# Chapter 8. Frequency Estimation

Published Online: 9 OCT 2001

DOI: 10.1002/0471200573.ch8

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) Frequency Estimation, in Digital Communication Receivers: Synchronization, Channel Estimation, and Signal Processing, John Wiley & Sons, Inc., New York, USA. doi: 10.1002/0471200573.ch8

#### 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:

- frequency estimation;
- classification independent operation;
- timing information;
- feedback;
- error;
- calculation;
- self-noise term;
- algorithms;
- modifications;
- feedforward carrier;
- additive noise;
- MSK estimators;
- performance analysis

### Summary

In this chapter we are concerned with frequency estimation. We could have studied this problem earlier (Chapter 5) by including an additional parameter Ω in the set **θ** = {θ, ε, **a**}. The main reason why we choose to include a separate chapter is that for a sizeable frequency offset Ω we must *first* compensate this frequency offset before the other parameters {θ, ε, **a**} can be estimated. This implies that frequency offset estimation algorithms must work independently of the values of the other parameters. The operation of the algorithms is nondata aided and nonclock aided. The only exception occurs for small frequency offset (Ω*T*) ≪ 1. In this case, timing-directed algorithms are possible.

This chapter is organized as follows. We first discuss the channel model modifications necessary to include the estimation of Ω. Then we derive estimators which work independently of the other parameters {θ, ε, **a**}. In a familiar way we obtain feedback algorithms by differentiating the likelihood function with respect to the parameter Ω. The algorithms of the first two sections operate on samples {*r _{f}*(

*kT*)} which are sufficient statistics. If the frequency offset is restricted to small values, roughly |Ω

_{s}*T*| < 0.15, timing can be recovered

*prior*to frequency compensation. Given the timing, frequency estimators are developed which work at symbol rate 1/

*T*. These algorithms have superior tracking performance compared to the algorithms operating with samples {

*r*(

_{f}*kT*)}. Direct frequency estimators are discussed. The corresponding error-feedback algorithms are studied. Frequency estimation for MSK signals is studied. In summary, the rate-1/

_{s}*T*algorithms can be regarded as coarse acquisition algorithms reducing the frequency offset to small fractions of the symbol rate. If necessary, timing-directed algorithms with improved accuracy can be employed in a second stage running at symbol rate 1/

_{s}*T*.