Peformance of mean-frequency estimators for Doppler radar and lidar

Abstract

The performance of mean-frequency estimators for Doppler radar and lidar measurements of winds is presented in terms of two basic parameters: Φ, the ratio of the average signal energy per estimate to the spectral noise level; and Ω, which is proportional to the number of independent samples per estimate. For fixed Φ and Ω, the Cramer-Rao bound (CRB) for unbiased estimators of mean frequency signal power, and spectral width are essentially independent of the number of data samples M. For large Φ, the estimators of mean frequency are unbiased and the performance is independent of M. For small Φ, the estimators are biased due to the effects of the uncorrelated noise (white noise), which results in uniformly distributed "bad' estimates. The friction of bad estimates is a function of Φ and M with weak dependence on the parameter Ω. For Doppler lidar and for large Φ, better performance is obtained by using many low-energy pulses instead of one pulse with the same total energy. For small Φ, the converse is true. -from Authors