The Theoretical Limit of Radar Target Detection

TL;DR

This paper applies Shannon's information theory to establish the theoretical limit of radar target detection, introducing detection information (DI) as a performance measure and proving its achievability.

Contribution

It derives an optimal detection framework using information theory, defining DI as the fundamental limit and proving the target detection theorem.

Findings

Detection information (DI) is an achievable theoretical limit.

Maximum a posteriori and Neyman-Pearson methods are bounded by DI.

Numerical simulations verify the theoretical results.

Abstract

In this paper, we solve the optimal target detection problem employing the thoughts and methodologies of Shannon's information theory. Introducing a target state variable into a general radar system model, an equivalent detection channel is derived, and the a posteriori probability distribution is given accordingly. Detection information (DI) is proposed for measuring system performance, which holds for any specific detection method. Moreover, we provide an analytic expression for the false alarm probability concerning the a priori probability. In particular, for a sufficiently large observation interval, the false alarm probability equals the a priori probability of the existing state. A stochastic detection method, the sampling a posteriori probability, is also proposed. The target detection theorem is proved mathematically, which indicates that DI is an achievable theoretical limit of target detection. Specifically, when empirical DI is gained from the sampling a posteriori detection method approaches the DI, the probability of failed decisions tends to be zero. Conversely, there is no detector whose empirical DI is more than DI. Numerical simulations are performed to verify the correctness of the theorems. The results demonstrate that the maximum a posteriori and the Neyman-Pearson detection methods are upper bounded by the theoretical limit.