ELEG5693 Wireless Communications Propagation and Noise Part II

Transcription

1 Deparme of Elecrical Egieerig Uiversiy of Arkasas ELEG5693 Wireless Commuicaios Propagaio ad Noise Par II Dr. Jigxia Wu

2 OUTLINE Wireless chael Pah loss Shadowig Small scale fadig Simulaio model Chael classificaios Noise ad ierferece

3 FADING: WHAT IS FADING? 3 Pah loss ad shadowig is caused by large objecs ha are disa from MS. Eve he MS is movig, he chage i he relaive posiio bewee MS ad hose disa large objecs is small. Therefore, he impairmes caused by hose large disa objecs chage very slow wih respec o w.r.. ime ad posiio. Shadowig is also referred o as large scale fadig. Small scale fadig is caused by he effecs of objecs ha are close o MS. The moveme of MS w.r.. earby small objecs will dramaically chage he reflecio or diffracios of propagaed sigals. The sigal a receiver sum of he sigals from all muliple pahs will chage rapidly wih he moveme of MS. Small scale fadig: rapid flucuaio of he received sigals over shor disace.

4 FADING: WHAT IS FADING? 4 Radom # of mulipah compoes The ampliude, phase, ad frequecy of each compoe chage w.r.. he moveme of MS. The sigal a he receiver is he summaio of all he mulipah compoes he ampliude, phase, ad frequecy of he received sigal a receiver chage w.r.. he moveme of MS. The moveme of surroudig objecs e.g. vehicles will also cause he ime variaio of he sigals.

5 FADING: AN EXAMPLE 5 The rae of variaio depeds o wo facors: Relaive moveme speed bewee Tx ad Rx Speed of surroudig objecs

6 FADING: DOPPLER 6 Wha is Doppler? The whisle of he rai comig from opposie direcio souds differe wih he rai passig by. The pich of he soud deermied by soud frequecy is chagig. Rx sigal frequecy will chage if he Rx is movig w.r.. Tx. Sigal frequecy chage due o he relaive moveme bewee Tx ad Rx is called Doppler effecs. =0 c b a c b a =0.5s c b a c b a =1s c b a c b a T = 1s T = 0.5s

7 FADING: DOPPLER 7 Cosider Tx seds ou a siusoid wih frequecy 1Hz If Rx moves oward Tx, he sigal observed by Rx will have a shorer period frequecy icreased If Rx moves away from Tx, he sigal observed by Rx will have a loger period frequecy decreased The amou of frequecy chage is called Doppler shif Doppler shif depeds o Relaive speed bewee Tx ad Rx The frequecy of he origial sigal

8 FADING: DOPPLER 8 Relaioship bewee speed ad Doppler shif q X Base Saio Maximum Doppler shif: v f v q cos v : relaive speed f D v : wavelegh Example: fid he maximum Doppler shif of 900MHz sysem wih mobile speed 10km/Hr

9 FADING: DOPPLER 9 A give frequecy v fd chael chages more rapidly fd = 0Hz fd = 100 Hz fd = 1000 Hz

10 FADING: IMPULSE RESPONSE 10 The impulse respose of fadig is ime-varyig! Relaive mulipah delay Time variaio N mulipah compoes f c N c, cos 1 f : sysem operaig frequecy e.g. 900MHz, 1.8GHz c : he ime variaio boh ampliude ad phase chages wih respec o ime : relaive delay bewee mulipah compoes f D : depeds o pah disace ad Doppler shif

11 11 FADING: IMPULSE RESPONSE Complex basebad represeaio Re, 1 N f j c e c Re 1 N j f j c e e, 1 N j e h Maximum delay spread The ime ierval bewee he firs mulipah ad he las mulipah max 1 N

12 1 FADING: FLAT FADING Fla fadig Maximum delay spread << sysem symbol period Ts Relaive o he symbol period, all he mulipah compoes arrive a almos he same ime Does eed o cosider he delay variable max N N N j j e h si cos N I h 1 cos Iphase compoe Quadraure compoe N Q h 1 si

13 FADING: FLAT FADING 13 h h j h I Q Boh hi ad hq are he sum of may mulipah compoes Each mulipah compoe is a radom process hi ad hq are radom processes Ceral limi heorem The sum of N idepede ad ideically disribued i.i.d. radom variables eds o Gaussia disribuio whe N is large eough. Based o ceral limi heorem, a ime ime, boh hi ad hq are Gaussia disribued!

14 FLAT FADING: RAYLEIGH FADING 14 If here is o LOS bewee Tx ad Rx hi ad hq are zero-mea Gaussia disribued ~ The ampliude or evelope of h N0, h h I h Q The fadig evelope h follows Rayleigh disribuio f h z z z exp Average power of fadig E h E h E h I Q

15 15 FLAT FADING: RICIAN FADING If here is LOS compoe hi ad hq are o-zero-mea Gaussia disribued ~ The fadig evelope follows Ricia disribuio, s N h h h Q I

16 FLAT FADING: TIME DOMAIN CORRELATION 16 The ime domai correlaio of h is R h * h P J f E h h 0 J0x: zero-order Bessel fucio of he firs kid D Fd = 10Hz Fd = 50Hz Geerally speakig, for give ime ierval Larger speed v larger fd smaller. R h

17 FLAT FADING: POWER SPECTRAL DENSITY 17 Power specral desiy is he Fourier rasform of auo-correlaio fucio. fc-fd fc fc+fd

18 OUTLINE 18 Wireless chael Pah loss Shadowig Small scale fadig Simulaio model Chael classificaios Noise ad ierferece

19 SIMULATOR 19 h h j h Fla Rayleigh fadig is a radom process I Q A ay ime isa, h h is Rayleigh disribued. I hq Boh he real par h I ad he imagiary par h Q are zero mea Gaussia disribued. The auo-correlaio fucio mus saisfy * h J f R E h 0 D

20 SIMULATOR 0 How o geerae fla Rayleigh fadig wih compuer program? Mehod 1: Filered Gaussia oise Rely o low-pass filer o iroduce he ime-domai correlaio amog symbols Whie Gaussia Low-pass Filer hi Whie Gaussia Low-pass Filer hq The low-pass filer is hard o desig.

21 SIMULATOR 1 Mehod : Sum-of-siusoid M 1 m 1 q h I Ts cos f D cos Ts m M m 1 4M h Q M 1 m 1 q T s si f D cos Ts m M m 1 4M h Ts hi Ts j hq Ts q, m, m : uiformly disribued i [ 0, ] M : a cosa. The larger, he more accurae. Usually 8 or 16. T : ime duraio bewee samples. s h = RayleighN, fd, Ts h h 0Ts, h1ts, hts,, h N 1 Ts

22 OUTLINE Wireless chael Pah loss Shadowig Small scale fadig Simulaio model Chael classificaios Noise ad ierferece

23 CLASSIFICATION 3 Fadig Ampliude ad phase disorios of rasmied sigal Classificaio crierios Scale Large scale fadig, small scale fadig Small scale fadig Fla fadig v.s. frequecy selecive fadig Fas fadig v.s. slow fadig Rayleigh fadig v.s. Ricia fadig

24 CLASSIFICATION: SCALE 4 Large scale fadig Pah loss sigal power loss as a fucio of disace Due o disace bewee Tx ad Rx, reflecio of large objecs Shadowig Obsrucio from large objecs Small scale fadig Ampliude ad phase disorios from local objecs highly sesiive o locaios of MS Due o he superposiio of muliple elecromageic waveforms Caused by wo idepede propagaio mechaisms 1 ime dispersio delay spread Deermies frequecy selecive or fla frequecy dispersio Doppler spread Deermies fas or slow

25 CLASSIFICATION: FAST FADING V.S. SLOW FADING 5 The ime domai variaio of fadig is deermied by maximum Doppler spread fd Doppler shif: sigal frequecy chage due o relaive moveme bewee Tx ad Rx. Larger speed v larger fd chael varies faser. Coherece ime Tc The ime period over which he chael is srogly correlaed did chage oo much Iverse proporioal o fd T c 1 f D Tc Tc

26 CLASSIFICATION: FAST FADING V.S. SLOW FADING 6 Sysem symbol period v.s. sigal badwidh Symbol Period = T s Sigal BW = B s 1 / T s Fas fadig If Ts > Tc, or Bs < fd Ts > Tc: chael chages wihi oe symbol period fas flucuaio Slow fadig If Ts << Tc, or Bs >> fd Ts << Tc : chael keeps cosa durig several symbol periods slow ampliude flucuaio. Coherece ime Tc, Doppler spread fd is relaed o fas fadig or slow fadig

27 7 CLASSIFICATION: FAST FADING V.S. SLOW FADING Example: A cell phoe user is i a vehicle moves a a speed of 10km/hr. The carrier frequecy is 1800MHz. a Wha is he maximum Doppler spread? b Wha is he coherece ime of he chael? c The symbol period of a sysem is 3ms. Is he sysem experiecig fas fadig or slow fadig? d The symbol rae of IS-136 sysem is 4.3ksym/s. Is he sysem experiecig fas fadig or slow fadig?

28 CLASSIFICATION: FLAT V.S. FREQUENCY SELECTIVE 8 Maximum delay spread The ime ierval bewee he firs mulipah ad he las mulipah max N 1 Mea delay spread N 1 P P oal Roo mea square rms delay spread P N P oal P 1 : he average power of he h mulipah : he oal power of he all mulipah rms N 1 P P oal N 1 P P oal

29 9 CLASSIFICATION: FLAT V.S. FREQUENCY SELECTIVE Coherece badwidh Bc The badwidh over which he chael is srogly correlaed did chage oo much The specrum over coherece badwidh is almos fla Iverse proporioal o rms delay spread B c 1 rms Bc f Coherece badwidh Bc, rms delay spread rms is relaed o fas fadig or slow fadig

30 CLASSIFICATION: FLAT V.S. FREQUENCY SELECTIVE 30 Fla fadig If Bs << Bc, or Ts >> rms Bs << Bc: sigal badwidh << chael badwidh rms Ts >> : relaive arrival ime bewee mulipah compoes is egligible Does eed o cosider delay variable h, h B c Frequecy selecive fadig If Bs >> Bc, or Ts << rms Bs >> Bc: sigal badwidh >> chael badwidh B s f c Sigal specrum will be seriously disored by chael! rms Ts << : symbol period smaller ha rms delay spread The relaive arrival ime bewee he mulipah compoes is o loger egligible! f

31 CLASSIFICATION: FREQUENCY SELECTIVE FADING 31 Frequecy selecive fadig rms rms delay spread > > sysem symbol period Ts The relaive arrival ime bewee he mulipah compoes is o loger egligible! The N mulipah compoes are divided io L clusers Wihi each cluser, here are sill may mulipah compoes Mulipah compoes belogig o he lh cluser arrives a approximaely he same ime. L l1 L h Il jhql h, h l l l hl is he sum of all he mulipah compoes wihi he same cluser Resolvable mulipah compoe The iphase ad quadraure compoes of hl are Gaussia disribued. l1 The frequecy selecive fadig ca be viewed as he combiaio of muliple fla fadig Each brach cluser hl ca be viewed as fla fadig l

32 3 CLASSIFICATION: FREQUENCY SELECTIVE FADING Each brach of frequecy selecive fadig ca be viewed as a fla fadig All he properies discussed for fla fadig ca be direcly applied o each brach of frequecy selecive fadig E.g. Iphase ad quadraure compoes are Gaussia disribued. fadig evelope: Rayleigh v.s. Ricia

33 CLASSIFICATION: FREQUENCY SELECTIVE FADING 33 Relaive mulipah delay Time variaio

34 34 CLASSIFICATION: FREQUENCY SELECTIVE FADING Power delay profile The average power of each resolvable mulipah compoe, w.r.. he relaive delay Relaive delay ms Average power

35 35 CLASSIFICATION: FREQUENCY SELECTIVE FADING Example: a Fid he maximum delay spread, mea delay spread, ad rms delay spread of he followig power delay profile. b Wha is he coherece badwidh of he chael? c For a sysem wih symbol rae 0.5KHz, is his a fla fadig or frequecy selecive fadig? d For a sysem wih symbol rae 1000KHz, is his a fla fadig or frequecy selecive fadig? Relaive delay ms 0 1 Average power

36 CLASSIFICATION: RAYLEIGH V.S. RICIAN 36 Fadig evelope h h I h Q Rayleigh fadig Fadig evelope h follows Rayleigh disribuio No LOS o domia mulipah compoes Ricia fadig Fadig evelope h follows Ricia disribuio Oe domia compoe LOS alog wih weaker mulipah sigals

37 OUTLINE 37 Wireless chael Pah loss Shadowig Small scale fadig Simulaio model Chael classificaios Noise ad ierferece

38 NOISE 38 Noise ad ierferece Uwaed elecrical sigals ierferig wih he desired sigal Arises from ouside aural or arificial sources Arificial source: oise from auomobile igiio, sigal from oher commuicaio sysem, ec. Naural source: hermal oise, amospheric disurbaces. Noise v.s. fadig Noise arises from ouside sources fadig arises from he sigal propagaio iself Noise is added o he desired sigal he desired sigal is buried by oise oise oly has egaive effecs o sigal. Fadig resuls i sigal power flucuaio sigal power may become larger or become smaller fadig migh beefi sysem performace. Noise is prese i all commuicaio sysems. Fadig is uique o wireless commuicaios.

39 NOISE: SIGNAL TO NOISE RATIO 39 Sigal o oise raio SNR: he raio of he sigal power o he oise power a he receiver. SNR = S/N, wih S beig he sigal power, ad N beig he oise power observed by he receiver. High SNR Sigal is srog, ad oise is weak Beer commuicaio qualiy. Improve SNR Improve Tx power More power cosumpio High SNR Low SNR

40 NOISE: THERMAL NOISE 40 Thermal oise A he emperaure above 0K absolue emperaure, =-73 ceigrade, he elecros iside he coducor will move radomly. This radom moveme of elecros will cause radom volage flucuaios of he rasmied sigals. Temperaure icrease elecros moveme becomes sroger oise power icrease

41 NOISE: THERMAL NOISE 41 Thermal oise is a radom process A ay ime isa, he radom volage due o hermal oise follows Gaussia disribuio wih zero mea. The radom volage is caused by he sum of he moios of a large umber of elecros ceral limi heorem. The oise samples a ay wo differe ime isas are ucorrelaed. Auocorrelaio fucio * N0 R x E

42 NOISE: THERMAL NOISE 4 Power specral desiy Fourier rasform of auocorrelaio fucio R X N0/ S x N0 j f N0 f e d S X f N0/ whie specrum f Addiive Whie Gaussia Noise AWGN

43 NOISE: COCHANNEL INTERFERENCE 43 Cochael ierferece CCI Due o frequecy reuse, cells usig he same frequecy rage will geerae ierferece wih each oher. Uique o cellular sysem.