In this paper, we derive an equivalent channel model for constant envelope, continuous phase (CECP) signals transmitted over the bandlimited additive white Gaussian noise (AWGN) channel. Using this equivalent channel model, it is proved that at high carrier-to-noise ratio (CNR), the capacity of coherent and non-coherent CECP-AWGN channel are the same. We then derive the main result of this paper, i.e., the capacity of the CECP-AWGN channel under Carson's rule bandwidth constraint. For comparison, the symmetric information rate (SIR) of several commonly used bandwidth efficient continuous phase modulation (CPM) signals are estimated using the method described in [8]. We conclude that under Carson's Rule bandwidth measure, the bandwidth efficiency of these CPM signals is still far below the CECP-AWGN capacity.
