An upper bound on the bit error probability of combined convolutional coding and continuous phase modulation

The bit error probability properties of signals consisting of convolutional coding combined with partial-response multilevel continuous phase modulation (CPM) are studied. It is assumed that the channel is an additive white Gaussian noise channel and that the receiver performs coherent maximum-likelihood sequence detection by means of the Viterbi algorithm. An upper bound on the bit error probability is derived, using the average generating function technique, and evaluated numerically for a number of coded multilevel full-response CPM schemes. Simulation results are also presented. It is concluded that the free Euclidean distance is the best one-parameter description of the error probability for the considered class of signals for high signal-to-noise ratios. However, the upper bound results show that the free distance alone yields pessimistic bit error probability behavior for some interesting cases