Hybrid digital transmission systems part I: Joint optimization of analog and digital repeaters

A hybrid digital transmission system consists of analog repeaters placed between digital repeaters. Joint optimization of the analog and digital repeaters is considered in this paper, using minimum mean-square error between the transmitted and received symbols as the performance criterion. A general hybrid system is considered. The joint optimization problem is solved in closed form for deterministic sampling under two usually satisfied conditions. From the results the minimum mean-square error and the optimum repeater characteristics can be computed for given system parameters. Timing error is also considered. From a general result, it is concluded that in many practical systems it is not only economical, but also optimum, to use identical analog repeaters, and that hybrid systems can be used for either digital or voice transmission with no compromise in theoretical performance.