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In this paper, we give a quite practical state formulation of the problem of CPM (Constant Phase Modulation) demodulation derived using an over-sampling procedure of the received signal. Consequently, the well-known Bayes filtering equations can be implemented to perform optimal demodulation using some variations of nonlinear optimal filters. Besides, due to the infinite horizon memory of the transmitted CPM signal, we propose to reconsider the direct observation equation into a differentiated observation vector eliminating thus the contribution of the tail of the symbol sequence to be detected. Simulations confirm further the efficiency of the optimal MAP Symbol-by-symbol Detector (MAPSD) [4] as an optimal demodulator whether in its differential or decision-feedback form. Robustness towards the over-sampling rate and the length of the partial response of the shaping filter is studied also numerically.

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