Frequency estimation in the presence of Doppler spread: Performance analysis

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.