Nonlinear multi-h phase codes for CPFSK signaling

Two novel trellis-coding techniques, called nonlinear multi-h signaling and nonlinear asymmetrical multi-h signaling, which achieve higher constraint length than ordinary multi-h signals, are introduced with CPFSK signals. In contrast to ordinary multi-h signaling where the modulation index is changed at the end of every symbol interval, nonlinear multi-h signals are constructed by changing the modulation index based on the previous symbol, and the current symbol interval. A class of nonlinear asymmetrical multi-h signals, which change the modulation index based on the current symbol too, is then constructed by extending nonlinear multi-h signals and combining them with asymmetrical multi-h signals. Binary full-response nonlinear multi-h and nonlinear asymmetrical multi-h CPFSK signals are constructed and analyzed. Minimum Euclidean distances and spectral properties of these signals are calculated at different phase states and various selected modulation index patterns. Numerical results indicate that nonlinear multi-h and nonlinear asymmetrical multi-h signals achieve significantly higher distance than other existing multi-h formats reported in the literature