Overview of Radio Links

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1 ece45c lecue noes Copyigh Mak odwell, 06 Oveview of adio Links Mak odwell, Univesiy of Califonia, Sana Babaa

2 Copyigh Mak odwell, 06 adio Waves, Popagaion, and Anennas

3 opical THz nea-i THz m The adio Specum Copyigh Mak odwell, 06 Wavelengh (mees MF* MHz m HF* 3-30 MHz 00-0 m HF* MHz 0- m UHF* GHz m-0 cm micowave SHF* 3-30 GHz 0- cm Fequency (Hz 0 - Wavelengh (mees micowave SHF* 3-30 GHz 0- cm 0 - mm-wave EHF* GHz 0- mm sub-mm-wave THF* 0.3-3THz -0. mm fa-i: THz 0-5 mid-i 6-00 THz 50-3 m Fequency (Hz *ITU band designaions ** I bands as pe ISO 0473

4 T T FM adio AM adio imaging wieless HDMI saellie links saellie T Fequencies of a Few Sevices (ough #s Copyigh Mak odwell, 06 Wavelengh (mees cell phones WiFi 0 0 Fequency (Hz 0 - Wavelengh (mees ada Fequency (Hz

5 Choice of Tansmission Fequency Copyigh Mak odwell, 06 Govenmen fequency allocaion. Amosphei c aenuaio n :good weahe and bad. equied anenna size. Ease of blocking beam. Cuvaue of he eah

6 Amospheic Aenuaion in Bad Weahe Copyigh Mak odwell, 06 Huicane opical deluge heavy ain vey heavy fog Liebe, Manabe, Huffod, IEEE Tans Anennas and Popagaion, Dec. 989 ain Olsen, oges, Hodge, IEEE Tans Anennas & Popagaion Ma 978 popagaion in bad weahe favos use of fequencies below ~0 GHz

7 Cuvaue of he eah, eflecion fom he ionosphee Copyigh Mak odwell, 06 Long - ange adio ansmiss ion is limied by he cuvaue of he eah. eflecion fom he ionosphee enables long - ange ansmiss ion This equies fequencie s below he elecon plasma esonance fequency, of ode 0 MHz in he ionosphee Ineconi nenal adio equies saellies o low - fequency caies (Maconi

8 Copyigh Mak odwell, 06 Fesnel Zone: Whee he adio Beam Caies The Signal Zone. Fesnel (fis he called is This. / caied in an aea is anennas beam beween The / / / / ( / ( / ( ( / / ( and assume Le us 4. / ( 4. / han less is in pah lenghs diffeence if - phase in add (almos Pahs H A H H H H H H H H H H H H H

9 Copyigh Mak odwell, 06 Fesnel Zone: Whee he adio Beam Caies The Signal Sill assuming and H, an objec of diamee H / hence aea A /. will block mos of he powe in he beam. Longe wavelengh (lowe - fequency ae less likely o be blocked. signals

10 Nealy Isoopic Anennas Copyigh Mak odwell, 06 Dipole anenna :adiaes effecively when lengh is ~ / Anenna can be educed : by using wide gound plane. "quae - wave anenna" in lengh adiaion paen is isoopic in veica l and vaies as ~ cos( in veica l plane plane, hp://en.wikipedia.og/wiki/file:elem-doub-ad-pa-pes.jpg

11 Diecional Anennas Copyigh Mak odwell, 06 Yagi - Uda log - peiodic hp://en.wikipedia.og/wiki/file:two_mee_yagi.jpg hp://en.wikipedia.og/wiki/log-peiodic_anenna paabolic efleco Typical plo of adiaion paen hp://en.wikipedia.og/wiki/adiaion_paen hp://en.wikipedia.og/wiki/file:supedish.jpg

12 Anenna Dieciviy Copyigh Mak odwell, 06 hp://en.wikipedia.og/wiki/adiaion_paen diecivi y peak inensiy adiaed adiaed inensiy of isoopic anenna diecivi solid angle of a sphee y angula beamwidh (solid angle in seadians 4 angula beamwidh (solid angle in seadians Simple half - wave dipole anennas have a diecivi y of.64.

13 Copyigh Mak odwell, 06 eceived Signal Sengh

14 Fiis Tansmission Fomula Copyigh Mak odwell, 06 P P eceived ansmie d D Ignoes objecs 4A scaeing cuvaue mulipah D D 6 many facos : in he fom eain of he plane beam pah popagaio n... D A e anenna dieciviy anenna effecive apeue aea ansmission ange amospheic aenuaion Whee do hese elaionships come fom?

15 Plane Wave Inciden on a Baie Copyigh Mak odwell, 06 Plane wave inciden on a baie wih an apeue :...wha is he fa - field paen?

16 Angula beamwidh of an apeue If / H sin, hen he op half of he apeue, of will adiae80 o ou - of - phase fom he lowe half. Null in beam null sin ( / H heigh H, Copyigh Mak odwell, 06 Small angle appoximaion : sin, Beamwidh a nulls ough guess a half null / H, null - powe beamwidh 3 / db / H H

17 Dieciviy vs Aea Copyigh Mak odwell, 06 We' ve jus deemined ha if he apeue heigh is H hen he veical half - powe beamwidh Similaly, if he apeue*widh *isw hen he * hoizonal* half - powe beamwidh 3dB, veical / H 3dB, hoizonal / W A a disance, he apeue will illuminae (ed ecangle an aea A illuminaed 3dB, hoizonal 3dB, veical

18 Dieciviy vs Aea Copyigh Mak odwell, 06 Aea of a sphee of adius : Anenna dieciviy D D Bu, 4 / 3dB, veical 3dB, hoizonal So : D 4WH / H, / A 3dB, veical 4A / A sphee / 4 (angles in adians 3dB, hoizonal sphee A illuminaed / W whee A is he apeaue aea

19 Tansmi vs eceive anenna Copyigh Mak odwell, 06 Tansmie apeue : heigh eceive apeue : heigh H H T, widh W, widh W T, aea, aea A A T, dieciviy, dieciviy D D Fo eihe : D 4A / 3dB, hoizonal 4 / / W, 3dB, hoizonal 3dB, veical 3dB, hoizonal / H (angles in adians

20 Copyigh Mak odwell, 06 eceived powe Fiis Tansmission Fomula ed ecangle: aea, a adius, illuminaed by ansmie Blue ecance: aea of eceiving anenna P P eceived asmied eceive aea illuminaed aea A 4 / D A D 4 Bu D 4A / and D 4A / So : P P eceived asmied A A D D 6

21 To summaize Copyigh Mak odwell, 06 P P eceived asmied eceive aea illuminaed aea A A D D 6 D D 4A 3dB, hoizonal 3dB, hoizonal 3dB, hoizonal 4,000 degees / W, 4 3dB, hoizonal Ignoes : amospheic loss eain scaeing loss beam blockage 3dB, hoizonal 3dB, veical (angles in adians / H (angles in adians

22 Phased Aays Copyigh Mak odwell, 06

23 An aay of anennas: Copyigh Mak odwell, 06 Take a small anenna : size h by w. Make a lage aay of hem : oveall size H by W. Dive hem in phase on ansmi, o on eceive. This is an *aay anenna * eical half - powe beamwidh, Hoizonal half - powe beamwidh, 3dB veical / H 3dB hoizonal / W

24 An aay of anennas: Copyigh Mak odwell, 06 Picue of an example Noe ha he aay is aimed by * mechanical* seeing * Eleconic* beamseeing is also possible.

25 Copyigh Mak odwell, 06 Beamwidh of anenna aay: elemen phases Dive he anennas in - phase : Physical angle. eical elemen sepaaion D Pah lengh diffeence l D Time delay diffeence ( D Elecical elaive phase shif v v. sin v / csin l /. If 0, signals do no add in - phase. This is why angula beamwidh is / H, no / h

26 Copyigh Mak odwell, 06 Eleconic Beamseeing, a.k.a. phased aay Add phase -shifes : bing signals back ino phase a physical angle. Elecical elaive phase shif Pah lengh diffeence l D v sin l /. eceive phased aay

27 Why phased aays? Copyigh Mak odwell, 06 Lage apeue, high dieciviy, naow beamwidh song eceived signal inefeence and muipah immuniy hps://en.wikipedia.og/wiki/phased_aay Bu, no need o mechanically aim naow beam. (eleconic beamseeing

28 Anenna & aay basics Copyigh Mak odwell, 06 Oveall aay ses beamwidh and hoizonal beamwidh aay widh veical beamwidh aay heigh Gain (diecivi y 4 aay aea gain (adians Individual elemen ses maximum beamseeing hoizonal seeing (adians elemen widh veical seeing elemen heigh ange. Fomulas assume ha aay elemens ouch each ohe; if hee ae spaces, we mus e - deive. A lage seeing angle, pojeced aay aea diminishes, inceasing beamdwidh. Again, mus e - deive.

29 Beamseeing eleconics: Achiecues Copyigh Mak odwell, 06 F phase - shifing phase - shifing

30 Beamseeing eleconics: Achiecues Copyigh Mak odwell, 06 muliple independen beams each caying diffeen daa each independenly aimed # beams = # aay elemens Hadwae: In effec, a sepaae phased aay fo each signal Signal pocessing: maix opeaions a baseband

31 MuliPah Popagaion Copyigh Mak odwell, 06

32 Mulipah Popagaion Copyigh Mak odwell, 06 Given lage angula beamwidh (low - dieciviy anennas Many objecs in anenna beam paen. Many signal pahs :"muli - pah popagaion" Each pah has diffeen lengh, diffeen delay. eflecing suface bounday condiion : possible phase shif. Each pah has diffeen signal sengh Dieciviy of anennas Sengh of eflecion

33 Copyigh Mak odwell, 06 Mulipah Popagaion: Delay Spead Delay spead use small- angle appoximaion. angles, small :, Lage above. use Pyhagous, wide angles, :, Low pah : Non - S (NS pah : sigh (S Line of H H c H H H H D D D D D H H D

34 Fading vs Inesymbol inefeence Copyigh Mak odwell, 06 (Delay spead Symbol peiod Fading S and NS signals aive wih symbol peiods ~ aligned Caies ae ou of phase inefeence possibly vey weak signal fix : wo eceiving anennas a appopiae sepaaion (Delay spead Symbol peiod Inesymbol inefeence One bi peiod inefes wih anohe need adapiive equalize in eceive o use ODFM :longe symbol peiods

35 Copyigh Mak odwell, 06 Signals o be Tansmied

36 Copyigh Mak odwell, 06 Signals we migh wan o ansmi by adio oice - qualiy sound ansmiss ion ange of human heaing (opimisi :0.4-4 khz c:0hz - 0kHz Uncompess ed HDT :abou.5 Gb/sec Compessed HDT : abou 5 Mb/s WiFi : ~00 Mb/s MP3 compessed audio :3-30 kb/s These signals mus be anslaed in fequency if we ae o ansmi hem by adio waves.

37 Geneaion of Digial Daa Seams Copyigh Mak odwell, 06 Samples mus hen be digiized wih some # of bis esoluion. If he digial seam conains edundancy, daa aes can be educed by compessio n. JPG, MPG, MP3,... (infomai on heoy

38 ecall he Sampling Theoem Copyigh Mak odwell, 06 image shifed by -f sample image shifed by +f sample To avoid specal aliasing, a signal of bandwidh limied o ( f, f mus be sampled a a ae sig. sig sample sig f f.

39 Bandlimiing of digial daa seams ( Copyigh Mak odwell, 06 Fileing a digial signal ounds he wavefom and educes he signal bandwidh A ain of impules has a fla specum A ecangula pulse ain has specum sin( bi / /( bi /

40 Bandlimiing of digial daa seams ( Copyigh Mak odwell, 06 If he daa seam is bick - wall fileed o bandwidh ( f / bi, f / hen each daa pulse has a shape sin( / /( / bi, bi bi. The funcion zeo fo sin( / bi,3 bi bi,4 /( /,ec., is so hee is zeo inesymbo l inefeence (ISI beween sucessive bis in he daa seam. bi bi

41 Bandlimiing of digial daa seams (3 Copyigh Mak odwell, 06 Oveall digial wavefom is a sum of hese pulses. This is had o daw. Hee is wha he wavefom looks like. This is an eye paen. Tajecoy is daw epeaedly fo all possible daa sequences.

42 Bandlimiing of digial daa seams (4 Copyigh Mak odwell, 06 Nyquis' s vesigal sideband heoem (NOT his sampling heoem : If he specum is symmeic wih a 80 degee hen he inesymbo l inefeen ce will be zeo. aion abou he indicaed poin, Minimum bandwidh is ( / bi, / minimum oal bandwidh is equal o he / - (/ he bi ae. Typical files ae boade, ypical equied bandwidh somewha geae han / - (/ he bi bi ae.

43 Pulses wih aised Cosine Speca : Fom Wikipedia. Copyigh Mak odwell, 06 hp://en.wikipedia.og/wiki/aised-cosine_file The aised - cosine pulse wavefom is a mahemaic alidealizai on of a family of zeo - ISI signals. These ae used in appoxima ing eal ansmiss ion sysems Fouie Tansfom of pulse Time wavefom of pulse As vaies fom 0 o, he fequency ange of he baseband digial will vay fom o ( / bi, / ( / bi bi i.e. ( f, / bi, f bi bi, i.e. ( f bi,fo. /, f bi /, fo 0, signal

44 Pulses wih aised Cosine Speca: Files Copyigh Mak odwell, 06 I is he *fileed pulse * which mus have he aised - cosine specum H( f. Since a ecangula pulse aleady has a sin( channel file (# mus have ansfe funcion bi / /( bi H( f ( / specum, he bi // sin( bi / Of couse, eal digial cicuis poduce ecangula pulses, so he fis file is no pesen in eal hadwae. no impulses,

45 Copyigh Mak odwell, 06 oo aised Cosine Speca in Tansmission Links In a adio link, we mus bandlimi We mus fuhe bandlimi he he ansmi e o say wihi n he allowed eceive so as o limi eceive noise. The final eceived signal mus also have zeo ISI; mus mee Nyquis cieion. fequency band. This is accomplish edusing *oo - aised - cosine *files.

46 Copyigh Mak odwell, 06 oo aised Cosine Speca in Tansmission Links H fileed H Choose a *oo - aised - cosine * specum fo he ansmi ed signal : H The eceive file mus hen also have oo - aised - cosine fequency esponse : H Given ha H ( j is a aised - cosine funcion : fileed T ( j F 3 F ( j H ( j H i is diven by ecangula pulses, he ansmi e file esponse is : ( j H H T C C C ( j ( j ( j ( j / H ec ( j H ( j ( / / sin( / C bi bi

47 Copyigh Mak odwell, 06 Modulaion and Fequency Convesion

48 Fequency Convesion / Modulaion Copyigh Mak odwell, 06 Depending on, he seam has a baseband specum beween (DCdaa f bi / o (DC- f bi. We ansmi he signal using adio fequencie s beween pehaps few MHz o00 GHz Fequency (Hz To do his, we mus impose ou signal on he high - fequency caie. This is called modulaion ; i is done by mixing (muliplic aion.

49 Copyigh Mak odwell, 06 Mixing = Muliplicaion cos( ( B I B cos( ( 0 / cos( cos( ( B I F e e e e e e e e e e e e e e e e z z z z z z z z z z z z z z e e z z e e B B j j j j j j j j j j j j j j j j B B B B B B B j j B B j j B B B B B B B B B B B ( cos ( cos ( ( ( ( cos( cos( 4 so cos( cos( y. efficienl funcions ig. wok wih We mus lean o sin( and cos( sin( cos( j j j j j e e j e e j e

50 Mixing = Muliplicaion Copyigh Mak odwell, 06 B cos( I B cos( F I ( I cos( F B / 0 F cos cos( / ( ( / cos( B 0 I F 0 B By a simila calculaio n... B sin( Q B cos( F Q ( Q sin( B / 0 sin cos( / ( ( / sin ( B 0 Q 0 B Muliplica ion geneaes sum and diffeence fequencie s

51 Copyigh Mak odwell, 06 Mixing Convoluion of Speca B ( ( 0 / ( ( ( b F ' ( ' ( ' ( ( and ( n of convoluio ( * ( ( j d j j j j j j j j b b b F ( ( ( ( ( So ( ha ecall / ( / ( cos( ( Suppose j j j j e e e Specum of he Local Oscillao

52 Mixing wih cosine ("I" local oscillao Copyigh Mak odwell, 06 B ( F ( j Suppose cos( Local oscillao specum Baseband signal specum (noe eal, imaginay pas F signal specum

53 Mixing wih sine ("Q" local oscillao Copyigh Mak odwell, 06 B ( F ( j Suppose sin( ( j ( j ( ( j ( Local oscillao specum Baseband signal specum (noe eal, imaginay pas F signal specum (noe he flipped phase of he sidebands

54 IQ Modulaion Copyigh Mak odwell, 06 B, I ( B, Q ( cos( F B, I I 0 cos( cos( Q B, Q sin( 0 sin( sin( and B, B, I Q ( ae independen, synchoniz ed daa seams

55 IQ Signal epesenaion Copyigh Mak odwell, 06 F j j e cos( sin( e I Q I Q Signal is epesened asa poin in a plane

56 IQ Signal epesenaion Copyigh Mak odwell, 06 F cos( sin( I cosine wave sine wave Q cos( cos( spins coune - clockwise angula fequency a

57 Quadaue Phase Shif Keying (QPSK Copyigh Mak odwell, 06 B I, B, Q ( cos( F B, I I 0 cos( cos( Q B, Q sin( 0 sin( sin( and B, B, I Q ( ae binay sequences Also known (less ofen as 4 - QAM

58 Copyigh Mak odwell, 06 6-Quadaue Ampliude Modulaion (6-QAM cos( sin( Thee is also 64 - QAM, 56 - QAM, ec.

59 Demodulaion Copyigh Mak odwell, 06 B, I ( cos( cos( ( i b, q ( S ( q ( S i sin( sin( cos( sin( B I 0 B, Q 0 S B, I B, I, 0 cos( cos ( 0 cos( sin( 0 B, I B, Q 0 0 sin( emoved B, Q cos( by LPF 0 Similaly, q B em a., Q 0

60 eceive Sensiiviy Copyigh Mak odwell, 06

61 Compuing eceive Sensiiviy ( Copyigh Mak odwell, 06 Fis, define he symbol wavefoms o be ansmied These ae jus a couple of possibiliies. Thee ae many

62 Compuing eceive Sensiiviy ( Copyigh Mak odwell, 06 Use hese as examples.les label hem (, (, (,3 (, is he fis of n possible wavefoms in ime slo #. ec. I is possible o have moe han one signal wavefom in each peiod Example: I( and Q( in QAM, ec

63 Enegy Pe Signal Copyigh Mak odwell, 06 Coecion :symbol peiod is sym (, Enegy pe Symbol E symbol Signal P signal Z 0 powe E bi / ols seconds Ohms d Joules, symbol E bi assuming we have one wavefom pe ime slo B Z 0 is he efeence impedance. Need no be physically coec. Will cancel ou in mah.

64 Nomalizaion: Uni Enegy Signals Copyigh Mak odwell, 06 Make hese * uni enegy*(no uni powe signals (, Enegy pe Symbol E symbol Z 0, d.0 Joules We have scaled he ampliude of he symbol enegy is.0 Joule., so ha Do ha fo *all* he symbol wavefoms

65 Non-inefeing wavefoms Copyigh Mak odwell, 06 These base signals should no inefee. We wan : Z 0 Z 0,,,, d d 0 ec. Zeo ovelap beween peiods 0 ec. Zeo ovelap wih a peiod (, (, (,3

66 Easie Noaion: do poducs Copyigh Mak odwell, 06 Hee is a moe compac noaion :,,,, Z 0 Z 0,, d d and so on These ae inne poducs. Jus like veco algeba.,,

67 Ou Se of Uni-Enegy singals: Copyigh Mak odwell, 06 Using ou moe compac noaion :,,,, ec. Joule,,,, ec. 0 Joules Take he do poduc wih he same wavefom. Take he do poduc wih a diffeen wavefom 0 even moe compacly: i, j whee k,l i,k Joule i,k isif is indices ae he same, 0 ohewise. (like a uni diagonal maix j,l (, (, (,3

68 A bi moe noaion and nomalizaion: Copyigh Mak odwell, 06 If we wee o ansmi *one* wavefom pe symbol peiod (caeful:qam has wo : Tansmi volage v m m,, m 3,3... Tansmi signal Enegy pe symbol peiod E m because Joule,, m m migh be / -(binay migh be 3/ / -/ 3 ( bis/wavefom m m 0.5(9 9 5

69 A bi moe noaion and nomalizaion: Copyigh Mak odwell, 06 eceived volage v m, I' veassumed only one wavefom pe symbol (caeful:qam has m wo, m 3,3... peiod eceived signal Enegy pe symbol peiod E m because Joule,,

70 Copyigh Mak odwell, 06 Opimum eceive (ohogonal signals, whie noise Le us no pove his ye, bu an opimum eceive simply muliplies v, wih he vaiousi, j( The op sucue illusaes his diecly, he boom sucue shows his in wo seps fo QAM

71 eceived Signal: no noise Copyigh Mak odwell, 06,( (, eceived Signal (no noise v m,, m,, m,, m,,... Oupu of muliplies : I v, m, because i, j k,l Joule i, j,k,l Q v, m, This is in he absence of noise. Noe : we ae now assuming ** basis wavefoms pe symbol peiod

72 eceived Signal: wih noise Copyigh Mak odwell, 06,( (, eceived Signal (wih noise v n( m,, m,, m,, m,,... Oupu of muliplies : I v, m, n, Q v, m, n, We need o know he vaiances and covaiances of n i, j

73 Noise popagaion hough he eceive Copyigh Mak odwell, 06 Noise oupu of basis basis basis wavefom, wavefom, wavefom, We need o know coelao (s :,( (, n, o moe geneally En i n E n imeslo : imeslo : imeslo :,, n n,, n, n(, n(, n(,,, j k, l

74 Noise popagaion hough he eceive Copyigh Mak odwell, 06 Coelaions of i, jnk, l E n( i,j n( k,l E Z n( d Z n( ( E n whee So, ( Bu n( has a powe specal densiy of S E Z Z Z nn nn because ( n( n( E[ n( n( ] ( is nn ktfz nn noise oupus i,j 0 i,j i,j he auocoelaion of (, ( and S i,j 0 k, l k, l whee nn of k, l coelao (s : ( dd ( dd F is k, l ( dd d n( nn ( jf ktfz he sysem noise figue. ( ( jf ae a Fouie ansfom pai. 0 / Hz

75 Noise popagaion hough he eceive Copyigh Mak odwell, 06,( (, Coelaions of noise oupus of coelao (s : E n i, j n k, l Z 0 Z 0 ktf Z ktf ktfz 0 i, k j, l 0 i,j nn ( ( k, l i,j i,j k, l k, l d ktf ( dd ( dd The coelaos have noise oupus wih vaiance ktf (Joules, and wih sasical independence of he noise signals beween coelaos i,j k, l

76 Signal o Noise aio Copyigh Mak odwell, 06 eceived Signal (wih noise : eceived signal Enegy pe symbol peiod : E Oupu of muliplies : I v whee he n, i, j m, n, v, Q n( m ae uncoelaed and have vaiance ktf v,,, m m m,, n m ( symbols/peiod,,,,... spacing m noise vaiance ktf

77 Pobabiliy of cossing decision bounday Copyigh Mak odwell, 06 eceived signal Enegy pe symbol peiod : I n i, j v, m n ae uncoelaed and have vaiance ktf,,, Q E v, m m, ( symbols/peiod n, Wha is he pobabiliy of a given signal veco cossing a specific bounday? Disance o bounday : m /, whee m /. Noise vaiance: ktf Pobabliy disibuion is Gaussian : n f N ( n exp Wha is he pobabiliy of n exceeding m /? noise vaiance ktf Noe :eo ae fo I o fo Q : P eo I is a P bounday 4 modeae coecion....5p bounday veco spacing m

78 Copyigh Mak odwell, 06 Pobabiliy of cossing decision bounday d Q ktf m Q m Q m n P n n f ktf m N exp ( whee / / / exceeding Pobabiliy of (cossing bounday exp ( Noise vaiance:, / Disance o bounday :

79 Eo Funcions Copyigh Mak odwell, 06 Q( Q( can be elaed o he moe well- known eo funcion * ef, bu Q( is moe diecly useful in I will povide a good abulaio n of bound fo lage : communcai ons poblems. Q(, bu hee is a vey good exp Q( exp * hps://en.wikipedia.og/wiki/eo_funcion

80 Tabulaed values of he Q-funcion Copyigh Mak odwell, 06 Some values of he Q-funcionae given below fo efeence. Q(0.0 = Q(0. = Q(0. = Q(0.3 = Q(0.4 = Q(0.5 = Q(0.6 = Q(0.7 = Q(0.8 = Q(0.9 = Q(.0 = Q(. = Q(. = Q(.3 = Q(.4 = Q(.5 = Q(.6 = Q(.7 = Q(.8 = Q(.9 = Q(.0 = Q(. = Q(. = Q(.3 = Q(.4 = Q(.5 = Q(.6 = Q(.7 = Q(.8 = Q(.9 = Q(3.0 = Q(3. = Q(3. = Q(3.3 = Q(3.4 = Q(3.5 = Q(3.6 = Q(3.7 = Q(3.8 = Q(3.9 = Q(4.0 = hp://en.wikipedia.og/wiki/q-funcion

81 Pobabiliy of Signal Cossing Bounday Copyigh Mak odwell, 06 Pocedue : Sa wih some pobabiliy of bounday - cossing.this is Q (. Deemine fom he plo o fomula fo Q (. Example: Q ( Q (6 0 m / 6 ktf ( m / 9 ktf ktf Bu he eceived signal enegy pe symbolis E E s s m m one wavefom pe symbol wo wavefoms pe symbol And m m wo - level coding 5 fou - level coding

82 eceive Sensiiviiy Copyigh Mak odwell, 06 BPSK : E P symbol eceived m ktf ktf B whee B is he *symbol* ae QPSK : E P symbol eceived m ktf ktf B bu he bi ae is B 6QAM : E P symbol eceived m ktf ktf B bu he bi ae is 4B

83 Copyigh Mak odwell, 06 Coelaos vs. Mached files

84 eceive using coelaos. Copyigh Mak odwell, 06 Oupu of coelaos I Wha if we insead pass he signal hough a mached file? Mached file impulse esponse : h Oupu of mached file : v Suppose we se Then If we sample v v ou v v ( T ou, v in ou v ( Z ( ( T ( T a T :, 0 h in, v, ou ( d Z d. ime evesal and delay. d 0, v v in Simila elaionship fo ( h, ( d Q

85 eceive using coelaos. Copyigh Mak odwell, 06 So we can eplace a coelao in he eceive Wih a mached file Pacical ealizaion : he oo - aised - cosine files discussed ealie. These can be analog files, o can bein DSP afe he ADC

86 eceive Tuning Copyigh Mak odwell, 06

87 Copyigh Mak odwell, 06 Ealy (90's eceive: Tuned adio Fequency A single LC file is has oo boad a bandwidh o sepaae saions Muliple cascaded files naowe uning bandwidh. Poblem : Mechanical acking of muliple files duing uning.

88 Copyigh Mak odwell, 06 Supeheeodyne eceive (Amsong, 98 eceive adio signal is conveed o an inemedia e fequency befoe deecion. eceived signal fequency is uned by vaying he fequency. Shap fixed - uned IF files ae used fo channel selecion.

89 Copyigh Mak odwell, 06 Oveall Block Diagams

90 QAM/QPSK ecieve Copyigh Mak odwell, 06 Diec convesion o clock and daa ecovey Supehee odyne

91 QAM/QPSK Tansmie Copyigh Mak odwell, 06 Diec convesion Supehee odyne

92 Copyigh Mak odwell, 06 Link Budge Calculaions

93 Quick link calculaions Copyigh Mak odwell, 06 I will pos on he class web sie

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