# Chapter 6. Performance Analysis of Synchronizers

Published Online: 9 OCT 2001

DOI: 10.1002/0471200573.ch6

Copyright © 1998 John Wiley & Sons, Inc

Book Title

## Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing

Additional Information

#### How to Cite

Meyr, H., Moeneclaey, M. and Fechtel, S. A. (2001) Performance Analysis of Synchronizers, in Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471200573.ch6

#### Publication History

- Published Online: 9 OCT 2001

#### Book Series:

#### Book Series Editors:

- John G. Proakis

#### Series Editor Information

Northeastern University

#### ISBN Information

Print ISBN: 9780471502753

Online ISBN: 9780471200574

- Summary
- Chapter

### Keywords:

- synchronizers;
- performance analysis;
- parameter errors;
- fisher information matrix;
- tracking performance;
- carrier synchronizers;
- symbol synchronizers;
- performance comparison;
- decision directed;
- non-decision directed;
- cycle slipping;
- feedforward;
- acquisition;
- carrier phase;
- symbol timing

### Summary

During data transmission the synchronizer provides an estimate which most of the time exhibits small fluctuations about the true value. The synchronizer is operating in the tracking mode. The performance measure of this mode is the variance of the estimate.

In this chapter, we derive a lower bound on the variance of these estimates. This bound will allow us to compare the variance of practical estimators to that of the theoretical optimum, and thus, assess the implementation loss.

We also compute the variance of carrier and symbol synchronizers of practical interest. The tracking performance is first computed under the assumption that the parameters are constant over the memory of the synchronizer. Later on we relax this prescription to investigate the effect of small random fluctuations (oscillator phase noise) and of a small frequency offset.

Occasionally, noise or other disturbances push the estimate away from the stable tracking point into the domain of attraction of a neighboring stable tracking point. This event is called cycle slip. Cycle slips have a disastrous effect since they affect many symbols. Their probability of occurrence must be at least a few orders of magnitude less frequent than the bit error rate. Cycle slipping is a highly nonlinear phenomenon which defies exact mathematical formalism in many cases. One must resort to computer simulation.

At the start of signal reception the synchronizer has no knowledge of the value of the parameters. During a start-up phase the synchronizer reduces the initial uncertainty to a small steady-state error. This process is called acquisition. To efficiently use the channel, the acquisition time should be short. Various methods to optimize the acquisition process are discussed.