Communicaions II Lecure 5: Eecs o Noise on FM Proessor Kin K. Leung EEE and Compuing Deparmens Imperial College London Copyrigh reserved
Ouline Recap o FM FM sysem model in noise Derivaion o oupu SNR Pre/de-emphasis Comparison wih AM Reerence: Lahi, Chap. 1.
Frequency Modulaion Fundamenal dierence beween AM and FM: AM: message inormaion conained in he signal ampliude Addiive noise: corrups direcly he modulaed signal. FM: message inormaion conained in he signal requency he eec o noise on an FM signal is deermined by he exen o which i changes he requency o he modulaed signal. Consequenly, FM signals is less aeced by noise han AM signals 3
REVISION: Frequency modulaion A carrier waveorm s = A cos[θ i ] where θ i : he insananeous phase angle. 4
When s = A cos θ i = We may say ha d d 1 d d Generalisaion: insananeous requency: i 1 di d 5
6 In FM: he insananeous requency o he carrier varies linearly wih he message: i = c +k m where k is he requency sensiiviy o he modulaor. Hence assuming θ i 0=0: Modulaed signal: Noe: a The envelope is consan b Signal s is a non-linear uncion o he message signal m. c i i d m k d 0 0 c d m k A s 0 cos
Bandwidh o FM m p max m : peak message ampliude c k m p < insananeous requency < c + k m p Deine: requency deviaion= he deviaion o he insananeous requency rom he carrier requency: Deine: deviaion raio: where W: he message bandwidh. k m p W 7
Small β: FM bandwidh x message bandwidh narrow-band FM Large β: FM bandwidh >> x message bandwidh wide-band FM Carson s rule o humb: B T = Wβ+1 = + W β <<1 B T W as in AM β >>1 B T, independen o W 8
Noise in FM Model o an FM receiver 9
Bandpass iler: removes any signals ouside he bandwidh o c ± B T / he predeecion noise a he receiver is bandpass wih a bandwidh o B T. FM signal has a consan envelope use a limier o remove any ampliude variaions Discriminaor: a device wih oupu proporional o he deviaion in he insananeous requency i recovers he message signal Final baseband low-pass iler: has a bandwidh o W i passes he message signal and removes ou-o-band noise. 10
Linear argumen a high SNR FM is nonlinear modulaion, meaning superposiion doesn hold. Noneheless, i can be shown see Chap. 9, Lahi ha or high SNR, noise oupu and message signal are approximaely independen o each oher: Oupu Message + Noise. Any smooh nonlinear sysems are locally linear! Noise does no aec power o he message signal a he oupu We can compue he signal power or he case wihou noise, and accep ha he resul holds or he case wih noise oo. 11
Power o signal a he oupu wihou noise: Insananeous requency o he inpu signal: i c k m Oupu o discriminaor: k m So, oupu signal power: P S k P where: P : he average power o he message signal 1
13 In he presence o addiive noise, he real predeecion signal is I can be shown by linear argumen: For high SNR, noise oupu: approximaely independen o he message signal We only have he carrier and noise signals presen In order o calculae he power o oupu noise, we may use: sin cos cos 0 n n d m k A x c s c c c sin cos cos ~ n n A x c s c c c
Phasor diagram o he FM carrier and noise signals 14
15 Insananeous phase: For large carrier power large A: Discriminaor oupu = insananeous requency: an 1 n A n c s i A n A n s s i an 1 d dn A d d s i i 1 1
The discriminaor oupu in he presence o signal and noise: k m 1 A dns d Wha is he PSD o dn s d Fourier heory: i hen x dx d X Diereniaion wih respec o ime = passing he signal hrough a sysem wih ranser uncion o H = j jx 16
I can be shown: S o H S i where: S i : PSD o inpu signal S o : PSD o oupu signal H : ranser uncion o he sysem 17
18 Then: Aer he baseband LPF, his is resriced in he band ±W wihin band PSD o PSD o PSD o 0 T s s s B N n n j d dn 1 1 PSD o PSD o 0 0 S N j A d dn A N j d dn D s i s
Power specral densiies or FM noise analysis 19
Average noise power a he receiver oupu: Thus, P S d N W W D W 1 0 PN j N0d W A N W 3A 3 Average noise power a he oupu o a FM receiver carrier 1 power A A Noise, called he quieing eec 0
Transmied power o an FM waveorm: From SNR baseband SNR PT : N 0 W O 3k 3A 3 N0W P SNR Valid when he carrier power is large compared wih he noise power k P T P A FM P SNRFM SNRbaseband 3 W mp SNR baseband 1
The FM deecor exhibis a more pronounced hreshold eec like he AM envelope deecor. The hreshold poin occurs around when signal power is 10 ime noise power: where A N 0 B T 10 B T = W β + 1 Carson s rule o humb
Qualiaive discussion o hreshold eec Phase noise c phase shi is caused by roaion around he origin 3
Pre-emphasis and De-emphasis: An alernaive way o increase SNR FM PSD o he noise a he deecor oupu square o requency. PSD o a ypical message ypically rolls o a around 6 db per decade 4
To increase SNR FM : Use a LPF o cu-o high requencies a he oupu Message is aenuaed oo No very saisacory Use pre-emphasis and de-emphasis Message is unchanged High requency componens o noise are suppressed 5
Pre-emphasis and de-emphasis in an FM sysem 6
H pe : used o ariicially emphasize he high requency componens o he message prior o modulaion, and hence, beore noise is inroduced. H de : used o de-emphasize he high requency componens a he receiver, and resore he original PSD o he message signal. In heory, H pe, H de 1/. This can improve he oupu SNR by around 13 db. Dolby noise reducion uses an analogous pre-emphasis echnique o reduce he eecs o noise hissing noise in audioape recording is also concenraed on high requency. 7
Simple linear pre-emphasis and de-emphasis circuis 8
Comparison o Analogue Communicaion Sysems Assumpions: 1 single-one modulaion, ie: m = A m cos m he message bandwidh W = m ; 3 or he AM sysem, µ = 1; 4 or he FM sysem, β = 5 which is wha is used in commercial FM ransmission, wih = 75 khz, and W = 15 khz. 9
Wih hese assumpions, we ind ha he SNR expressions or he various modulaion schemes become: SNR DSBSC = SNR baseband 1 SNR AM SNR baseband 3 SNR FM 3 SNR baseband 75 SNR baseband where we used = 5 30
Noise perormance o analog communicaion sysems 31
Conclusions AM: The SNR perormance is 4.8 db worse han a baseband sysem, and he ransmission bandwidh is B T = W. DSB: The SNR perormance is idenical o a baseband sysem, and he ransmission bandwidh is B T = W or SSB, he SNR perormance is again idenical, bu he ransmission bandwidh is only B T = W. FM: The SNR perormance is 15.7 db beer han a baseband sysem, and he ransmission bandwidh is B T = β + 1W = 1W wih pre- and deemphasis he SNR perormance is increased by abou 13 db wih he same ransmission bandwidh. 3