Minimal PAM decompositions of CPM signals with separable phase

This letter proposes a new pulse amplitude modulation decomposition of continuous phase modulation (CPM) signals under the constraint of phase response separability. The separability condition is met by a broad class of CPM signals, including full-response signals. We show that the proposed decomposition has minimal cardinality of N_c=L(M-1), where M is the alphabet size and L is the CPM memory length. The cardinality increases linearly with L, while previous proposed decompositions have cardinalities M^L-M^L-1, which grow exponentially with L.