Effect of Directional Antennas at Both Ends of

the Radio Link on the Doppler Power Spectrum

Saeed Iqbal, Bilal Hasan Qureshi and Noor M. Khan, Member IEEE

Center for Advanced Research in Wireless Communications (CARWiC)

Mohammad Ali Jinnah University, Islamabad, 44000, Pakistan

saeedwattoo@gmail.com, bilal_oct@yahoo.com, noor@ieee.org

Abstract --- This paper presents the Doppler Power spectrum

density (PSD) of a cellular mobile channel when directional

antennas are deployed at both ends of the radio link. A

macrocellular environment is modeled by assuming Gaussian

and uniform scatter density around mobile station. The statistics

of angle of arrival are used to explain the Doppler power density

spectrum for macrocellular environment. Results are shown for

various scenarios and the impact of the beamwidth of the

directional antennas as well as the direction of motion of the

mobile on Doppler PSD is investigated.

I. INTRODUCTION

In wireless communication systems more attention has been

paid to minimize the interference between multipath

components. To achieve this goal directional antennas

employed at either end of the link have been shown to be

useful [1]. Moreover, the performance of wireless

communication system may be enhanced by employing

directional antennas at base station (BS) and mobile station

(MS) simultaneously. The directional antenna at BS has been

used for spatial filtering whereas directional antenna at MS

provides the selectivity of the spectrum.

In order to assess the behavior of the radio channel the

Doppler PSD may be used as the key function. In [2] the

Doppler PSD has been found with omnidirectional antennas

used at both ends of the radio link. In [3], Petrus has evaluated

the effect of directional antenna used at BS on Doppler PSD.

A similar kind of work has been done in [4] by assuming

Gaussian scatter density around MS instead of uniform scatter

density. Directional antennas have also been used in [5], to

show their effect on the Doppler PSD. Part of their work has

been corrected by Dubey et al. in [6]. Whereas, the effect of

directional antennas at MS and BS on the Doppler PSD

investigated wrongly in [5] still awaits correction. Also the

discrepancies of the first part need to be explained in a more

theoretical way.

In this paper, we investigate the effect of directional antennas

used at both ends of the radio link on the Doppler PSD of the

macrocellular mobile channel. The approach adopted in this

paper differs from the work done in [5] and [6] where the

Fig. 1 A Communication System with directional antennas at BS and MS

effect of directional antennas on Doppler PSD has been

investigated and corrected respectively. In this paper we use

the PDF of the angle of arrival (AoA) at MS and BS with

assumption of uniform and Gaussian distribution of the

scatterers around the MS while directional antennas are

employed at both ends of the radio link. Respective PDFs of

AoA seen at BS and MS have been derived in [7]. The rest of the paper is organized as follows: System Model

for Doppler spectrum is described in Section II. Results of

Doppler PSD are described in Section III. Finally conclusions

are shown in Section IV.

II. SYSTEM MODEL and DOPPLER SPECTRUM

This section presents the system model used for Doppler

spectrum while directional antennas are used at BS and MS as

shown in Fig. 1. The BS and MS are separated by distance d.

The beamwidth of the directional antennas employed at BS

and MS are and respectively. The system model shown in

Fig. 1 is similar to the model used in [7] for the derivations of

PDFs of AoA seen at BS and MS. When the directional

antennas are used at both ends of the link the scatterers inside

the region PQST would be illuminated. This illuminated

region is shown with broad line in the system model. Fig. 2

represents a situation when MS is moving with some velocity

in the direction v with respect to line-of-sight (LOS) and a

multipath coming from a scatter is shown making an angle i

with respect to LOS.

978-1-4244-4873-9/09/$25.00 ©2009 IEEE

Fig. 2 Explanation of the Geometry of MS and arrival of multipath component

It is shown in the expression below that the Doppler shift

experienced by multipath components depends upon the PDF

of AoA seen at MS as well as the direction of motion of the

mobile.

( )vimi ff ϕϕ −= cos, += −

v

m

ii

f

f ϕϕ 1cos

(1)

In above equation fm is the maximum Doppler shift. It can be

calculated as fm = ( v / ) where v is the velocity of the mobile

and is the wavelength of the carrier frequency. The Doppler

PSD using PDF of AoA is found in [2] as shown below.

( )( )

2

112

1

|cos||cos|

−

−++

=

−−

m

m

m

v

m

vio

r

f

ff

f

ff

f

ffGA

fS

ϕϕϕ ϕϕ

; | f | < fm (2)

Where f (.) is the PDF of angle of arrival seen at MS and

G ( i) is the pattern of the received antenna. In [2] it has been

shown that if only omnidirectional antennas are used then the

Doppler PSD can be expressed as show below.

( )2

2

1 −

=

m

m

or

f

ff

AfS

π

(3)

III. RESULTS And DESCRIPTIONS

The work in this Section is divided in two parts. The first part

comprised of Doppler spectrum with assumption that MS is

surrounded by uniform distributed scatterers, while the second

part illustrates the Doppler spectrum using Gaussian scatter

density.

A. Doppler PSD Using Uniform Scatter Density

The Doppler PSD can be found using PDF of AoA while

directional antennas are deployed at both ends of radio link.

The PDF of AoA using uniform scatter density found in [7] is

seen to useful in this regard. The Doppler PSD found in this

-100 -80 -60 -40 -20 0 20 40 60 80 100-50

-40

-30

-20

-10

0

10

20

30

40

Dopler frequency

PSD(d

B)

alpha = 2

alpha = 5alpha = 19

Fig. 3 Doppler PSD with v = 0o

-100 -80 -60 -40 -20 0 20 40 60 80 100-50

-40

-30

-20

-10

0

10

20

30

40

Dopler frequency

PS

D(d

B)

alpha = 2

alpha = 5alpha = 19

Fig. 4 Doppler PSD with v = 180o

way is being used to observe the effect of directional antennas

on Doppler spectrum by varying the beamwidths of the

directional antennas used at BS and MS.

≤<

+Ω

≤<Ω

=

||||;

2

tancossin

tan

-;2

)(

1

Density

2

11

Density

2

βθη

αθθα

ηθη

θθ

A

d

A

R

f

s

(4)

In the above expression the term ADensity represents the area of

the scattering region around MS whose scatterers are

illuminated as found in [7] which can be shown below.

−+−×

++

−+=

−

−

αααβ

αββα

ααα

2

2

21

2

2

212

sin1cossincossin

tancossin

tan

sin1cossincosDensity

ss

s

ss

s

R

d

R

d

dR

R

d

R

dRA

(5)

-100 -80 -60 -40 -20 0 20 40 60 80 100-40

-30

-20

-10

0

10

20

30

40

Dopler frequency

PS

D(d

B)

alpha = 2

alpha = 5alpha = 19

clark

Fig. 5 Doppler PSD with v = 90o

-100 -80 -60 -40 -20 0 20 40 60 80 100-80

-70

-60

-50

-40

-30

-20

-10

0

Dopler frequency

PS

D(d

B)

beta = 60

beta = 30

Fig. 6 Doppler PSD for v = 0oand = 60o, 30o

Combining (2) and (4), the Doppler PSD can be obtained for

mobile channel for uniform scatter density. To assess the time

variations in the channel and the effect of mobility, we assume

that mobile is moving with the velocity 54 Km/hr and the

carrier frequency is taken as 2 GHz, from this data the

maximum Doppler shit fm can easily be calculated as 100 Hz.

The distance d between BS and MS is taken as 3000m and the

radius of the scattering region is taken as 1000m for

theoretical results. The beamwidth of the MS antenna is

taken as 60o. For these parameters the maximum range of AoA

of multipath is 2 =38.9o.

We have shown the results with three direction of motion of

the mobile station v = 0o, 180

oand 90

o. These results are

shown in Fig 3 to 5, by varying the beamwidth of directional

antenna used at BS as = 2o, 5

o and 19

o for each direction of

motion of mobile. It has been observed for the direction of

mobile v = 0o

and 180o that the Doppler spectrum is shifted in

positive and negative side respectively as shown in Fig. 3 and

Fig. 4. Similarly when the mobile is moving perpendicular to

the line joining BS and MS i.e v = 90o

most of the spectral

components lies near central frequencies. Moreover it has

been observed in Fig. 5 that as we increases the beamwidth

of the directional antenna used at BS the Doppler PSD

continued towards Clark's model. It is due to the fact that with

the increase in the PDF of AoA at MS becomes more and

more uniform and flat as was explained in [7].

The behavior of Doppler PSD is shown in Fig. 6 with different

value of = 60o, 30

o for fixed value of . It has been observed

that by decreasing the spread of Doppler spectrum is

reduced significantly. The same effect can also be checked for

different values of v.

B. Doppler PSD Using Gaussian Scatter Density

The Doppler PSD can be found using PDF of AoA seen at MS

with assumption that Gaussian distributed scatterers are

present around MS. The system model shown in Fig. 1 can

also be used for Gaussian scatter density. The PDF of AoA at

MS using Gaussian scatter density around MS when

directional antennas are used at both ends of the link is found

in [7] is written in (6).

Combining (2) and (6) we get the expression for Doppler PSD

which is being used to observe the effect of directional

antennas. To check the performance of the system we have

_______________________________________________________________________________________________________

( )

( ) ( ) ( ) ( )( )

( )

( ) ( )

( ) ( ) ( ) ( )( )

( )

||||;

sin1cos

sin

cossin2

sincscerf4

sin1cos

sincos8

2

sincscerf

;

sin1cos

sin

cossin2

sincscerf4

sin1cos

sincos8

22erf

)(

1

2

22

2

12

2

222

12

2

2

11

2

22

2

12

2

222

12

22

≤<

−−−++−−

+Ω

≤<−

−−−++−−

Ω

=

−−

−−

βθη

αα

α

βσ

αβασααασ

σαθασ

ηθη

αα

α

βσ

αβασααασ

σ

θθ

s

s

s

s

ss

s

s

s

s

s

s

s

ss

s

s

R

d

R

d

d

R

d

R

d

d

R

d

R

d

d

R

d

R

d

f

(6)

-100 -80 -60 -40 -20 0 20 40 60 80 100-40

-35

-30

-25

-20

-15

-10

-5

0

5

Dopler frequency

PS

D(d

B)

alpha = 2

alpha = 5alpha = 10

Fig. 7 Doppler PSD with v = 0o

-100 -80 -60 -40 -20 0 20 40 60 80 100-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

Dopler frequency

PSD(d

B)

alpha = 2

alpha = 5alpha = 10

Fig. 8 Doppler PSD with v =180o

shown the theoretical results with d = 2000 m, s = 400 m,

Rs = 400 m and maximum Doppler shift fm is taken as 100Hz.

Plots of the Doppler PSD are presented in Fig. 7 and Fig. 8

with two values of direction of motion of the mobile i.e.

v = 0o

and 180o. The results are obtained for fixed value of

= 60o and varying values of = 2

o, 5

o, and 10

o. In Fig. 9 the

results are also presented for the same data set with v =90o.

The results show that the behavior of the Doppler PSD can be

explain in the same manner as it has been done in case of

uniform scatter density. The effect of changing the beamwidth

is elaborated in Fig. 10 for fixed values of with v = 0o. It

can be seen that by decreasing the Doppler PSD has been

reduced significantly. It can also be checked for other values

of v.

IV. CONCLUSION

In this paper the effect of directional antennas at MS and BS

on Doppler PSD has been observed assuming uniform and

Gaussian distribution of scatterers around MS. The approach

adopted in this paper differs from the work done in [5] and [6],

where the effect of directional antennas on Doppler PSD has

been investigated and corrected respectively. The results have

been shown for uniform and Gaussian scatter density by

varying the beamwidths of antennas and direction of motion of

the MS simultaneously.

-100 -80 -60 -40 -20 0 20 40 60 80 100-80

-60

-40

-20

0

20

40

Dopler frequency

PS

D(d

B)

alpha = 2

alpha = 5alpha = 19

clark

Fig. 9 Doppler PSD with v = 90o

-100 -80 -60 -40 -20 0 20 40 60 80 100-45

-40

-35

-30

-25

-20

Dopler frequency

PS

D(d

B)

beta = 30

beta = 60

Fig. 10 Doppler PSD for v = 0o and = 60o , 90o

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statistical macrocell channel model for mobile environments"

IEEE Trans. Commun., vol. 50, no. 3, pp. 495-502, March 2002. [4] C. A . Lopez, D. H. Corvarrbias, D. Munoz and M. A. Panduro

"Statistical cellular Gaussian Scatter density channel model

employing a directional antenna for mobile environments" Int. J. Electron. Commun. vol. 59 pp. 195-199, 2005

[5] C. Q. Le, S. Yoshida "On the Doppler Power Spectrum at the

Mobile Unit Employing a Direction Antenna" IEEE Commun. Letter., vol. 5, no. 2, January 2001.

[6] W. Teck, V. K. Dubey “Comment on “On the Doppler Power Spectrum at the Mobile Unit Employing a Direction Antenna"

IEEE Commun. Letters., vol. 6, no.11, pp. 472-474 November,

2002. [7] Bilal Hasan Qureshi, Saeed Iqbal and Noor M. Khan "Effect of

Directional Antennas at Both Ends of the Link on the Spatial

Characteristics of Cellular and Mobile Channel", Accepted in 5th

International IEEE Conf. on Emerging Technol., October, 2009.