Chapter 14: Bandpass Digital Transmission. A. Bruce Carlson Paul B. Crilly 2010 The McGraw-Hill Companies

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1 Communicaion Sysems, 5e Chaper 4: Bandpass Digial Transmission A. Bruce Carlson Paul B. Crilly The McGraw-Hill Companies

2 Chaper 4: Bandpass Digial Transmission Digial CW modulaion Coheren binary sysems Noncoheren binary sysems Quadraure-carrier and M-ary sysems Orhogonal frequency division muliplexing Trellis-coded modulaion The McGraw-Hill Companies

3 Signal Deecion Coheren Deecion All he simulaion have used coheren mached received signal deecion As good as i can ge Non-coheren Deecion Usually easier o implemen wih less requiremens, BUT i does no perform as well. 3

4 Opimum binary deecion (a) parallel mached filers (b) correlaion deecor: 4

5 Opimal Deecion Concenraing on a single bi inerval he symbol represenaion can be described as ( ) ( ) b m c T k s x = The opimal deecor is a mached filer () ( ) ( ) ( ) ( ) [ ] f p Q f p I A s c q k c i k c m = π π sin cos The opimal deecor is a mached filer ( ) ( ) ( ) [ ] ( ) = + = b b k T T k b m k m h T k s z This generaes a deecion saisic for each ransmied ( ) ( ) ( ) ( ) = = b b m T k k b m d T h s d h T k s λ λ λ λ λ λ symbol wih opimal oupu energy. 5

6 Deecion Threshold Once he opimal symbol oupu power is known, he deecion hreshold h can be se based on probabiliy. P ( H ) Pe + P ( H ) Pe P = P + error ( H ) p ( V H ) = P( H ) p ( V ) Y op Y op H For binary, equally probable bl symbols p ( y H ) = p ( y z ) p ( y H ) = p ( y - ) Y k N k Y ( z z ) V op = + k N k z P error z z = Q σ 6

7 Condiional PDFs Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure 4.- 7

8 Opimum binary deecion (a) parallel mached filers (b) correlaion deecor: 8

9 An Alernae Form Insead of one filer per symbol, for binary we can combine he opimal filer for deecion as h op ( ) K s ( T ) K s ( T ) = b h op ( ) h ( ) h ( ) = op op Whichever form is used: he opimal deecor physically performs a correlaion of he incoming waveform wih he ransmied symbols Therefore, hey are called correlaion deecors! b 9

10 Bandpass binary receiver Using superposiion of he parallel mached filers, he BPF is he difference of he wo filers. ( ) = h ( ) h ( ) h BPF This resuls in an opimal binary deecor

11 h () = h () h ( ) h BPF OOK BPSK BPF Binary Receiver h h ( ) = K s( T ) ( ) K s ( T ) = ( ) = h ( ) = K s ( T ) cos ( π f ( T ) ) h BPF BFSK h ( ) = h ( ) h ( ) = h ( ) = K s ( T ) cos( π f ( T ) ) BPF h ( ) h ( ) h ( ) = K s ( T ) K s ( T ) h BPF = () [ cos( π( f + f ) ( T ) ) cos( π( f f ) ( T ) )] h BPF c d () sin( π f ( T ) ) sin( π f ( T ) ) c c c d d c

12 Correlaion receiver for OOK or BPSK Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Since boh opimal filers consis of cosine waveforms, mix and inegrae insead of filer an opimally sample. Noe ha he inegraor can be a recangular window filer ha is opimally sampled. (Provides funcionaliy near synchronizaion as well.)

13 Opimal Parallel Mached Filer Receiver Error Analysis Error Analysis () () [ ] d s s E z z T Evaluaing he expeced value max N z z = σ Evaluaing he expeced value ( ) ( ) [ ] ( ) ( ) ( ) ( ) + = T T T T d s E d s s E d s E d s s E () () [ ] E E E d s s E T + = ( ) E E E b + = E E E E z z b b = = 3 max N N σ

14 Opimal Parallel Mached Filer Receiver Error Analysis T E b = ρ Eb = E s E E E () s () d OOK E = z E b z = σ N max PSK E = ( ) Eb z z E = σ N max b FSK E = z z E = σ N max b 4

15 Generalized Probabiliy of Error Using he opimal BPF filer and sampling for each symbol, he relaionship will be based on: z Eb E Eb z = = σ N N max The BER is hen based on ( ρ) P e z z Eb = Q = Q σ N ( ρ) Therefore picking arbirary symbols is possible, bu he symbol correlaion coefficien will drive he BER performance. 5

16 Generalized FSK s s () = Ac cos( π( fc fd ) + θ) ( ) = A cos ( π ( f + f ) + θ ) E c c T = Ac E cos Ac E d ( π( f + f ) ) cos( π( f f ) ) d c d T = cos π fc + cos π fd [ ( ) ( ) ] T c d d Eb E = d T E b exp ρ Eb = T iπ fd [ exp( iπ f ) + exp( iπ f ) ] d d ( iπ f T ) exp( iπ f T ) d d b ( π f T ) iπ f There are muliple orhogonal one separaions. fd = k 4 The correlaion coefficien can go negaive! The minimum occurs a approximaely sinc(.) = -.66 d T = r E b sin d ρ Eb = = Eb sinc 4 T π f d ( ) = d 4 f d T Eb sinc rb r b 6 f

17 Noncoheren Binary Sysems Synchronous coheren receiver can be very difficul o design. Can noncoheren sysems be more easily designed wihou giving i up significan ifi BER performance? For a - db E b /N o performance loss, YES! 7

18 Noncoheren OOK receiver Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure 4.3- Using an envelope deecor, he noise pdf for a zero symbol becomes Rician and is non-longer Gaussian. The noise pdf for a one symbol remains Gaussian 8

19 Condiional PDFs for noncoheren OOK Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure ( V ) P ( V ) P e op e op P e exp Eb N P e = b ( P ) ( ) e + Pe Pe exp N E V op A c 9

20 Noncoheren deecion of binary FSK Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure 4.3-5

21 Noncoheren FSK Qualiaive commens Using envelope deecors on each symbol oupu, he Rician error disribuion effecs he z deecion saisic. P e exp Eb N

22 Binary error probabiliy curves Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. (a) coheren BPSK (b) DPSK (c) coheren OOK or FSK (d) noncoheren FSK (e) () noncoheren OOK: Figure BER Simulaion for BPSK and BFSK - - BER BPSK simulaion BPSK (heoreical) BFSK simulaion BFSK (heoreical) E b /N o (db)

23 Deecion for M-ary Sysems Deermine he deecion saisic for all symbols Selec he maximum saisic Decode he binary values from he seleced symbol 3

24 Quadraure-carrier receiver wih correlaion deecors Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure 4.4- Applicable for: M-QAM M-PSK 4

25 Carrier synchronizaion for quad-carrier receiver Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure 4.4-5

26 Coheren M-ary PSK receiver Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure PreDecode, E s /N (db)=9 5 5 MPSK_Demo.m Fixed N, varying signal E b Imag Real 6

27 Decision hresholds for M-ary PSK Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. Figure PreDecode, Es /N (db)=9 5 Imag Real 5 5 7

28 PSK signal consellaions (a) M=4 (b) M=8 Figure 4.5- MPSK Symbols are ypically y Gray-code encoded prior o ransmission In he Gray-code, adjacen symbols are only differen by bi value! 8 Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display.

29 MPSK Eb/N Examples PreDecode, Es /N (db)= PreDecode, Es /N (db)= Imag Imag PreDecode, Es /N (db)=9 Real Symbol Error Rae, M=8 Real Bi Error Rae, M= BER SER Imag Real Es/No (db) - - Eb/No (db) 9

30 Simulaed Performance MPSK MPSK_Ber and MPSK_PP_Plo MPSK Symbol Error Rae MPSK Bi Error Rae SER M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound E s /N (db) BER M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound E b /N (db) 3

31 Simulaed Performance MFSK MFSK_Ber and MFSK_PP_Plo MFSK Symbol Error Rae MFSK Bi Error Rae SER M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound E s /N (db) BER M= Sim M= Bound M=4 Sim M=4 Bound M=8 Sim M=8 Bound M=6 Sim M=6 Bound E b /N (db) 3

32 Comparing MPSK and MFSK MPSK More E b /N required for higher M for symbol error rae - and 4-PSK have he same BER MFSK Oherwise higher BER for higher M More E b /N required for higher M for symbol error rae, BUT i does no increase as fas as MPSK Less E b /N required for higher M for BER! How could his be? The symbols are all orhogonal! 3

33 M-ary QAM sysem Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. (a) ransmier (b) receiver (c) square signal consellaion and hresholds wih M=6 Figure

34 Performance comparisons of M-ary modulaion sysems P == be 4 Copyrigh The McGraw-Hill Companies, Inc. Permission required for reproducion or display. 34

35 Wha if quesion? Could you ake he MFSK or MPSK simulaions and use hem o develop a M-QAM simulaion? i Define consellaion Modulae symbols I,Q correlaors Map I,Q resuls o consellaion Deermine symbol errors and bi errors 35

36 OFDM Muliplexing in boh phase and frequency domains Wihou he cosly hardware of convenional FDM Can be implemened using IFFT/FFT hardware OFDM form of Mulicarrier (MC) modulaion Carriers are muual orhogonal We parse up a given message ino separae componens o OFDM hem ono a channel a symbol is ransmied a a lower rae increased immuniy o mulipah may no have o employ equalizaion The McGraw-Hill Companies

37 Applicaions IEEE 8. (Wi-Fi) and IEEE-8.6 (WiMax) Modems, DSLs OFDM sysem of parsing symbols ono separae frequencies and phases can be exended o muliple access (MA) applicaions. The McGraw-Hill Companies

38 OFDM Sysem Wihou QAM The McGraw-Hill Companies

39 Trellis-coded modulaion (TCM) Combinaion of coding and modulaion Uses sysemaic convoluional coding Lower bi error rae in exchange for increased complexiy Maximize Euclidean disance (no necessarily Hamming) )beween consellaion poins o minimize errors Does no reduce overall message rae Coding gain achieved by incorporaing more bis The McGraw-Hill Companies

40 Telephone-line Modem Formas 4