Evolutionary Optimization of CPM Schemes over a Range of Spectral Efficiencies

We consider the optimization of coded continuous phase modulation (CPM) systems operating at the spectral efficiencies 0.5bps/Hz, 1.0bps/Hz, 1.5bps/Hz and 2.0bps/Hz. Due to the difficulty of defining an analytic fitness function and the discreteness of the CPM parameters, we opt for an evolutionary optimization, which easily deals with such limitations. We apply a bi-objective instance of the non-dominated sorting genetic algorithm II (NSGA-II) where the mutual information between the transmit bits and soft bits at the output of the CPM detector as well as the complexity are taken as objective functions. This enables us to quantify the trade-off between complexity and performance. The results show that for all considered spectral efficiencies, the best schemes are usually quaternary or octal with a frequency pulse length not exceeding 2 symbol durations and a code rate ranging between 0.7−0.8.