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This paper establishes an optimal generic function model in order to obtain a continuous phase modulated (CPM) signal with a smoother phase modulation function. This is achieved by finding the solution to the symbol signals at different lengths of the CPM function. In the solution process, the unknown amount that needs to be solved is reduced by using the even function symmetry characteristic of the signal to be solved. For each different form of the signal, the time domain form of the CPM function and the corresponding normalized energy spectral density are compared under the influence of the phase modulation signal length and the generic function parameter n. The data transmission rate is improved by introducing inter-symbol interference, and the modulation process is realized using six-way parallel transmission when the CPM function is 6T. The simulation results show that the CPM function obtained by establishing an optimal generic function model has high-quality time-frequency characteristics. The real-time phase trajectory and the high-order derivative are both continuous, and the modulated signal has constant envelope characteristics. The CPM function has a fast rolling-off in the frequency domain and small out-of-band radiation, which greatly improves the characteristics of the frequency band utilization.

Research on an Optimization Method for a Partially Responsive Continuous Phase Modulated (CPM) Signal Based on an Optimal Generic Function