Communications II Lecture 4: Effects of Noise on AM. Professor Kin K. Leung EEE and Computing Departments Imperial College London Copyright reserved

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1 Commuiaio II Leure 4: Effe of Noie o M Profeor Ki K. Leug EEE ad Compuig Deparme Imperial College Lodo Copyrigh reerved

2 Noie i alog Commuiaio Syem How do variou aalog modulaio heme perform i he preee of oie? Whih heme perform be? How a we meaure i performae?

3 We mu fid a way o quaify =o meaure he performae of a modulaio heme. We ue he igal-o-oie raio SNR a he oupu of he reeiver: SNR 0 average power of meage igal a he reeiver oupu average power of oie a he reeiver oupu P P S N 3

4 Model of a aalog ommuiaio yem 4

5 P T : The ramied power Limied by: equipme apabiliy, o, goverme reriio, ierferee wih oher hael, e The higher i i, he more he reeived power PS, he higher he SNR For a fair ompario bewee differe modulaio heme: P T hould be he ame for all We ue he baebad igal o oie raio SNR baebad o alibrae he SNR value we obai 5

6 Baebad Commuiaio Syem I doe o ue modulaio I i uiable for ramiio over wire The power i rami i ideial o he meage power: P T = P The reul arry over o bad-pa yem 6

7 7

8 verage igal=meage power: P =he area uder he riagular urve ume: ddiive, whie oie wih power peral deiy PSD=N 0 / verage oie power a he reeiver: P N = area uder he raigh lie = WN0/ = WN 0 8

9 SNR a he reeiver oupu: SNR baebad PT N W 0 Noe: ume o propagaio lo PT P S Improve he SNR by: a ireaig he ramied power P T, b reriig he meage badwidh W, makig he reeiver le oiy N 0. 9

10 REVISION: mpliude Modulaio Geeral form of a M igal: [ m ]of M : he ampliude of he arrier f : he arrier frequey m: he meage igal 10

11 Modulaio idex: m p m p : he peak ampliude of m, i.e., m p = max m 11

12 Sigal reovery 1 1 m p : ue a evelope deeor Oherwie: ue yhroou deeio=produ demodulaio=ohere deeio 1

13 Syhroou deeio Muliply he waveform a he reeiver wih a loal arrier of he ame frequey ad phae a he arrier ued a he ramier: Ue a LPF o reover m + / ad fially m Problem: he reeiver you eed a igal perfely yhroized wih he ramied arrier 13

14 REVISION mpliude Modulaio: Double-idebad uppreed arrier DSB-SC m of DSBS Sigal reovery: Wih yhroou deeio oly 14

15 15 Noie i DSB-SC The rue igal reeived i: i ]o [ i o o i o f f m f f f m f f x

16 For yhroou deeio: muliply wih oπf : y of m o x m [1 o4f i4f f Ue a LPF o keep ~ y m ] o f [1 o4f i4f ] 16

17 Sigal power a he reeiver oupu: P S E{ m } E{ m } P Power of he oie igal : P W N0df N W N 0 W 17

18 SNR a he reeiver oupu: SNR 0 P N W 0 To whih ramied power doe hi orrepod? P T E{ P m o f } 18

19 So SNR 0 PT N W 0 SNR DSBSC Compario wih SNR baebad PT N W 0 SNR DSBSC SNR baebad Coluio: a DSB-SC yem provide o SNR performae gai over a baebad yem. 19

20 0 Noie i adard M, Syhroou Deeio Pre-deeio igal: i ]o [ i o ]o [ ]o [ f f m f f f m f m x

21 Sigal Reovery: Muliply wih oπf : y [1 o4f [1 o4f ] m [1 ] o4f i4f ] LPF ~ y m 1

22 Sigal power a he reeiver oupu: P S E{ m } P Noie power: P N N 0 W

23 SNR a he reeiver oupu: SNR 0 P N W 0 SNR M Tramied power: P T P P SNR of a baebad igal wih he ame ramied power: P N W SNR baebad 0 3

24 Thu: SNR M SNR baebad P P Noe: P 1 P Coluio: he performae of adard M wih yhroou reovery i wore ha ha of a baebad yem. 4

25 Noie i adard M, Evelope Deeio Phaor diagram of he igal pree a a M reeiver E i : reeiver oupu= y 5

26 y evelope of x [ m ] 95 Equaio oo ompliaed Mu ue limiig ae o pu i i a form where oie ad meage are added 6

27 1 pproximaio: a Small Noie Cae [ m ] The The [ m ] y [ m ] 7

28 Thu SNR 0 P N W 0 SNR ev d i erm of baebad SNR: SNR Valid for mall oie oly! ev SNR baebad P P 8

29 9 ] [ m d pproximaio: b Large Noie Cae Iolae he mall quaiy i 95: 1 ] [ ] [ m m m m m y

30 30 where : he evelope of he oie E ] [ 1 ] [ 1 ] [ E m E m y

31 31 From he phaor diagram: = E oθ The: Ue : 1 for 1 1 x x x ]o [ 1 E m E y ]o [ ]o [ 1 m E E m E y

32 Noie i mulipliaive here! No erm proporioal o he meage! Reul: a hrehold effe, a below ome arrier power level very low, he performae of he deeor deeriorae very rapidly. 3

33 SSB modulaio Sigle lower idebad M: where mˆ mˆ SSB m of mˆ i f i he Hilber raform of m. i obaied by paig m hrough a liear filer wih rafer fuio jgf. mˆ ad m have he ame power P. The average power i P/4. 33

34 34 Noie i SSB Reeiver igal x = +. pply a bad-pa filer o he lower idebad. Uig ohere deeio: fer low-pa filerig, i4 ˆ o4 o f m f m m f x y m y

35 Sigal power P/4 Noie power for = ha for bad-pa oie = N 0 W SNR a oupu P 4N W SNR SSB 0 For a baebad yem wih he ame ramied power P/4 P 4N W SNR baebad 0 Coluio: SSB ahieve he ame SNR performae a DSB-SC ad he baebad model bu oly require half he bad-widh. 35

36 Summary 36