Overview of performance lower bounds for blind frequency-offset estimation

This paper focuses on performance bounds for estimating the frequency and the phase of a received signal when the complex amplitude of the signal is non-constant and unknown. Receivers need to perform such an estimation in many application fields, including digital communications, direction-of-arrival estimation, and Doppler radar. While in digital communications the non-constant complex-signal amplitude is a discrete random variable related to the transmitted information bits, in many other signal-processing fields this non-constant amplitude is typically modeled as multiplicative Gaussian noise. Fundamental lower bounds on the mean square error of any frequency-offset and phase-shift estimator are continuously employed in all these application fields. They serve as a useful benchmark for judging the performance of practical estimators. We present an overview of such bounds with their respective areas of interest, and their associated derivations in closed form.