Theoretical Limits of Joint Detection and Estimation for Radar Target

This paper proposes a joint detection and estimation (JDE) scheme based on mutual information for the radar work, whose goal is to choose the true one between target existent and target absence, and to estimate the unknown distance parameter when the target is existent. Inspired by the thoughts of Shannon information theory, the JDE system model is established in the presence of complex white Gaussian noise. We make several main contributions: (1) the equivalent JDE channel and the posterior probability density function are derived based on the priori statistical characteristic of the noise, target scattering and joint target parameter; (2) the performance of the JDE system is measured by the joint entropy deviation and the joint information that is defined as the mutual information between received signal and the joint target parameter; (3) the sampling a posterior probability and cascaded JDEers are proposed, and their performance is measured by the empirical joint entropy deviation the empirical joint information; (4) the joint theorem is proved that the joint information is the available limit of the overall performance, that is, the joint information is available, and the empirical joint information of any JDEer is no greater than the joint information; (5) the cascaded theorem is proved that the sum of empirical detection information and empirical estimation information can approximate the joint information, i.e., the performance limit of cascaded JDEer is available. Simulation results verify the correctness of the joint and the cascaded theorems, and show that the performance of the sampling a posterior probability JDEer is asymptotically optimal. Moreover, the performance of cascaded JDEer can approximate the system performance of JDE system.