L A-B-C dei Segnali Spread-Spectrum

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1 L A-B-C dei Segnali Spread-Specrum Marco Luise Universiy of Pisa, Ialy Diparimeno Ingegneria dell Informazione hp://

2 PAM Signal +A -A s() a 0 a 1 a 2 a 3 a 4 {a k }=+1 Binary Symbols Binary Pulse-Ampliude Modulaion (PAM) Symbol Inerval: = Bi Inerval: b Basic Pulse p(): Symbol Rae: R=1/ = Bi Rae: R b =1/ b p() Bipolar Forma s() a k p( k ) k A LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 2

3 Norm.PSD S s (f)/ (db) Power Specral Densiy (PSD) of he PAM Signal p() A=1 A db Normalized Frequency, f S s ( f ) A2 P( f ) Normalized Frequency, f LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 3

4 Direc-Sequence Spread Specrum p() Daa Pulse s() x SS () A s() a k p( k) k q() c() SPREADING CODE PAM Signal Chip ime 1 Chip Pulse M=Spreading Facor PSEUDO-NOISE Sequence =/M c c() c m q( m c ) m LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 4

5 Spreading he Specrum s() s() x SS () +A -A c() SPREADING CODE M=8 c +1 c() Wha is he PSD of he SS signal? (o be coninued ) -1 LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 5

6 Anoher view of he SS signal s() +A -A Compuing he produc of he daa symbol a k wih he code chip c m we ge c() +1-1 x ( ) s( ) c( ) q( m ) SS m c m where +1 x ss () c a m m in( m / M ) -1 is iid binary and runs a he chip rae LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 6

7 Spread Specrum!! 1.2 Linear Scale Daa PSD M=8 Spreading Code PSD M= Normalized Frequency, f Log (db) Scale Normalized Frequency, f GPS: chip rae Mchip/s bi rae 50 bi/s M=20460 LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 7

8 he DS/SS Receiver x SS () r() z() (k+1) 1 ( ) d k â k Mached filer w() Code Sync c() De-spreader Correlaor z() s()c() w() c() s()c 2 () w' () LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 8 =1!

9 iming Error- Spread-Specrum Modulaion x SS () r() z() 1 (k+1) k ( ) d z k â k w() Code Sync c(-) z( ) s( ) c( ) w( ) c( ) s( ) c() c( ) w() De-spreader Correlaor ( k1) 1 z a c() c( ) d w a Rc ( ) w k k k k k k LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 9

10 BER of he DS/SS Receiver P Q e b C N 0 / 2 Q 2 E b N 0 NO difference w.r. a narrowband modulaion! Specrum spreading/despreading is a ransparen operaion LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 10

11 Narrowband Inerference Rejecion In-band Inerfering Power P i P 1/ c 1 P c P M Narrowband Inerference Power P De-spread SS signal SS signal BEFORE Despreading Spread Inerference AFER Despreading 1/ c Frequency 1/ 1/ c LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 11

12 Muliplexing: ime- and Frequency-Division Slo #1 Slo #2 Slo #N... IME User Daa #1 DMA: he user signals are separaed in IME(overlapped in frequency) User Daa #2 User daa signals o be muliplexed. User Daa #N FDMA: he user signals are separaed in FREQUENCY (overlap in ime) Carrier #1 Carrier #2 Carrier #N... FREQUENCY LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 12

13 Code Division Muliplexing User Daa #1 Each user is assigned a signaure code used o spread his/her own daa signal IME User Daa #2.. Spreading Code #1 Spreading Code #2 he he users usersare are overlapped boh bohin in ime ime and and frequency --hey heycan be beseparaed only onlyvia via de-spreading wih wih he he appropriae code code User Daa #N Spreading Code #N Spread Specrums FREQUENCY LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 13

14 Orhogonal Codes (0) c () m L=2 =4 0 c ( i ) ( ) c ( k ) ( ) d 0, i k =L c H H WALSH-HADAMARD Marices & Funcions (1) c () (2) c () Chip ime H H H H/ 2 H H/ 2 H H/ 2 H H / 2 (3) c () LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 14

15 (Synchronous) Orhogonal CDMA c i ()c k ()d=0, ik he user signals are ORHOGONAL (bu synchroniciy is needed) c () 0 c () 1 c () 2 c () 3 ime c () 4 c () 5 Frequency c () 6 CODE c () 7 able of Walsh-Hadamard Funcions L=8 LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 15

16 Flexible Bi-Rae wih CDMA (symbol repeiion) s() Full Rae R=1/ +A E b =P max. MAI N users -A M=8 c c() +1 Chip-rae and DS/SS signal bandwidh is he same! -1 +A s() Half Rae R =1/2 E b =P 2=2E b half power 2 half MAI 2N -A M=16 LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 16

17 OVSF Codes Orhogonal Variable Spreading-Facor Codes ree C 0 (0) = + C 1 (0) = + + C 1 (1) = + - C 2 (0) = C 2 (1) = C 2 (2) = C 2 (3) = C 3 (0) C 3 (1) C 3 (2) C 3 (3) C 3 (4) C 3 (5) C 3 (6) C 3 (7) Orhogonal wihin he same layer Orhogonal beween differen layers provided ha he shorer is no ancesor of he longer LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 17

18 Mulirae ransmission wih OVSF Codes R b Code C (3) 3 Daa L=8 a (k) 1 ime 4R b Code C (1) 1 L=2 a (k) 2 ime Each repeiion of he shor code is orhogonal o any of he sub-codes of he long code over a shor-symbol period he long code is orhogonal o he repeiions of he shor code over a longsymbol period (basic rae) LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 18

19 Code-Division Muliplexing and Muliple Access Synchronous muliplexing: all users share he same daa and chip clock Co-locaed user signals Asynchronous MULIPLE ACCESS: no user synchronizaion (sor of random access) LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 19

20 Wideband Inerference (A-CDMA) P i De-spread SS signal In-band Inerfering Power P 1/ c 1 P c P M Wideband Inerference Power P BEFORE Despreading (SILL) Spread Inerference AFER Despreading SS signal 1/ c Frequency 1/ 1/ c LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 20

21 Asynchronous Code-Division Muliplexing DS/SS-BPSK Modulaor #1 2P exp{ j} he desired signal is corruped by DS/SS-BPSK Modulaor #2 2P (2) exp{ j 2 } 2 w() r() Muliple-Access Inerference (MAI) DS/SS-BPSK Modulaor #U 2P (N) U exp{ j U } Equivalen Noise PSD of I() DS/SS-BPSK Modulaor #1 2P exp{ j} w() y() I 0 =(U-1)P/(1/ c ) Equivalen Gaussian Channel (Cenral Limi heorem) LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 21 I()

22 BER BER Capaciy of CDMA db U=1 9.6 db E b /N 0 =11.3 db M=128 M= E b /N 0 (db) # of Acive Channels, U LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 22

23 !? Band-Limied Spread Specrum!? a k d m Pulse x () SS M Shaping 1/ 1/ c 1/ q() c 1/ c q() is now an SRC pulse c Q(f) c m w.r. he chip ime c IA s IS-95: =0.2, R c = Mc/s B=1.475 MHz - Carrier spacing=1.5 MHz 1 2 c Roll-off Region / c Bandwidh (1+ )/2 c f ESI s WCDMA: =0.22, R c =3.840 Mc/s B= MHz-Carrier spacing=5 MHz LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 23

24 Modulaion / Spreading Arrangemens I a k Pulse Shaping q() x() SS-BPSK c() cos( 2f 0 ) cos( 2f 0 ) a k S/P a 2k c() Pulse Shaping q() x() SS-QPSK a 2k+1 Pulse Shaping q() -sin( 2f 0 ) LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 24

25 he RAKE Receiver r() (k+ 1) 1 ( ) d k c() 1 z k (k+ 1)+ 1 ( ) d k+ c(-) Aexp{-j} Received Signal ou of he 2-ray channel j r( ) c( ) Ae c( ) Overall Response of he Mached Filer: Oupu of he overall MF a =: jus z k!! LM Ing. LC ABC dei Segnali Spread-Specrum M. LUISE 25

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