uwb isbc2010 full paper

8/6/2019 Uwb Isbc2010 Full Paper

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Geometrical-based Channel Simulation Model for Ultra

Wideband Environment

Uche A.K. Okonkwo

1

, Razali Ngah

2

, Zabih Ghassemlooy

3

, and Tharek A. Rahman

4

1,2,4Wireless Communication Center (WCC), Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor3School of Computing, Engineering & Information Sciences, University of Northumbria, Newcastle, UK

Keywords: Ultra-wideband (UWB) channel, geometrical

model, multipath, power delay profile (PDP).

Abstract

A geometrical-based method for the characterization of the

ultra wideband time-invariant channel (UWB) is presented.This model arises primarily from the integration of

geometrical and statistical assumptions from a physical

propagation point of view to account for clusters in the

channel response of the UWB channel. The accuracy of this

model is verified by comparison with the measured data.

1 Introduction

In order to design and analyze the ultra-wideband (UWB)

system, a good knowledge of the channel properties is

necessary. A considerable amount of experimental

measurement campaign has been conducted in order to

characterize and model the UWB channel [1]-[3]. The IEEE802.15.3a and 802.15.4a Task Groups also developed UWB

channel models for the simulation of the UWB system [4]. In

the simulation model the mathematical representation of the

channel response using the Saleh-Valenzuela (SV) model [5]

is assumed:

)()()( thtxty UWB=

(1)

where )(tx and )(ty are the transmitted and received

signals, respectively. The term )(thUWB is the UWB

channel response in complex baseband:

= =

=

L

l

K

k

lkllklkUWB Ttjath

0 0

,,, )()exp()(

(2)

where lka , is the tap weight of the kth component in the lth

cluster, lT is the delay of the lth cluster, lk, is the delay

of the kth multipath component (MPC) relative to the lth

cluster arrival time lT . Some modifications to the above

model were proposed by Chong et al [6] and Spenser et al [7].

The SV model (2) has been widely used in order to fit in

and account for the appearance of clusters in the response

pattern [5], [8]. In this paper, we combine the elliptical

geometrical model [9] and statistical assumptions to derive a

computationally efficient and tractable algorithm for the

characterization of the UWB channel. This model primarily

uses three parameters: transmitter-receiver distance, number

of scatterers and physical dimension of the environment for

the simulation.The proposed geometrical-based model is discussed in

Section 2. And some numerical results are presented in

Section 3.

2 Proposed Channel Model

The geometrical-based elliptical model represents an ideal

model of indoor wireless propagation environment. This

model considers the geometric description of the spatial

relationship among the access point (AP), scatterers and the

user equipment (UE) within defined elliptical loops as shown

in Fig. 1.

Fig. 1: Elliptical model for UWB radio propagation channel

For AP-UE separation distance of D, the major and minor

axes are indicated by amax and b max, respectively).

Each scatterer is defined as a vector ns in a hypothetical

space-frequency coordinate ),,,( eyx , where ke is

the specific elliptical area within which the scatterers

),( yxsn with frequency characteristics lie. For the

UWB channel, we make the following additional assumptions

to those in [9]:

1. The propagation medium from the UE to AP withthe exception of the scattering volume has the


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intrinsic electromagnetic properties of free space.

2. The scatterers may not have identical scattering

coefficients; hence the frequency dependence of the

scattering coefficients is taken into account.

From the physical propagation point of view, the single

channel can be fully characterized in the time-domain withthe knowledge of the delays and composite powers associated

with the MPCs. Let the numberNand the coordinates of the

scatterers Nnyx ..,2,1),( = in the propagation environment

have known statistical distributions within the region bounded

by hypothetical bi-centric ellipses }{ ke with foci at the AP

and UE. For a system bandwidth BW, the metric separation

between two bi-centric ellipses ie and je ,

}1..,2,1,0{, = Kkji is given by:

= c (3)

where )2/(1 BW= is the time delay resolution. The

large bandwidth of UWB implies a very high resolution. All

MPCs received from scatterers within the same elliptical

separation ie

have the same delay. However their power

gain may vary due to the intrinsic electromagnetic properties

of the associated scatterers which define the scattering

coefficients.

The major a and minor b axes half-lengths of the

ellipses are given by:

= kck .5.0a (4)

= 22).(5.0 Dkck b

(5)

where c is the speed of electromagnetic wave, = ki is the delay associated with the i th ellipse. The maximum

delay = )1(max K occurs at the boundary of the

biggest ellipse of consideration 1Ke . Thus all multipath

components that arrive after max are considered

insignificant. This is justifies since such signal components

will experience greater path loss and hence will haverelatively low power compared to those with shorter delays.

Therefore max should be chosen sufficiently large so that

nearly all multipath components with significant power level

will be accounted for.

The geometric distribution ),( yxf of the Nscatterers

can be defined using any of the appropriate known statistical

distribution functions where ),( yxf is independent of

frequency. The choice of the appropriate ),( yxf follows

the physical architecture and positioning/dimension of the

objects within the propagation environment. The bounds of

),( yxf depends on the choice and physical dimension of1Ka , and the value of 1Kb derived from (5) for a given

D .

To obtain the delays associated with all MPCs, we first of

all obtain the total path length by considering Fig. 2.

Fig. 2: Coordinate diagram of the scatterers, AP and UE. Thephysical channel are bounded by A, B and C.

Let the reference point )0,0( be the receiver position

)0,0(AP . The path length R from )0,(DUE to

)0,0(AP through ),,( knnn eyxs is given by:

{ }knnknn

gfR +=|, , Nn ,..,2,1=

(6)

where:

( ) 21

22nnn yxf +=

(7)

22 )( nnn xDyg += (8)

If we classify all scatterers within an area defined by ellipse

1e as NQqeyxs qqq = ),..,2,1(),,,( 1 , then the

total path length 1H is :

=

qqqq

q

q

RRR

RRR

RRR

H

..

:::

..

..

21

22221

11211

1 (9)

Thus for all the bi-centric ellipses }{ ke the composite path

length can be concatenated into a rectangular matrix W :

[ ]121 ...... = KHHHW (10)

The matrix W has Q -by- ))1(( KQ dimension. Its

elements are either 0s or 1s. The sum of all the elements inkH represents the magnitude of the resolved MPC


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associated with the ith ellipse (delay of .k ) if we

assume a lossless medium. Thus we can reduce the matrix

W to a 1-by- )1( K matrix dW .

In the case of time-varying UWB system, the required

angle-of-arrival (AOA)

can be obtained from theknowledge of the perimeter defined from UE through ns

to AP :

( ) ( )22211 )2cos nnnn gfDDf += (11)

For the ke the power associated with each element of

kH is given by:

.(log10)(log20),( 101

00 ddNPdP dnn ++=

(12)

where knnRd |, , and 0P , 0 and 0d are the

reference power, frequency and distance, respectively. The

term Nd is the path loss exponent while U is the lognormal

shadowing. Thus for scatterers defined by

),,,( nknn eyxs we can express the received scattered

power by:

[ ]121 ...... = KT PPPP(13)

where kP is:

=

qqqq

q

q

k

EEE

EEE

EEE

P

..

:::

..

..

21

22221

11211

(14)

The values of kP with elements E can be accurately

determined if the statistics of the material scattering objects

are available. For simulation purposes, we can employ theempirical expression in [3]:

+

=

mddd

mdddPk

11,).log(7456

11,).log(4.201

0

10

knnRd |,

(15)

Hence the average powers profile associated with the

resolvable MPCs are expressed in the matrix:

TPW = (16)

where is an element-by-element multiplicationoperator and

2

UWBh= .

3 Numerical Results and Discussions

In this section we illustrate the reliability of our method by

comparison with measured data as shown in Table 1. The

resultant measured and simulated channel responses are

shown in Fig. 3, 4 and 5. The measured channel is an office

lobby and the considered bandwidth is 500 MHz in the

frequency band 3.5 to 4.5 GHz for ChannelsA, B and C.

Channel A: 4 meters line-of-sight (LOS) indoor channel.

Channel B: 6 meters line-of-sight (LOS) indoor channel.

Channel C: 10 meters line-of-sight (LOS) indoor channel.

Channel A

0 5 10 15 20 25 30 35 40 45 50-20

-15

-10

-5

0

Delay(ns)

NormalizedPower(dB)

(a) MeasuredPDPat D=4m

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

Delay(ns)

Normalizedaveragepower(dB muate at =4m

Fig. 3: (a) Simulated PDP for Tx-Rx separation distance of 4m and (b) measured PDP for Tx-Rx separation distance of 4

m.

Channel B

0 10 20 30 40 50-20

-15

-10

-5

0

Delay (ns)

NormalizedPower(dB)

(a) Measured PDP at D= 6 m


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0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

1

Delay(ns)

Norm

alizedaveragepower(d

(b)SimulatedPDPat D=6m

Fig. 4: (a) Simulated PDP for Tx-Rx separation distance of 6

m and (b) measured PDP for Tx-Rx separation distance of 6

m.

Channel C

0 10 20 30 40 50 60 70 80 90

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

Delay(ns)

NormalizedPower(dB)

a easure at =10m

0 5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

Delay(ns)

Normalizedaveragepower( muae a = m

Fig. 5: (a) Simulated PDP for Tx-Rx separation distance of 10

m and (b) Measured PDP for Tx-Rx separation distance of 10

m.

Channel A D

(m)

amax

(m)

Mean no.

ofscatterers

max

(ns)

rms

(ns)

Simulation 4 7 35 9.75 3.504

Measurement 4 - - 9.9 3.660

Channel B D(m)

amax(m)

Mean no.

of

scatterers

max

(ns)

rms

(ns)

Simulation 6 10 35 13.7 4.507

Measurement 6 - - 13.5 4.701

Channel C D

(m)

amax(m)

Mean no.

of

scatterers

max

(ns)

rms

(ns)

Simulation 10 18 35 24.45 8.127

Measurement 10 - - 23.3 8.014

Table 1: Comparison between measured and simulated

models

To obtain the simulated results, the scatterers are assumed to

be uniformly distributed. This assumption and the choice of

the approximate number of scatterers arise from the

observation of the physical distributions of the various objects

in the propagation environment. Of course the use of different

statistical distributions can result in different results. Thus the

choice of appropriate distribution function must be made

carefully. In both the measured and simulated results, the

appearance of clusters can be observed. The close match

between the measured and simulated results indicates

provides the degree of confidence offered by our method.

4 Conclusion

A geometrical-based computationally tractable simulation

model for UWB channel characterization was presented. This

approach emphasizes on viewing the channel behavior from

the physical propagation point. The appearance of MPC

clusters follow naturally from the model. In a future paper we

will address the case of time-varying UWB channel using this

model. In that case the summation of MPCs that fall within

the same bin has to be carried out with consideration to the

different Doppler shifts experienced by each MPC.

Acknowledgements

The authors thank the Ministry of Higher Education

(MOHE), Malaysia for providing financial support and

wonderful hospitality through the course of this work. The

Grant (78368) is managed by Research Management Center

(RMC), Universiti Teknologi Malaysia (UTM).

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http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10511http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10511http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10511http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10511http://ieeexplore.ieee.org/xpl/RecentCon.jsp?punumber=10511

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