The problems of fast channel estimation and fast start-up equalization in synchronous digital communication systems are considered from the viewpoint of the optimization of the training sequence to be transmitted. Various types of periodic sequences having uniform discrete power spectra are studied. Some of them are new and may be generated with data sets commonly used in phase modulation systems. As a consequence of their power spectra being flat, these sequences ensure maximum protection against noise when initial equalizer settings are computed via channel estimates and noniterative techniques. 8 Copyright 1983 by International Business Machines Corporation. Copying in printed form for private use is permitted without payment of royalty provided that (1) each reproduction is done without alteration and (2) the Journal reference and IBM copyright notice are included on the first page. The title and abstract, but no other portions, of this paper may be copied or distributed royalty free without further permission by computer-based and other information-service systems. Permission to republish any other portion of this paper must be obtained from the 426 Editor.

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