Giuseppe Bianchi, Ilenia Tinnirello

Transcription

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2 Powe units - ecibel Decibel (B): logaithmic unit of intensity use to inicate powe lost o gaine between two signals Name afte Alexane Gaham Bell. ( ) log P P 1 /

3 Decibels - Bm» Not much use by us 1BW30Bm µ! " # " $ #! % & % & & % %

4 Quick evaluations!"#"$ %$"& ' ( ) * # $ ) ' ( * '&()*(+,) ++)*++ )++

5 Computation with B -$ +, - Es. 33 Bm.$ +, - Es. Bm ". * /, +, - 0,,, 1 * / Es. 43 B attenuation by facto 0.000

6 Attenuation moel fo LOS /"$ - ), - * 0 3" 0 "., ) /, 4 3, *,.$& 5 ), * 3 ), *, 6 * / 3, /,, 7 - P ( ) ( istance between sene an eceive)

7 fee space moel ieal antennas 0 8, 9 -, * 9,, - 3*, $1 / : 33 * / P P ( ) A e a λ 4π ( ) P a P t 4π ( ) A e

8 fee space moel eal antennas ' ; P a ( ) G P t 4π t ' ; P ( ) P ( ) G A a e PG t t λ G 4π 4π

9 Fiis Fee-Space Moel summaizing all pevious consieations PG t tgλ Gt G c P ( ) P t (4π ) L L 4πf P t tansmitte powe (W o mw) G t tansmitte antenna gain G tansmitte antenna gain (imensionless) λ c/f RF wavelength (m) c spee of light (3x 8 m/s) f RF fequency (Hz) P ( ) 0 log [ Bm] P [ Bm] λ 0log t + log (4π ) 0 log G t + log > 0 P t G t Equivalent Isotopic Raiate Powe (EIRP) L othe system losses (hawae) L >1 (imensionless) istance between tansmitte an eceive (m) log G L +

10 Example nomalize fequency [MHz] spee of light [Km lamba (m) 0, gain Tx 1 Gain Rx 1 Loss 1 Ptx [W] 5 istance (Km) Px W Px Bm 00 8,80E-08-40,55 400,0E-08-46, ,77E-09-50, 800 5,50E-09-5, ,5E-09-54,54 0,44E-09-56, ,79E-09-57, ,37E-09-58, ,09E-09-59, ,80E- -60, ,7E- -61, ,11E- -6, ,0E- -6, ,49E- -63, ,91E- -64, ,44E- -64, ,04E- -65, ,71E- -65, ,44E- -66, ,0E- -66, ,99E- -67, ,8E- -67, ,66E- -67, ,53E- -68, ,41E- -68,5-30,00-40,00-50,00-60,00-70,00 eceive powe (B istance (m)

11 Path Loss (popagation loss) positive value in B PL( ) [ B ] log 0 log 0 log 0 log P t L 4 log π P Gt G λ Gt G λ log 0log L 4π Gt G + 0 log f log 0log L Gt G + 0 log f log L c 4π

12 Fee space loss same as path loss, but pat ue to attenuation in fee space only (in B) L fee ( ) λ 4 π L fee ( ) [ B] λ c/ f 0log 0log 4 π 4π 0log + 0log f

13 Refeence istance 0$$ * * * - 3 < P ( )( Bm) o P ( ) P ( o ) o log P ( o ) + 0log P ( o)( Bm) + 0 log o 3"1 $1) 3"*#" ",,, ) <, - <, * -1 + &++*+++

14 Example P ( + ++% 0 )( Bm) 30 + log +++ Gt G Pt ( Bm) + log + 0log L log 34,5Bm 0π 0 P ( 00m) P ( 0) + 0log 34,5 Bm 0B 54,5Bm λ 4π

15 Refeence istance + fequency 41%1 $ P (, 51 + PG G λ PG G ( c/ f ) f ) (4π ) P ( t 0 t, f 0 ) L (4π ) 0 [ ] ( ) ( ) Bm t t 0log 0 L f / f 0 f00 f 0log / 0 33, * <, *, < * < + >? < *

16 Moe ealistic popagation moels 05$$ <, * *,. 9η P ( ) η -, - *, η7 If tough envionment (e.g., lots of foliage), < * / -, 9 η fo small istances (0 B/ecae) η3 to η4 (40 B/ecae) fo mobile telephone istances η *, - ), Aη, - ) - ) -, η

17 Extene fomulae P ( )( Bm) log P ( o ) + η log _ef 1 Km P_ef -51,566 Bm (PtxW; 900 MHz; 00m) o istance px (eta)px (eta3,5) px (eta4) 1-51,566-51, ,566 1, -53,1-54, ,6939 1,4-54,449-56, ,3717 1,6-55,609-58, ,6914 1,8-56,631-60, , ,547-6, ,5678, -58, , ,35,4-59, , ,7351,6-59,861-66, ,156,8-60, , , ,069-68, ,6115 3, -61,696-69, ,736 3,4-6,156-70, ,7858 3,6-6,657-70, ,7787 3,8-63,13-71, , ,5678-7, ,609 4, -63, , ,4566 4,4-64, , ,647 4,6-64, , ,0369 4,8-65, , , ,506-75, ,4854 eceive powe (Bm) η η3,5 η istance (Km)

18 Realistic scenaios $" 3 * 633* 6, *, < 3- * ) < / ) - * *, *, 6 /, < 6 / 3 * * - *, 3 * /, A * - *, ), ), < $". /, / * / 3 33 *, 33 <,.## ##,, * *, - * / <, -,,, - * / <, -,,, /,,

19 Example scenaios: LOS path non necessaily existing (an unique) : B 9* < ) -, A # 0 5# : C " 5; > 8 A D 33* A 3 * 33* 3 *

20 Example scenaios 0 5# : C " 5; > 8 % D 33* 6 3 * 6, * 0 "

21 Two-Ray Goun Popagation Moel -"η6 8 <,, -, * 0 " 3 * * * /, 3* :, <, / h t 0 3" < 3 * < h 8, * /, 33

22 Two-ay moel geomety >> h t, h θ θ iect + ( h h ) t ht h 1 + 1/ ht h eflect + ( h + h ) t ht h 1/ ht + h

23 Two ay moel path analysis ht + h 1 + eflect iect 1 ht h ht h 3$ " , E iect ay Acos πf t - * eflect ay B cosπf t - 3 * 3 * 6 iect c eflect c

24 Two ay moel fiel stength " π ϕ πf c λ.#" 0 : * ) 3, / ) < * < 8 ρ* E E E [ ] j ϕ + ρ E E iect 1 e iect E iect E 4πh h t λ [ ] j ϕ 1 e E [ 1 cos sin ] iect ϕ + j ϕ [ 1 cos cos sin ] 1/ + ϕ ϕ + ϕ iect 1 cos ϕ E iect ϕ sin

25 Two ay moel powe computation.$ F: F P 4 E iect sin ( ϕ / ) P ( ) PG t tg L λ πht h 4sin 4π λ

26 Two ay moel - conclusion -1& G 3, 3 G * - 3, λ G 3, 3* G -, sin h h h h small h h t t t λ π λ π λ π ) ( h h L PG G h h L PG G P t t t t t t λ π π λ 4 ) ( P

27 Design notes -1 1 η - 3,, *, Fee space moel η4-3, *, LOS + eflecte ay moel H,, /, * I I % (e.g., > (h t + h ))

28 Empiical moels! J ) -, * < 6- +, ) < * ), 4 < < *, 0 " 6 3 * 633* 6, *, - 3 *, -, C 7 - * < A, A, * 33* - -, 64, 6,, 6, 6 *! " # $ % & ' (

29 Okumua-Hata moel 789+&1 : " 0 *, A" - *, A. -, 0 9I 4 & f caie fequency (MHz) istance BS MS (Km) h bs (effective) heigh of base station antenna (m) h ms height of mobile antenna (m) : 33 * / "

30 Okumua-Hata: uban aea L path ( B) ( log h ) 13.8 log log h bs a bs ( h ) ms log f + + lage " # *) 34"#" cities : a small - me ( ) [ ( )] hms 3. log 11.75hms 4.97 f 400MHz : a( h ) [ 1.1log f 0.7] h [ 1.56 log f 0.8] cities ms ms

31 Okumua-Hata: sububan & ual aeas 4" sububan : ual : L L path path ( B) ( B) L L p p log 4.78 f [ ] log f log f

32 Okumua-Hata: examples path loss (B) istance (km) C K + >? 6 ), L 6, lage cities small cities sububs ual aea

33 Okumua-Hata an η!#1" +η -""#""4%"$"η η base station height (m)

34 Othe empiical moels ; J, K + > M C, *, I 4,, -, 4 *, * - + * B 4- - > "*0# C * < L + >? N 3 * * -, *, 1 4 ) < : - H 3 3" * 3* 8 * * H " 8, *, 3 * 3 ;, <,, 0# 5 * - - 3*, - ) - * * ) 3, 63, 6 3 *,, 6 *,?,? 6? 6,? 6 *?

35 Execises < $,+ ##%" ##"+#1 #1 ;++ #$"""#"#" +++"$#" -"# "$ ""$ -"$(" 6<7 %#+ "" $"5$"#"" #*1A" "#" 1$%" $*(+ " ""#A>*?+%*6+%

36 Execises 7##99+37# &,B (C( 9(#" D66 8*?,,#" # 7$""#$"" "#"(+++ #$,,A>9 8##@

37 ( #

38 Statistical natue of eceive powe 4##" Long tem faing Shot tem faing Mean value peicte by attenuation moel (constant at given ) Time (o movement)

39 Multipath: shot tem faing 4"*#, 9-3, 9,, * 3, 93 <1 # ## 1".#& e ( t) N a k k cos 1 0 ) ) ) φ ( π f t + φ ) k 3"#5 " /, 3B B 3Oλ change intefeence patten astic fluctuations in signal stength ue to constuctive/estuctive intefeence 15-0 cm fo 900 MHz "

40 Multipath analysis e ( t) ( f t + φ ) N a k k cos π 1 0 k X N ( πf 0t) a ( f t ) k k cosφk sin π 1 0 ( πf t) Y sin( πf t) cos cos k ecall cos that :cos( πf 0t + φk ) ( πf t) cos( φ ) sin( πf t) sin ( φ ) 0 N k a k sin φ k 0 k 5,, -, 9 # <, φ 4-3 <, ) - 6π 4 * ) /, - *, 0 " $ 6P -,, 6 * <, ) - / ), " / 9 X + Y. <, ) -

41 pobability istibution E 0,7 0,6 0,5 0,4 0,3 0, 0,1 0 Rayleigh istibution amplitue sigma1 sigma sigma4 σ [ ] x a x e x σ 1. 53σ Va 0 x σ π f a (x) [ ] x σ a x e σ σ 0.49σ 0 x σ π π P x σ σ / * 3$ P ; -,, / ( x a < x + x) e x x σ

42 Signal powe amplitue : a X + Y : ayleigh istibuti on powe : p a X + Y : exponential istibuti on #$& σ / / 0$. / ) 6 9 pobability ensity function: Pobability istibution function: f p F p ( x) ( x) 1 x σ e σ x σ 1 e

43 Outage pobability 1"$$ "#"" *, * ) * * < * / #$ + σ 3$""γ outage pobability : : B 9 / µ A, µ A - ) ) < B 6K Q P( p γ ) P0 ( γ ) 1 F p e : B 9 / A, A - ) ) < B 6K L Q γ

44 Long-tem faing 4#1E #" " ##""# $".&#*# 3,

45 Long-tem faing statistics lognomal istibution P ( )( Bm) log P ( o ) + η log o + F+# $"σ 11& Y f Y ' 1 ( ) σ B ( ) p Bm π σ B e p Bm P av

46 Long-tem faing an attenuation plot attenuation: η4 afte 0m; η befoe 0m -30 eceive powe (Bm) istance (m) no shaowing sigma3 B sigma8 B

47 nomal istibution 0.4 σ σ σ3 " 9 µ0; σ f X µ 1 ( x µ ) ( x) e σ π σ

48 Cumulative nomal istibution µ0; σ1 (stana) x t 1 Q e ( x) FX ( x) π t

49 ef - efc x ef ( x) e π efc( x) 1 0 t t ef ( x) Popeties: ef ( x) ef ( x) efc( x) efc( x)

50 ef ( x-) efc e ef π x 0 t t #, ) - µ 6σ, 7 ef ( x) π 1 x x t t e t e t 0 π x π 1 ( 1/ ) x x e t ( 1/ ) t 1 ef ( x) 1 efc( x) x

51 ef - efc F X ( m, σ ) ( x) 1 m x efc PX0, σ 1 > m x σ ef efc an nomal stana istibution: F X (0,1) 1 1 ( x) efc 1 efc x nomal stana istibution to efc: 1 x efc 1 FX (0,1) ( x) x

52 Cumulative nomal (st) istibution an efc 1 x efc efc x x

53 Outage pobability examples aveage eceive powe (Bm) -80 lognomal stana eviation (B) 6 outage theshol outage pob ,87% -88 9,1% -90 4,78% -9,8% -94 0,98% -96 0,38% -98 0,13% -0 0,04% : B * * - 9 DISTRIB.NORM( th, me,stev, VERO) ; *, * - 9 H /,!, γ g th P γ σ B av < 0 > 0 : / - ) 6 R : 3 : 3γ - : 3 : 3* : 3 : 3

54 Nomal istibution (stana) -4 0,003% -3,9 0,005% -3,8 0,007% -3,7 0,011% -3,6 0,016% -3,5 0,03% -3,4 0,034% -3,3 0,048% -3, 0,069% -3,1 0,097% -3 0,135% -,9 0,187% -,8 0,56% -,7 0,347% -,6 0,466% -,5 0,61% -,4 0,80% -,3 1,07% -, 1,390% -,1 1,786% -,75% -1,9,87% -1,8 3,593% -1,7 4,457% -1,6 5,480% -1,5 6,681% -1,4 8,076% -1,3 9,680% -1, 11,507% -1,1 13,567% -1 15,866% outage pob 0,000%,000% 1,000% 0,0% 0,0% 0,001% n x sigma

55 Esecizi & σ! "!#"$!#"% &'#()* &! " # ##$ #!% &'(σ)*&)+ (& ' σ),##$ # - % " ##$ #./ # 01