Theoretical Performance Limit for Radar Parameter Estimation

TL;DR

This paper applies Shannon's information theory to establish the fundamental performance limits of radar parameter estimation, deriving bounds and demonstrating the optimality of certain estimators across all SNR levels.

Contribution

It introduces a theoretical framework for radar parameter estimation using information theory, deriving performance bounds and proving the achievability of the theoretical range information.

Findings

Theoretical range information (RI) is achievable.

The entropy error (EE) bound is tighter than classical bounds.

EE degenerates to MSE at high SNR.

Abstract

In this paper, we employ the thoughts and methodologies of Shannon's information theory to solve the problem of the optimal radar parameter estimation. Based on a general radar system model, the \textit{a posteriori} probability density function of targets' parameters is derived. Range information (RI) and entropy error (EE) are defined to evaluate the performance. It is proved that acquiring 1 bit of the range information is equivalent to reducing estimation deviation by half. The closed-form approximation for the EE is deduced in all signal-to-noise ratio (SNR) regions, which demonstrates that the EE degenerates to the mean square error (MSE) when the SNR is tending to infinity. Parameter estimation theorem is then proved, which claims that the theoretical RI is achievable. The converse claims that there exists no unbiased estimator whose empirical RI is larger than the theoretical RI. Simulation result demonstrates that the theoretical EE is tighter than the commonly used Cram\'er-Rao bound and the ZivZakai bound.