
It is observed that the actual errors of the estimation (n) from
the ideal value (n) are computed in each step and are used foradjustment of estimation in the next step.
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4. SIMULATIONS AND RESULTSIn order to compare the ICI cancellation schemes,
BER curves were used to evaluate the performance of each
scheme. For the simulations in this project, MATLAB was
employed. The simulations were performed using an AWGNchannel.
Table 1: Simulation Parameters
PARAMETERS VALUES
Number of carriers (N) 1705
Modulation (M) BPSK
Frequency offset [0.25,0.5,0.75]
No. of OFDM symbols 100
Bits per OFDM symbol N*log2(M)
Eb-No 1:20
IFFT size 2048
Figure 3: BER performance with ICI
Cancellation for =0.25
Figure 3 shows that for small frequency offset
values, ML and SC methods have a similar performance.
However, ML method has a lower bit error rate for increasing
values of Eb/No.
Figure 4: BER performance with ICICancellation for =0.5
Figure 4 illustrates that for frequency offset value of0.5, BER increases for both th