Reduced-Complexity PAM-based Timing Recovery
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Reduced-Complexity PAM-based Timing Recovery for Continuous Phase Modulation Dr. Erik Perrins( ), Sayak Bose. Solution to Symbol Timing Recovery. Motivation.

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Simulation results
Reduced-Complexity PAM-based Timing Recoveryfor Continuous Phase ModulationDr.Erik Perrins(, Sayak Bose

Solution to Symbol Timing Recovery


  • Continuous phase modulation (CPM) is a jointly power and bandwidth efficient digital modulation scheme used for data transmission over band-limited non-linear channels.

  • However, its deployment has been limited to a large extent because of its nonlinear nature and the complexity and synchronization problems that arise therefore.

  • Pulse Amplitude Modulation is a method of “linearizing” CPM that was first proposed for binary CPMs in the well-known paper by Laurent. This method has since been extended to M-ary CPM, and cases such as multi-h CPM and data dependent pulses, among others. The PAM representation of CPM can be applied to the problemof symbol timing recovery for CPMs in general.

  • The decision-directed nature of the algorithm has been exploited to develop two formulations of the reduced-complexity PAM-based timing error detectors (TED) that have different arrangements of the front-end matched filters.

  • The PAM Based CPM model is represented as:

  • Discrete-time implementation of PAM based decision-directed symbol timing recovery for CPM is given in the following diagram:

    Where e[n-D] are the TED outputs of two separate implementations.

Simulation Results

Timing Error Variance performances and Conclusion

  • S-curve - GMSK L=4 and B=1/4 |k|=2 S-Curve – 4-ary 2RC CPM |k|=2

  • S-curve computed via simulation for decision-directed case as well as analytically. For a small timing error, simulated curves show strong agreement with analytical curve with strong agreement with the values of slope Kp.

  • The DD-TED has stable lock points when equals integer multiples of Ts.

  • The S-curve for 4-ary CPM shows the possibility of false lock points although repeated simulation never seemed to result in one.

  • MCRB vs. Normalized timing error variance with GMSK MCRB vs. Normalized timing error variance with 4-ary 2RC

  • (L=4, Pulse parameter B=1/4 and BTs=1X CPM with h=1/4 and BTs=1X

  • Simulation results for GMSK show that, for GMSK, the normalized timing error variances are very close to MCRB for most values of Es/No. Also, TED-A is more effective than TED-B for smaller values of Es/No, its performance deviates for large Es/No although that has no practical impact on BER. No appreciable performance gap between

  • Simulation results for 4-ary 2RC CPM, TED-B outperforms TED-A, especially for the extreme low and high values of Es/No. BER is impacted for low values of Es/No. Also, for the timing error variance is closer to MCRB than for

  • In general, both TED formulations have low complexity at the receiver and are able to perform close to the MCRB. So the proposed TEDs provide important timing synchronization component for reduced complexity PAM- based CPM receivers which was previously missing.