Linear models and capacity bounds for continuous phase modulation

We derive upper bounds on the capacity of an additive Gaussian noise channel with continuous phase modulation (CPM). We propose an MMSE approximation to Laurent´s (1986) linear decomposition using an arbitrary number of filtered, linearly modulated pulses. Using this linear modulation structure, we derive capacity bounds for both white and colored noise channels with CPM modulation by showing the system is equivalent to a multiple access channel (MAC) with intersymbol interference (ISI). The rate sum capacity of this cooperative MAC is used for the upper bound. Numerical results are presented for a channel using CPM with both white and colored noise. The bounds show a significant gap between a channel using CPM and a channel with unconstrained modulation.