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Communications Part I

0. Introduction: Stochastic Processes Principles of Digital Transmission Structure of Data Trans. Systems Spectra of Data Signals Nyquist Criterion Partial Response Transmission Matched Filter Bit Error Probability 2. Digital Modulation Lowpass – Bandpass Transform

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Communications Part I

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  1. 0.Introduction: Stochastic Processes Principles of Digital Transmission Structure of Data Trans. Systems Spectra of Data Signals Nyquist Criterion Partial Response Transmission Matched Filter Bit Error Probability 2.Digital Modulation Lowpass – Bandpass Transform Linear Modulation Methods 3.Nonlinear Modulation Methods 4. Spectral Characteristics Demodulation of Dig. Waveforms Coherent Demodulation Noncoherent Demodulation Carrier Recovery Timing Synchronisation Communications Part I Contents

  2. Disadvantage: delay in synchroni-sation loop caused by group delay of lowpass filters Advantage: fast synchronisation loop 3.1 Coherent DemodulationBasic Structures of Coherent Receivers Lowpass Filter - Structure Quadrature filter-Structure Coherent Demodulation

  3. Coherent DQPSK Demodulator Coherent Demodulation

  4. Coherent Demodulation of MSK Signals Reminder: FSK with  Interpretation as Offset-QPSK Decoding: Coherent Demodulation

  5. Coherent Demodulation of MSK Signals with Precoding Description of MSK as Offset-QPSK Coherent Demodulation

  6. Coherent Demodulation of MSK Signals with Precoding Avoid decoding of data  differential, nonrecursive Precoding Coherent Demodulation

  7. Coherent Demodulation of MSK Signals with Precoding Precoding Multiplication with results in derotation Coherent Demodulation

  8. Linear Model for nonlinear CPM SignalsLaurent Approximation Exact CPM signal: For limited L and define a limited phase impulse and a base impulse as well as timeshifted version Coherent Demodulation

  9. Laurent Approximation (ctd.) From the basic impulse and its timeshifted versions we can derive elementary impulses where . For the definition of we need in a binary representation: The elementary impulses are defined as: Coherent Demodulation

  10. Laurent Approximation (ctd.) Elementary impulses for 2 REC with Coherent Demodulation

  11. Laurent Approximation (ctd.) Construction of elementary impulses Coherent Demodulation

  12. Laurent Approximation (ctd.) Elementary impulses for GMSK and 4REC Coherent Demodulation

  13. Laurent Approximation (ctd.) Defining For : Under previously given conditions a CPM signal can be described as Assuming that elementary impulse has significantly greater energy than all other impulses ( to ) we get the approximation Coherent Demodulation

  14. Laurent Approximation: Complex envelopes of GFSK signals Coherent Demodulation

  15. Laurent Approximation: S/N-Ratio Coherent Demodulation

  16. Eyepatterns for coherent demodulation of GMSK Coherent Demodulation

  17. Coherent Demodulation of CPM Signals Coherent Demodulation

  18. transfering received signal into baseband without carrier synchronisation noncoherent structure: 3.2 Noncoherent Demodulation definition: typical: use of nonlinear systems for demodulation  example: FM demodulation problem: linear channel distortion  nonlinear distortion after demodulation  difficult equalization Noncoherent Demodulation

  19. Noncoherent DPSK Receiver compared with coherent structure: differential demodulation before decision phase error due to carrier frequency offset Noncoherent Demodulation

  20. Noncoherent DPSK Receiver (cont.) (otherwise: decision errors)  M-ary PSK: drawbacks of noncoherent DPSK demodulation: • 2. Nyquist criterion is not fulfilled • influence of noise (multiplication of noisy signal) Noncoherent Demodulation

  21. Eyepatterns of noncoherent DQPSK Demodulation Noncoherent Demodulation

  22. Signal Constellation of noncoherent DQPSK Demodulation Noncoherent Demodulation

  23. Differential Demodulation of CPM signals Complex envelope of CPM signal Where is the deviation of the carrier frequency used at the receiver compared to the true FSK carrier frequency Multiplication with the complex conjugate signal delayed by one symbol intervall results in for 1-REC-FSK signal Noncoherent Demodulation

  24. Sampling at symbol rate under concideration of finite length of results in By taking the argument of the above expression data value can be extracted Noncoherent Demodulation

  25. The demodulator is optimal for , i.e. MSK signals. Of disadvantage are values of close to 1 because does not contain phase information ( or ) Noncoherent Demodulation

  26. Example: GMSK demodulation ; nonrecursive approximation is broadened compared to ð increase of ISI Measurements: Equalization, Viterbi detection Noncoherent Demodulation

  27. Discriminator demodulator for CPM signals CPM signals are frequency modulated signals ð demodulation with conventional FM demodulator Ideal: derivation in time of instantaneous phase For FSK signal with after sampling at data decision possible Noncoherent Demodulation

  28. Discriminator demodulator for CPM signals Integration over one symbol intervall is not in terms of matched filtering Limit of when using a digital FM demodulator: is limited by and thus much larger than for differential demodulator Noncoherent Demodulation

  29. 3.2 Carrier SynchronisationCarrier Synchronisation on RF Example: 2 ASK • spectrum doesn´t contain carrier frequency • extracting carrier frequency out of RF signal with squaring loop Carrier Synchronisation

  30. Carrier Synchronisation: Phase locked loop (PLL) block diagramm: PLL: Phase Locked Loop phase detector BP LP loopfilter 90° VCO: Voltage Controlled Oscillator VCO Carrier Synchronisation

  31. PLL contains of • phase detector • loop filter • voltage controlled oscillator (VCO) Phase Locked Loop (cont.) • squaring input signal (removing data): • removing DC (bandpass filtering): • synchronisation in phase locked loop (PLL) VCO output: Carrier Synchronisation

  32. Phase Locked Loop (cont.) and phase detector compares phase of  multiplication loop filter suppresses noise and higher frequency signal components VCO input: ~ phase error because is small (VCO center frequency ) loop islocked:   (remaining phase error) instead of M-PSK: Carrier Synchronisation

  33. (during )  rotation of signal constellation in complex plane due to frequency offset is Decision Feedback Carrier Synchronisation (Baseband) Idea: Receiver knows correct phases out of modulation alphabet  comparing input and output of decider decision feedback carrier synchronisation demodulation of received signal with  frequency offset Carrier Synchronisation

  34.  integrating by filter yields to phase error signal at decider input: estimating (condition: correct decision, ) DF Carrier Synchronisation (cont.) correction term is accumulation of : Carrier Synchronisation

  35. DF Carrier Synchronisation: Block Diagram : received signal (baseband) decider + + - + Carrier Synchronisation

  36. DF Carrier Synchronisation: Example signal constellation without synchronisation: QPSK: correction term: if rotation of signal constellation during T is greater than : wrong decision ( )  carrier synchronisation failes!! Carrier Synchronisation

  37. frequency offset  • phase jitter  additionally: phase error estimation is disturbed by channel noise noise at decider input: Carrier Synchronisation Loop – Linearized Model up to now: only frequency offset now: phase error results of  phase error (ramp) instantanous phase error after correction: Carrier Synchronisation

  38. Carrier Synchronisation Loop noisy phase error estimation: power of phase noise: linearized model for carrier synchronisation loop (considering only phase): + remaining phase error - noise Carrier Synchronisation

  39. example: first order loop filter Remaining Phase Error (only Frequency Offset)  using z-transformation: loop transfer function: Carrier Synchronisation

  40. Remaining Phase Error with 1st Order Loop Filter remaining phase errordue to a frequency offset (steady state, 1st order loop filter):  Carrier Synchronisation

  41. but: for loop stability ! Remaining Phase Error (cont.) as big as possible small remaining phase error : choose   M-ary PSK: (= all decisions correct) Carrier Synchronisation

  42. 4 3 2 1 stability: -3 -2 -1 0 Remaining Phase Error with 2nd Order Loop Filter no remaining phase error: choose 2nd order loop filter stability Carrier Synchronisation

  43. phase jitter: : jitter frequency : amplitude jitter transfer function: (1st order loop filter) remaining phase jitter: Remaining Phase Error with Phase Jitter (Phase Noise) assumption: Carrier Synchronisation

  44. Phase Jitter, Phase Noise 2nd order loop filter: noise transfer function: , 1st order: power of remaining phase noise: Carrier Synchronisation

  45. Phase Noise Carrier Synchronisation

  46.  system impulse response fits 1st Nyquist condition idea: synchronisation on zeros of : sampling error 3.4 Timing Synchronisation: Decision Feedback Rate Control assumption: received signal is equalized (cross correlation : before and after decision) criterion for symbol clock correction: inphase component: where Synchronisation

  47. no decision errors Decision Feedback Rate Control  Synchronisation

  48. else ~ ! Decision Feedback Rate Control uncorrelated zero mean data:  with :  Synchronisation

  49. - + DCO mean Decision Feedback Rate Control block diagram: sample time tracking  time averaging ~ t Synchronisation

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