COMM70: Modulaion II Leure 4 - Coheren and non-oheren inary pass-and daa ransmission
Binary Digial Modulaion Sinusoidal Carrier Digial Message ASK FSK PSK
Parameers o Digial Pass-and ransmission Proailiy o rror: he goal is o oain opimum reeiver so as o minimize he average proailiy o error. Power Spera: I is imporan in: - Oupany o B.W - Cohannel inererene in muliplexed sysems 3 Bandwidh Speral eiieny: he ojeive o eiien modulaion is o maximize he andwidh eiieny deined y: Where R R B is he i rae and B is he signal andwidh.
Deeion o Digial Communiaions Coheren -he reeiver generaes a arrier signal wih he same phase and requeny as he ransmied one. -I is omplex u has eer perormane han non-oheren deeion. Non-Coheren - he reeiver is equipped wih an envelope deeor -he envelope deeor demodulaes he inoming signal wihou need o a phase. -I is simpler han he oheren deeion u is perormane is lower han he oheren deeor.
Binary Ampliude Shi Keying ime Domain Represenaion: A inary ampliude shi keying signal BASK an e deined as: s m os Where m is reangular pulses and is he arrier requeny. m s
ime Domain Represenaion o BASK Nex igure shows OOK OOK On-o keying OOK OOK
Power speral densiy o OOK he PSD o OOK signal is given y: Where is he PSD o whih is a random unipolar inary waveorm wih ampliude 0 and. he PSD o m is: hen, rom and, he PSD o OOK signal is: S m m sin 4 m S Reerene: Page 394 Digial & analog Communiaion Sysems, K. Sam. ] [ m m s S S S sin sin ] [ 8 S S
Power speral densiy o BASK 8 sin A 6 8
ASK Bandwidh Null-o-null andwidh: B. W R Where R is he i rae [is/se]. R is he i duraion [se]
Generaion o BASK m s os s m os
Coheren Deeion o BASK S os
x 0 hreshold Coheren Deeion o BASK Con. 0 0, ] 4 4 sin [ 4 os os os, 0 inerval he in is i ransmied he Assume 0 0 0 x zero is i ransmied he When d d d s x m hen n nr Sine 0
Non-Coheren Deeion o ASK s m os nvelope Deeor m Deision Blok mˆ Sine he inormaion is onveyed in he ampliude or he envelope o he modulaed signal, hen an envelope deeor an e used o exra i. Advanages o non-oheren deeion: - No need or arrier synhronizaion - Simple implemenaion. H.W: Calulae he hreshold in his ase Disadvanages o non-oheren deeion: - Is perormane is lower han he oheren one in presene o noise.
Perormane o digial modulaions in presene o noise he addiive noise o he signal is assumed o e saionary Gaussian random proess signal wih zero mean and variane No/. he perormane o a digial ommuniaion sysem is desried y he proailiy o i error and he proailiy o symol error as a union o he reeived /No raio. For inary modulaion sysems, symol and i error proailiy are he same. he mehod o oain he proailiy o error o oheren digial modulaions is as ollows: We express he digial signal as a linear ominaion o orhonormal waveorms and hen we draw he signal veors or onsellaion diagram as a union o hese orhonormal waveorms and hen alulae he disane eween he veor poins as desried eore.
Proailiy o rror o Coheren OOK I he ransmied i is, hen s os 0 hen s an e expressed as: s where os I he ransmied i is 0, hen S=0 he disane eween So and S is: d hen he proailiy o error o oheren ASK is given y: P e Q d N Q o N o
Binary Phase Shi Keying BPSK In PSK, he inormaion is onained in he insananeous phase o he modulaed arrier. For inary PSK, phase saes o 0 and 80 are used. here is no non-oheren PSK insead we have dierenially oheren PSK. ime domain represenaion: 0
Generaion o BPSK
Coheren Deeion o BPSK here is no non-oheren deeor or PSK. he oheren deeor requires pere knowledge o he arrier phase a he reeiver. S
Coheren Deeion o BPSK s x 0 hreshold x d d x d s x 0 0 0 ransmiing 0, or Similarly 4 sin4 os 4 os os os s hen ransmied, is Assume 0
Proailiy o rror o Coheren BPSK he disane eween So and S is: d o o N Q N d Q e P
Binary Frequeny Shi Keying BFSK - FSK is reaed as non-linear modulaion sine inormaion is pu ino he requeny. ime domain represenaion: he ransmied signal an e represened as: S represens symol. S represens symol 0. s i 0, os i, 0 elsewhere i, Where: 4 4 - he minimum requeny spaing eween wo adjaen requeny slos o ensure orhogonaliy or he oninuous phase BFSK is
Phase Disoninuous Frequeny Shi Keying
Phase Coninuous Frequeny Shi Keying
Generaion o BFSK
Coheren Deeion o BFSK S H.W: derive he expressions or x, x, and y
Proailiy o error o Coheren BFSK here are wo asis unions wrien as Sine: As a resul, he signal veors are elsewhere 0, 0, os i i elsewhere 0, 0, os i i s
Proailiy o rror o Coheren BFSK Con. From he igure, we have d In ase o Pr0=Pr, he proailiy o error is given y P e Q N 0 We oserve ha a a given value o P e, he BFSK sysem requires wie as muh power as he BPSK sysem.
Non-Coheren Deeion o BFSK
Non-Coheren Deeion o BFSK Con.
Non-Coheren Deeion o BFSK Con.
Proailiy o rror o non-oheren BFSK Proailiy o rror: Bandwidh o FSK: P e exp N0 he null o null andwidh o FSK is B. W R
Comparison o proailiy o error o oheren and non-oheren FSK P nonoh P oheren exp Q N 0 N 0
Comparison o proailiy o error o oheren BFSK and oheren PSK he proailiy o error o oheren FSK: P Coh FSK Q N 0 he proailiy o error o oheren PSK: P oh PSK Q N o Case: For he same energy per i : Case: For he same, he FSK needs o doule o ahieve he same P e P e P ohfsk P ohpsk hus he oheren BFSK is poorer y 3 db han oheren PSK
Comparison o BR o Dieren Binary Digial Modulaions