Synthesis of Synchronization Algorithms In this chapter we derive maximum-likelihood (ML) synchronization algorithms for time and phase. Frequency estimation and synchronization will be treated in Chapter 8. The algorithms are obtained as the solution to a mathematical optimization problem. The performance criterion we choose is the ML criterion. In analogy to filter design we speak of synthesis of synchronization algorithms to emphasize that we use mathematics to find algorithms - as opposed to analyzing their performance. Derivation of ML Synchronization Algorithms Conceptually, the systematic derivation of ML synchronizers is straightforward. The likelihood function must be averaged over the unwanted parameters. For example, joint. | Digital Communication Receivers Synchronization Channel Estimation and Signal Processing Heinrich Meyr Marc Moeneclaey Stefan A. Fechtel Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-50275-8 Online ISBN 0-471-20057-3 Chapter 5 Synthesis of Synchronization Algorithms In this chapter we derive maximum-likelihood ML synchronization algorithms for time and phase. Frequency estimation and synchronization will be treated in Chapter 8. The algorithms are obtained as the solution to a mathematical optimization problem. The performance criterion we choose is the ML criterion. In analogy to filter design we speak of synthesis of synchronization algorithms to emphasize that we use mathematics to find algorithms - as opposed to analyzing their performance. Derivation of ML Synchronization Algorithms Conceptually the systematic derivation of ML synchronizers is straightforward. The likelihood function must be averaged over the unwanted parameters. For example joint estimation of 0 e pWW P a p r a 0 all sequences a phase estimation P rf 0 j 52 P a p r a p de 5-1 Lail sequences a timing estimation P k 52 p a P r la MPOT dd .all sequences a With the exception of a few isolated cases it is not possible to perform these averaging operations in closed form and one has to resort to approximation techniques. Systematically deriving synchronization algorithms may therefore be 271 272 Synthesis of Synchronization Algorithms understood as the task of finding suitable approximations. The various algorithms are then the result of applying these techniques which can be systematic or ad hoc. The synchronizers can be classified into two main categories 1. Class DD DA Decision-directed DD or data-aided DA 2. Class NDA Non-data-aided NDA The classification emerges from the way the data dependency is eliminated. When the data sequence is known for example a preamble a0 during acquisition we speak of data-aided synchronization algorithms. Since the sequence ao is known only one term of
