An adaptive view of synchronization

There are four basic synchronization tasks in communications systems: the receiver must determine the phase and frequency of the carrier signal, and it must determine the timing and period of the symbol clock. All four of these tasks can be solved via gradient methods, and many common algorithms such as the phase locked loop, Costas loop, cluster variance minimization and output energy maximization (for clock recovery) can be viewed as a gradient algorithm applied to specific cost functions. This paper presents an overview of synchronization by stating a formal definition of an "adaptive element". By looking at the cost functions, insight can be gained as to how the various elements can be combined, sequenced, and compared.