Synchronization and Digital Receivers

Transcription

1 Synchronization and Digital Receivers Marie-Laure BOUCHERET IRIT/ENSEEIHT Marie-Laure.Boucheret@enseeiht.fr Synchronization (SC, Gaussian) 1

2 Synchronization algorithms (Single carrier systems, Gaussian channels) Synchronization (SC, Gaussian) 2

3 Contents Impact of synchronization errors Analog vs digital demodulators Baseband signal generation Lielihood functions Carrier phase recovery Timing recovery Carrier frequency recovery Digital demodulators examples Advanced topics References Synchronization (SC, Gaussian) 3

4 Impact of synchronization errors (1) Carrier phase error: BPSK, «NRZ»filter Maximum phase jitter is determined by the implementation loss in the lin budget. Synchronization (SC, Gaussian) 4

5 Impact of synchronization errors (2) Timing error BPSK, «NRZ»filter Maximum timing jitter is determined by the implementation loss in the lin budget. Synchronization (SC, Gaussian) 5

6 Demodulation Functions to be implemented Baseband conversion I,Q generation Carrier recovery Timing recovery Matched filtering Demodulation/decoding Synchronization (SC, Gaussian) 6

7 Analog demodulators Typical analog demodulator architecture PLL : baseband conversion + carrier frequency/phase correction IF input PLL Timing correction Decoder data PLL : baseband conversion + carrier frequency/phase correction Timing correction : FF/FB structure AFTER PLL Synchronization (SC, Gaussian) 7

8 Digital demodulators A digital demodulator is NOT the sampled version of the equivalent analog demodulator. Specific algorithms suited to digital implementation have been developped. Main differences between digital and analog demodulators: Down conversion is INDEPENDENT from phase recovery Timing recovery is performed BEFORE phase recovery Synchronization (SC, Gaussian) 8

9 Receiver input signal ( 2 jπ f t ) ( 2 jπ f t ) yt () = Re xte () + Re nte () jϕ () t xt () = e dht ( T τ ) ϕ() t = 2π ft+ ϕ f 0 : carrier frequency, Df :carrier frequency uncertainty φ 0 : phase offset, τ : timing offset d : emitted symbols h(t): emission filter (wideband channel assumed) Synchronization (SC, Gaussian) 9

10 Baseband signal generation (1) Analog implementation LPF Real part π/2 f 0 LPF Imag part This process can be digitally implemented (DAF : digital anti aliasing filter) Synchronization (SC, Gaussian) 10

11 Baseband signal generation (2) Digital implementation (1) s(t) is the real received passband signal (allocated bandwidth : FI, centred at f 0 =FI) s(t) s s r d x H PB 2 Fe=4FI -FI H PB (f) 0 Fe/8 Fe/4 f Synchronization (SC, Gaussian) 11

12 Baseband signal generation (3) Digital implementation (2) s(t) h O (n) Re(x(n)) F e =4Fi +/-1 z -n Im(x(n)) Synchronization (SC, Gaussian) 12

13 Lielihood functions (1) rt () = xt () + nt () jϕ () t xt () = e dht ( T τ ) ϕ() t = 2π ft+ ϕ 0 ρ(t 0 ) : signal observed during a period of duration T 0 Φ = { ϕ, f, τ,{ d }} 0 { ϕ ˆ { ˆ }} 0 f ˆ τ d Φ= ˆ ˆ,,, Vector of unnown parameters Vector of parameters estimates Synchronization (SC, Gaussian) 13

14 Lielihood functions (1) Λ( Φ ) = Pr( ρ( T )/ Φ ) In Gaussian channel: ΛΦ ( ) = exp rt ( ) st (, Φ) dt N0 T0 2 jπ ft + j ϕ stφ = Ae dht T 0 (, ) ( τ ) st (, Φ ) : signal replica Synchronization (SC, Gaussian) 14

15 Lielihood functions (2) Sub-optimal lielihood functions : - DD : Decision Directed - NDA : Non-data aided (depends on modulation) These sub-optimal lielihood functions are derived for timing, phase and frequency. Synchronization (SC, Gaussian) 15

16 Lielihood functions (3) Timing : L NDA ( τ ) r(t) = p(, τ ) h*(-t) 2 p(, τ ) T + τ Timing recovery is performed prior to phase recovery Synchronization (SC, Gaussian) 16

17 Lielihood functions (4) Carrier phase: DD lielihood function ( j ϕ ) ˆ ( j ϕ ) L ( ϕ) = aˆ Re p (, ˆ τ) e + b Im p (, ˆ τ) e DD NDA loelihood function for general rotationnaly symetric signal constellation (2p/N symetry) ( ) * N N jn ϕ LNDA( ϕ) = Re E d p (, ˆ τ) e Synchronization (SC, Gaussian) 17

18 Lielihood functions (5) Examples of general rotationnaly symetric signal constellation QPSK N=4 16QAM N=4 Synchronization (SC, Gaussian) 18

19 Synchronization (SC, Gaussian) 19 Lielihood functions (6) Carrier frequency recovery { } { },, 2 2 * 2 * (, ) 2 Re (, ) ˆ (, ) Re (, ) ˆ a a j ft j ft QAM L f d p d e PSK L f p d e π ϕ π ϕ ϕ τ ϕ τ + + = + =

20 Carrier phase recovery : DDMLFB (1) Derivation of detector expression from Lielihood function d L d ϕ DD ( ϕ) = 0 for ϕ = ˆ ϕ ( * j d ˆ ) p e ϕ Im (, τ ) = 0 for ϕ = ˆ ϕ ( ) ( * j ˆ ) τ u = Im d p(, ) e ϕ is a phase detector Synchronization (SC, Gaussian) 20

21 Carrier phase recovery : DDMLFB (2) S curve (example for QPSK) => Phase ambiguity (solved by using differential encoding/decoding) Synchronization (SC, Gaussian) 21

22 Carrier phase recovery : DDMLFB (3) DPLL pt (,) ˆ decision phase detector 1/(z-1) F(z) Synchronization (SC, Gaussian) 22

23 Carrier phase recovery : DDMLFB (4) Other possible detectors p(,) ˆ τ = w() ( ) Im * ( ).sgn ( ) 1 u = w w dˆ u dˆ w dˆ ( ) Im * = ( ) 2 ( ) Im *. sgn ( ) 3 u = d c w dˆ u dˆ w dˆ ( ) Im * = sgn ( ) 4 Synchronization (SC, Gaussian) 23

24 Carrier phase recovery : DDMLFB (5) Phase equivalent scheme j j F(z) 1/(z-1) ˆ( ϕ z) H( z) = ϕ( z) 1 * 1 2 BT L = H( zh ) ( z ) 2 jπ σ 2 BT L E / N s 0 γ dz z Synchronization (SC, Gaussian) 24

25 Carrier phase recovery : NDAMLFB (1) Example for QPSK d L d ϕ NDA ( ϕ) = 0 for ϕ = ˆ ϕ Im { j p (, ˆ τ ) e ϕ } 4 = 0 for ϕ = ˆ ϕ ( ) { j u Im = p(, ˆ τ ) e ϕ } 4 is a phase detector Synchronization (SC, Gaussian) 25

26 Carrier phase recovery : NDAMLFB (2) Synchronization (SC, Gaussian) 26

27 Carrier phase recovery : NDAMLFB (3) p(,) tˆ decision phase detector 1/(z-1) F(z) Synchronization (SC, Gaussian) 27

28 Carrier phase recovery : NDAMLFF (1) Suited for burst transmission Two types of structures : bloc window, sliding window Example for QPSK 4 = = { j ϕ p ˆ e } Im (, τ ) 0 for ϕ ˆ ϕ 1 4 π ˆ ϕ = Arg p (, ˆ) 4 τ + 2 Phase ambiguity ( π /2) Synchronization (SC, Gaussian) 28

29 Carrier phase recovery : NDAMLFF (2) «Sliding window» estimator p(,) tˆ Delay (L samples) decision Exp(-j.) Phase estimator (*) (*): averaging over 2L+1 samples Synchronization (SC, Gaussian) 29

30 Carrier phase recovery : NDAMLFF (3) «Bloc» estimator p(,) tˆ Delay (L samples) decision Exp(-j.) Phase estimator (*) L hold Synchronization (SC, Gaussian) 30

31 FF structures vs FB structures Advantage No acquisition time Drawbacs Smaller B L T => higher jitter, higher cycle slip probability Sensitivity to frequency deviation Synchronization (SC, Gaussian) 31

32 Timing recovery (1) ( ) ( ) LNDA() τ = p (, τ) = Re p (, τ) + Im p (, τ) d L ( ) 2 Re( (, )) d Re( (, )) 2 Im( (, )) d NDA τ = p τ p τ p τ Im( p(, τ)) dτ + dτ d τ Derivative vs timing is approximated by a difference Re( p (, τ )) Re( p ( + λτ, )) Re( p ( λτ, )) Im( p (, τ )) Im( p ( + λτ, )) Im( p ( λτ, )) Synchronization (SC, Gaussian) 32

33 Timing recovery (2) Gardner: l=1/2 => detector output is independent from carrier phase error. GA( ) = Re( p( + 1/2, τ))re( p(, τ)) Re( p( + 1, τ)) + Im( p ( + 1/2, τ ))Im( p (, τ)) Im( p ( + 1, τ)) Synchronization (SC, Gaussian) 33

34 Timing recovery (3) Matched filter Fractionnal delay 2 to DPLL τˆ updating TED Loop filter is implented by polyphasing the matched filter Synchronization (SC, Gaussian) 34

35 Timing recovery (4) S curve (Gardner, quantized) Synchronization (SC, Gaussian) 35

36 Timing recovery (5) Timing estimator (Oerder and Meyr) L 1N jπn N ˆ τ 1 = Arg p(,) n e T 2π = 0 n= 0 pn (,) pt ( + nt/ N) where N is the number of samples per second Example : N=4 L ˆ 1 Arg p(,) n j T τ = 2π = 0n= 0 n Synchronization (SC, Gaussian) 36

37 Timing recovery (6) Implementation of Oerder and Meyr * ˆ 1 T τ 2π L 1 L = Arg { p (,0) p (,2) } + j { p (,1) p (,3) } = 0 = 0 4 Rs D E M U X (1/4) * * - - Rs Σ Σ Rs /K a t a n 2 π τ / Ts * Rs Synchronization (SC, Gaussian) 37

38 Frequency recovery : general Feedbac structures «Frequency» detectors «Time» detectors Feedforward structures Type 1 Type 2 Synchronization (SC, Gaussian) 38

39 Frequency recovery:fb structures (1) «Frequency» detector (1) SMF x(n) VCO 2Rs FMF F(z) y(n) FED e(n) Synchronization (SC, Gaussian) 39

40 Frequency recovery:fb structures (2) «Frequency» detector (2) SMF : signal matched filter : g(t) FMF : frequency matched filter : -2jptg(-t) e(n)=im(x(n)y*(n)) A simpler filter (SFMF) derived from FMF can be used (g(t)=-j sgn(t) g(-t) Acquisition range : +/-(1+a)R s No prior timing correction required Synchronization (SC, Gaussian) 40

41 Frequency recovery:fb structures (3) Synchronization (SC, Gaussian) 41

42 Frequency recovery:fb structures (3) «Time» detectors Any estimator can be used as a time detector. Frequency offset range is +/- R s /M Timing has to be corrected prior to frequency detection 1 sample/symbol is sufficient. Synchronization (SC, Gaussian) 42

43 Frequency recovery:ff structures (1) Bellini 2 N N = i N N ft ˆ iα /8πT i => Cycle slip a i : unwrapped phase RCFE (reduced complexity frequency estimator) 2π ft ˆ = r = p(,) ˆ τ 1 Arg d r r MD * D M Large D leads to better performances but to lower frequency range. Synchronization (SC, Gaussian) 43

44 Digital demodulators (1) Synchronization (SC, Gaussian) 44

45 Digital demodulators (2) Choice of algorithms depends on specifications such as: Acquisition time (=> FF/FB structures) Maximum frequency deviation (=> frequency circuitry needed) Eb/No (=> use of TD if low)... Synchronization (SC, Gaussian) 45

46 Digital demodulators (3) FED Example: Receiver for TCM (in cooperation with CNES) Synchronization (SC, Gaussian) 46

47 Advanced topics Evolutions of input specifications (for satellite communications) Low Eb/No (use of efficient coding schemes such as Turbo-Codes and LDPC) Bursty transmission Large frequency deviation (low-cost terminals, non GEO sat.) Critical function : phase recovery (classical algorithms fail) There is a need to develop new synchronisation schemes Synchronization (SC, Gaussian) 47

48 References (1) Reports, boos on synchronization F.M Gardner «Demodulator reference recovery techniques suited for digital implementation» ESTEC contract n 6847/86/NL/GG,1988 F.M Gardner «Frequency detectors for digital demodulators via ML derivation», ESTEC contract n 8022/88/NL/DG,part 2, june 1990 T Jesuprret, M Moeneclaey, G Asheid «Digital demodulator synchronization : performance analysis», ESTEC contract n 8437/89/NL/RE, June 1991 H. Meyr, M Moeneclaey, S.A Fechtel «Digital communications receivers : synchronization, channel estimation and signal processing», J. Wiley and Sons, 1998 PhD Dissaertations D Mottier «Association des fonctions d égalisation, de synchronisation et de décodage canal pour les transmissions numériques à grande efficacité spectrale», PhD disertation (in French), INSA de Rennes Ivar Mortensen "Traitement en bande de base pour charges utiles à régénération bord",phd dissertation (in French), ENST, 1997 Synchronization (SC, Gaussian) 48

49 References (2) Catherine Morlet " Démodulateur embarqué multiporteuses pour applications multimédia par satellites», PhD dissertation (in French), ENST, 2000 Phase estimation A.J Viterbi and A.M Viterbi «Non-linear Estimation of PSK-modulated carrier phase with applications to burst digital transmission», IEEE on IT, 1983 M Moeneclaey, G de Jonghe, «ML oriented NDA carrier Synchronization for General Rotationnally Symmetric Signal Constellations», IEEE on COM, August 1994 C.N Georghiades «Blind carrier Phase Acquisition for QAM constellations»,ieee on COM, November 1997 Frequency estimation S Bellini and al «Digital frequency estimation in burst mode QPSK transmission», IEEE on COM, vol COM 38, July 1990 A.N D Andrea, U mengali «Performance of a frequency detector based on the Maximu Lielihood principle» F Classen and al. «Maximum Lielihood Open Loop Carrier Synchronizer for Digital Radio», ICC 93 J Zhang and al «Data-Aided estimation of carrier frequency for burst detection of QAM», Electronics Lettters, October 200 Synchronization (SC, Gaussian) 49

50 References (3) Timing estimation F.M Gardner «A BPSK/QPSK timing error detector for sampled reciver», IEEE on COM, may 1986 Oerder, Meyr «Digital filter and square timing recovery», IEEE on COM, May 1988 M.K Nezami, R Sudhaar «New schemes for improving Non-Data-Aided symbol Timing Recovery for QAM receivers in flat fading channels», 2000 Synchronization (SC, Gaussian) 50