CRAMER-RAO BOUND FOR GAUSSIAN RANDOM-PROCESSES AND APPLICATIONS TO RADAR PROCESSING OF ATMOSPHERIC SIGNALS

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.