Theoretical Limit of Radar Parameter Estimation

In the field of radar parameter estimation, Cramer-Rao bound (CRB) is a commonly used theoretical limit. However, CRB is only achievable under high signal-to-noise (SNR) and does not adequately characterize performance in low and medium SNRs. In this paper, we employ the thoughts and methodologies of Shannon's information theory to study the theoretical limit of radar parameter estimation. Based on the posteriori probability density function of targets' parameters, joint range-scattering information and entropy error (EE) are defined to evaluate the performance. The closed-form approximation of EE is derived, which indicates that EE degenerates to the CRB in the high SNR region. For radar ranging, it is proved that the range information and the entropy error can be achieved by the sampling a posterior probability estimator, whose performance is entirely determined by the theoretical posteriori probability density function of the radar parameter estimation system. The range information and the entropy error are simulated with sampling a posterior probability estimator, where they are shown to outperform the CRB as they can be achieved under all SNR conditions