Investigation of the Nonlinear Characteristic of Costas Loop based Carrier Recovery Systems

Transkript

1 Investigation of the Nonlinear Characteristic of Costas Loop based Carrier Recovery Systems Semjon Schaefer International Workshop on Optical Phase-locked-Loop Techniques Kiel Technische Fakultät Christian-Albrechts-Universität zu Kiel

2 Motivation Data Channel Coherent Data Data Transmitter Receiver Recovery e.g. Fiber Free-space Atmosphere Carrier Recovery (=PLL) Receiver Main focus: 1) Carrier recovery system nonlinear OPLL characteristic 2) Influence of the carrier recovery (OPLL) on the data recovery -2-

3 Content 1. Introduction 2. Optical Phase-Locked Loop 3. Nonlinear OPLL Characteristic 4. Noise Sources & Cycle Slip Phenomena 5. Conclusion -3-

4 Content 1. Introduction 2. Optical Phase-Locked Loop 3. Nonlinear OPLL Characteristic 4. Noise Sources & Cycle Slip Phenomena 5. Conclusion -4-

5 Introduction Why coherent detection? Pros: Full amplitude and phase recovery High flexibility Cons: Requires local oscillator with same carrier frequency as transmitter High complexity Carrier recovery structures: Digital carrier frequency estimation (D. Clausen) Phase-locked loop techniques University of Kiel: Optical PLL based on Costas-loop in optical intersatellite links -5-

6 Optical Intersatellite Link (OISL) Current RF Scenario: OISL Scenario: LEO: Low-Earth Orbit GEO: Geostationary Orbit LEO GS: Low data rate Short time window -6- LEO GEO GS: High data rate (LEO GEO) Long time window (GEO GS)

7 OISL Transmission System Typical Laser Communication Terminal (LCT) Setup: PM 1064 nm YDFA Free- space Channel Tx/Rx Antenna Coherent Receiver I Q Data Recov. Diff. Decod. Data Diff. Encoding Pulse Shaper Data modulation: Binary phase shift keying (BPSK) Phase of the laser is switched: Bit Bit 0 0 Frequency mismatch between LO and input signal due to Natural frequency drift Phase noise Doppler shift Transmitter -7- Fast Tuneable LO(VCO) OPLL Electronic OPLL PM: Phase modulator YDFA: Ytterbium-doped fiber amplifier OPLL: Optical phase-locked loop LO: Local oscillator Optical Electrical Digital Receiver

8 Doppler Frequency Shift Caused by the relative velocity between the satellites frx f Tx 1 v c 2 2 v 1 cos c f f Tx Rx : Transmitted frequency : Received frequency c : Speed of light in vacuum v : Relative velocity Maximum frequency offset of approx. 7 GHz Coarse compensation by using satellite trajectory data Fine compensation by optical phase-locked loop (OPLL) Residual Doppler shift, natural frequency drift and phase noise -8-

9 Content 1. Introduction 2. Optical Phase-Locked Loop 3. Nonlinear OPLL Characteristic 4. Noise Sources & Cycle Slip Phenomena 5. Conclusion -9-

10 Optical PLL based on Costas loop Fundamentals of Costas PLL ˆ sin ( ) ˆ sin ( ) s t s t t s t s t t with () t t 1 2,0 2,0 Frequency offset Phase offset I I t s t s t 1 2 ss ˆˆ 1 2 cos 1( ) 2( ) cos 2 0 1( ) 2( ) 2 t t t t t ss ˆˆ 1 2 IQ t sin 1 ( t) 2( t) sin 2 0t 1 ( t) 2( t) 2 LP Filter Error signal: ( t) I ( t) I ( t) I Q ~ sin 2 ( t) ( t)

11 Optical Phase-Locked Loop Optical phase-locked loop for BPSK transmission based on Costas loop BPSK modulation: ( t ) 0, M Coherent Receiver AGC: Automatic gain control TIA: Transimpedance amplifier LO: Local oscillator Demodulated data signal after coherent detection: U ( t) ~ cos ( t) ( t) ( t) I 1 2 U ( t) ~ sin ( t) ( t) ( t) Q 1 2 M M ( t) U ( t) U ( t) I Q ~ sin 2 ( t) ( t) 1 2 Phase error -11-

12 Frequency Acquisition Example: Residual frequency offset of 5 MHz Damping: Natural Frequency: D MHz n Error Signal () t Frequency Error -12-

13 Content 1. Introduction 2. Optical Phase-Locked Loop 3. Nonlinear OPLL Characteristic 4. Noise Sources & Cycle Slip Phenomena 5. Conclusion -13-

14 Mathematical description of Costas-PLL Error signal: ( t) K D sin 2 Loop filter: e.g. passive PI filter (lag-lead) Phase error: Nonlinear differential equation system: d dt Xs () 1sT1 1sT1 T1 F( s), with m T1 E( s) 1 st 1 s T 2 m 2 ( t) ( t) ( t) ( t) K x( t) dt d d1 xt () K dt dt 0 d 1 1 2KDK0mcos2 KDK0m sin 2 dt T2 T1 T2 d 1 d 1 x( t) ( t) m dt T dt T 2 1 K D : Phase discriminator gain [V/rad] K 0 : LO (VCO) gain [MHz/V] No analytical solutions exist Numerical approximation Phase plane -14-

15 Phase Plane Diagram Each solution of the NLDE system is represented by a trajectory in the phase plane L : All trajectories end in a stable point P H L Hold-in range Lock-in range -15-

16 Phase Plane Diagram Each solution of the NLDE system is represented by a trajectory in the phase plane L H : Not all trajectories end in a stable point P A stable periodic state exists H L Hold-in range Lock-in range -16-

17 Phase Plane Diagram Each solution of the NLDE system is represented by a trajectory in the phase plane H : No trajectories end in a stable point P but in the stable periodic state H L Hold-in range Lock-in range -17-

18 Content 1. Introduction 2. Optical Phase-Locked Loop 3. Nonlinear OPLL Characteristic 4. Noise Sources & Cycle Slip Phenomena 5. Conclusion -18-

19 Noise Sources Shot noise Results from transformation of optical power into photo current Phase noise Due to laser linewidth (Tx and LO laser) Laser spectrum: (Ideal) (Measurement) Main focus: noise influence on the phase error (i.e. carrier frequency offset) 1 2 noise distortion affects directly the carrier recovery -19-

20 Equivalent mathematical block diagram Both noise sources influence the phase error Phase error variance a b B 2 L BL PRx Phase noise Shot noise a,b const. PLL bandwidth B L influences the noise performance: Variance due to shot noise increases with B L Variance due to phase noise decreases with B L Optimum bandwidth exists -20-

21 Cycle Slip phenomena Caused by nonlinear OPLL characteristic: ( t) sin(2 ) High phase errors may drive the PLL in the nonlinear regime sin(2 ) 2 OPLL unlocks from stable point P and relocks after several jumps OPLL may lose lock without relock -21-

22 Noise Influence Cycle slips will impair data demodulation U ( t) ~ cos ( t) ( t) I U ( t) ~ sin ( t) ( t) Q M M T 1 <T 2 <T 3 Phase jumps in () t Bit errors! will flip the data Solution: Observe relative changes of bits and not absolute values Differential Encoding T: Observing time per simulation n: No. of simulations -22-

23 Conclusions Coherent detection requires carrier frequency recovery OPLL as carrier recovery in optical communication systems Investigation of the nonlinear characteristic Shot and phase noise impair the (nonlinear) OPLL performance Cycle slips influence the communication system and data recovery -23-

24 Thank you! -24-