In this paper, we are concerned with the estimation of the frequency of a c
omplex sinusoid that has been corrupted by complex-valued multiplicative an
d additive noises. This problem is important in many applications including
array processing in the case of spatially distributed sources and synchron
ization in the context of time-selective channels. The multiplicative noise
smears the spectral line due to the sinusoid. This smearing, which is ofte
n called Doppler spreading, may significantly degrade the estimation accura
cy. The goal of this paper is to analytically assess this degradation. The
finite-sample Cramer-Rao bounds (CRBs) are derived, and closed-form express
ions are given for the large-sample CRB. The latter gives insights into the
effective coherent and noncoherent SNRs for frequency estimation. We then
analyze the accuracy of frequency estimators that are based on the angles o
f the sample covariances, Simulations results are presented to illustrate t
he theoretical results.