The role of spectral correlation in design and performance analysis of synchronizers
Abstract
The popular class of synchronizers that consist of a quadratic nonlinearity followed by a phase-lock loop is investigated, and it is shown that the optimum design of the quadratic transformation is characterized in terms of a spectral correlation function for the signal to be synchronized to. It is also shown that the SNR performance of this quadratic transformation, and the mean-square phase jitter of the phase-lock loop are both characterized in terms of spectral correlation functions. The conditions under which the optimum quadratic transformations, for symbol synchronization of BPSK, QPSK, SQPSK, and MSK, and for carrier synchronization of BPSK, reduce to the well-known matched-filter-squarer are identified. In addition, the well-known zero-mean-square-phase-jitter condition is generalized from PAM to all synchronizable signals, and is characterized in terms of the spectral correlation function. The low-SNR maximum-likelihood synchronizer for all quadratically synchronizable signals is characterized in terms of a multiplicity of maximum-SNR quadratic spectral-line generators. A closed form implementation in terms of a matched filter, squarer, and symbol-rate-synchronized averager is obtained for BPSK and QPSK signals.
- Publication:
-
IEEE Transactions on Communications
- Pub Date:
- November 1986
- Bibcode:
- 1986ITCom..34.1089G
- Keywords:
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- Communication Theory;
- Performance Prediction;
- Spectral Correlation;
- Synchronizers;
- Synchrophasing;
- Maximum Likelihood Estimates;
- Phase Locked Systems;
- Signal To Noise Ratios;
- Transformations (Mathematics);
- Communications and Radar