Chapter 4 Frequency Correction

Over the years, much effort has been spent in the search for optimum synchronization schemes that are robust and simple to implement [1,2]. These schemes were derived based on maximum-likelihood (ML) estimation theory. In many cases, the derived openor closed-loop synchronizers are nonlinear. Linear approximation provides a useful tool for the prediction of synchronizer performance. In this semi-tutorial chapter, we elaborate on these schemes for frequency acquisition and tracking. Various low-complexity frequency estimator schemes are presented in this chapter. The theory of ML estimation provides the optimum schemes for frequency estimation. However, the derived ML-based scheme might be too complex for implementation. One approach is to use theory to derive the best scheme and then try to reduce the complexity such that the loss in performance remains small. Organization of this chapter is as follows: In Section 4.1, we show the derivation of openand closed-loop frequency estimators when a pilot (residual) carrier is available. In Section 4.2, frequency estimators are derived for known data-modulated signals (data-aided estimation). In Section 4.3, non-data-aided frequency estimators are discussed. This refers to the frequency estimators when the data are unknown at the receiver.