Topics in matrix analysis
Cyclic spectral analysis of continuous-phase modulated signals
IEEE Transactions on Signal Processing
Decomposition of M-ary CPM signals into PAM waveforms
IEEE Transactions on Information Theory
Space-time code design with continuous phase modulation
IEEE Journal on Selected Areas in Communications
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In 1986, Laurent showed that binary continuous phase modulated (CPM) signals can be decomposed into pulse amplitude modulated (PAM) waveforms. This result, later extended to multilevel CPM signals by Mengali and Morelli, has attracted much attention, especially for the design of simplified receivers. The paper proceeds from the premise that the decomposition into PAM waveforms is not unique, and follows a system-theory approach that leads to a natural formulation. First, the CPM modulator is represented by a nonlinear part (encoder) followed by a linear part (bank of PAM modulators). The two parts are then rearranged with the aim of obtaining real-valued continuous PAM waveforms and to reduce their number. Several classes of decompositions arise with this approach, each of which admits an infinite number of different decompositions of the same CPM signal, among which the Laurent and Mengali-Morelli results appear as special cases. Throughout the paper, a systematic use is made of the Kronecker product, which appears to be the natural tool for dealing with CPM decompositions and for expressing results in a very simple form.