R. Frehlich, CRAMER-RAO BOUND FOR GAUSSIAN RANDOM-PROCESSES AND APPLICATIONS TO RADAR PROCESSING OF ATMOSPHERIC SIGNALS, IEEE transactions on geoscience and remote sensing, 31(6), 1993, pp. 1123-1131
Calculations of the exact Cramer-Rao Bound (CRB) for unbiased estimate
s of the mean frequency, signal power, and spectral width of Doppler r
adar/lidar signals (a Gaussian random process) are presented. Approxim
ate CRB's are derived using the Discrete Fourier Transform (DFT). Thes
e approximate results are equal to the exact CRB when the DFT coeffici
ents are mutually uncorrelated. Previous high SNR limits for CRB's are
shown to be inaccurate because the discrete summations cannot be appr
oximated with integration. The performance of an approximate maximum l
ikelihood estimator for mean frequency approaches the exact CRB for mo
derate signal to noise ratio and moderate spectral width.