Principles of Communications

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1 Sae Key Lab. on ISN, Xidian Universiy Principles of Communicaions Chaper VI: Elemenary Digial Modulaion Sysem Xidian Universiy Sae Key Lab. on ISN December 13, 2013

2 Sae Key Lab. on ISN, Xidian Universiy 6.1 Inroducion Desinaions Move he signal o he suiable frequency band. In wireless communicaions, he reasonable size of anenna is desired, which is proporional o he wavelengh. Classificaions Carrier Acosω c +φ is applied and in i here are hree changeable parameers: ampliude A, carrier frequency f c, and phase ϕ. There are hree elemenary digial modulaion sysem: Ampliude shif keying (ASK): linear modulaion; Frequency shif keying (FSK): nonlinear modulaion; Phase shif keying (PSK): linear modulaion. There are also some advanced modulaions, such as QAM, OFDM,....

3 Sae Key Lab. on ISN, Xidian Universiy 6.2 Binary Ampliude shif Keying 1. 2ASK Modulaion bi 1 cosω c bi 0 zero level. Uni-polar no reurn-o-zero waveform s() e2 ASK ( ) cos c ( ) e2 ASK cos c

4 Sae Key Lab. on ISN, Xidian Universiy 2. 2ASK Demodulaion Envelope deecor e2 ASK ( ) a Full-vave b c Samping& oupu BPF LPF recifier decision Envelope deecion noncoheren demodulaion Timing e2 ASK ( ) a b c BPF LPF cos c Coheren demodulaion Samping& decision Timing oupu

5 Sae Key Lab. on ISN, Xidian Universiy Waveforms in he Demodulaor a b c A A V 2 A V 2 1 0

6 Sae Key Lab. on ISN, Xidian Universiy 3. Power Specral Densiy of 2ASK Signals Time expression: e 2ASK = s()cosω c Power Specral Densiy: P 2ASK = 1 4 [P s(f +f c )+P s (f f c )]. Because s() is unipolar waveform, PSD of s() is P s (f) = Ts 4 Sa2 (πft s )+ 1 4 δ(f). P s (f ) B f f s f s P2 ASK ( f ) f fcf s f c fcf s 0 fcf s f c fcf s Frequency band widh: B 2ASK = 2f s.

7 Sae Key Lab. on ISN, Xidian Universiy 6.3 Binary Frequency Shif Keying (2FSK) Basic Principle Modulaion bi 1 cosω 1 bi 0 cosω 2 f1 f f f f2 f f f f f f f 2 f2 f2 f f Swiching circui cos 2 Bipolar Baseband Signal Inverer e 2FSK cos 1

8 Sae Key Lab. on ISN, Xidian Universiy Basic Principle 2FSK Demodulaion BPF 1 Envelope deecion e2 FSK ( ) Timing Sampling Comparison &decision oupu BPF 2 Evnelope deecion Non-coheren demodulaion BPF 1 LPF e2 FSK ( ) cos 1 Timing Sampling Comparison &decision oupu BPF 2 LPF cos 2 Coheren demodulaion

9 Sae Key Lab. on ISN, Xidian Universiy FSK Power Specral Densiy 2FSK signal can be regarded as consising of wo 2ASK signals. P s (f ) B f f s f s B2 FSK f 2B f1 1 P2 FSK ( f ) f f 2 f s f f 2 1 f 1 f s 1 f 1 f 2 f2f s f f s f1 f 2 2 f 1 f 2 < f s, one peak; f 1 f 2 < f s, wo peaks.

10 Sae Key Lab. on ISN, Xidian Universiy 6.4 Binary Phase Shif Keying 2BPSK 1. Modulaion bi 1 0 o cosω c bi 0 π cosω c Bipolar waveform s() cos c e2 PSK ( ) 0 cos c ( ) e2 PSK

11 Sae Key Lab. on ISN, Xidian Universiy 2. 2PSK Demodulaion e2 PSK ( ) BPF a c LPF d Sampling &Decision Oupu b cos c Timing a b c V 0 V 0 1 0

12 Sae Key Lab. on ISN, Xidian Universiy 3. Power specral densiy Because e 2psk () = s()cosω c, we have P 2psk (f) = 1 4 [P s(f +f c )+P s (f f c )]. We also know ha s() is, specifically, bipolar recify waveform. Power specral densiy of s() is P s (f) = T s Sa 2 (πft s ). So B 2PSK = 2f s and PSD of e 2psk () P s (f ) B f f s f s P2 PSK ( f ) B2PSK 2B 2f s f fcf s f c fcfs fcf s f c fcfs Bandwidh: B = 2f s Only coninuous specral and no discree specral.

13 Sae Key Lab. on ISN, Xidian Universiy 4. Performance of Ani-Noise Symbol Error Probabiliy e2 PSK ( ) r( ) n ( ) cos c In [0, T s ], he received signal { r() = e 2psk +n() = Acosω c +n() 1 Acosω c +n() 0. 2PSK signal, e 2psk (), can pass hrough he BPF; Afer passing hrough he BPF, he noise, n(), becomes narrow band whie noise, i.e.,. n i () = n c ()cosω c n s ()sinω c

14 Sae Key Lab. on ISN, Xidian Universiy Assume ha he curren symbol in [0, T s ] is 1. For signal, e 2psk 2cosω c = 2Acos 2 ω c = A+Acos2ω c LPF A. For noise, n i () 2cosω c = 2n c ()cos 2 ω c 2n s ()sinω c cosω c = n c ()cosω c +n c ()cos2ω c n s ()sin2ω c LPF n c () The inpu of he sampling&decision uni is x = A+n c and he 1-dim pdf is f(x) = 1 2πσ exp [ (x A)2 2σ 2 ] f (x) 0 A x

15 Sae Key Lab. on ISN, Xidian Universiy Le he decision hreshold V d = 0, and hen he error probabiliy of he ransmied symbol 1 is Pe 1 = 0 f(x)dx = 1 2πσ 0 = 1 2 erfc( A 2σ ). exp [ (x A)2 ] dx 2σ 2 Le signal-o-noise raio (SNR) r = S N = 1 2 A2 σ 2. We have Pe 1 = 1 2 erfc( r). Similar we derive Pe 0 = 1 2 erfc( r). While P(0) = P(1) = 1 2, symbol error rae of 2BPSK sysem is Pe = 1 2 erfc( r).

16 Sae Key Lab. on ISN, Xidian Universiy 5. Phase ambiguiy In he receiver, he square-loop is used widely o recover carrier cosω c. I is also named inver-π case. If he recovered carrier is cosω c +π, he demodulaed bis are invered in comparison wih he ransmied bis. The soluion is he use of differenial phase keying (2DPSK).

17 Sae Key Lab. on ISN, Xidian Universiy 6.5 Binary differenial Phase Shif Keying (2DPSK) 1. Modulaion he relaive value of he carrier phases of he adjacen symbols is used o express bis ϕ = 0 0 ; ϕ = π 1, y i = x i 1 Relaive phase ϕ π π 0 π 0 0 π Info. bis x i Carrier phase ϕ π 0 0 π π π 0 Relaive code y i cos c ( ) e2 DPSK Code converer Informaion bis x i T s Relaive code y x y i i i1 s() y i1

18 Sae Key Lab. on ISN, Xidian Universiy 2. 2DPSK demodulaion Coheren demodulaion e2 PSK ( ) BPF a c b cos c LPF d Sampling& Decision iming Inverse code conversion oupu x i Relaive code y i Informaion bis x y y i i i1 T s y i1 Phase comparison mehod e2 PSK ( ) BPF a c LPF d Sampling& decision oupu b iming delayt s

19 Sae Key Lab. on ISN, Xidian Universiy Waveforms in he Phase comparison mehod a b c V 0 V How abou PSD of 2DPSK signals.

20 Sae Key Lab. on ISN, Xidian Universiy 3. Performance of Ani-noise Pe 2DPSK = 2Pe 2PSK (1 Pe 2PSK ).

21 Sae Key Lab. on ISN, Xidian Universiy 6.6 Performance Comparison of Binary Digial Modulaions 1.Pe Comparison Bi Error Rae Pe Keying modes Coheren Noncoheren 1 2ASK 2 erfc( r 4 ) 1 2 e r/4 1 2FSK 2 erfc( r 2 ) 1 2 e r/2 1 2PSK 2 erfc( 1 r) 2 e r 2DPSK Pe 2DPSK = 2Pe 2PSK (1 Pe 2PSK ) Performance of ani-noise: 2PSK > 2DPSK > 2FSK > 2ASK, 3dB difference. 2. Frequency band widh: B 2ASK = B 2PSK = 2f s, B 2FSK = f 2 f T s.

22 Sae Key Lab. on ISN, Xidian Universiy 3. Robusness: Decision Sensiive o Channel? Conclusions 2ASK 2FSK 2PSK A 2 fading values of wo 0 Compare he signals sensiive insensiive insensiive Signals of 2PSK and 2DPSK have he bes BER performance and he bes frequency band efficiency. They can be used widely in consan parameers channel. 2FSK signal is insensiive o channel s variaion. I can be applied o random parameer channel.

23 Sae Key Lab. on ISN, Xidian Universiy 6.7 M-ary Digial Keying 1. Inroducion R B = R b log 2 M Baud Under he condiion of consan informaion ransmission rae (bi/s), he symbol ransmission rae or he bandwidh of he signal can be reduced by increasing he ary number M; Under he condiion of consan symbol ransmission rae (Baud) or given frequency band, he informaion ransmission rae can be higher.

24 Sae Key Lab. on ISN, Xidian Universiy 2. M-ary ASK and 3. M-ary FSK MASK: Use he differen ampliude of he carrier o denoe he digial informaion. The carrier ampliudes is of M values. In [0, T s ], one of he M values is sen. MFSK: Use he differen frequency of he carrier o denoe he digial informaion. The carrier frequency is of M values. In [0, T s ], one of he M values is sen. 3A 2A A A s ( ) MASK Ts s ( ) MFSK Ts

25 Sae Key Lab. on ISN, Xidian Universiy 4. M-ary PSK In [0,T s ], he MPSK symbol can be expressed as s() = Acosω c +ϕ = Re(Ae j(ωc+ϕ) ) Each symbol can be described by vecor. (consellaion) QPSK: vecor diagram Reference phase Reference phase Mode A Mode B Info. Bis cosφ + + sin φ + +

26 Sae Key Lab. on ISN, Xidian Universiy 2. QPSK Modulaion Approach I: Phase selecion Serial-oparallel Phase selecion BPF e4 PSK ( ) phase carrier generaion Approach II: I-Q modulaion a Inpu Serialoparallel carrier cos c 2 e4 PSK ( ) b cosω c +φ = cosω c cosϕ sinω c sinϕ

27 Sae Key Lab. on ISN, Xidian Universiy 3. QPSK Demodulaion 1 1 cosc cosc cos 2c cos 2 2 cosc cosc cos sinc sin Samping& a LPF Decision Inpu BPF cos c iming Parraelo-serial oupu sin c Carrier recover LPF Samping& Decision 1 1 cosc sinc sin sin 2c 2 2 b furher on he way: QAM, OFDM.