Principles, Methods and Performance Limits

This chapter lays the groundwork for the material in the book and addresses three major themes. Section 2.2 describes synchronization functions in a digital receiver and indicates methods to pinpoint design limits on the synchronization errors. Section 2.3 is an overview of maximum likelihood parameter estimation theory, with emphasis on synchronization applications. A distinction is made between wanted and unwanted parameters, the former being those of interest in a given situation and with respect to which the maximum of a likelihood function is to be sought. The computation of likelihood functions for wanted parameters is investigated. Section 2.4 establishes limits to the performance of practical synchronizers. The most popular limit is the Cramer-Rao bound to the variance of unbiased estimators. It is argued that this limit is difficult to compute in most practical cases. A simpler limit is the modified Cramer-Rao bound, which is used as a benchmark in performance evaluations throughout the book.

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