final - volume 3 no 2

8/14/2019 Final - Volume 3 No 2

1/89

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.

UbiCC Journal - Volume 3 1


2/89

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



3/89

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



4/89

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



5/89

-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

)


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

)


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.



6/89


7/89

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



8/89


9/89

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


10/89

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:


11/89

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


12/89


13/89

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


14/89

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.


15/89

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


16/89

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.


17/89

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


18/89

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


19/89

[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


20/89


21/89

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.


22/89

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


23/89

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


24/89

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


25/89


26/89

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.

7. References

[1] AmitSingh,H.F. and Tosun,A.S. (2003) High

dimensional reverse nearest neighbor queries.

Proceedings of the 20th

International

Conference on Information and Knowledge

Management (CIKM03), NewOrleans, LA,USA, pp.9198.

[2] Barbara,D. (1999) Mobile computing and

databases-a survey.IEEE Transactions on

Knowledge and Data Engineering, 11, 108117.

[3] Benetis,R.,Jensen, C.S.,Karciauskas,G., and

Saltenis,S. (2002) Nearest neighbor and reverse

nearest neighbor queries for moving objects.

International Database Engineering and Applications Symposium, Canada, July17-19,

pp.4453.

[4] Chaudhuri,S. and Gravano,L. (1999) Evaluating

top-k selection queries. Proceedings of the 25th

IEEE International Conference on Very Large

Data Bases, pp.397410.

[5] Civilis,A., Jensen,C.S., and Pakalnis,S. (2005)Techniques for efficient road-network-based

tracking of moving objects. IEEE Transactions

on Knowledge and Data Engineering, 17, 698

712.

[6] Computer Science and Telecommunication

Board.IT Roadmap to a geospatial future, thenational academies press,2003.

[7] http://gist.cs.berkeley.edu/.

[8] Guttman,A. (1984) R-trees:A dynamic index

structure for spatial searching. Proceedings of

the 1984 ACM SIGMOD international

conference on Management of data, pp.4757.

[9] Hjaltason,G.R. and Samet,H. (1999) Distance

browsing in spatial data bases. ACM

Transactions on Database Systems (TODS), 24,

265318.

[10] Korn,F. and Muthukrishnan,S. (2000) Influence

sets based on reverse nearest neighbor queries.

Proceedings of the 2000 ACM SIGMOD International Conference on Management of

Data, Dallas, Texas, USA, May16-18, pp.201

212.

[11] Korn,F.,Muthukrishnan, S.,and Srivastava.,D.(2002) Reverse nearest neighbor aggregates

over data streams. Proceedings of the

International Conference on Very Large

DataBases (VLDB02), Hong Kong, China,

August, pp.9198.

[12] Korn,F., Sidiropoulos, N.,Faloutsos, C.,Siegel,E.,

and Protopapas,Z. (1996) Fast nearest neighbor

search in medical image database. In

Proceedings of the 22th InternationalConference on Very Large Data Bases

(CLDB96), pp. 215226.

[13] Lee,D.L., chien Lee, W.,Xu,J., and Zheng, B.

(2002) Data management in location dependent

services.IEEE Pervasive Computing,1, 6572.[14] Roussopoulos,N., Kelley,S. ,and Vincent,

F.(1995) Nearest neighbor queries.

Proceedings of ACM Sigmod InternationalConference on Management of Data , Illinois,

USA, June, pp.7179.

[15] Ross,S.(2000) Introduction to Probability andStatistics for Engineers and Scientists.

[16] Stanoi,I., Agrawal,D., and Abbadi,A.E. (2000)Reverse nearest neighbor queries for dynamic

databases. ACM SIGMOD Workshop on

Research Issues in Data Mining and

Knowledge Discovery, pp.4453.

[17] Song,Z. and Roussopoulos,N. (2001) K-nearest

neighbor search for moving query point.

Proceedings of 7th International Symposium on

Advances in Spatial and Temporal Databases,LNCS2121, RedondoBeach, CA, USA, July12-

15, pp.7996.

[18] Stanoi,I.,Riedewald, M.,Agrawal,D., and

Abbadi,A.E. (2001) Discovery of influence sets

in frequently updated databases. Proceedings of

the 27th VLDB Conference, Roma, Italy, pp.99

108.[18] Tao,Y., Papadias,D., and Lian,X. (2004) Reverse

knn search in arbitrary dimensionality.

Proceedings of 30th

Very Large Data Bases,

Toronto, Canada, August29-September3,

pp.279290.

[20]Tao,Y., Papadias, D., and Shen,Q. (2002)Continuous nearest neighbor search.

International Conference on Very Large Data

Bases, Hong Kong, China, August 20-23,

pp.279290.

[21] Xu,J., Zheng,B., Lee,W.-C.,, and Lee,D.L. (2003)

Energy efficient index for energy query

location-dependent data in mobile

environments.In Proceedings of the 19th IEEE

International Conference on Data Engineering

(ICDE03), Bangalore, India, March, pp.239

250.

[22] Yang,C. and Lin,K.-I. (2001) An index structurefor efficient reverse nearest neighbor queries.

Proceedings of the 17th

International

Conference on Data Engineering, pp.485492.

[23] Yiu,M.L., Papadias,D., Manoulis,N., and Tao,Y.(2005) Reverse nearest neighbors in large

graphs. Proceedings of 21st IEEE International

Conference on Data Engineering (ICDE),

Tokyo, Japan, April5-8, pp.186187.

[24] Yu,C.,Ooi,B.C., Tan,K.-L., and Jagadish,H.V.

(2001) Indexing the distance: An efficient

method to knn processing. Proceedings of the

27th

VLDB Conference, Roma, Italy, pp. 421

430.[25] Zheng,B.,Lee, W.-C., and Lee,D.L. (2003)
http://gist.cs.berkeley.edu/http://gist.cs.berkeley.edu/


27/89

Search k nearest neighbors on air. Proceedings

of the 4th

International Conferenceon Mobile

Data Management, Melbourne, Australia,

January, pp.181195.[26] Zheng,B., Xu,J., chien Lee, W., and Lee,D.L.

(2004) Energy conserving air indexes for

nearest neighbor search. Proceedings of the 9th

International Conference on Extending

Database Technology (EDBT04), Heraklion,

Crete, Greece,March, pp.4866.

[27] Zhang,J., Zhu,M., Papadias,D., Tao,Y., and

Lee,D.L. (2003) Location-based spatial queries.

In Proceedings of the 2003 ACM SIGMOD

international conference on Management of

data, SanDiego, California, USA, June9-12,

pp.443454.


28/89

REDUCTION OF INTERCARRIER INTERFERENCE IN OFDM

SYSTEMSR.Kumar Dr. S.Malarvizhi

* Dept. of Electronics and Comm. Engg., SRM University, Chennai, India-603203

[email protected]

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



29/89

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)|


30/89

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.



31/89

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

final - volume 3 no 2

Documents