Timing Recovery in PAM Systems

The problem of symbol synchronization in digital data transmission in the presence of intersymbol interference is extremely complicated. The best sampling instants are channel dependent and are in general difficult to determine. Consequently, the problem of timing recovery in high-speed data transmission is intimately tied in with adaptive 1645 1646 T H E BELL SYSTEM TECHNICAL J O U R N A L , M A Y - J U N E 1971 equalization. Since general methods for simultaneous optimum determination of the receiver parameters arc not known, these parameters are independently determined. Timing information is usually obtained directly from the data wave in a variety of ways. 1-3 Our objectives in this paper are: (i) To indicate the optimum method (maximum likelihood) for estimating an unknown timing parameter from random data for a certain class of PAM data transmission systems; (ii) To show t h a t a variety of timing recovery methods currently in use are reasonable approximations of the optimum method, and to note that the generation of an error signal from the received signal is a feature common to these methods; (Hi) To demonstrate that timing recovery dynamics can often be studied and controlled through the application of stochastic approximation theory. 4 - 6 Identifying the desired timing parameter as the solution of a regression equation will allow us to apply stochastic approximation theory to the symbol synchronization problem. For purposes of illustration we analyze a stochastic approximation timing recovery procedure for square-wave modulation.