Carrier and Timing Synchronization in Digital Modems

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1 Carrier and Timing Synchronization in Digital Modems Synchronization-3 Carrier Phase Lock fred harris June, 218

2 Locking to Carrier of Modulated Signal with Suppressed Carrier 2

3 How Can One Lock to a Carrier That s Not There? Phase Jump f f Frequency Jump 3 f Non Linea rity Forms Line f f f

4 Estimate Modulation and Remove it from Modulated Waveform. m( t) x( t) j y( t) R( t) exp( j ( t)) Baseband Modulation signal s( t) [ x( t) j y( t)] exp( j t) R( t) exp( j ( t)) exp( j t) v( t) s( t) exp( j( t )) R( t) exp( j ( t)) exp( j t) exp( j( ˆ t )) mˆ ( t) slice [ v( t)] slice [ R( t) exp( j ( t)) exp( j )] Rˆ ( t) exp( j ˆ ( t)) R( t) exp( j ( t)) exp( j ) ( ) ˆ ( ) ( ) exp( ( )) exp( ) ˆ( ) exp( ˆ( )) * v t m t R t j t j R t j t 4 Up-Converted Signal, Modulation Signal On Carrier R( t) Rˆ ( t) exp( j( ( t) ˆ ( t))) exp( j ) Estimate of Modulated Signal Component R( t) Rˆ( t) exp( j )exp( j ) R( t) Rˆ( t) exp( j( )) is Phase Error Due to Additive Noise Down-Convert Received Signal With Phase Error in Local Oscillator Remove Estimated Modulated Signal Component from Down Converted Signal

5 Computation Are Performed in Cartesian Coordinates not Polar Coordinates ( ) ˆ ( ) ( ) exp( ( )) exp( ) ˆ ( ) exp( ˆ( )) * v t m t R t j t j R t j t R exp( j ) exp( j ) R exp( j ) R R exp( j( )) exp( j ) R R exp( j ) exp( j ) 1 2 R R exp( j( )) 1 2 R R [cos( ) j sin( )] 1 2 is Phase Error Due to Additive Noise * v t () mˆ ( t) [ x ( t) j y ( t)] [ x ( t) j y ( t)] [ x j y ] [ x j y ] [ x x y y ] j [ x y x y ] [ x y x y ] R R sin( )

6 Phase Measurement with Modulated Signal Constellation Points Noise Cloud s(n) Noise cloud N(n) Rotated Data Decision Boundaries s(n) e j r(n)= s(n) e j + N(n) r(n) Slic er s(n) * d(n) 6

7 Angle Varianc e Due to Noise Cloud for Small Signal Decision Aided Acquisition Noise Cloud Angle Varianc e Due to Noise Cloud for Large Signal r(n) e j (n) Matc hed Filter Equalizer Filter r(n) Detector (Slic er) s(n) (n) * -j (n) e DDS Loop Filter SNR ATAN d(n) 7

8 Decision Aided Acquisition Angle Varianc e Due to Noise Cloud for Small Signal Noise Cloud Angle Varianc e Due to Noise Cloud for Large Signal r(n) e j (n) Phase Detector, Estimates Modulation and Removes it Matc hed Filter Equalizer Filter r(n) Detector (Slic er) s(n) (n) * -j (n) e DDS Loop Filter SNR ATAN d(n) 8 Water Pistol Cleverly Disguised as a PLL Phase Detector

9 BPSK Phase Error y A sin( ) A exp(j ) x A cos( ) Consider x(n) y(n) x n y n A 2 ( )* ( ) cos( )*sin( ) A 2 2 sin(2 ) 9

10 BPSK Phase Error Option 1: x(n) y(n) x n y n A 2 ( )* ( ) cos( )*sin( ) A 2 2 sin(2 ) A sin( ) y Phase Error Down Converted Modulation Component With Carrier Phase Error A cos( ) A exp(j ) x BPSK Slicer Output. Estimate of Modulation Component Option 2: sgn(x(n)) y(n) x + j y Estimated Constellation point = A sgn(x ) = A sgn(cos( )) x + j y Observed Constellation point = A cos( )+ j A sin( ) [ x1 y2 x2 y1] A sgn(cos( )) A sin( ) A sgn(cos( )) sin( ) 1

11 I-Q Product Phase Detectors for Modulated BPSK Inputs to Product Detector Inputs to Product Detector sgn(cosine) cosine S-Curve Product detector x*y S-Curve Product Detector sign(x)*y No Multiplies in sgn(x) y -

12 12 I-Q Product Phase Detectors for Modulated BPSK

13 I-Q Product Phase Detectors for Modulated QPSK Inputs to Phase Detector y(n)*sign(x(n-1))-x(n)*sign(y(n-1)) and y(n-1)*sign(x(n))-x(n-1)*sign(y(n)) S-Curve Product Phase Detector: sign(x)*y-sign(y)*x [y(n)*sign(x(n-1))-x(n)*sign(y(n-1))]- [y(n-1)*sign(x(n))-x(n-1)*sign(y(n))] Quadricorrelator (Frequency Estimator) No Multiplies in sgn(x) y-sgn(y) x No Multiplies in Frequency Estimator

14 I-Q Product Phase Detectors for Modulated QPSK Det ( 4 ) sgn( I( )) Q( ) sgn( Q( )) I( ) Det ( ) 3 2 [ I( ) Q( )] [ I( ) Q( )] I( ) Q( ) 14

15 Tanh( SNR I( )) Q( ) Tanh( SNR Q( )) I( ) QPSK S-Curves for Range of SNR 15

16 Non Data Aided BPSK Low SNR TIME SYNCH r(t) T ( ) dt cos( t + ) SAMPLE Output I k Quadrature VCO sin( t + ) T ( ) dt LOOP FILTER SAMPLE e(t) TIME SYNCH 16

17 Non Data Aided BPSK High SNR TIME SYNCH T ( ) dt SAMPLE Output I k r(t) cos( t + ) SIGN Quadrature VCO sin( t + ) LOOP FILTER e(t) T ( ) dt SAMPLE TIME SYNCH 17

18 Costas Loop PLL r(t) T ( ) dt cos( t + ) Quadrature VCO sin( t + ) T ( ) dt LOOP FILTER e(t) Output S(t) 18

19 Digital PLL for Sinusoid r(n) cos( + ) FIR LPF Down Sam ple x(n) ATAN k P Loop Filter -Sin( + ) FIR LPF Y(n) K I Z -1 Sin-Cos Table Z -1 Direc t Digital Synthesizer If we replace ATAN with a product, we have a Costas Loop! 19

20 QPSK PLL I(n)+ jq(n) (n) Loops Differ in Phase Detectors That Change Slicers to Match Constellation r(n) cos( + ) FIR LPF x(n) x(n)+ jy(n) I(n) + -Sin( + ) FIR LPF y(n) Q(n) - DDS Loop Filter I(n)y(n)-Q(n)x(n) ~ sin( (n)) 2 Direc t Digital Synthesizer

21 QPSK PLL-II r(n) cos( + ) FIR LPF x(n) SNR I(n) Tanh(-) + -Sin( + ) Trig Table FIR LPF Loop Filter y(n) Direc t Digital Synthesizer SNR Tanh(-) Q(n) I(n)y(n)-Q(n)x(n) ~ sin( (n)) -

22 I(n)+ jq(n) (n) x(n)+ jy(n) 16-QAM PLL r(n) -sin( + ) DDS cos( + ) FIR LPF FIR LPF Loop Filter x(n) y(n) 2-D Slic er + - I(n) Q(n) Gain Det Loops Differ in Phase Detectors That Change Slicers to Match Constellation Slicer Boundaries 22

Carrier Synchronization

Chapter 8 Carrier Synchronization Marvin K. Simon and Jon Hamkins Traditionally, carrier synchronization (sync) techniques have been developed assuming that the modulation format and signal constellation