UNIT IV DIGITAL MODULATION SCHEME

Transcription

1 UNI IV DIGIAL MODULAION SCHEME

2 Geomeric Represenaion of Signals Ojecive: o represen any se of M energy signals {s i (} as linear cominaions of N orhogonal asis funcions, where N M Real value energy signals s 1 (, s 2 (,..s M (, each of duraion sec Orhogonal asis funcion N 0 si ( sij j (, ( j1 i==1,2,...,m Energy signal coefficien

3 Coefficiens: i=1,2,...,m sij s ( (, (5.6 0 i j d j=1,2,...,m Real-valued asis funcions: 0 1 if i j i ( j ( d ij (5.7 0 if i j

4 he se of coefficiens can e viewed as a N-dimensional vecor, denoed y s i Bears a one-o-one relaionship wih he ransmied signal s i (

5 (a Synhesizer for generaing he signal s i (. ( Analyzer for generaing he se of signal vecors s i.

6 So, Each signal in he se s i ( is compleely deermined y he vecor of is coefficiens 1 2 i. s, 1,2,...,M (5.8.. i i in s s i s

7 Finally, he signal vecor s i concep can e exended o 2D, 3D ec. N-dimensional Euclidian space Provides mahemaical asis for he geomeric represenaion of energy signals ha is used in noise analysis Allows definiion of Lengh of vecors (asolue value Angles eween vecors Squared value (inner produc of s i wih iself s i 2 s i s i Marix ransposiion N 2 = sij, i1,2,...,m (5.9 j1

8 Figure 5.4 Illusraing he geomeric represenaion of signals for he case when N 2 and M 3. (wo dimensional space, hree signals

9 Also, Wha is he relaion eween he vecor represenaion of a signal and is energy value? sar wih he definiion of average energy in a signal Where s i ( is 2 E i s i ( d ( N s ( s (, (5.5 i ij j j1

10 Afer susiuion: Afer regrouping: E i s ( s ( d i N N ij j ikk 0 j1 k1 N N ij ik j k j1 k1 0 E s s ( ( d (5.11 Φ j ( is orhogonal, so finally we have: N 2 2 E i sij = s i (5.12 j1 he energy of a signal is equal o he squared lengh of is vecor

11 Formulas for wo signals Assume we have a pair of signals: s i ( and s j (, each represened y is vecor, hen: ij 0 i k i s s ( s ( d s s (5.13 k Inner produc of he signals is equal o he inner produc of heir vecor represenaions [0,] Inner produc is invarian o he selecion of asis funcions

12 Euclidian Disance he Euclidean disance eween wo poins represened y vecors (signal vecors is equal o s i -s k and he squared value is given y: i N 2 2 k sij skj j1 s s = ( - (5.14 = ( ( ( 0 2 si sk d

13 BPSK - BINARY PHASE Generaion of BPSK: SHIF KEYING Consider a sinusoidal carrier. If i is modulaed y a i-polar i sream, is polariy will e reversed every ime he i sream changes polariy. his, for a sinewave, is equivalen o a phase reversal (shif. he muliplier oupu is a BPSK 1 signal.

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15 BPSK signal in ime domain

16 sychronous demodulaion of BPSK

17 Frequency Shif Keying (FSK Binary FSK Frequency of he consan ampliude carrier is changed according o he message sae high (1 or low (0 Disconinuous / Coninuous Phase 0 (i 0 1 (i 0 f f A s f f A s c c 2 cos(2 ( 2 cos(2 ( 2 1

18 Disconinuous Phase FSK Swiching eween 2 independen oscillaors for inary 1 & 0 cos w 1 inpu daa phase jumps swich cos w 2 inary 1 s BFSK (= v H ( = 2E cos(2f H 0 1 inary 0 s BFSK (= v L ( 2E = cos(2f L 2 0 resuls in phase disconinuiies disconinuiies causes specral spreading & spurious ransmission no suied for ighly designed sysems

19 Coninuous Phase FSK single carrier ha is frequency modulaed using m( 2E s BFSK ( = cos(2f ( = 2E where ( = c cos 2 f c 2k FSK m( d FSK 2 k m( d m( = disconinuous i sream ( = coninuous phase funcion proporional o inegral of m(

20 FSK Example Daa FSK Signal x a 0 a VCO cos w c modulaed composie signal

21 Specrum & Bandwidh of BFSK Signals complex envelope of BFSK is nonlinear funcion of m( specrum evaluaion - difficul - performed using acual ime averaged measuremens PSD of BFSK consiss of discree frequency componens a f c f c nf, n is an ineger PSD decay rae (inversely proporional o specrum PSD decay rae for CP-BFSK PSD decay rae for non CP-BFSK f = frequency offse from f c 1 f 4 1 f 2

22 Specrum & Bandwidh of BFSK Signals ransmission Bandwidh of BFSK Signals (from Carson s Rule B = andwidh of digial aseand signal B = ransmission andwidh of BFSK signal B = 2f +2B assume 1 s null andwidh used for digial signal, B - andwidh for recangular pulses is given y B = R - andwidh of BFSK using recangular pulse ecomes B = 2(f + R if RC pulse shaping used, andwidh reduced o: B = 2f +(1+ R

23 General FSK signal and orhogonaliy wo FSK signals, V H ( and V L ( are orhogonal if 0 ( ( 0 d V V L H inerference eween V H ( and V L ( will average o 0 during demodulaion and inegraion of received symol 0 ( ( 0 d V V L H received signal will conain V H ( and V L ( demodulaion of V H ( resuls in (V H ( + V L (V H ( 0 ( ( 0 d V V H H??

24 (2 cos(2 (2 2 cos( f f E c = ( cos(2 ( cos(2 2 f f f f E c c v H ( v L ( = hen = c c f f f f E 0 4 sin(4 4 sin(4 f f f f E c c 4 sin(4 4 sin(4 = d f f E d V V c L H 0 0 cos(4 cos(4 ( ( and v H ( v L ( are orhogonal if Δf sin(4πf c = -f c (sin(4πδf An FSK signal for 0 v H ( = ( cos(2 2 f f E c v L ( = ( cos(2 2 f f E c and

25 QPSK Quadraure Phase Shif Keying (QPSK can e inerpreed as wo independen BPSK sysems (one on he I-channel and one on Q-channel, and hus he same performance u wice he andwidh (specrum efficiency.

26 QPSK Consellaion Diagram Q Q I I Carrier phases {0, /2,, 3/2} Carrier phases {/4, 3/4, 5/4, 7/4} Quadraure Phase Shif Keying has wice he andwidh efficiency of BPSK since 2 is are ransmied in a single modulaion symol

27 Convenional QPSK has ransiions hrough zero (i.e phase ransiion. Highly linear amplifiers required. In Offse QPSK, he phase ransiions are limied o 90 0, he ransiions on he I and Q channels are saggered. In /4 QPSK he se of consellaion poins are oggled each symol, so ransiions hrough zero canno occur. his scheme produces he lowes envelope variaions. All QPSK schemes require linear power amplifiers ypes of QPSK Q Q Q I I I Convenional QPSK Offse QPSK /4 QPSK

28 Quadraure Phase Shif Keying (QPSK: Also a ype of linear modulaion scheme Quadraure Phase Shif Keying (QPSK has wice he andwidh efficiency of BPSK, since 2 is are ransmied in a single modulaion symol. he phase of he carrier akes on 1 of 4 equally spaced values, such as where each value of phase corresponds o a unique pair of message is. he QPSK signal for his se of symol saes may e defined as:

29 QPSK he sriking resul is ha he i error proailiy of QPSK is idenical o BPSK, u wice as much daa can e sen in he same andwidh. hus, when compared o BPSK, QPSK provides wice he specral efficiency wih exacly he same energy efficiency. Similar o BPSK, QPSK can also e differenially encoded o allow noncoheren deecion.

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31 Quadraure ampliude modulaion Quadraure ampliude modulaion (QAM is oh an analog and a digial modulaion scheme. I conveys wo analog message signals, or wo digial i sreams, y changing (modulaing he ampliudes of wo carrier waves, using he ampliude-shif keying(ask digial modulaion scheme or ampliude modulaion (AM analog modulaion scheme. he wo carrier waves, usually sinusoids, are ou of phase wih each oher y 90 and are hus called quadraure carriers or quadraure componens hence he name of he scheme.

32 QAM ransmier

33 Firs he flow of is o e ransmied is spli ino wo equal pars: his process generaes wo independen signals o e ransmied. hey are encoded separaely jus like hey were in an ampliude-shif keying (ASK modulaor. hen one channel (he one "in phase" is muliplied y a cosine, while he oher channel (in "quadraure" is muliplied y a sine. his way here is a phase of 90 eween hem. hey are simply added one o he oher and sen hrough he real channel.

34 QAM Receiver

35 he receiver simply performs he inverse operaion of he ransmier. Muliplying y a cosine (or a sine and y a low-pass filer i is possile o exrac he componen in phase (or in quadraure. hen here is only an ASK demodulaor and he wo flows of daa are merged ack.

36 Carrier Synchronizaion Synchronizaion is one of he mos criical funcions of a communicaion sysem wih coheren receiver. o some exen, i is he asis of a synchronous communicaion sysem. Carrier synchronizaion Symol/Bi synchronizaion Frame synchronizaion

37 Receiver needs esimae and compensae for frequency and phase differences eween a received signal s carrier wave and he receiver s local oscillaor for he purpose of coheren demodulaion, no maer i is analog or digial communicaion sysems. o exrac he carrier: 1. Pilo-one inserion mehod Sending a carrier componen a specific specral-line along wih he signal componen. Since he insered carrier componen has high frequency sailiy, i is called pilo. 2. Direc exracion mehod Direcly exrac he synchronizaion informaion from he received signal componen.

38 1. Pilo-one inserion mehod -inser pilo o he modulaed signal x( Modulaor Bandpass filer Add s( -asin( c cos( c /2phase shif he pilo signal is generaed y shif he carrier y 90 0 and decrease y several db, hen add o he modulaed signal. Assume he modulaed signal has 0 DC componen, hen he pilo sis f a cos sin c c

39 2. Direc exracion mehod If he specrum of he received signal already conains carrier componen, hen he carrier componen can e exraced simply y a narrowand filer or a PLL. If he modulaed signal supresses he carrier componen, hen he carrier componen may e exraced y performing nonlinear ransformaion or using a PLL wih specific design

40 DPSK DPSK is a kind of phase shif keying which avoids he need for a coheren reference signal a he receiver. Differenial BPSK 0 = same phase as las signal elemen 1 = 180º shif from las signal elemen

41 DPSK modulaion and demodulaion

42 hank you