Indi an Jo urnal o f Radio & Space Phys ics Vo l. 33, June 2004, pp. 180- 184

Double knife edge diffraction propagation studies over irregular terrain

M V S N Prasad 1• S V Bhaskara Rao2

, T Rama Rao3, S K Sarkar1 & Suresh Sharma4

1Radio & Atmospheric Sc iences Di visio n, National Phys ical Laboratory, Dr K S Kri shnan Road, New Delhi 11 0 0 12

E-mai 1: mvprasad @ mail.nplindia.ernet.in 2Department o f Physics, S V Uni versity, Tirupati 5 17 502

3Departmatode Teoria de Ja Senaly Communications, Uni versidad Carlos lii de Madrid , Spai n 4 Direc torate of All India Radio, Prasar Bharati , Parliament Street, New De lhi 110 00 1

Received 27 May 2003: revised 18 August 2003; accepted 30 December 2003

Mountain c li ffs constituting knife edges inOuence radio wave propagating fro m VH F to microwave frequenc ies. The d iffraction phenomena caused by these sing le or multi ple kn ife edges are a do minant propagation mechanism that has to be taken into account in planning TV, FM networks, ce llul ar radio, microwave network, e tc., in mountainous regions. In order to in vesti gate the above mechani sm fi e ld strength measurements were conducted over fi ve double knife edge paths and the measured signal levels are compared with several predic ti on techniques. T he deviations of the predic tio n techni ques and their suitabil ity are presented in this paper. It is seen that out of a ll the predic tion methods G iovane ll i's method gives best agreement with the observed results.

Keywords: Kn ife edge diffrac tion, Field strength measurements, Path loss, Pred ic tion techniques PACS No.: 92.60.Ta; 94. 10.Gb; 84.40.Ua IPC Code: H 04 H 1/00; H 04 B 7/00; G 01 S 1/08

1 Introduction Radio wave propagati o n o ve r irregular terrai n

consisting o f mounta ins and hill s is o f considerable interes t to comm un icatio n eng ineers in volved in planning TV, FM and mobil e co mmunicati on ne tworks. At VHF and UH F, propagati on by diffrac ti on over terra in obstructions can be impo rtan t at larger di s tances. Cellular mobile radio, mi crowave links utili zing mounta in c liffs as knife edges can communi cate signals us ing di ffractio n as the propagatio n mechani sm. Thi s is evident in urban mobile radi o predicti on methods where vari ous bu ildings are taken as knife edge obstac les' . 1n another approach kn ife edges were replaced by wedges to model obstacles in the te rra in pro fil es2

. The ri s ing and falling terrain is approximated by a wedge and Lopez3 presented formulae fo r ca lcul ating the signal strength using wedge diffractio n and es timated the effec ts of shadowing caused by ri sing and fa lling terrain between base s tati o n and use r. In micro cellul ar propagati on where base s tatio n antenn a he ig t is less than roof- to p he ight , diffrac ti on caused by the bu ild ings becomes the dominant propagati on mechanis nf 1

. In dealing with te rrain di ffraction, Whitteker5 underlines the impo rtance o f physica l opti cs principles, especially w hen the terrain or

buildings o n it can be modelled as kni fe edges. In the present study an atte mpt is made to evaluate di ffe re nt do uble knife edge diffractio n predictio n techniques by comparing them with experimenta lly observed field strength values o ver five paths in western Indi a.

2 Experimental details Fi eld strength measurements were conducted over

multiple kn ife edge paths (mostly double) utili z ing Mumbai (earlier known as Bo mbay) and Pune TV

transmi ss ions. Measurements were conducted over fi ve paths, four around Mumbai transmitter and one around Pune transmitter. The Mumbai TV transmitte r operated on channel-4 (61-68 MHz band) and Pune TV transmitter operated o n channel-S (174- I 8 1 MHz) with effecti ve isotropic radiated power (EJRP) o f 5.6 and 7.2 kW, respective ly . The antenna gains o f Mumbai and Pune transmitter are 7 dB and 8 dB , respecti vely. At a g iven site, 50 samples of signal level, each of 15 min duratio n, were collected. Final signal level was averaged over the entire period. A ll the path profiles are sho wn in Figs I -5 . They are M umbai-Kasara, Mumbai-Karj at, Mumbai-Chauk, Mumbai -Bulsar, Pune (Simhagarh)-M ahabaleswar. A ll these pl aces are located in wes tern Indi a.

PRASAD eta/.: KNIFE EDGE DIFFRACTION PROPAGATION STUDIES OYER IRREGULAR TERRAIN 181

T-MUMBAI 700 R-KASARA

E t-.:'50() X C)

i:i;,oo X

100

20 0 40 60 DISTANCE 1 km

Fig. !-Path profile between Mumbai and Kasara

900

E

0

T-MUMBAI R- KARJAT

20 40 DISTANCE

1 km

60

Fig. 2-Path profile between Mumbai and Katjat

3 Prediction techniques

80

The field strength values are converted into path loss values using transmitter power and gain of antennae, and compared with the path loss values deduced from different prediction methods. The prediction methods utilized in the present study are: (i) Epstein-Peterson6 (i i) ITU-R (Ref.7), (iii) Deygout8,

(iv) Edward and Durkins9 and (v) Giovanelli 10.

3.1 Epstein-Peterson method

In this method, ground reflections are neglected and the overall propagation loss is calcul ated as the sum of propagation factors for each obstacle. In the case oft wo obstacles the diffraction loss is calcu Ia ted as

... (I)

where a 1 is the distance between the transmitter and centre of the first knife edge, a2 the distance between the first and second knife edges, II 1 is the height of the first knife edge from the line joining the transmitter to second knife edge, lz 2 is the height of second knife

T-MUMBAI R-CHAUK

32 64 96 DISTANCE, km

Fig. 3-Path profile between Mumbai and Chauk

edge from the line joining first knife edge and the receiver point. The function F(a,b,h) is the well­known Fresnei-Kirchhoff diffraction propagation facto r for a perfectly absorbing knife edge. This is g iven by

F(a,b,!J)=-6.02-9.!1 V+ 1.27 vforO~ V<2.4

=-12.95-201og 10 (v)for v>2.4 ... (2)

where v is the well-known terrain diffraction parameter. It is defined as

... (3)

Here, h is the height of obstacle from the transmitter­receiver line, and a~. a 2 are defined above. This method tends to overestimate the diffraction loss of two or more knife edges, especially, if they are nearly in line-of-s ight range.

3.2 ITU-R method

Here also the diffraction parameter is calculated as in the above case. Utilizing that the terrain diffraction loss is calculated as

182 INDIAN J RADIO & SPACE PHYS, JUNE 2004

700 E - 500

1-J: Cl

1.1.1 :r 100

DISTANCE, km

T-MUMBAI R-BULSAR

Fig. 4- Path pro lile between Mumbai and Bulsar

R-MAHABALESHWAR T -SIMHAGARH

1~00

1300

E ~ 1100

1-J: <.!) 900 Ul J:

700

!500

10 0 10 30 DISTANCE, km

70

Fig. 5- Path prolile between Pune and Mahabaleshwar

J(v) = 6.4 + 20 log [ ( v" + 1) 112 + v] dB ... (4)

This loss is added to free-space loss to give total loss .

3.3 Edward and Durkin 's method Here again the terrain di ffraction parameter is

defined as in the Epstein- Peterson method. The total loss is the sum of free-space loss and terrain diffraction loss. The terrain diffraction loss is given by

Floss = 20 log10 (E!Eo ) ... (5)

where E/£0 is the ratio of field strength at the recei ving point to its free-space value. This is g iven by Fresnel integral

E!E0 =(l+i)!2J; e-;<nt 2Jv dv ... (6)

This holds good for the va lues of v in the range 0 ~ v < 2. For values of v > 2, E/£0 is approximated as E/£0 = 0.225/v; ... (7)

3.4 Deygout's method Here also the to tal path loss is the sum of free space

loss and terra in diffraction loss . The terrain diffraction parameter is defined a

.. . (8)

where f is the frequency in MHz. This differs from that defined earlier by a factor of ...J2.

For h > V; , the terrain d iffraction loss is g iven by

F = 20 log 10 (hlv) + 16 ... (9)

3.5 Giovanelli's method The terrain diffraction parameter is calculated in

the same manner as that of Epstei n-Peterson method. Heights of obstacles from the transmitter-receiver line and their distances are calculated also in the same manner. The obstacle whi.ch has the larger individual loss, i.e. the greatest ra tio of hlr, where r is the radius of the first Fresnel zone at the position of the hill , is considered as the main obstacle. Its associated diffraction loss is computed first, as if that hill is alone, using the Fresnei-Kirchhoff fo rmulation for a single edge as in the case of Edward and Durkin 's method. The diffraction loss associated with the second obstacle is then computed by considering the propagation path between the top of the main obstacle and the receiving point, with an effective height h1 for the secondary obstacle. The overall path loss is then the composite of these individual losses.

4 Results and discussion The methods of Epstein-Peterson and Giovanelli

compute multiple knife edge diffraction in different manners. Giovanelli uses modifed Deygout procedures by introducing a kind of virtual transmitter and receiver antenna he ight. In the case of Deygout' s method, path losses are calculated using both sol ution

PR ASAD er a/.: KNI FE EDGE DIFFRACTION PROPAGATION STUDIES OVER IRREGULAR TERR AIN 183

C and solution D and final path loss is the average o f losses due to both the methods. Solution B is based on the approach of Bullington and solution C is based un the approach of Epstein-Peterson. Deygout's own approach is class ified as so lution D. In the case of solution C the total di ffrac tion loss due to both the obstacles are calculated separately as if they are ex isting separate ly and the total loss is obtained by adding the indi vidual losses . In the case of solution D, the obstacle which has the g reatest rati o lzlr (where It is the height and r is the rad iu s o f Fresnel zone, i.e., the main indi vidual loss), is calllecl the main hill and its associated di ffraction loss is computed first as if that hill was alone. The diffraction loss associ ated with the second obstacle is then computed by considering the propagation around receiver and first obstacle with virtual sources above the main obstac le.

Solutions fo r the case of two or more edges have been availabl e. Nevertheless, different approxima­tions to the problem have been suggested and because of the length and mathematical intricacy of the exact solution their use has become w idespread. Existing predi ction models diffe r in their applicability; others are restri cted to more speci fie situations. What is certain is that there is no one mode l which stands out as being idea lly to a ll environments. The use of diffraction calculations based on kni fe edge theory to account fo r losses caused by real obstacles and the empirical methods of estimating losses over paths with many obstruc tions are de monstrably unjustifi abl e on any grounds other than they prov ide a reasonably accurate, simple and effi c ient solution 11

•

The extension of the sing le knife edge diffracti on theory to two or three or more obstac les is not an easy task. The problem is complicated mathe mati cally , but reduces to a double integral of the Fresnel fo rm over a plane above each kni fe edges. Bullington's method 12

is very simple, but almost in vari ably produces results that underes timate the path loss. The primary limitation of Bullington's method, that the important obstac les can be ignored is overcome by Epste in­Peterson technique, which computes the attenuation due to each obstac le in turn and sums them up to obtain the overall loss. Japanese postal service 13

proposed a technique, which is simil ar in concept to Epstein-Peterson method . Deygout 's method gives good agreement with the ri gorous theory for two edges, but overestimates the path loss when multi ple obstacles are close together. Gi ovane lli has devi sed a techn ique, an approach using a di fferent geometry whi ch maintains the proper diffraction angles and

remains in good agreement w ith the values obtained by Vogler even when several obstructi ons are considered. Vogler presented a complete representation of multiple edge di ffracted field where the attenuation fun ction is expressed as a multi ple integral whose dimension is equal to the nu mber of edges 14

• But the method is cumbersome fo r implementation. Thi s method is regarded as a reference for comparing other methods because of its accuracy. It is usually di scarded fo r practi ca l system predic ti on due to large computati on time and complex prediction procedure. The UTD (uniform theory of diffraction) method is charac terized by same accuracy as the Vogler' s solution. Gi ovane lli 's method can be extended to paths w ith several obstacles, incl uding sub-path obstacles.

Table 1 shows the five paths, their d istances, free­space losses, observed losses relati ve to free-space, di ffraction parameter (defined in the predict ion methods) and the predicted path losses clue to Epstei n­Peterson, IT U-R, Deygout , Eclwarcl-Durkins and Giovanelli methods. Epstein-Peterson method gives reasonable agreeme nt in the case o f Mumbai-Kasara (erro r = Pc - P111 is - 0 .63 dB , where Pc is calculated path loss and Pm the path loss dcclucecl from measure ments of signal levels) and Mumbai-Ka1jat (error is - 3.32 dB ). The same method gives large deviations in the case of Mumbai-Chauk (error is -11 .33 dB), Mumbai-Bulsar (eiTor is + 52.29 dB) and Pune-Mahabaleshwar (erro r is + 15.25 dB). A perusal of the Table I and errors showed that Epstein­Peterson method gives good agreement in those paths which are hav ing prominent knife edges (indi cated by the large values of d iffraction parameter). T he largest devi ation of 52.29 dB is observed in the case of Mumbai-Bulsar path . In thi s case there are fo ur knife edges. It appears that the method is suitable fo r paths hav ing not more than two knife edges and moderate di stances (less than 100 km). The dev iati on of ITU-R method precisely fo llows the same trend of Epstein­Peterson method. Deygout ' s method gives poor agreement with all. The largest dev iati on is seen for Mumbai-Karsat (erro r is -23.73 dB) and Mumbai ­Chauk (error is - 24 .00 dB) and the smalles t dev iation fo r Pune-Mahabaleswar paths (erro r is + 2.52 dB) . Edward-Durkin ' s method g ives reasonable agreement fo r paths I ,2,3 with a deviation of around 5 dB and shows largest dev iat ion of- 68.48 dB fo r Mu mbai­Bulsar path and a dev iati on of +2 1 dB fo r Pune­Mahabaleswar path. Gi ovanelli 's method gives a dev iat ion of 0.87 dB fo r Mumbai -Kasara path. 10 dB

184 INDIAN J RADIO & SPACE PHYS, JUNE 2004

Table !- Comparison of observed and predicted path losses for five knife edge diffraction paths along with path characteristics

Path Distance Free-space Diffr Observed Epstein- ITU-R Deygout Edward & Giovanelli km loss( dB) parameter loss( dB) Peterson Durkins

Mumbai - Kasara 97 108.4 0.77 34.10 33.46 33.50 46.41 39.28 34.97 2.57

Mumbai- Ka~jat 55 103.45 1.80 47.03 43.71 43.12 23.30 56.61 37.71 4.18

Mumbai- Chauk 47 102. 10 2.50 42 .39 31.06 31.18 18.40 36.48 45.13 0.48

Mumbai- 13ulsar 170 113.26 1.98 42.22 94.50 94.42 24.33 110.70 42.50 3.6

6.67 3.28

Pune- Mahabaleshwar 48 111.90 0.71 22.68 37.93 37.80 25.20 43.66 55.31

for Mumbai-Katjat path, 2.74 dB for Mumbai-Chauk path and 0.28 dB for Mumbai-Bulsar path . This method gives very good agreement for all the paths except the Pune-Mahabaleswar path, where a deviation of + 32 dB was observed (the deviation otherwise is less than one dB). Hence, this method is found to be more suitable.

Tzaras and Saunders 15 conducted extensive investigations with the help of 20,000 path profiles and the comparison of measurements with predicted methods showed that Deygout and Giovaneli solutions were very sensitive to the number of edges selected for prediction . They concluded that these methods cannot be regarded as reliable since it is difficult to know how many edges have to be considered. These types of extensive investigations were not possible in this country due to lack of infrastructure and other facilities. According to them 15

, slope-UTD and Vogler's methods gave high accuracy and computation time is very high for these methods. Causebrook's method performed better than Deygout and Giovanelli. For the total number of sites the Causebrook solution had a standard deviation o:F error of approximately 8 dB with a mean error of -3 dB , whereas the Vogler and slope-UTD solutions had a standard deviation of prediction error of 7.5 dB with a mean error of - 1.8 dB and -2 dB, respectively. Deygout and Giovanelli have performed poorly when large number of edges are involved.

5 Conclusions A comparison of double knife edge diffraction

prediction techniques is carried out by comparing the predicted losses against the path losses deduced from the experimental measurements conducted in western India. Whenever the number of knife edges are more,

like in the case of Mumbai-Bulsar the total path loss in the case of Epstein-Peterson and Edward-Durkins and also ITU-R methods are much more than the observed loss. The Epstein-Peterson method gives good agreement when the knife edges are prominent. Out of all the methods Giovanelli's method gives best agreement and can be used for predicted losses for designing diffraction links over mountainous regions.

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