Multi-pulse continuous phase modulation

A generalization of multi-level continuous phase modulation (CPM) called multi-pulse CPM (mpCPM) is proposed. We show how to find the minimum Euclidean distance and how to calculate the power spectral density. We compare the performance with standard CPM by numerically searching for phase pulses that maximizes the minimum Euclidean distance under a power spectral density requirement defined by a spectrum mask. There is a small gain in the minimum Euclidean distance over standard CPM for a spectrally efficient system, and the gain increases with less spectral efficiency. Furthermore, we demonstrate that mpCPM can be used to control the bit error probability of the individual bit streams in multi-level CPM.