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Rec. ITU-R P.526-8 1

RECOMMENDATION ITU-R P.526-8

Propagation by diffraction

(Question ITU-R 202/3

(!"#8-!"82-!""2-!""$-!""5-!""#-!"""-200!-2003

T%e ITU R&'ioo))uni&tion Asse)*+,

considering

& t%&t t%ee is & nee' to oi'e en1ineein1 ino)&tion o t%e &+u+&tion o ie+' sten1t%s

oe 'i&tion &t%s

recommends

1 t%&t t%e )et%o's 'esi*e' in Anne ! *e use' o t%e &+u+&tion o ie+' sten1t%s oe

'i&tion &t%s 4%i% )&, in+u'e & s%ei&+ e&t% su&e o ie1u+& te&in 4it% 'ieent

in's o o*st&+es.

Annex 1

1 Introduction

A+t%ou1% 'i&tion is o'ue' on+, *, t%e su&e o t%e 1oun' o ot%e o*st&+es &ount )ust

*e t&en o t%e )e&n &t)os%ei e&tion on t%e t&ns)ission &t% to e&+u&te t%e 1eo)eti&+

&&)etes situ&te' in t%e eti&+ +&ne o t%e &t% (&n1+e o 'i&tion &'ius o u&tue %ei1%t

o o*st&+e. o t%is uose t%e &t% oi+e %&s to *e t&e' 4it% t%e &oi&te e7ui&+ent E&t%

&'ius (Reo))en'&tion ITU-R P.83$. I no ot%e ino)&tion is &&i+&*+e &n e7ui&+ent E&t%

&'ius o 8500 ) )&, *e t&en &s & *&sis.

2 Frene! e!!ipoid and Frene! "one

In stu',in1 &'io4&e o&1&tion *et4een t4o oints A &n' t%e inteenin1 s&e &n *e

su*'ii'e' *, & &)i+, o e++isoi's no4n &s esne+ e++isoi's &++ %&in1 t%ei o&+ oints &t A

&n' su% t%&t &n, oint M on one e++isoi' s&tisies t%e e+&tion9

2AMAM

+=+ n (!

4%ee nis & 4%o+e nu)*e %&&tei:in1 t%e e++isoi' &n' n=! oeson's to t%e ist esne+

e++isoi' et. &n' is t%e 4&e+en1t%.

As & &ti&+ u+e o&1&tion is &ssu)e' to ou in +ine-o-si1%t i.e. 4it% ne1+i1i*+e 'i&tion

%eno)en& i t%ee is no o*st&+e 4it%in t%e ist esne+ e++isoi'.

T%e &'ius o &n e++isoi' &t & oint *et4een t%e t&ns)itte &n' t%e eeie is 1ien *, t%e

o++o4in1 o)u+&9

2/!

2!

2!

+=

dd

ddnRn (2

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2 Rec. ITU-R P.526-8

o in &ti&+ units9

2/!

2!

2!

(550

+

=fdd

ddnRn (3

4%ee f is t%e e7uen, (M;: &n' d! &n' d2&e t%e 'ist&nes () *et4een t&ns)itte &n'eeie &t t%e oint 4%ee t%e e++isoi' &'ius () is &+u+&te'.

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Rec. ITU-R P.526-8 #

[ ]$/!=

223/!=/000!8(!=((36.0 ffaK eH +=

($&

[ ]2/!

22 /000!8( fKK HV +=(5&

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* Rec. ITU-R P.526-8

4%ee9

ae9 eetie &'ius o t%e E&t% ()

9 eetie e+&tie e)ittiit,

9 eetie on'utiit, (;: !0 >;:

5

2

2

5

2

5

2

5

!0

!

=2!0

=3!0

=!!0

=30=!0 =2

=3=!0 =$=!5

=!0 =3

=30=!0 =2

=3=!0=$

=!5=!0=3

I>URE !

+a!cu!ation of K

=80=5

No.)&+i:e'2&to.2o.su.2&e&')itt&ne-K

e7uen,

@eti&+

;oi:ont&+

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Rec. ITU-R P.526-8 5

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6 Rec. ITU-R P.526-8

IKis +ess t%&n 0.00! t%e e+eti&+ %&&teistis o t%e E&t% &e not i)ot&nt. o &+ues o K

1e&te t%&n 0.00! t%e &oi&te o)u+&e 1ien *e+o4 s%ou+' *e use'.

#.1.2 $iffraction fie!d trengt& for(u!ae

T%e 'i&tion ie+' sten1t%E e+&tie to t%e ee-s&e ie+' sten1t%E0 is 1ien *, t%e o)u+&9

'(((+o120 2!0

YGYGXFE

E++= (6

4%eeXis t%e no)&+i:e' +en1t% o t%e &t% *et4een t%e &ntenn&s &t no)&+i:e' %ei1%ts Y!&n' Y2

(&n' 4%ee +o120 E

is 1ene&++, ne1&tie.

In se+-onsistent units9

da

X

e

3/!

2C

= (#

ha

Y

e

3/!

2

2C2

= (8

o in &ti&+ units9

dafX e3/2=3/!C2.2= (#&

hafY e3/!=3/23=

C!06." = (8&

4%ee9

d

9 &t% +en1t% ()

ae9 e7ui&+ent E&t%s &'ius ()

h

9 &ntenn& %ei1%t ()

f9 e7uen, (M;:.

is & &&)ete &++o4in1 o t%e t,e o 1oun' &n' o o+&i:&tion. It is e+&te' to K*, t%e

o++o4in1 se)i-e)ii&+ o)u+&9

$2

$2

35.!5.$!

#5.06.!!

KK

KK

++

++= ("

o %oi:ont&+ o+&i:&tion &t &++ e7uenies &n' o eti&+ o+&i:&tion &*oe 20 M;: oe +&n'

o 300 M;: oe se& )&, *e t&en &s e7u&+ to !.

o eti&+ o+&i:&tion *e+o4 20 M;: oe +&n' o 300 M;: oe se& )ust *e &+u+&te' &s &

untion oK. ;o4ee it is t%en ossi*+e to 'ise1&' &n' 4ite9

3/53/2

28".6

fkK

("&

4%ee is eesse' in

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7/27

Rec. ITU-R P.526-8 ,

T%e 'ist&ne te) is 1ien *, t%e o)u+&9

XXXF 6.!#=(+o1!0!!( += (!0

T%e %ei1%t 1&in te) G(Y is 1ien *, t%e o++o4in1 o)u+&e9

8=!.!=(+o15=!.!=(6.!#(2/!

YYYG o Y > 2 (!!o Y

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8 Rec. ITU-R P.526-8

0526-02

!00

"0

80

#0

60

50

$0

30

20

!0

!5

!00"0

80

#0

60

50

$0

30

20

!0

!5

8

"

!50

200

300

$00

500

600

#00

800

"00! 000

!

2

3

$

5

6

#

8

"

20

!5

!0

5

0

= 5

= !0

= !5

= 20

= !0

= !5

= 20

= 25

= 30

= 35

= $0

= 50

= 60

= #0

= 80

= "0

= !00

= !50

= 200

= 250

= 300

= 35030

$0

50

60

#0

80

"0!00 M;:

!50

200

300

$00

500

600

#00

800

"00! >;:

2

3

$

5

6

#

8

"!0 >;:

!5

>;: !0"

8

#

6

5

$

3

2

"00

800

#00

600

500

$00

300

200

!50

M;: !00"0

80

#0

60

50

$0

30

>;: !

20

I>URE 2

$iffraction by a p&erica! eart& effect of ditance

!.5

!.5

!.5

6.e7uen,2o.kF!

6.e7uen,2o.kF$/3

Dist&ne(5)

Ge0e

+('8in.e+&tionto2.ees&e

;oi:ont&+ o+&i:&tion oe +&n' &n' se&@eti&+ o+&i:&tion oe +&n'

(T%e s&+es oine' *, &o4s s%ou+' *e use' to1et%e

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9/27

Rec. ITU-R P.526-8

0526-03

2 000

! 500

! 000"00

800

#00

600

500

$00

300

200

!50

!00"0

80

#0

60

50

$0

30

20

!5

!0"

8

#6

5

$

3

!80

!60

!$0

!20

!00"0

80

#0

60

50

$0

30

20

!0

0

= !0

= 20

= 30

!5

>;: !0"

8

#

6

5

$

3

2

"00

800

#00

600

500

$00

300

200

!50

M;: !00"0

80

#0

60

50

$0

30

30

$0

50

60

#0

80

"0!00 M;:

!50

200

300

$00

500

600

#00

800

"00! >;:

2

3

$

5

6

#

8

"

!0 >;:

!5

>;: !

!.5

!.5

I>URE 3

$iffraction by a p&erica! eart& &eig&t-gain

;ei1%t o &ntenn&&*oe 1oun' ()

;ei1%t-1&in (';(h

;oi:ont&+ o+&i:&tion = +&n' &n' se&@eti&+ o+&i:&tion = +&n'

e7uen, o

k =! k F $/3

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10/27

1/ Rec. ITU-R P.526-8

0526-0$

!00

"0

80

#0

60

50

$0

30

20

!0

!5

!00"0

80

#0

60

50

$0

30

20

!0

!5

8

"

!50

200

300

$00

500

600

#00

800

"00! 000

!

2

3

$

5

6

#

8

"

20

!5

!0

5

0

= 5

= !0

= !5

= 20

= !0

= !5

= 20

= 25

= 30

= 35

= $0

= 50

= 60

= #0

= 80

= "0

= !00

= !50

= 200

= 250

= 300

= 350

>;: !0"

8

#

6

5

$

3

2

"00800

#00

600

500

$00

300

200

!50

M;: !00

"0

80

#0

60

50

$0

30

30

$0

50

60

#0

80

"0

!00 M;:

!50

200

300

$00

500

600

#00

800

"00! >;:

2

3

$

5

6

#

8

"!0 >;:

!5

>;: !

I>URE $

$iffraction by a p&erica! eart& effect of ditance

6.e7uen,2o.kF!

6.e7uen,2o.kF$/3

Dist&ne(5)

G

e0e+('8.e+&ti0eto2.ees&e

@eti&+ o+&i:&tion oe se&

(T%e s&+es oine' *, &o4s s%ou+' *e use' to1et%e

!.5

!.5

!.5

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Rec. ITU-R P.526-8 11

0526-05

2 000

! 500

! 000

"00

800

#00

600

500

$00

300

200

!50

!00"0

80

#0

60

50

$0

30

20

!5

!0"

8

#6

5

$

3

!80

!60

!$0

!20

!00"0

80

#0

60

50

$0

30

20

!0

0

= !0

= 20

= 30

A

!00 M;:

! >;:

!0 >;:

!5

>;: !0"

8

#

6

5

$

3

2

"00

800

#00

600

500

$00

300

200

!50

M;: !00

"0

80

#0

60

50

$0

30

30

$0

50

60

#0

80

"0

!50

200

300

$00

500

600

#00

800

"00

2

3

$

5

6

#

8

"

!5

>;: !

!.5

!.5

I>URE 5

$iffraction by a p&erica! eart& &eig&t-gain

;ei1%t o &ntenn&&*oe 1oun' ()

;ei1%t-1&in (';(h

@eti&+ o+&i:&tion = se&

e7uen, o

k F ! kF $/3

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12 Rec. ITU-R P.526-8

* $iffraction o%er obtac!e and irregu!ar terrain

M&n, o&1&tion &t%s enounte one o*st&+e o see&+ se&&te o*st&+es &n' it is useu+ to

esti)&te t%e +osses &use' *, su% o*st&+es. To )&e su% &+u+&tions it is neess&, to i'e&+i:e

t%e o) o t%e o*st&+es eit%e &ssu)in1 & nie-e'1e o ne1+i1i*+e t%iness o & t%i s)oot%o*st&+e 4it% & 4e++-'eine' &'ius o u&tue &t t%e to. Re&+ o*st&+es %&e o ouse )oe

o)+e o)s so t%&t t%e in'i&tions oi'e' in t%is Reo))en'&tion s%ou+' *e e1&'e' on+, &s

&n &oi)&tion.

In t%ose &ses 4%ee t%e 'iet &t% *et4een t%e te)in&+s is )u% s%ote t%&n t%e 'i&tion &t%

it is neess&, to &+u+&te t%e &''ition&+ t&ns)ission +oss 'ue to t%e +on1e &t%.

T%e '&t& 1ien *e+o4 &+, 4%en t%e 4&e+en1t% is &i+, s)&++ in e+&tion to t%e si:e o t%e

o*st&+es i.e. )&in+, to @; &n' s%ote 4&es (f>30 M;:.

*.1 0ing!e nife-edge obtac!e

In t%is ete)e+, i'e&+i:e' &se (i1s. 6& &n' 6* &++ t%e 1eo)eti&+ &&)etes &e o)*ine'

to1et%e in & sin1+e 'i)ension+ess &&)ete no)&++, 'enote' *, 4%i% )&, &ssu)e & &iet, o

e7ui&+ent o)s &o'in1 to t%e 1eo)eti&+ &&)etes se+ete'9

+

=

2!

!!2

ddh (!3

+

=

2!

!!

2

dd

(!$

H,osi1nt%e%&s(2

hh

= (!5

&n'osi1nt%e%&s(2

2!2! = d

(!6

4%ee9

h

9 %ei1%t o t%e to o t%e o*st&+e &*oe t%e st&i1%t +ine oinin1 t%e t4o en's o

t%e &t%. I t%e %ei1%t is *e+o4 t%is +ine his ne1&tie

d!&n'd29 'ist&nes o t%e t4o en's o t%e &t% o) t%e to o t%e o*st&+e

d9 +en1t% o t%e &t%

9 &n1+e o 'i&tion (&'B its si1n is t%e s&)e &s t%&t o h. T%e &n1+e is

&ssu)e' to *e +ess t%&n &*out 0.2 &' o ou1%+, !2

!&n'29 &n1+es *et4een t%e to o t%e o*st&+e &n' one en' &s seen o) t%e ot%e en'.

!&n' 2&e o t%e si1n o hin t%e &*oe e7u&tions.

NOTE ! = In e7u&tions (!3 to (!6 in+usie h d d! d2&n' s%ou+' *e in se+-onsistent units.

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Rec. ITU-R P.526-8 1#

0526-06

h > 0

> 0

2

d2

&

!

d!

d2

d!

h

R

! 2

d

!d!

h 0

< 0

2

*

d2

I>URE 6

2eo(etrica! e!e(ent

! 2 ! 2(o 'einitions o , , , d d d &n'R,see A $.! &n' $.3

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1* Rec. ITU-R P.526-8

i1ue # 1ies &s & untion o t%e +oss (' &use' *, t%e esene o t%e o*st&+e. o 1e&te

t%&n =0.# &n &oi)&te &+ue &n *e o*t&ine' o) t%e eession9

'8!.0=!!.0=(+o120".6(2

+++=J (!#

0526-0#

= 3 = 2 = ! 0 ! 2 3

= 2

0

2

$

6

8

!0

!2

!$

!6

!8

20

22

2$

J(('8

I>URE #

3nife-edge diffraction !o

*.2 Finite-4idt& creen

Inteeene suession o & eeiin1 site (e.1. & s)&++ e&t% st&tion )&, *e o*t&ine' *, &n

&tiii&+ seen o inite 4i't% t&nsese to t%e 'ietion o o&1&tion. o t%is &se t%e ie+' in

t%e s%&'o4 o t%e seen )&, *e &+u+&te' *, onsi'ein1 t%ee nie-e'1es i.e. t%e to &n' t%e

t4o si'es o t%e seen. Constutie &n' 'estutie inteeene o t%e t%ee in'een'entonti*utions 4i++ esu+t in &i' +utu&tions o t%e ie+' sten1t% oe 'ist&nes o t%e o'e o &

4&e+en1t%. T%e o++o4in1 si)+iie' )o'e+ oi'es esti)&tes o t%e &e&1e &n' )ini)u)

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Rec. ITU-R P.526-8 15

'i&tion +oss &s & untion o +o&tion. It onsists o &''in1 t%e &)+itu'es o t%e in'ii'u&+

onti*utions o &n esti)&te o t%e )ini)u) 'i&tion +oss &n' & o4e &''ition to o*t&in &n

esti)&te o t%e &e&1e 'i&tion +oss. T%e )o'e+ %&s *een teste' &1&inst &u&te &+u+&tions

usin1 t%e unio) t%eo, o 'i&tion (UTD &n' %i1%-eision )e&sue)ents.

Ste !" C&+u+&te t%e 1eo)eti&+ &&)ete o e&% o t%e t%ee nie-e'1es (to +et si'e &n'i1%t si'e usin1 &n, o e7u&tions (!3 to (!6.

Ste #" C&+u+&te t%e +oss &to$( =!0J(/20&ssoi&te' 4it% e&% e'1e o) e7u&tion (!#.

Ste %" C&+u+&te )ini)u) 'i&tion +ossJmino)9

+

+

=(

!

(

!

(

!+o120=(

32! $$$Jmin ' (!8

o &+ten&tie+,

Ste &" C&+u+&te &e&1e 'i&tion +ossJa'o)9

'(

!

(

!

(

!+o1!0=(

23

22

2!

+

+

=

$$$Ja (!"

*.# 0ing!e rounded obtac!e

T%e 1eo)et, o & oun'e' o*st&+e o &'iusRis i++ust&te' in i1. 6. Note t%&t t%e 'ist&nes d!&n' d2 &n' t%e %ei1%t h&*oe t%e *&se+ine &e &++ )e&sue' to t%e ete 4%ee t%e oete' &,s

inteset &*oe t%e o*st&+e. T%e 'i&tion +oss o t%is 1eo)et, )&, *e &+u+&te' &s9

'(( nmTJ( += (20

4%ee9& J( is t%e esne+-Ji%o +oss 'ue to &n e7ui&+ent nie-e'1e +&e' 4it% its e& &t t%e

ete oint. T%e 'i)ension+ess &&)ete )&, *e e&+u&te' o) &n, o e7u&tions (!3

to (!6 in+usie. o e&)+e in &ti&+ units e7u&tion (!3 )&, *e 4itten9

2/!

2!

2! (203!6.0

+=

dd

ddh (2!

4%ee h&n' &e in )etes &n' d!&n' d2&e in i+o)etes.

J( )&, *e o*t&ine' o) i1. # o o) e7u&tion (!#. Note t%&t o &n o*stution to +ine-

o-si1%t o&1&tionis ositie &n' e7u&tion (!# is &+i'.* T(mn is t%e &''ition&+ &ttenu&tion 'ue to t%e u&tue o t%e o*st&+e9

T(mn = k m) (22&

4%ee9

k = 8.2 + !2.0 n (22*

) = 0.#3 + 0.2# K! = e (= !.$3 nL (22

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16 Rec. ITU-R P.526-8

&n'

3/!

2!

2!

+=

R

dd

ddRm (23

RRhn

3/2

= (2$

&n'R d! d2 h&n' &e in se+-onsistent units.

T(mn &n &+so *e 'eie' o) i1. 8.

Note t%&t &sRten's to :eo m &n' %ene T(mn &+so ten' to :eo. T%us e7u&tion (20 e'ues to

nie-e'1e 'i&tion o & ,+in'e o :eo &'ius.

It s%ou+' *e note' t%&t t%e ,+in'e )o'e+ is inten'e' o t,i&+ te&in o*stutions. It is not

suit&*+e o t&ns-%oi:on &t%s oe 4&te o oe e, +&t te&in 4%en t%e )et%o' o 3 s%ou+'

*e use'.

0526-08

50

$5

$0

35

30

25

20

!5

!0

5

0

0

n F !0!00

T(m-n

('8

0.$ 0.8 !.2 !.6 2 2.$ 2.8 3.2 3.6 $

0.5

0.25

0.0

I>URE 8

T&e %a!ue of T5m6n7 5d87 a a function of mand n

m

5.0 2.0 !.0

7/30/2019 R-REC-P.526-8-200304-I!!MSW-E.doc

17/27

Rec. ITU-R P.526-8 1,

*.* $oub!e io!ated edge

T%is )et%o' onsists o &+,in1 sin1+e nie-e'1e 'i&tion t%eo, suessie+, to t%e t4o

o*st&+es 4it% t%e to o t%e ist o*st&+e &tin1 &s & soue o 'i&tion oe t%e seon' o*st&+e

(see i1. ". T%e ist 'i&tion &t% 'eine' *, t%e 'ist&nes a&n' )&n' t%e %ei1%t -!h 1ies &

+oss*!('. T%e seon' 'i&tion &t% 'eine' *, t%e 'ist&nes )&n' c&n' t%e %ei1%t -2h 1ies& +oss*2('.*!&n'*2&e &+u+&te' usin1 o)u+&e o $.!. A oetion te) *c(' )ust *e

&''e' to t&e into &ount t%e se&&tion )*et4een t%e e'1es.*c)&, *e esti)&te' *, t%e o++o4in1

o)u+&9

++

++=(

((+o1!0

c)a)

c))a*c (25

4%i% is &+i' 4%en e&% o*!&n'*2eee's &*out !5 '. T%e tot&+ 'i&tion +oss is t%en 1ien

*,9

* =*! +*2 +*c (26T%e &*oe )et%o' is &tiu+&+, useu+ 4%en t%e t4o e'1es 1ie si)i+& +osses.

0526-0"

h+!

h+2

) ca

I>URE "

9et&od for doub!e io!ated edge

I one e'1e is e'o)in&nt (see i1. !0 t%e ist 'i&tion &t% is 'eine' *, t%e 'ist&nes a&n'

)+c&n' t%e %ei1%t h!. T%e seon' 'i&tion &t% is 'eine' *, t%e 'ist&nes ) &n' c &n' t%e%ei1%t 2h .

0526-!0)a c

h! h2

RT

M

h+2

I>URE !0

Figure &o4ing t&e (ain and t&e econd obtac!e

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18/27

18 Rec. ITU-R P.526-8

T%e )et%o' onsists o &+,in1 sin1+e nie-e'1e 'i&tion t%eo, suessie+, to t%e t4o

o*st&+es. ist t%e %i1%e h/r&tio 'ete)ines t%e )&in o*st&+e M 4%ee his t%e e'1e %ei1%t

o) t%e 'iet &t% TR &s s%o4n in i1. !0 &n' ris t%e ist esne+ e++isoi' &'ius 1ien *,

e7u&tion (2. T%en 2h t%e %ei1%t o t%e seon'&, o*st&+e o) t%e su*-&t% MR is use' to&+u+&te t%e +oss &use' *, t%is seon'&, o*st&+e. A oetion te) Tc(' )ust *e su*t&te'

in o'e to t&e into &ount t%e se&&tion *et4een t%e t4o e'1es &s 4e++ &s t%ei %ei1%t. Tc('

)&, *e esti)&te' *, t%e o++o4in1 o)u+&9

c ,

aT

2

!0

=!

2+o120=!2

= (2#

4it%9

2/!

2

2/!

!

2/!(

t&n(

(2

(

(2

++=

+

++

=

+

++

=ac

c)a)h

c)a

c)a,h

ac)

c)a (28

h!&n' h2&e t%e e'1e %ei1%ts o) t%e 'iet &t% t&ns)itte-eeie.

T%e tot&+ 'i&tion +oss is 1ien *,9

cT*** =2!+= (2"

T%e s&)e )et%o' )&, *e &+ie' to t%e &se o oun'e' o*st&+es usin1 $.3.

In &ses 4%ee t%e 'i&tin1 o*st&+e )&, *e +e&+, i'entiie' &s & +&t-ooe' *ui+'in1 & sin1+e

nie-e'1e &oi)&tion is not suiient. It is neess&, to &+u+&te t%e %&so su) o t4o

o)onents9 one un'e1oin1 & 'ou*+e nie-e'1e 'i&tion &n' t%e ot%e su*et to &n &''ition&+

e+etion o) t%e oo su&e. It %&s *een s%o4n t%&t 4%ee t%e e+etiit, o t%e oo su&e

&n' &n, 'ieene in %ei1%t *et4een t%e oo su&e &n' t%e si'e 4&++s &e not &u&te+, no4n

t%en & 'ou*+e nie-e'1e )o'e+ o'ues & 1oo' e'ition o t%e 'i&te' ie+' sten1t% i1noin1

t%e e+ete' o)onent.

*.5 enera! (et&od for one or (ore obtac!e

T%e o++o4in1 )et%o' is eo))en'e' o t%e 'i&tion +oss oe ie1u+& te&in 4%i% o)s

one o )oe o*st&+es to +ine-o-si1%t o&1&tion. T%e &+u+&tion t&es E&t% u&tue into

&ount i& t%e onet o &n eetie E&t% &'ius (see Reo))en'&tion ITU-R P.$52 $.3. T%is

)et%o' is suit&*+e in &ses 4%ee & sin1+e 1ene&+ oe'ue is e7uie' o teesti&+ &t%s oe

+&n' o se& &n' o *ot% +ine-o-si1%t &n' t&ns%oi:on.

A oi+e o t%e &'io &t% s%ou+' *e &&i+&*+e onsistin1 o & set o s&)+es o 1oun' %ei1%t &*oe

se& +ee+ o'ee' &t inte&+s &+on1 t%e &t% t%e ist &n' +&st *ein1 t%e %ei1%ts o t%e t&ns)itte

&n' eeie &*oe se& +ee+ &n' & oeson'in1 set o %oi:ont&+ 'ist&nes o) t%e t&ns)itte.

E&% %ei1%t &n' 'ist&ne &i &e eee' to &s & oi+e oint &n' 1ien &n in'e 4it% in'ies

ine)entin1 o) one en' o t%e &t% to t%e ot%e. A+t%ou1% it is not essenti&+ to t%e )et%o' in t%e

o++o4in1 'esition it is &ssu)e' t%&t in'ies ine)ent o) t%e t&ns)itte to t%e eeie. It is

ee&*+e *ut not essenti&+ o t%e oi+e s&)+es to *e e7u&++, s&e' %oi:ont&++,.

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Rec. ITU-R P.526-8 1

T%e )et%o' is *&se' on & oe'ue 4%i% is use' o) ! to 3 ti)es 'een'in1 on t%e &t% oi+e.

T%e oe'ue onsists o in'in1 t%e oint 4it%in & 1ien setion o t%e oi+e 4it% t%e %i1%est

&+ue o t%e 1eo)eti&+ &&)ete &s 'esi*e' in $.!. T%e setion o t%e oi+e to *e

onsi'ee' is 'eine' o) oint in'e & to oint in'e * (& 0.#8 &n' is ot%e4ise :eo.

Note t%&t e7u&tion (30 is 'eie' 'iet+, o) e7u&tion (!3. T%e 1eo)et, o e7u&tion (30& is

i++ust&te' in i1. !!. T%e seon' te) in e7u&tion (30& is & 1oo' &oi)&tion to t%e &''ition&+

%ei1%t &t oint n 'ue to E&t% u&tue.

0526-!!

h)hn

ha

h

dan dn)

da)

re

Point &

Point n

Point *

URE !!

2eo(etry for a ing!e edge

7/30/2019 R-REC-P.526-8-200304-I!!MSW-E.doc

20/27

2/ Rec. ITU-R P.526-8

T%e &*oe oe'ue is ist &+ie' to t%e entie oi+e o) t&ns)itte to eeie. T%e oint 4it%

t%e %i1%est &+ue o is te)e' t%e ini&+ e'1e &n' t%e oeson'in1 +oss isJ(

.

I>=0.#8 t%e oe'ue is &+ie' t4ie )oe9

= o) t%e t&ns)itte to oint to o*t&int &n' %eneJ(tB

= o) oint to t%e eeie to o*t&inr&n' %eneJ(r.

T%e eess 'i&tion +oss o t%e &t% is t%en 1ien *,9

* =J( + TKJ(t +J(r + -L o > =0.#8 (3!&

* = 0 o =0.#8 (3!*

4%ee9

-

9 e)ii&+ oetion

- = !0.0 + 0.0$. (32

.9 tot&+ &t% +en1t% ()

&n'

T = !.0 = e K=J(/6.0L (33

Note t%&t t%e &*oe oe'ue o t&ns%oi:on &t%s is *&se' on t%e De,1out )et%o' +i)ite' to &

)&i)u) o 3 e'1es. o +ine-o-si1%t &t%s it 'ies o) t%e De,1out onstution in t%&t

t4o seon'&, e'1es &e sti++ use' in &ses 4%ee t%e ini&+ e'1e esu+ts in & non-:eo

'i&tion +oss.

?%ee t%is )et%o' is use' to e'it 'i&tion +oss o 'ieent &+ues o eetie E&t% &'ius

oe t%e s&)e &t% oi+e it is eo))en'e' t%&t t%e ini&+ e'1e &n' i t%e, eist t%e &ui+i&,

e'1es on eit%e si'e &e ist oun' o )e'i&n eetie E&t% &'ius. T%ese e'1es s%ou+' t%en *euse' 4%en &+u+&tin1 'i&tion +osses o ot%e &+ues o eetie E&t% &'ius 4it%out ee&tin1

t%e oe'ue o +o&tin1 t%ese oints. T%is &oi's t%e ossi*i+it, 4%i% )&, ou in & e4 &ses

o & 'isontinuit, in e'ite' 'i&tion +oss &s & untion o eetie E&t% &'ius 'ue to 'ieent

e'1es *ein1 se+ete'.

*.6 Finite!y conducting 4edge obtac!e

T%e )et%o' 'esi*e' *e+o4 &n *e use' to e'it t%e 'i&tion +oss 'ue to & inite+, on'utin1

4e'1e.

7/30/2019 R-REC-P.526-8-200304-I!!MSW-E.doc

21/27

Rec. ITU-R P.526-8 21

0526-!2

0 n

s!

n

!

2

s2

I>URE !2

2eo(etry for app!ication of UT$ 4edge diffraction

0 &e n&e

7/30/2019 R-REC-P.526-8-200304-I!!MSW-E.doc

22/27

22 Rec. ITU-R P.526-8

( )

+

+++

+

++

+

+

=

+

+

((2

(ot

((2

(ot

((2

(ot

((2

(ot

22

/$Ee

!2!2

!2!2

!2

!2

!2!2

0

k*aFn

R

k*aFn

R

k*aFn

k*aFn

kn.

n

(35

7/30/2019 R-REC-P.526-8-200304-I!!MSW-E.doc

23/27

Rec. ITU-R P.526-8 2#

4%ee9

!9 ini'ene &n1+e )e&sue' o) ini'ene &e (0 &e

29 'i&tion &n1+e )e&sue' o) ini'ene &e (0 &e

n

9 eten&+ 4e'1e &n1+e &s & )u+ti+e o &'i&ns (&tu&+ &n1+e =n(&' = !

&n' 4%eeF(0 is & esne+ inte1&+9

=0

tt000F 'Ee3/(=Ee3/(E2( 2 (36

= 0

0

tttt

0

22 'Ee(==E=!(8

'Ee(= (3#

T%e inte1&+ )&, *e &+u+&te' *, nu)ei&+ inte1&tion.

A+ten&tie+, & useu+ &oi)&tion is 1ien *,9

(2

O'Ee( 2 0(tt

0

=

(38

4%ee9

+