Coherent & Non Coherent Detection

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1 Coheren & Non Coheren Deecon 1

2 Bandpass Modulaon and Demodulaon Bandpass Modulaon s he process by whch some characerscs of a snusodal waveform s vared accordng o he message sgnal. Modulaon shfs he specrum of a baseband sgnal o some hgh frequency. Demodulaor/Decoder baseband waveform recovery 2

3 Why Modulae? Mos channels requre ha he baseband sgnal be shfed o a hgher frequency For example n case of a wreless channel anenna sze s nversely proporonal o he cener frequency, hs s dffcul o realze for baseband sgnals. For speech sgnal f = 3 khz =c/f=(3x10 8) /(3x10 3 ) Anenna sze whou modulaon /4=10 5 /4 meers = 15 mles - praccally unrealzable Same speech sgnal f amplude modulaed usng f c =900MHz wll requre an anenna sze of abou 8cm. Ths s evden ha effcen anenna of realsc physcal sze s needed for rado communcaon sysem Modulaon also requred f channel has o be shared by several ransmers (Frequency dvson mulplexng). 3

4 4.2 Dgal Bandpass Modulaon Technques Three ways of represenng bandpass sgnal: (1) Magnude and Phase (M & P) Any bandpass sgnal can be represened as: s( ) A( ) cos[ A( ) cos[ 0 ( )] A() 0 s real valued sgnal represenng he magnude Θ() s he genarlzed angle φ() s he phase The represenaon s easy o nerpre physcally, bu ofen s no mahemacally convenen In hs form, he modulaed sgnal can represen nformaon hrough changng hree parameers of he sgnal namely: Amplude A() : as n Amplude Shf Keyng (ASK) Phase φ() : as n Phase Shf Keyng (PSK) Frequency dθ()/ d : as n Frequency Shf Keyng (FSK) 4

5 Angle Modulaon Consder a sgnal wh consan frequency: s( ) A( ) cos( ( )) A( )cos( ) Is nsananeous frequency can be wren as: d ( ) ( ) 0 d 0 or ( ) ( ) d 5

6 Phase Shf Keyng (PSK) or PM Consder a message sgnal m(), we can wre he phase modulaed sgnal as ( ) c K m( ) p s PM ( ) Acos[ K m( )] c p d ( ) c K pm( ) d 6

7 Frequency Shf Keyng (FSK) or FM In case of Frequency Modulaon ( ) K m( ) 0 f ( ) [ K m( )] d 0 f 0 K f m( ) d s ( ) Acos[ K m( ) d] FM 0 0 f f Acos[ K a( )] where: a( ) m( ) d 7

8 Example 1 The message sgnal The modulaed sgnal Tme 8

9 4.2.1 Phasor Represenaon of Snusod Consder he rgonomerc deny called he Euler s heorem: j0 e j cos( ) sn( ) 0 0 Usng hs deny we can have he phasor represenaon of he snusods. Fgure 4.2 below shows such relaon: 11

10 Phasor Represenaon of Amplude Modulaon Consder he AM sgnal n phasor form: s m j e e ( ) Re e 1 j j m 12

11 Phasor Represenaon of FM Consder he FM sgnal n phasor form: s e e e j j j j e m 0 m m ( ) Re

12 Dgal Modulaon Schemes Basc Dgal Modulaon Schemes: Amplude Shf Keyng (ASK) Frequency Shf Keyng (FSK) Phase Shf Keyng (PSK) Amplude Phase Keyng (APK) For Bnary sgnals (M = 2), we have Bnary Amplude Shf Keyng (BASK) Bnary Phase Shf Keyng (BPSK) Bnary Frequency Shf Keyng (BFSK) For M > 2, many varaons of he above echnques ex usually classfed as M-ary Modulaon/deecon 18

13 Fgure4.5: dgal modulaons, (a) PSK (b) FSK (c) ASK (d) ASK/PSK (APK) 20

(also called ON-OFF Keyng (OOK)), one and

14 Amplude Shf Keyng Modulaon Process In Amplude Shf Keyng (ASK), he amplude of he carrer s swched beween wo (or more) levels accordng o he dgal daa For BASK (also called ON-OFF Keyng (OOK)), one and zero are represened by wo amplude levels A 1 and A 0 21

15 Analycal Expresson: s( ) where A = peak amplude A cos( 0, c ), 0 T bnary 1 0 T bnary 0 2 s( ) Acos( ) 2Arms cos( 0) 2A cos( 0 Hence, 0 2E 2P cos( 0 ) cos( 0) P T 2E ( ) s ( ) cos( ), 0 T bnary 1 T, 0,2,... M 1 0, 0 T bnary 0 where E T 0 s 2 ( ) d, 0,2,... M 1 rms V R 2 ) 22

16 Where for bnary ASK (also known as ON OFF Keyng (OOK)) s1( ) Ac m( )cos( c ), 0 T bnary 1 s0( ) 0, 0 T bnary 0 Mahemacal ASK Sgnal Represenaon The complex envelope of an ASK sgnal s: g( ) A m( ) c The magnude and phase of an ASK sgnal are: A( ) Ac m( ), ( ) 0 The n-phase and quadraure componens are: x( ) A m( ) c y( ) 0, he quadraure componen s wased. 23

17 I can be seen ha he bandwdh of ASK modulaed s wce ha occuped by he source baseband sream Bandwdh of ASK Bandwdh of ASK can be found from s power specral densy The bandwdh of an ASK sgnal s wce ha of he unpolar NRZ lne code used o creae.,.e., B 2R Ths s he null-o-null bandwdh of ASK b 2 T b 24

18 If rased cosne rolloff pulse shapng s used, hen he bandwdh s: Specral effcency of ASK s half ha of a baseband unpolar NRZ lne code 1 B ( 1 r) R W (1 r) 2 Ths s because he quadraure componen s wased 95% energy bandwdh b R b 3 B 3R T b b 25

Deecors for ASK Coheren Recever Coheren deecon requres he phase nformaon A coheren deecor mxes he ncomng sgnal wh a locally generaed carrer reference Mulplyng he receved sgnal r() by he recever local

19 Deecors for ASK Coheren Recever Coheren deecon requres he phase nformaon A coheren deecor mxes he ncomng sgnal wh a locally generaed carrer reference Mulplyng he receved sgnal r() by he recever local oscllaor (say A c cos(w c )) yelds a sgnal wh a baseband componen plus a componen a 2f c Passng hs sgnal hrough a low pass fler elmnaes he hgh frequency componen In pracce an negraor s used as he LPF 26

as he roo rased cosne fler can hus be used o shape he source and receved baseband

20 The oupu of he LPF s sampled once per b perod Ths sample z(t) s appled o a decson rule z(t) s called he decson sasc Mached fler recever of OOK sgnal A MF par such as he roo rased cosne fler can hus be used o shape he source and receved baseband symbols In fac hs s a very common approach n sgnal deecon n mos bandpass daa modems 27

21 Noncoheren Recever Does no requre a phase reference a he recever If we do no know he phase and frequency of he carrer, we can use a noncoheren recever o recover ASK sgnal Envelope Deecor: The smples mplemenaon of an envelope deecor comprses a dode recfer and smoohng fler 28

Frequency Shf Keyng (FSK) In FSK, he nsananeous carrer frequency s swched beween 2 or more levels accordng o he baseband dgal daa daa bs selec a carrer a one of wo frequences he daa s encoded n he

22 Frequency Shf Keyng (FSK) In FSK, he nsananeous carrer frequency s swched beween 2 or more levels accordng o he baseband dgal daa daa bs selec a carrer a one of wo frequences he daa s encoded n he frequency Unl recenly, FSK has been he mos wdely used form of dgal modulaon;why? Smple boh o generae and deec Insensve o amplude flucuaons n he channel FSK conveys he daa usng dsnc carrer frequences o represen symbol saes An mporan propery of FSK s ha he amplude of he modulaed wave s consan Waveform 29

23 30 Analycal Expresson General expresson s Where 1 0,1,... ), cos( 2 ) ( M T E s s s Analog form ) ( ) ( ] ) ( [ ) ( 0 0 m f f d d f d m d d b s b s kt T ke E and f f f, 0 1 f f f 1 0,1,... ), 2 cos(2 2 ) ( 0 M f f T E s s s

24 Bnary FSK In BFSK, 2 dfferen frequences, f1 and f2 = f1 + f are used o ransm bnary nformaon Daa s encoded n he frequences Tha s, m() s used o selec beween 2 frequences: f1 s he mark frequency, and f2 s he space frequency 2Es s0( ) cos 2 ( f1 1), 0 Tb T b s 2E s 1( ) cos 2 ( f2 2), 0 Tb T b 31

25 s( ) Ac cos( 1 Ac cos( 2 ), 1 ), 2 when m( ) when m( ) 1 or 1or X X n n 1 0 Bnary Orhogonal Phase FSK When w 0 an w 1 are chosen so ha f 1 () and f 2 () are orhogonal,.e., ) ( ) 1( 2 0 form a se of K = 2 bass orhonormal bass funcons 32

26 Phase Shf Keyng (PSK) General expresson s s Where 2Es ( ) cos[2f 0 ( )], 0,1,... M 1 T s 2 ( ) 0,1,... M 1 M 33

27 3. Coheren Deecon of Bnary FSK Coheren deecon of Bnary FSK s smlar o ha for ASK bu n hs case here are 2 deecors uned o he 2 carrer frequences Recovery of fc n recever s made smple f he frequency spacng beween symbols s made equal o he symbol rae. 34

28 Non-coheren Deecon One of he smples ways of deecng bnary FSK s o pass he sgnal hrough 2 BPF uned o he 2 sgnalng freqs and deec whch has he larger oupu averaged over a symbol perod 35

Phase Shf Keyng (PSK) In PSK, he phase of he carrer sgnal s swched beween 2 (for BPSK) or more (for MPSK) n response o he baseband dgal daa Wh PSK he nformaon s conaned n he nsananeous

29 Phase Shf Keyng (PSK) In PSK, he phase of he carrer sgnal s swched beween 2 (for BPSK) or more (for MPSK) n response o he baseband dgal daa Wh PSK he nformaon s conaned n he nsananeous phase of he modulaed carrer Usually hs phase s mposed and measured wh respec o a fxed carrer of known phase Coheren PSK For bnary PSK, phase saes of 0 o and 180 o are used Waveform: 36

30 Analycal expresson can be wren as where s ( ) A g( )cos[ ( )], 0 T, 1,2,..., M c b g() s sgnal pulse shape A = amplude of he sgnal ø = carrer phase The range of he carrer phase can be deermned usng For a recangular pulse, we oban g( ) 2 ( 1) ( ) 1,... M M 2, 0 Tb ; T b and assume A E b 37

31 We can now wre he analycal expresson as 2Eb 2 ( 1) s ( ) cos c, 0 Tb, and 1,2,... M T M b Consan envelope carrer phase changes abruply a he begnnng of each sgnal nerval In PSK he carrer phase changes abruply a he begnnng of each sgnal nerval whle he amplude remans consan 38

ECE5713 : Advanced Digital Communications

ECE5713 : Advanced Digital Communications Bandpass Modulation MPSK MASK, OOK MFSK 04-May-15 Advanced Digital Communications, Spring-2015, Week-8 1 In-phase and Quadrature (I&Q) Representation Any bandpass