Symbol timing tracking for continuous phase modulation over fast flat-fading channels

The symbol timing tracking problem for a class of continuous phase modulation (CPM) schemes transmitted over unfaded and fast flat-fading channels is studied. The specific family of CPM considered is that of M-ary continuous-phase modulation with a modulation index of h=1/M. A particular symbol synchronizer structure that constructs a tone at the symbol frequency by passing the received signal through an Mth power law nonlinearity and multiband filter followed by a squared-envelope nonlinearity and narrowband filter is proposed. The operation and parameters of this symbol synchronizer are discussed as well as the performance of the synchronizer. Simulation results giving the root-mean-square timing jitter of this system for several binary, quaternary and 8-ary instances of modulation using rectangular, raised-cosine, truncated Nyquist III, and truncated tamed FM pulse shapes are presented to illustrate the synchronizer performance