Maliuzhinets Diffraction Coefficient Applied to Hilly Terrain Scenario

Sanjay Soni Electronics and Electrical Communication Engg.

Indian Institute of Technology Kharagpur, India

sanjoo_ksoni@yahoo.co.uk

Amitabha Bhattacharya Electronics and Electrical Communication Engg.

Indian Institute of Technology Kharagpur, India

amitabha@ece.iitkgp.ernet.in

Abstract—In this paper, Maliuzhinets diffraction coefficient has been applied to hilly terrain propagation channel. In hill scenario, terrain is modeled as series of wedges with arbitrary angle. This needs Maliuzhinets solution with arbitrary wedge angle. The prediction result is compared with published measurement. The comparison between prediction and measurement shows good agreement

Keywords- UTD, Propagation channel,Wedge

I. INTRODUCTION

Efficient and reliable propagation model can optimize the network planning and reduce unnecessary interference. This can enhance the economy of mobile industry by providing reliable communication and by increasing number of services per cell. Deterministic propagation model is a viable and most reliable solution to modeling of wireless propagation channel [1]. Modeling of hilly terrain scenario has a special significance as in this scenario non line-of-sight (NLOS) situation is often encountered and hence the diffraction and scattering are the dominant mode of propagation. Linear-piece wise model has been widely used to model the terrain profile. Geometrical Theory of Diffraction (GTD) [2] and its extension Uniform Theory of Diffraction (UTD) [3] have been successfully tested by several authors to model irregular terrain [4-6]. In [4], [5], UTD is applied to linear piece-wise terrain model to compute pathloss. In [6], heuristic diffraction coefficient is used to model terrain structure with finite conductivity and permittivity. All these used manual linear piece-wise model. Modeling of terrain has the significant impact on the accuracy of the prediction. Several papers have appeared to show the importance of optimum linear-piece-wise model on the prediction accuracy [7]. In [7], it is emphasized that with optimum selection of linear piece-wise model, greater prediction accuracy can be obtained.

In general, the propagation environment can be modeled by lossy wedges. The rigorous solution to the imperfectly conducting wedges problem was given by Maliuzhinets [8]. The main hurdle in implementing rigorous Maliuzhinets coefficient in propagation channel tool was its computational complexity. In [9], the Maliuzhinets coefficient has been verified in urban scenario whereas in [10], it is compared with some known heuristic coefficient and it is shown that heuristic coefficients are invalid for 270 0 wedge. In hill scenario, terrain is modeled as series of wedges with arbitrary angle. This needs Maliuzhinets solution with arbitrary wedge angle. Though, simple formula for some definite shape of wedge such as 900, 1800 and 2700 are available [9], [10], but the complexity for other values of wedge angle has been a major deterrent to the use of this coefficient for propagation channel modeling. With the work reported in [11], Maliuzhinets function can be expressed in the simple cosine form, thus, making the coefficient computationally efficient.

In this paper, our goal is to verify the Maliuzhinets coefficient in hilly terrain scenario. This Maliuzhinets coefficient uses the cosine form of Maliuzhinets function given in [11]

II. UTD-LIKE MALIUZHINETS DIFFRACTION COEFFICIENT FOR DIELECTRIC WEDGE

Maliuzhinets formulation in UTD format is given as:

(1) (3) (2) (4)(n /2+ - ) (n /2- - )=(n /2- ') (n /2- ')

D D D D D� � � � � � � �� � � � � �

� � �� � � �

(1) Where is given as [3]: ( ) , 1,...4iD i �

( ) ( )

( ) 2 2 ( )0

( , , , ')-exp(-j* /4) = cot (2 sin )

2 2

i i

i i

D D L n

F kLnn k

� �� � ��

�

0 ( )F x =Transition function ___________________________________ 978-1-4244-4076-4/09/$25.00 ©2009 IEEE

2 2 (2 sin ix kLn )��

k=wave number

L = '( ' )

s ss s�

Detailed information about parameters used can be found in [9].

( )� =Auxiliary function expressed as

/ 2 0

/ 2

/ 2 0

/ 2

( ) ( / 2 / 2 ) ( / 2 / 2 ) ( / 2 / 2 ) ( / 2 / 2 )

n

n n

n

n

nnnn

�

�

�

� n

� � � � �� � � �� � � �� � � �

� � � �� � � �

� � � �� � � �

(2)

0 500 1000 15000.5

1

1.5

2

Frequency, MHz

Diff

ract

ed fi

eld,

dB

Holm's Heuristic CoefficientFDTDMaliuzhinets

Simplified analytical formulation of Maliuzhinets

function is given as [12]:

� � (2 ) / 4n /2 ( ) cos /(2 )z z

�

�� � ��

� �� � (3) where

1/v n�

A. Comparison of Maliuzhinets diffraction coefficient with FDTD for 900 wedge

In Fig. 1, the Maliuzhinets coefficient is compared with FDTD [12, Fig 8, Fig 9] for wedge angle=900, incidence angle=262.370. Both the TM and TE polarizations are considered. It is noted that the maximum error between FDTD and Maliuzhinets coefficient is 0.02 whereas there is significant discrepancy between FDTD and heuristic coefficient.

Fig.1 Maliuzhinets coefficient vs. frequency for wedge angle=90

Almost same trend is observed in Fig (4) also. Here, the gap is more pronounced in the illumination region. The significant gap can also be observed in transition region.

0,incident angle= 80 0,diffracted angle=262.37 0,TM

Fig.2 Maliuzhinet coefficient vs. frequency for wedge angle=900, incident angle=800, diffracted angle=262.37 0,TE B. Comparison between Maliuzhinets and Heuristic diffraction Coefficients [13],[14] for 1700 wedge angle

Here, Wedge=170o, incidence angle=45o. Both TE and TM mode are considered. The selection of wedge with this angle was done intentionally as it is the mostly encountered wedge in hilly scenario. Regarding Fig. 3, two points are noted: First, heuristic coefficients in illumination and deep shadow region can lead to inaccurate result. Second, even in the transition region, heuristic coefficients are predicting higher diffracted field. Hence, in the transition region, which is mostly encountered in hilly scenario, there exists significant gap between heuristic and rigorous diffraction coefficient.

0 50 100 150-100

-80

-60

-40

-20

0

Diffraction angle, degree

Diff

ract

ed fi

eld,

dB

DanielaMaliuzhinetsHolmUTD

0 500 1000 15000.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

Frequency, MHz

Diff

ract

ed fi

eld,

dB

HolmFDTDMaliuzhinets

Fig 3 Comparison of diffraction coefficients: wedge

angle=170, incidence angle=45, TM

Fig 4: Comparison of diffraction coefficients: Wedge angle=170o, incidence angle=45o, TE

C. Comparison with heuristic coefficient for 2100 wedge Interior wedges with arbitrary interior angle are often encountered in hilly scenario. It is observed that in Fig 5, the discrepancy between Maliuzhinets and heuristic coefficient is quite significant in deep shadow region.

Fig 5 Comparison of diffraction coefficients: Wedge angle=210, incidence angle=145, TM

Fig 6: Comparison of diffraction coefficients: Wedge angle=210, incidence angle=145, TE

a

MERICAL RESULTS AND DISCUSSION

tracing tool using ray tube method [16] is used to ed path for hill scenario.

Following ray types are considered: direct, reflected, reflected-reflected, reflected-diffracted, diffracted,

cted, and diffracted-diffracted. Hill is ies of wedges with arbitrary wedge angle

hilly terrain wedge: n, we consider simple hilly terrain

g linear piece-wise model, terrain is ge with wedge angle 177.60.Here, the the single dominant wedge is the n means. Pathloss prediction is done

cy 230 MHz and polarization was considered ontal.

son of prediction with Measurement [5,

mparison with hilly terrain applied to terrain in

In Fig 6, the discrepancy is significant in both illumination

III. NU

Ray trace the reflected and diffract

nd shadow region.

0 50 100 150-100

-80

-60

-40

-20

0

Diffraction angle, degree

Diff

ract

ed fi

eld,

dB

HolmMaliuzhinetsDanielaUTD

diffracted-reflemodeled as ser

A Comparison withIn this sectio

[5, Fig. 6]. Usinconsidered as wedpropagation from primary propagatioat frequenas horiz

Fig 7: CompariFig 7]

B CoThe proposed propagation model is [15, Fig.8, Fig.9] and predicted pathloss is compared with the measured results [15].In all cases, relative permittivity of 15r� � and conductivity �=0.012S/m are considered.

-2 0 2 4 6 8 10 12 14-155

-150

-145

Fig 8: Comparison of Prediction with Measurement [15, Fig 8]

0 50 100 150-80

-60

-40

-20

0

Diffraction angle, degree

Diff

ract

ed fi

eld,

dB

HolmMaliuzhinetsUTDDaniela

0 50 100 150-100

-80

-60

-40

-20

0

Diffraction angle, degree

Diff

ract

ed fi

eld,

dB

HolmMaliuzhinetsUTDDaniela

-140

-135

-130

-125

-120

receiver height above ground (m)

Pat

h Lo

ss (d

B)

MaliuzhinetsMeasurement [5] GTD

0 2000 4000 6000 8000 10000 120000

50

100

150

200

Distance from Transmitter(m)

Pat

hlos

s (d

B),H

eigh

t(m)

ath loss vs Tx-Rx distanceP

terrainMaliuzhinet modelmeasured

The receiver is allowed to move along the path profile with a height of 2.4 m above the ground whereas the transmitter has a height of 10.4m. Frequency ofoperation is 1.9GHz and vertically polarized antenna is used. In Fig 7, improvement of about 5 dB can clearly be observed when Maliuzhinets diffraction coefficient is applied to terrain structure In Fig. 8 and 9, it is observed that the proposed model closely follows the measured result. It is able to account the multipath propagation which has led to the peaks and falls in the measured result. Here, the linearized terrain profile was created manually. Further improvement in these results is possible by accurate linearized profile of the terrain as reported in [7].

Fig 9: Comparison of Prediction with Measurement [15, Fig 9]

IV. CONCLUSION In this paper, ray model based on Maliuzhinets’ coefficient has been proposed to model hilly terrain scenario. Maliuzhinets Coefficient is compared with heuristic coefficients of [13], [14] for the wedges of angle 170o and 210o , that are frequently used in hill scenario. It is shown that for 170o and 210o wedges, heuristic coefficients can lead to inaccurate result in illuminated region and shadow region respectively.

Maliuzhinets diffraction coefficient is applied to hilly terrain scenario published in [5], [15]. Predictions are found to be close to the available measurement.

It is hoped that the Maliuzhinets coefficient can be successfully used as propagation tool to accurately characterize the radio propagation channel.

ACKNOWLEDGMENT

The authors are thankful to Prof. S. Sanyal, department of Electronics and Electrical Communication Engg. IIT Kharagpur, for valuable suggestion.

REFERENCES

[1] COST Action 273, “Mobile Broadband multimedia networks; techniques, models and tools for 4G”, ISBN 0-12-369422-1(2006).

[2] J. B. Keller, “Geometrical theory of Diffraction,” J. Opt. Soc. Amer., vol. 52, no. 2, pp. 116-130, Feb 1962.

[3] R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE, vol. 62, no. 11, pp. 1448-1461, Nov. 1974.

[4] K.A. Chamberlin and R. J. Luebbers. “An evalualion of Longley-Rice and GTD propagation models,” IEEE Trans. Antennas Prop. vol. 30. pp. 1093- 1098. Nov. 1982.

[5] R. J. Luebbers. “Finite conductivity uniform GTD versus knife edge diffraction in prediction of propagation path loss,” IEEE Trans. Antennas Prop., vol. 32, pp.70-76. Jan. 1984.

[6] R. J. Luebbers. “Propagation prediction for hilly terrain using GTD wedge diffraction.” lEEE Trans. Antems propagat. vol. 32. pp. 951-955. Sep. 1984M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.

[7] Kent Chamberlin and Shahaji Bhosle, “A Robust Solution for

Preprocessin Terrain Profiles for Use With Ray-Tracing Propagation Models,” lEEE Trans. Antennas propagat., vol. 52, no. 10, Oct. 2004

[8] G. D. Maliuzhinets, “Excitation, reflection and emission of

surface waves from a wedge with given face impedances,” Sov. Phys. Dokf.,Vol.3, pp. 752-755,1958

[9] Christian Bergljung and Lars G. Olsson,“Rigourous Diffraction

coefficient Theory Applied to Street Microcell Propagation”,IEEE Global Telecommunications Conference ,1991

[10] Xiongwen Zhao, Ioannis, and Pertti Vainikainen,“A

Recommended Maliuzhinets Diffraction Coefficient for Right Angle Lossy Wedge” IEE Proceeding,2003

[11] Andrey V. Osipov A Simple Approximation of the Maliuzhinets

Function for Describing Wedge Diffraction IEEE Transactions on Antennas and Propagation, vol. 53, no. 8, Aug. 2005.

[12] Glafkos Stratis, Veeraraghawan Anantha, and Allen Taflove,“Numerical Calculation of Diffraction Coefficients of Generic Conducting and Dielectric Wedges Using FDTD” IEEE Trans. Antennas Propagat., vol. 45, no. 10, pp. 1525-1529, Aug. 1997.

[13] P. Holm, “A new heuristic UTD diffraction coefficient for nonperfectly conducting wedges,” IEEE Trans. Antennas Propagat., vol. 48, no. 8, pp. 1211–1219, Aug. 2000.

[14] Daniela N. Schettino, Fernando J.S. Moreira, Kleber L. Boges, and Cassio G. rego, “Novel heuristic UTD coefficients for the characterization of radio channels,’ IEEE Trans. Magnetics, vol. 43, no.4, pp. 1301-1304, April 2007.

[15] George Koutitas, Costas Tzaras, “Slope UTD solution for Cascade of Multishaped Canonical Objects” IEEE Trans. Antennas Propagat., vol. 54, no. 10, pp. 2969–2976, Aug. 2006.

[16] Hae-won Son and Noh-Hoon Myung, “A deterministic ray tube

method for Microcellular Wave propagation prediction model”, IEEE Trans. Antennas Prop.vol. 47, pp. 1344–1350,Aug. 1999.

0 2000 4000 6000 80000

50

100

150

200Path loss vs Tx-Rx distance

Distance from Transmitter(m)

Pat

hlos

s (d

B),H

eigh

t(m)

terrainMaliuzhinet modelmeasured