Trellis termination of Multi-h CPM and the Diophantine Frobenius Problem

This paper presents a method for terminating the phase trellis in Multi-h Continuous Phase modulation (CPM). It is shown that tilted phase trellis for a Multi-h CPM signal is periodic and enables the representation of the modulator as the cascade of a periodic recursive continuous phase encoder (CPE) and a phase modulator (PM). We then pose the problem of finding the number of symbols that will terminate the tilted phase trellis, and establish a connection of its solution to the Diophantine Frobenius Problem (FP). Results are derived for the existence of a terminating sequence (TS), and bounds are established on its length in terms of the modulation parameters.