Politecnico di Milano Facoltà di Ingegneria dell Informazione. 2 Wireless channel. Wireless Networks Prof. Antonio Capone

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1 Politecnico i Milano Facoltà i Ingegneria ell Informazione Wireless cannel Wireless Networks Prof. Antonio Capone

2 Wireless cannel See H. Walke: Mobile aio Networks, cap.. sect. 1 o Generally speaking, wit respect to wire meia, te wireless cannel as worse caracteristics (strong attenuation, caracteristics varying over time, istortion, etc.) o Signals propagating in te raio meium are affecte by: n Attenuation ue to istance among transmitter an receiver n Attenuation ue to obstacles n Propagation over multiple pats A. Capone: Wireless Networks

3 e raio spectrum o aio wave n Wave lengt n Ligt spee l c 3 c f 10 8 m/s s( t) cos(p ft + j) n Frequency f A. Capone: Wireless Networks 3

4 e raio spectrum A. Capone: Wireless Networks 4

5 e raio spectrum o Mobile raio networks n MHz (VHF-UHF) n Simple an small antennas (few cm) n Wit emitte powers aroun 1W we can cover up to few kilometers an penetrate builing walls o Point-to-point links an satellite links n 3-30 GHz (SHF) n Plenty of banwit available but strong attenuation ue to meteorological effects (rain, fog, etc.) o Data wireless networks (WLAN, WPAN, etc.) n.4 GHz e 5GHz (ISM ban) n Interference wit oter systems (microwave ovens, remote controls, etc.) n In te 5 GHz attenuation ue to rain an fog. A. Capone: Wireless Networks 5

6 e raio spectrum o Hig frequencies n Hig banwit availability n Spectrum is less crowe by oter systems n Propagation is ifficult ue to low penetration of obstacles (wic appear as opaque) o Low frequencies n Low banwit availability n Big antennas n Many interference sources ue to oter uman activities A. Capone: Wireless Networks 6

7 Antennas o e antennas are conuctors or systems of conuctors able to: n In transmission: irraiate electromagnetic energy in te space n In reception: capture electromagnetic energy from te space o In te biirectional communication systems, te same antenna can be use bot for transmission an reception A. Capone: Wireless Networks 7

8 Antennas o A point source (isotropic raiator) transmitting a signal of power P irraiate it uniformly in all irections Distance Source Area o e power ensity on te surface of a spere centere in te isotropic raiator an wit raius is given by: F( ) P 4p [W/m ] A. Capone: Wireless Networks 8

9 Antennas o In many cases we aopt antennas tat are able to concentrate raiate power mainly in some irections o is caracteristic is expresses troug te antenna gain g(q) in te irection q g( q ) P( q )4p o Were P is te transmitte power an P(q) is te power ensity in te irection q at a reference istance 1 o Usually, we assume tat te maximum gain is in te main irection of te antenna (main lobe) corresponing conventionally to q 0. P A. Capone: Wireless Networks 9

10 Antennas o Antenna gain: ratio between te power ensity in te irection of maximum raiation an te power ensity of a isotropic raiator at reference istance (usually in Bi ecibel over isotropic) o Antenna irectivity: ratio between te power ensity in te irection of maximum raiation an te average power ensity at a reference istance o For te gain we calculate te ensity of te isotropic raiator as P 4p o Wile for te irectivity we consier te average power ensity, excluing ten te losses A. Capone: Wireless Networks 10

11 Antennas o Directional antennas: n Improve receive power n euce interference from oter sources n ey are more complex an require pointing o Examples of raiation iagrams g(q): A. Capone: Wireless Networks 11

12 eceive power o Denoting wit g te antenna gain we ave tat te power ensity in te main irection is given by P g F( ) [W/m ] 4p o e prouct P g is calle EIP (Effective Isotropically aiate Power) an represents te power necessary wit a isotropic raiator to get te same power ensity of te irective antenna A. Capone: Wireless Networks 1

13 eceive power o e power capture by te antenna epens on te incient power ensity an te effective area A e of te antenna o In te case of te isotropic raiator we ave: P F( ) A e A e l 4p o e capacity to concentrate te energy of a irective antenna is translate into a iger capacity of capturing incient power in reception equal to te antenna gain: P F( ) g A e A. Capone: Wireless Networks 13

14 eceive power o e receive power at te receiver can ten be expresse as P P g g æ ç è l 4p o Were P is te power raiate by te transmitter, g e g are te antenna gains of te transmitter an receiver respectively, l te wave lengt an te istance o Assuming tat g(q) is uniform in te angle of te antenna (main lobe of te raiation power), tis formula can be use in mobile raio systems were transmitter an receive are not always aligne in te irection of te maximum raiation power. ö ø A. Capone: Wireless Networks 14

15 Free space moel (Friis) o Summarizing: P P g g æ ç è l 4p ö ø P g g æ ç è c 4pf ö ø P transmitte power (W or mw) P receive power (W or mw) g tx antenna gain g rx antenna gain lc/f wave lengt (m) istance (m) P g EIP A. Capone: Wireless Networks 15

16 Free space moel (Friis) o e expression: L æ ç è l 4p ö ø - o epresents te free space attenuation. o e formula is vali in free space propagation, witout obstacles an reflections affecting signal propagation from transmitter to receiver. A. Capone: Wireless Networks 16

17 Line-of-sigt o One of te practical case were te formula of free-space propagation is vali is te propagation in line-of-sigt eart o Satellite communications (over 30 MHz oterwise reflections in te ionospere) o errestrial communications wit irective antennas witin te raio orizon A. Capone: Wireless Networks 17

18 Line-of-sigt o aio orizon ifferent from te optical orizon ue to te eviation of raio waves in te low atmospere optical orizon 3.57 orizon raio orizon: 3.57 K K 4 / 3 [Km], [m] 3.57( K + K ) A. Capone: Wireless Networks 18

19 Propagation effects o e free-space attenuation is not te only one affecting a raio signal propagating near te eart surface o Oter attenuations may be present ue to atmospere (epening on te frequency, fog, rain, etc.) an obstacles. o Moreover, propagation near te eart surface as some funamental ifferences wit respect to free-space A. Capone: Wireless Networks 19

20 Propagation effects o eflections o Saowing A. Capone: Wireless Networks 0

21 Propagation effects o Diffraction Wen wave meets a sarp ege of an obstacle, te ege acts as a linear emitter o Scattering Wen wave meets a small object wit respect to wave lengt, te object acts like a point emitter A. Capone: Wireless Networks 1

22 wo-ray moel o If ue to reflections, iffraction an scattering more copies of te same signal arrive to te receiver, tey combines vectorially o In te case of propagation wit two rays, a irect ray an a completely reflecte one, it is possible to calculate te attenuation of te receive signal in close form A. Capone: Wireless Networks

23 wo-ray moel A. Capone: Wireless Networks 3 >>, q irect reflect ú ú û ù ê ê ë é ø ö ç è æ + +» ú ú û ù ê ê ë é ø ö ç è æ ú ú û ù ê ê ë é ø ö ç è æ - +» ú ú û ù ê ê ë é ø ö ç è æ / reflect 1/ irect ) ( ) (

24 wo-ray moel o Signals travel ifferent istances an ten arrive wit ifferent pases: irect reflect ú ú û ù ê ê ë é ø ö ç è æ ú ú û ù ê ê ë é ø ö ç è æ + +» - irect ray: Acos π f t irect c " # $ % & ' ( ) * +, - reflecte ray: Bcos π f t reflect c " # $ % & ' ( ) * +, - A. Capone: Wireless Networks 4

25 wo-ray moel D o Pase ifference: Dj pf 4p c l o Denoting wit E irect te amplitue of te irect signal an wit E tat of te compose E Eirect 1+ o Assuming perfect reflection (r-1): E E E E irect E irect irect A. Capone: Wireless Networks 5 [ ] - jdj re [ ] - jdj 1- e E [ ] irect 1- cos( Dj) + j sin( Dj) [ 1 cos ( ) cos( ) sin ( )] 1/ + Dj - Dj + Dj 1- cos( Dj) E irect Dj sin

26 wo-ray moel o e receive power is ten: P o erefore: P ( ) µ E 4 E 4P D j irect sin g g æ ç è l ö æ p sin ç 4p ø è l π o If is small, ten λ æ p ö æ p ö sin ç» ç è l ø è l ø A. Capone: Wireless Networks 6 ö ø

27 wo-ray moel o en: A. Capone: Wireless Networks ) ( g g P g g P P ø ö ç è æ ø ö ç è æ» l p p l o erefore in te two-ray moel we ave: 4 ) ( - µ P

28 wo-ray moel o Summarizing: 1 o e ratio between receive power an transmitte power is given by: P P g g 1 A. Capone: Wireless Networks 8 æ ç è ö ø

29 Attenuation ue to istance o Assuming a two-ray propagation, te receive power ecreases ue to istance muc faster (~1/ 4 ) tan in te case of free space propagation (~1/ ) o Actually, te typical propagation in wireless systems is often ifferent an more complex tan in tese two cases o Neverteless, a common approac to propagation moeling in wireless systems assumes propagation is given by a formula similar to te above two cases were owever te exponent of te istance is ifferent (propagation coefficient ) tat can get values between (free-space) an 5 (strong attenuation in urban environment): P P g g æ ç è l ö 4p ø 1 A. Capone: Wireless Networks 9

30 Empirical moels o ere are several more sopisticate tecniques for te estimation of te receive power tat are base on te etaile moeling of te caracteristics of te area in wic signal propagates an propagation simulation (ray tracing tecniques) o ese tecnique are usually very complex in terms of computation an ifficult to use because of non accurate moeling of propagation environment o For tis reason, quite often empirical moels are aopte tat calculate attenuation ue to istance wit approximate formulas just capturing general caracteristics of te propagation area A. Capone: Wireless Networks 30

31 Empirical moels o eference scenarios consiere n Urban areas (big-meium-small cities), rural areas n Combinations of elementary moels (LOS, reflecte ray, etc.) n Parameters set using a large number of empirical measurements o Consiere parameters n Frequency, antenna eigt, istance, etc. o Correction parameters n Mountains, lakes, streets, etc. o First moel: n Hata (1968) very complex wit many paramaters A. Capone: Wireless Networks 31

32 Empirical moels o e most famous empirical moel moeling istance attenuation is te Okumura-Hata (1980) o It provies te attenuation formulas in several reference scenarios n Big cities; meium-small cities; rural areas n Distances > 1 km A. Capone: Wireless Networks 3

33 Empirical moels o Okumura-Hata: urban area L P log log ( log ) log [B] - a( ) + o were n f is te frequency in MHz (vali from 150 to 1500 MHz) n is te eigt of te base station (in m) n is te eigt of te mobile terminal (in m) n a( ) correction parameter ue to area type n is te istance(in km) o Big cities: a( ) 3.[ log10( )] o Small-meium cities: A. Capone: Wireless Networks 33 f [ 1.1log f - 0.7] -[ 1.56 log 0.8] a( ) 10 f 10 -

34 Empirical moels o Okumura-Hata: sub-urban & rural areas o Calculate starting from tat of urban areas (L P ) o Sub-urban: L pat L P - é ê log ë f ù 8ú û o ural: L pat [ f ] log LP log 10 f 10 - A. Capone: Wireless Networks 34

35 Empirical moels o Okumura-Hata: numerical example A. Capone: Wireless Networks 35

36 Empirical moels o Okumura-Hata: propagation factor n Propagation factor epens only on te eigt of te base stations: ( log ) log ( log ) 10 Þ A. Capone: Wireless Networks 36

37 Empirical moels o Oter empirical moels n Lee s moel o Frequency aroun 900 MHz o Distance > 1 km o More complex tan Okumura-Hata n Walfis-Ikegami s moel o Frequency MHz o Vali for small istances 0 m 5 km o eference moels for 3G systems n Inoor moels o Several moels o ey inclue attenuation for walls penetration o Base on zones (small spaces, meium spaces, big spaces) A. Capone: Wireless Networks 37

38 Multi-pat faing o o o In te propagation between transmitter an receiver, signal can follow ifferent pats ue to total or partial reflection over obstacles e beavior of te waves wen interacting wit objects epens on teir frequency an te caracteristics an size of te objects Generally speaking, signals at low frequency can cross many objects (tat appear as transparent) wit small attenuation, wile as frequency increases signals ten to be absorbe or reflecte by obstacles (at very ig frequencies over 5 GHz it is possible basically only irect propagation). A. Capone: Wireless Networks 38

39 Multi-pat faing o o As we alreay know from two-ray moel, replicas combines at te receive e resulting signal epens on: n Number of replicas (N) n elative pases (j k ) n Amplitues (a k ) n Frequency (f 0 ) e ( t) N å a k 1 k cos(p f t + j ) 0 k A. Capone: Wireless Networks 39

40 1,5 1 0,5 0-0,5-1 Multi-pat faing s(t) s(t+) s(t)+s(t+) o Signal can be attenuate 4/5p -1,5,5 1,5 1 0,5 0-0,5-1 -1,5 - -, s(t) s(t+) s(t)+s(t+) o Or even amplifie p /6 A. Capone: Wireless Networks 40

41 Multi-pat faing o If terminal moves, te caracteristics of te compose signal cange wit time o Faing notces ten to occur regularly at intervals corresponing to te time necessary for covering alf of te wave lengt A. Capone: Wireless Networks 41

42 Multi-pat faing o In some simplifie scenarios it is possible to give a statistical representation of te multipat faing: A. Capone: Wireless Networks 4 ) sin( ) cos( sin ) sin( cos ) cos( ) cos( ) ( t f Y t f X a t f a t f t f a t e k N k k k N k k k N k k p p j p j p j p å å å

43 Multi-pat faing o ayleig Faing n If we assume o An infinite number of pats o No ominating component (a k comparable) [usually verifie wen tere are only reflecte pats] o anom pases uniform in [0,p] n e two signal components X an Y are inepenent Gaussian variables f ( x-m) 1 - s X ( x) fy ( x) e ps A. Capone: Wireless Networks 43

44 Multi-pat faing n e amplitue of te vector: n Wit Gaussian components as a ayleig istribution: n wit n Usually a normalize istribution is consiere A. Capone: Wireless Networks 44 0, ) ( ³ - x e x x f x s s. 4, ) (, ) ( ø ö ç è æ - p s s s p s x E x E 1 ) ( x E Y X +

45 Multi-pat faing n e power P of a signal wit ayleig istribute amplitue as an exponential istribution A. Capone: Wireless Networks 45 / / 1 ) (, 1 ) ( s s s x P x P e x F e x f Average power: s

46 Multi-pat faing o Outage probability n Probability tat te signal power is below a given receiver tresol n Average power P 0 n resol g F P ( g ) 1- e -g / P 0 Example 1: Average power 100 µw resol 5 µw Outage prob. 4.9% Example : Average power -75 Bm resol -90 Bm Outage prob. 3.1% A. Capone: Wireless Networks 46

47 Multi-pat faing o ice faing n e assumptions of te ayleig moel are not verifie wen tere is a irect pat an many reflecte pats n In tis case usually te amplitue of te signal is represente as a ice ranom variable: p( r) r s r + r - s æ rrs ç ès n r s is te power of te irect ray wile s is te cumulative power of all te oters n I 0 is te Bessel function of 1 st kin an orer 0 e s I 0 ö ø A. Capone: Wireless Networks 47

48 Multi-pat faing n Factor K r s s n Denotes ow muc te irect components ominates te oters n Wit K0 we get te ayleig istribution n Figure sows istributions wit s 1 an ifferent values of K K0 1 3 A. Capone: Wireless Networks 48

49 Saowing o In te propagation te signal crosses or is partially reflecte an iffracte by obstacles o is generates a furter attenuation tat is usually inicate wit te name of saowing o is is a slowly varying faing tat canges only wen te move is big enoug to moify te components of te signal o In practice saowing is use to moel all te oter effects not capture by istance base moels an multi-pat A. Capone: Wireless Networks 49

50 Saowing o Saowing is usually moele as a log-normal ranom variable x, o So te power in B (average value P B ) as an attenuation component Zlog (x) wic is a Guassian variable wit stanar eviation s B tat usually gets values between 0 an 1 B f Z 1 -( x-p ) / B ( x) e B s p s B A. Capone: Wireless Networks 50

51 Saowing o Outage probability: n We nee to convert te tresol into anoter one for normal istribution: g Prob P B s -g B [1 - erf ( g)]/ erfc( g) / Example 1: Average power -75 Bm resol -85 Bm s B 6 B Outage prob. 4.8% Example : Average power -75 Bm resol -90 Bm s B 8 B Outage prob. 3% A. Capone: Wireless Networks 51

52 Saowing A. Capone: Wireless Networks 5