On the representation of CPM signals by linear superposition of impulses in the bandpass domain

Abstract
A novel signal generation concept for continuous phase modulations (CPMs) with modulation index 1/2 based on real impulses is presented. With this concept, bandpass CPM signals can be generated directly in one step instead of the two consecutive steps, namely, the generation of the complex envelope and the modulation of the carrier by the complex envelope, which are necessary in conventional signal generators. Mathematical expressions for both the real impulses and the bandpass CPM signals are derived and a simple modulator structure is discussed. Examples for the real impulses are given. Among these are the well-known CPM schemes of minimum shift keying (MSK), sinusoidal frequency shift keying (SFSK), and Gaussian minimum shift keying (GMSK). As an example, the validity of the novel signal generation concept is shown for the latter CPM scheme