Conditional maximum likelihood frequency estimation for staggered modulations

The use of spectrally efficient continuous phase modulations for mobile communications may lead to a serious performance degradation of the classical frequency error detectors (FEDs) due to the presence of self-noise. This article presents a new statistically efficient frequency estimation algorithm for staggered modulations. The cancellation of the self-noise is accomplished by the use of the conditional ML principle, well known in the context of array processing, as an alternative to the unconditional ML, typically applied in the communications field. The paper also provides a new Cramer Rao bound (CRB) which is more accurate than the so-called modified CRB (MCRB) extensively applied to synchronization problems.