The Cramer-Rao bound for pole and amplitude estimates of damped exponential signals in noise

Expressions are derived for the Cramer-Rao bounds (CRBs) of the parameters of an exponential model with one set of poles and multiple sets of amplitude coefficients. The poles of this model may lie anywhere in the complex plane. The CRB for pole angle is log-symmetric about the unit circle with minimum on the unit circle, while the CRB for pole magnitude has its minimum inside the unit circle for finite-length datasets and is not symmetric. Simulation results show that error-standard-deviation ellipses about poles turn out to be circular. The CRBs for estimates of the amplitude coefficients of real and imaginary parts are also available