An equivalence principle for separable CPM signals

A continuous phase modulation (CPM) is specified by the size M of the input alphabet, the modulation index h, the phase response φ(t) and the duration LT of the active part of φ(t). The integer L indicates the memory and, roughly, the complexity of a CPM system. In this contribution we show that a CPM with an arbitrary memory L is equivalent to a CPM with a unitary memory and a bigger alphabet with size L(M - 1) + 1. The assumption is that the phase response φ(t) is "separable", a requirement verified in some practical implementations. We discuss some consequences of this equivalence on modulator and demodulator structure.