Optimizing Performance of Spectrally Constrained Partial Response CPM

Optimized phase pulses, which maximizes the minimum Euclidean distance in spectrally constrained partial response CPM for di erent pulse lengths and di erent alphabet sizes, are numerically found. The channel is an AWGN channel constrained by a narrow spectrum mask, which puts hard requirements on both the width of the spectral main lobe and the size of the spectral side lobes. The phase pulse is parameterized by equidistant sample points connected by cubic spline interpolation and the modulation index is also treated as a free parameter. It is found that the optimized phase pulses are smooth pulses and in many cases similar to the GMSK phase pulse family. A gain of up to 0.9 dB is obtained for the optimized phase pulses compared to the GMSK phase pulses and a useful property for reduced complexity detection is found for some phase pulses.