Optimal Design Of Pulse Shapes By Means Of Constrained Criteria

Abstract

A primary concern in the early days of pulse shaping was the construction of an analog circuit to generate the optimal pulse shape, and this has been a limiting constraint. With the recent developments in the DSP hardware, however, it is possible to use almost any pulse shape for digital data transmission. This resulted in a search for design algorithms capable of constructing pulse shapes matching to the properties of a given channel. Such properties can be translated to certain constrained criteria in the design of pulse shapes. The projection onto convex sets technique is suitable for the solution of this problem particularly because of its flexibility in modeling a variety of constraints. The use of the technique for the optimal pulse design problem is demonstrated through a detailed example from power line communications.