Soft-output detection of CPM signals transmitted over channels affected by phase noise

We consider continuous phase modulations (CPMs) and their transmission over a typical satellite channel affected by phase noise. By modeling the phase noise as a Wiener process and adopting a simplified representation of an M-ary CPM signal based on the principal pulses of its Laurent decomposition, we derive the MAP symbol detection strategy. Since it is not possible to derive the exact detection rule by means of a probabilistic reasoning, the framework of factor graphs (FGs) and the sum-product algorithm is used. By pursuing the principal approach to manage continuous random variable in a FG, i.e., the canonical distribution approach, two algorithms are derived which do not require the presence of known (pilot) symbols, thanks to the intrinsic differential encoder embedded in the CPM modulator.