The Channel Capacity of Phase Modulation Systems

For a particular digital phase modulation system (PMS), its channel capacity (CC) has already been derived. However, the CC of the general PMS has not been sufficiently studied, and the theoretical expression is still unavailable. In this paper, we consider the demodulation of PMS as a parameter estimation problem. Suppose that a priori distribution of the phase obeys a uniform distribution, and the CC of the PMS is the mutual information between the received signal and the unknown phase. In the additive complex Gaussian white noise, the phase modulation system model and the equivalent channel model are first developed. Based on the Bayesian formula, the analytical expression of the CC of the analog PMS is derived. And the asymptote of the CC in the high signal-to-noise ratio (SNR) is derived, which shows that for every 6 dB increase in SNR, the CC increases by 1 bit. Simulations are conducted to illustrate the CC of the general PMS and the particular digital PMS versus SNR. Results show the validity of the theoretical derivations presented in this paper.