New results on the spectral analysis of multi-h CPM signals

This paper deals with the spectral analysis of multi-h continuous phase modulation (CPM) signals. A new solution to the problem is obtained by identifying an inner hidden Markov model in the CPM signal, which can be accomplished by expressing the modulator as the cascade of a sequential machine (SM), and a bank of PAM modulators. An in-depth study of the resulting Markov chain shows that it is both cyclostationary and reducible, and proper tools are identified to address these peculiarities. As a result, the multi-h CPM spectrum is expressed as a combination of Fourier transforms of portions of a CPM signal, thus allowing an efficient numerical evaluation through fast Fourier transforms (FFTs).