Performance analysis for convolutional coded CPM over rings

In this paper, we present upper bounds on the symbol error probability for convolutional encoded continuous phase modulation (CPM) over rings with maximum likelihood sequence detection (MLSD). Both coded CPM schemes with and without feedback from the CPM encoder to the ring convolutional encoder are considered. The bounds are based on the transfer function technique. The paper contribution is in the development of the analytical upper bound on the symbol error probability for the investigated system. The bound can be used as a tool to analyze and design ring convolutional encoded CPM systems.