Reduced-complexity detection and phase synchronization of CPM signals

Based on an extension of Laurent (1986) decomposition of continuous phase modulation (CPM) signals into a sum of linearly modulated components, we derive a class of reduced-complexity maximum-likelihood (ML) coherent detection and closed-loop phase synchronization schemes. The complexity of the resulting detection schemes, expressed in terms of the number of matched filters and states of a Viterbi algorithm, is significantly reduced with respect to that of optimal coherent receivers with negligible performance loss. This result extends a known one valid for the binary case to multilevel CPM. The proposed synchronization schemes do not require an increased number of matched filters, and are perfectly suitable to be used in conjunction with these receivers. Based on the phase-locked loop (PLL) equivalent linear model, a method for optimizing the parameters of digital second-order PLL's is presented. Numerical examples, based on theoretical analysis and computer simulation, are provided for two specific formats in the CPM class: tamed frequency modulation (TFM) and a quaternary raised-cosine (RC) modulation.