Inherent limitation in data-aided time synchronization of continuous phase-modulation signals over time-selective fading channels

Time synchronization of continuous phase modulation (CPM) signals over time selective, Rayleigh fading channels is considered. The Cramér-Rao lower bound (CRLB) for this problem is studied for data-aided (DA) synchronization (i.e., known symbol sequence transmission) over a time-selective Rayleigh fading (i.e., Gaussian multiplicative noise) channel. Exact expressions for the bound are derived as well as simplified, approximate forms that enable derivation of a number of properties that describe the bound's dependence on key parameters such as signal-to-noise ratio (SNR), channel correlation, sampling rate, sequence length, and sequence choice. Comparison with the well-known slow fading (i.e., constant) channel bound is emphasized. Further simplifications are obtained for the special case of minimum phase keying (MSK), wherein it is shown how the bound may be used as a sequence design tool to optimize synchronization performance.