Frequency domain interpretation of the Cramer-Rao bound for carrier and clock synchronization

The Cramer-Rao bound is a fundamental lower bound on the variance of unbiased estimates. Applied to carrier phase and clock phase synchronization for digital communications, it is shown that the corresponding bounds can be derived from the power density spectrum of the transmitted signal-irrespective of the particular modulation scheme. This allows the localization of the available information about the parameters in the frequency domain. If the incoming signal is only partly exploited, the resulting performance loss is now easily attainable.<>