ITU-R P.56- (0/0 P
ITU-R P.56- ii.. (IPR (ITU-T/ITU-R/ISO/IEC.ITU-R ttp://www.itu.int/itu-r/go/patents/en. (ttp://www.itu.int/publ/r-rec/en ( ( BO BR BS BT F M P RA RS S SA SF SM SNG TF V 0.ITU-R ITU 0..(ITU
ITU-R P.56- ITU-R P.56- (ITU-R 0/3 (0-009-007-005-003-00-999-997-995-99-99-98-978.. (..(.(ITU-R P.83.km 8 500..
ITU-R P.56- (Fresnel B A M B A : (. λ λ AM MB AB n n n. (LoS. : ( (3 R n n λ (km (MHz f.(m n.. n n n Rn 550 ( f (. (W (.. : ( w λa e π /3.(m m (m :λ :a e
3 ITU-R P.56- w P.056-0 %60 (5 [ ] / 3.. (LoS. (R Δ Δ 0.0 Rλ m 3 3.. (m :R.(m :λ. :. - 0,6 -. - (ITU-R P.30 Δ 5. 6. ( R 0,R..(3
ITU-R P.56-.. (6 ITU-R P.56.. F c ν 0 πs ( ν ep j s C( ν js( ν : S(ν C(ν ( ( 7. : j ( 7 ( 7 ν ν 0 ν 0 πs C( ν cos s πs S( ν sin s F c (ν : ( 8 F ( ν c ep( j n 0 ( a n n jbn for 0 < ( 8 F ( ν c j ep( j n 0 ( c n j n n for (9 0.5π ν (Boersma n c n b n a n, a 0,5957690 b 0-0,000000033 c 0 0,000000000 0 0,9970 a -0,0000070 b,553875 c -0,0933975 0,00000003 a -6,80856885 b -0,0000980 c 0,000003936-0,009353 a 3-0,00057636 b 3-7,7800000 c 3 0,005770956 3 0,00003006 a 6,906990 b -0,00950895 c 0,00068989 0,008566 a 5-0,06898657 b 5 5,075698 c 5-0,0099736 5 0,009038 a 6-3,05085660 b 6-0,38397 c 6 0,098809 6-0,079 a 7-0,075759 b 7 -,36379 c 7-0,00678873 7 0,0906067 a 8 0,85066378 b 8-0,033976 c 8 0,00060 8-0,0798955 a 9-0,056390 b 9 0,7006 c 9 0,000967 9 0,0697308 a 0-0,5030960 b 0-0,69599 c 0-0,007930 0-0,00559855 a 0,030779 b 0,095703 c 0,00033939 0,000838386
5 ITU-R P.56- : ν S(ν C(ν ( 0 ( 0 C( ν C(ν S( ν S(ν.. (ITU GRWAVE ITU-R P.368.(. MHz 0..3. GRWAVE MHz 0.3...3..3. MHz 0...3. B..3..3.G R G T F.( K...3 : ( / K H for orizontal polarization λ /3 πa ( e [( ε (60λ σ ] ( [ ] / K K ε ( 60 λ σ for vertical polarization V H 3.3..3 /3 ( K 0.36( a f [( ε (8000σ / f ] H ( [ ] / KV e KH ε ( 8000σ / f /
ITU-R P.56-6 (km (S/m.(MHz :a e :ε :σ :f. K 0 K 5 5 ε 80 σ 5 K 0 5 ε 30 σ 0 ε 5 σ 0 3 ε 3 σ 0 0 5 ε 3 σ 0 ε 5 σ 0 3 ε 30 σ 0 3 0 0 khz 5 00 khz 5 MHz 5 0 MHz 5 00 MHz 5 GHz 5 0 GHz P.056-0
7 ITU-R P.56- K. 0,00 K K...3 0,00...3. K GRWAVE.K GRWAVE khz 00 MHz 0....3. : E 0...3 E (3.( 0 log E E 0 E 0 log F( X G( Y G( Y E 0 Y Y B X ( X β π λ a e /3 (5 Y β π λ a e /3 ( X.88 β f / 3 /3 ae ( 5 Y 9.575 0 3 β f /3 ae / 3 (km (km (m.(mhz : :a e : :f : K. β (6 β.6 K.5 K 0.67 K.53 K. MHz 300 β MHz 0
ITU-R P.56-8 β MHz 300 : MHz 0 ε.k ( 6 K 6.89 k /3 σ f 5/3. k (MHz f S/m σ : ( 7 F(X 0 log (X 7.6 X for X.6 ( 7 F(X 0 log (X 5.688X.5 for X <.6 : G(Y (8 / G( Y 7.6( B. 5log( B. 8 for B > ( 8 3 G ( Y 0log( B 0.B for B If G( Y < 0 log K, set G(Y to te value 0log K ( 8 B βy (3 : Y Y X B (3. (9 / / ( X βy Δ( Y, K (βy Δ( Y, K > X lim ( 9 X.096.80 ( β lim ( 9 Δ ( Y, K Δ( Y,0.779 ( β[ Δ( Y, Δ( Y,0] Δ(Y, Δ(Y,0 ( 9 Δ( Y,0 0.5 0.5 log(βy tan 0.3 0.55 ( 9 Δ( Y, 0.5 : 0.5 log(βy tan 0.5 (3 0.55 min ( 9 X min X lim / / ( βy Δ( Y, K (βy Δ( Y, K.( X min min
9 ITU-R P.56- : (..3 (0 E 0 log F( H( H( B E0. : E : E 0 : :.6 5 3 ( H ( F k (6 3 k. MHz 30 /3 k k.itu-r P.30 f / k 5 3 f / k k.6.. AB 6. AB.A (0. (0...3 -. AB -
ITU-R P.56-0 3 - GHz 0 9 8 7 5 8 9 0 0 0 6 5 3 0 GHz 9 8 7 6 5 5 0 5 0 5 3 30 3 5 30 k GHz 900 800 700 600 500 00 300 00 50 GHz 900 800 700 600 500 00 300 /3 k (km 0 50 60 70 80 90 00 50 00 5 6 7 8 9 0 5 0 (B 35 0 50 60 70 80 90 00 0 5 0 MHz 00 90 80 70 60 50 0 30 0 00 50 00 MHz 90 80 70 60 50 0 30 300 00 500 600 700 800 900 000 30 0 50 60 70 80 90 00 50 00 50 300 350 5 0 5 0 ( P.056-03
ITU-R P.56- - k Frequency for /3k k k /3 5 5 Heigt of antenna above groun (m (m 000 500 GHz 0 9 8 7 6 5 3.5 0 GHz 9 8 7 6 5 3.5 (B 80 60 0 0 00 90 80 70 60 50 0 000 900 800 700 600 500 00 300 00 50 GHz 900 800 700 600 500 00 300 GHz 900 800 700 600 500 00 300 30 0 0 0 00 90 80 70 60 50 0 30 00 50 00 50 0 0 5 MHz 00 90 80 70 60 50 0 30 00 MHz 90 80 70 60 50 0 30 0 30 0 9 8 7 6 5 3 - - P.056-0
ITU-R P.56-5 - GHz 0 9 8 7 5 8 9 0 0 0 6 5 3 0 GHz 9 8 7 6 5 5 0.5 5 0 5 k.5 GHz 900 800 700 600 500 00 300 00 3.5 GHz 900 800 700 600 500 00 300 /3 k (km 30 0 50 60 70 80 90 00 50 00 3 5 6 7 8 9 0 5 0 (B 5 30 35 0 50 60 70 80 90 00 0 5 0 50 MHz 00 90 80 00 50 300 00 30 0 50 5 70 60 50 0 30 00 MHz 90 80 70 60 50 0 500 600 700 800 900 000 50 60 70 80 90 00 00 50 300 350 0 5 0 30 ( P.056-05
3 ITU-R P.56-6 - k /3k (m (B - P.056-06
ITU-R P.56- MHz 0.MHz 0 -..3. : (. (7...3 ( los ae los :.3 ( ae a e ( ( b ( ( b m cos 3m π 3 3 arccos 3c 3m ( m 3 ( c ( m ae ( : req (3 req λ 0.55.. req <
5 ITU-R P.56- ( a em : a em a em 0.5..3.A a e. : (B A A (5 [ req ] A A /.....(MHz 30 < f (VHF 7 P :P P.056-07
ITU-R P.56-6 ( 8 8 : ν. (6 v λ (7 v θ λ (8 ν θ λ ( ν as te sign of an θ (9 ν λ αα ( ν as tesign of α an α. ra 0, α α θ. (ra...(9 (6 λ : : : :θ :α α -
7 ITU-R P.56-8 R (.. α α θ (For efinitions of θ, α, α,,, an R, see. an. θ > 0 α > 0 α ( a α < 0 θ < 0 α ( b R α α c P.056-08
ITU-R P.56-8.(B J(v v 9 : J(v (30 J ( ν 0 log [ C( ν S( ν ] [ C( ν S( ν ].7. F(v S(ν : 0,78- v C(ν (3 J ( ν 6.9 0 log ( ν 0. ν 0. B 9 0 6 8 J( ν (B 0 6 8 0 3 0 3 ν P.056-09
9 ITU-R P.56-.R 8c. (3 A J( v T( m, n B Fresnel-Kircff J(v (.(9 (6 v. (6. (33 v 0, 036 ( λ. λ.(3 9 J(v. (3 v : T(m,n ( / 3/ ( 3 T( m, n 7.m (.5n m 3.6m 0.8m B for mn / 3/ ( 3 T( m, n 6 0 log ( mn 7.m ( 7n m 3.6m 0.8m B for mn > (35 m R πr λ /3 (36 π R n λ /3 R (3 T(m,n. λ R R.. 0. (37 i yi r i
ITU-R P.56-0. i r i : N (38 r N N i y i 0 y i i P.056-0 b a.( c b.(b L (B L c.. L L.(B L : L c. b 3. (39 (0 :. L c 0log ( a b ( b c ba ( b c B 5 L L L L c L L.
ITU-R P.56- ' ' a b c P.056- b c a. c (. b M ' T a b c R P.056- /r. r TR M (MR.( (B T c. : (B T c. ( q Tc 0log0 a p π p
ITU-R P.56- ( ( ( ( a b c p λ ( b c a / / ( a b c q λ ( a b c b( a b c tan α ac / (3.3. L L L.- : :....... N N : " " i-t.j-t i-t i-t. " ".. T c : i : i : ij.
3 ITU-R P.56-.. 5. : s (i>s i-t ( e [( i s / si ] [ si / a e ] : k 6 37 (km. :k. m 50.. 8.(3 3 s s. 8. s 5 s :ae
ITU-R P.56-3 ( ( a a a 3 A B C ( a A s s B s s 3 C b ( s s P.0506-3 3. 8.. :.. :w : :y :z :v
5 ITU-R P.56- v y w z w v vy yz 056-. z y w. y. w z y..r s s.z y w - ( -. - B (5. z y L N i w L' L"( w i L"( y z 0logC i-t. i. N i L" N B :L' i : L"(w :L"(y z i :C N
ITU-R P.56-6 (6 C N (P a / P b 0.5 : C N (7 (8 N N P a s ( i i j [ s ] s j [( s ] N P b ( s ( s N i i i [( s ( s ] j.. (Bullington...3 (,... ( n, n..... (..(... : (..3 5. (..
7 ITU-R P.56- m/km i m km i i-t. n n i.km r km e /r e C e. rs ts.λ.. (9 S tim ma i 500Cei ( i ts [ ] i. n m/km i.5. (50 S tr rs ts m/km... S tim < S tr :ν (5 (5 (53 ( ( ( ts i rsi ν i Cei 0. 00 ma ma 500 i λi i. S rim. n i L uc J ( ν ma B 0,78- ν b (3 J.. S tim S tr. i 500Cei ( i rs ma m/km i. n i
ITU-R P.56-8 (5 (55 b rs ts S S S tim rim rim ( km : ts b rs b νb ts Stimb 0. 00 λb ( b ν b (56 (56 ( ν (5 B (57 L b L uc [ ep( L uc /6](0 0.0..(57 L b L uc J b.5. L uc.5. B L ba. : n (58 a ( i i i ( i i masl n (59 m [ 3( ( ( ( ( ] ( 60 ( 60 ( 6 ( 6 ( 6 α obr 3 i α obt i i i i i i a i i i i m/km stip a 0. 5m srip a 0. 5 m masl masl obs ma{ } α obr obt obs obi { } ma / obi α ma / { ( } obi i i m mra mra
9 ITU-R P.56- ( 6 ( 6 ( 6 ( 6 ( 6 ( 6 ( 6 ( 63 ( 63 ( 63 ( 63 [ ( ] obi i ts i rs i / m. n i obs stp srp stp stip srp srip gt gr stip srip obs obs α / obt α / g t masl masl masl masl stp st obr st stp sr n sr srp g r ( α α obt obr ( α α obt obr masl masl masl masl n srp i.5. : ( 6 ' ts rs st masl ( 6 ' rs rs sr masl.(57 L b B L bs
ITU-R P.56-30 ( 65 km.3 ' ts m ( 65.(5 ' rs A B m L sp (66 L Lba ma{ Lsp Lbs,0} B.. (...... (UTD ( ν :.(9 (6.(3 j(ν 0 J(ν/0 : : J min :3 (67 J ( ν 0 log min j( ν j( ν j3( ν B : J av 5.5 : (68 J a ν ( ν 0log ( ( 3 ( j ν j ν j ν B
3 ITU-R P.56-. " "..5.. " " 5 5.5..5 ( y y T Y X O R P.056-5 R T Z y R T. y : e a (69 e a (,,y,y 0.5(C C y S S y j 0.5 (C S y S C y ( 70 C C(ν C(ν ( 70 C y C(ν y C(ν y ( 70 S S(ν S(ν ( 70 S y S(ν y S(ν y
(7,0 j 0,0 (7 S(ν C(ν.( 8 ( 8 ITU-R P.56-3 y y (6 v ( 7 ( 7 : L a L a 0 log (e a..5 (69 : ( e s e s,0 e a. (69 e a -.(7 (69 -. v j 0,5 0,5 S(ν C(ν -. (50 B...... 6 6
33 ITU-R P.56-6 Φ nπ s s Φ 0 0 n nπ P.056-6 (UTD : ep( jks (73 s e UTD e0 D ep( jks s s( s s π/λ ( :. λ s s :e UTD :e 0 :s :s :k D : (7 D ep n ( jπ/ πk π ( Φ Φ cot F( kla ( Φ Φ n π ( Φ Φ cot F( kla ( Φ Φ n π ( Φ Φ R cot ( ( Φ Φ 0 F kla n π ( Φ Φ R cot n F( kla ( Φ Φ n
ITU-R P.56-3 :Φ (0 :Φ (0 :n π (nπ (ra j. F( (75 (76. (77 (78 a b c.7. (79 (80 (8 (5 : (8 t t F ep( j ep(j j ( π t t t t 0 ep( j j ( 8 ep( j ( π j ep( A t t < 0 0 oterwise j ( j ep( if j ( j ep( j ( n n n n n n n n c b a A s s s s L β π β ± ± cos ( N n a β Φ ± Φ ± N π π β n N ± ±
35 ITU-R P.56- : R n R 0 (83 R sin( Φ sin( Φ η η cos( Φ cos( Φ (8 R R n η η sin( Φ sin( Φ η cos( Φ η cos( Φ R 0 (S/m.(Hz :ε r :σ :f.. (7. ε (85 (86 (87 ε π β πnn for β Φ Φ ε π β πnn for β Φ Φ : ε. : ( Φ Φ π e LD (88 π ± β ± cot F( kla (β n n e LD < e e (7 UTD UTD ep( jks s Φ ( nπ Φ η ε Φ Φ r j 9 8 0 σ / [ πkl sign(ε klε ep(jπ/ ] ep(jπ/ for for Φ Φ < Φ Φ π π. :s ( Φ Φ π.(85 f D
(73 (89 ITU-R P.56-36 e 0 ( B (B. :s n.(9.matcad (UTD. 3 E UTD s e 0log UTD ep( jks 7. 7
37 ITU-R P.56-7 6. 6. 6..3 (.3 (.3 (.. (. 3. (. ( 3. ( 5. P.056-7
ITU-R P.56-38 8... 5 (90. θ α w α z α e : z w y : α z α w (9 α w ( w w a w e (9 α z ( y yz z yz a e : z w α e (93 (9 ( 95 ( 95 (96 α e a wz e w wv w. α z αe wz z w wv for θ a e y 0 ( w wy wv for θ a e < y vz wz wv : z.
39 ITU-R P.56- (97 v : (98 v wv α w a e w wv 8c. ( : (99 (00 v wv a e vz ( wvz z wz wv :. p y : q p :p :q : : (0 q y y-q p- (0 p p (03 yq q y (0 pq q p q p..q p :( y-q p- (05 t ( p p ( y yq q a pq e. ae
ITU-R P.56-0 (06 R [ / ] [ ep( ν ] 3 t pq.(3 : v (06.(LoS. z w w. 3..z y. v u v u.v u q p v u. u p -. p p < p v > p -. - v q -. q q < q u < q -..0 q p : z /F C F. : z :F
ITU-R P.56- (07 (08 q min z i [( / ( F ] C F i p ( z i ( r i ( t i i (09 ( F λ / i ui iv uv : i-t v u ( r i (0 ( r i ( u iv v ui / uv v u ( t i : i-t ( ( t i i ui iv / a e ( ν.9 (3 C (L" F.. L"