Bounds on frequency estimation under additive and multiplicative noise

This paper provides a comprehensive performance analysis of frequency estimation in additive and multiplicative noise environments. A general multiplicative and additive noise model is considered with the signal. The colored noise is modeled as an AR or MA process. The exact Cramer-Rao bound (CRB) is derived for short data lengths. A frequency domain evaluation of the CRB is also discussed and it is shown that the frequency domain evaluation provides in-sight that could be used for approximating the CRB in the presence of singularities in the covariance of the multiplicative noise model. This approach has been successfully used in obtaining the CRB for a Jakes´ fading environment.