Commuiaio Sysems Leure 5 Dog I Kim Shool o Io/Comm Egieerig Sugkyukwa Uiversiy 1
Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM
Review o Agle Modulaio Geeral orm o agle modulaed sigal: PM: ( = os é w + ( x A ë x( = Aos éw+ kpm( ù ë û ( ( m : ormalized message wih max m = 1. é ù FM: x ( = Aos w+ p ò d m ( a d a êë úû 1 P= A. Trasmied Power: Demodulaio oupu: PM: T 1 d yd( = KD(, FM: yd( = KD p d ù û ( 3
Noise i Agle Modulaio ( x + Noise w(: AWGN N 0 / Predeeio Filer 1( ( e Demodulaio Badwidh o he predeeio iler: Carso s rule: B T = (D+1W. ( = éw + ( From x Aos ù ë û, To aalyze he ee o he oise, we eed o wrie ( ( e1 ( = R(os éw q e ù ë + + + û, where e ( is he oise added o (. Posdeeio Filer Rd Redue oise (explaied laer 4
Noise i Agle Modulaio Predeeio iler oupu: ( = os é w + q + ( ù + ( os ( w + q - ( si ( w + q e1 Aos ë û ( os s( si = A os é w q ( ù ë + + û + r( os( w+ q+ ( os éw q ( ù ( os( w q ( ( ( = A ë + + û + r + + - + ( ( ( ( ( w + q+ ( si( ( ( ( ù ( = A os é ë w+ q+ û + r( os w+ q+ os - - r (si + + si( - ( ( ( ( A r(os oséw q ( = + - ë + + - r (si ( w + q+ ( si( ( -( ù û 5
Noise i Agle Modulaio ( ( ( ( éw q ( e1 ( = A + r (os - os ë + + e ( ( w + q+ ( si ( ( ( - r (si + + - ( ( = R(os é ë w+ q+ + e = a ù û ( ( ( ( ( r (si 1 A + r (os - - - ( Phase deviaio rom he arrier: ( ( y( = + e Oly yphase deviaio aes he demodulaio. Ampliude a be kep osa by a limier (pp. 143. 6 ù û
Agle Modulaio wih High SNR High SNR: A r( mos o he ime. r (si ( ( (si ( ( - r - -1 ( -1 ( e ( = a» a A+ r(os ( ( -( A r (si ( ( - ( r (si ( ( - ( (si -1 (si(» si» A A r ( y( = + e» + si - A A ( ( ( ( ( ( Sill domiaed by he sigal ( ireases, he ee o r ( redues! 7
Agle Modulaio wih Low SNR Low SNR: A r ( mos o he ime. y (: domiaed by (. y ( = ( -a (. a ( Need expressio o a ( i erms o ( ad (. Noe: e ( is wrog i Fig. 6.13. e 8
Agle Modulaio wih Low SNR Low SNR: y ( = ( -a (. a( very small i A r (. a ( a(» si a(» a a(» A y(» ( si q( r ( A - si ( ( r ( - ( 9
Agle Modulaio wih Low SNR Low SNR: A» - ( - y ( ( si ( ( r ( Message sigal is los a low SNR! Threshold ee. 10
Agle Modulaio Phase deviaio e ( (os 1 = R é ë w+ q+ y ù û ( High SNR: r ( y (» ( + si ( ( - ( (1 ( Low SNR: A Small mos o he ime A y(» ( - si ( ( - ( ( r ( Noe: Eq ( a be obaied rom (1 by swihig ( «(, ad A «r (. 11
Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM 1
PM Oupu SNR ( = éw + q+ ( ù+ ( ( w + q - ( i ( w + q e1 Aos ë û (os s(si ( ( (os ( = R(os éw q ù R éw q ù ë + + + e û ( ë + + y û r ( y (» + si - A PM Demodulaio oupu: ( High SNR: ( ( ( ( = y( = ( + ( y K K K D D D D e r ( = KD ( + KD si ( - ( A ( = K k m + ( D p P ( P ( 13
PM Oupu SNR PM Demodulaio oupu: r yd ( = KD kp m ( + KD si ( - ( A ( si ( Demod Sigal power: S = P ( K k P DP D p m To ompue oise power: le ( = 0 (message is 0 r( s( P( = KD si( = KD A A r ( ( ( s 14
PM Oupu SNR Reall: NBNoise N 0 / S ( S (- +B/ S (+ ( = Lp é ( - + ( + B/ S S s S ù ë û S s ( N 0 B/ 15
PM Oupu SNR PM Demodulaio oupu: s ( P ( KD A D = S ( = N P 0 A Sperum o s ( is i [-1/ B T, 1/ B T ] ( = ( + ( y K k m D D p P B T : Badwidh o predeeio iler (by Carso s rule. Oupu oise power: N DP = K D 0 A K N B T 16
PM Oupu SNR Pos-deeio i iler: Sie B T = (D+1W > W, he oupu oise power a be redued by applyig a pos-deeio iler wih badwidh W Predeeio Filer e1( Demodulaio Posdeeio Filer N DP = K D A N B 0 T N DP = K D A N W 0 17
PM Oupu SNR Trasmied power Per ui message badwidh 1 P= A. Trasmied Power: Oupu oise power: T D ç T 0 D A è 0 A PT = N W N W 0 0-1 K æ P ö N = DP N W = K. ç N W ø Ireasig rasmied power redues oupu oise power! Diere rom liear modulaio. PM Demod Oupu SNR: K k P SNR = = k P DP K P N W - NW ( SNR D D p m P T k ppm T / ( 0 0 ( 1 18
PM Oupu SNR PM: x A é ë kpm ( = os w + ( PM Demod Oupu SNR: Sigle-oe Modulaio ( = k siw bsiw p m m ù û P SNR = k P DP NW ( SNR m ( = si w or osw m m T p m 0 b k p : Modulaio Idex SNR PT = b P m : ireasig b ireases oupu SNR. DP NW ( 0 ( b + Bb Bu badwidh B = + 1 W is also ireased. T Ipu oise power will be ireased. Eveually large ipu SNR assumpio is ivalid hreshold ee. 19
Oulie Noise i Agle Modulaio Phase deviaio Large SNR Small SNR Oupu SNR PM FM 0
FM Oupu SNR ( = A éw + q + ( ù + ( ( w + q - ( i ( w + q e1 Aos ë û (os s(si ( ( (os ( r ( y(» ( + si( ( ( - A = R(os éw + q+ + ù R éw + q+ y ù ë e û ë û High SNR: FM Demodulaio oupu: y D ( ( A K d y D = p d K d ( ì ü D KD d r ( = + í ï si ( ( ( - ý ï p d p d ï A î ïþ ( = K m + ( D d F F ( 1
FM Oupu SNR FM Demodulaio oupu: K ( D d ì r ü y ( ( ï si ( ( ( ï D = KD dm + í p d A - ý ï î ïþ Demod Sigal power: S F ( DF = KD d Pm To ompue oise power: le ( = 0 (message is 0 ( K ì ü (si D d r KD ds ( F ( = ï í ï ý= p d ïî A ïþ pa d (: quadraure ompoe o oise. s How o id oise psd? r ( ( ( s
FM Oupu SNR ( K (si D d ì r ü KD ds ( F ( = ï í ï ý= p d ï î A ï þ pa d dx( j p X ( d ( s «d/d is a liear iler d d u ( S ( = H( S ( KD KD 1 1 NF = ç ( p 0 0 T T pa = Îê- A æ ö é ù S ( N N, B, B. èç ø ê ë ú û u s 3
FM Oupu SNR K é 1 1 ù D SNF ( = N 0, Î - BT, BT. A ê ë úû The oise has less ee o low-req message sigals. Aer Pos-deeio iler wih badwidh W: K K NDF = N ò d = N W A W D D 3 0 0. -W 3A ò 4
FM Oupu SNR 1 P= A. Trasmied Power: Oupu oise power: N DF T K K W æ P ö = 3A = 3 ç N W ø D 3 D T N 0W ç è 0 A PT = N W N W -1 0 0 Noise power is iversely proporioal p o FM Demod Oupu SNR: ( SNR DF K D d P æ m ö 3 d PT P -1 m æ P ö èç W ø D T 0 = = K W 3 ç èn W ø 0 N W P T NW 0 5
FM Oupu SNR FM Demod Oupu SNR: ( SNR DF æ ö = ç P N W d T 3 Pm ç èw ø 0 Reall: Deviaio Raio or geeral m(: peak requey deviaio max '( D = = badwidh o m( W é ù FM: x ( = Aos w+ p ò d m ( a d a êë úû d max m( D = d SNR W = ( DF W P SNR = D P NW T 3D Pm 0 6
FM Oupu SNR FM Demod Oupu SNR: P SNR = D P DF NW ( SNR T 3D Pm 0 For D 1, B =(D+1W» DW: T ( SNR DF 3æB ö T PT Pm 4 ç çèw ø 0 = N W Ireasig badwidh a improve he oupu SNR. Ipu oise power will be ireased. Eveually large ipu SNR assumpio is ivalid hreshold ee. 7
Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Demod oupu: Noise K ì ü D d r ( y ( ( si ( ( ( D = KD dm + í ï - ý ï p d ï A î ïþ Umodulaed arrier: F dx ( «d F ( ( 0 (message is 0 = ( K ì ü (si D d r KD ds ( ( = í ï ý ï= p d ïî A ïþ pa d K é 1 1 ù D j p X ( SNF ( = N 0, Î - BT, BT. A ê ë úû 8
Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise K 1 1 D é ù SNF ( = N0, - B,. T BT A Îê ê ë úû Assume de-emphasis iler is a 1 s -order lowpass RC iler: 1 HDE ( = 1 + ( / 3 W Noise power aer de-emphasis iler: W DF DE NF W N = ò H ( S ( d - 3 ò 9
ò 1 1 u du = a -1 a + u a a Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise Noise power aer de-emphasis emphasis iler: W NDF = ò HDE ( SNF ( d - W K K = N d = N d A A W W D ò D ò 0 0 3 W W - 1 + ( / - 3 3 + K æw Wö K æw pö K = N - a» N -» N W A A A D 3-1 D 3 D 0 3 0 3 0 3 ç è 3 3ø ç è 3 ø 30
Pre-emphasis ad De-emphasis or Noise A PT = N W N W 0 0 Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise ( = ( + ( y K m D D d F Demod Sigal power: Noise power aer de-emphasis: Oupu SNR: ( ( / P = Oupu SNR: SNR wihou deemphasis: S N DF = KD d Pm DF» SNR P T DF d 3 m NW 0 SNR PT = 3 d / W P DF m NW ( ( 0 K D A N W 0 3 31
Pre-emphasis ad De-emphasis or Noise Pre emphasis Mod + Pre deeio Demod Pos deeio Deemphasis Noise Oupu SNR wih de-emphasis: emphasis: ( = ( / SNR P T DF _ DE d 3 m NW 0 Oupu SNR wihou de-emphasis: 3 W ( = 3 ( / P PT SNR 3 d / W P DF m NW SNR a be improved sigiialy by de-emphasis iler. 0 3
Pre-emphasis ad De-emphasis or Noise SNR wih de-emphasis: SNR wihou de-emphasis: ( ( / P = SNR P T DF _ DE d 3 m NW 0 ( = 3 ( / P SNR W P T DF d m NW Example: FM: = 75 khz, W=15kHz, D = 5. ( SNR ( d =.1 khz, P =0.1. 3 m PT PT SNR = 375/15 01 0.1 = 7.5 75 DF NW 0 NW 0 PT PT SNR = 75/.1 0.1 = 18 DF_ DE NW NW ( ( 0 0 Trasmied power a be redued by 17 imes, wih he same oise perormae. 0 33