The Theoretical Limit of Radar Target Detection

In the field of radar target detection, the false alarm and detection probabilities are used as the universal indicator for detection performance evaluation so far, such as Neyman Person detector. In this paper, inspired by the thoughts of Shannon's information theory, the new system model introducing the target existent state variable v into a general radar system model is established for target detection in the presence of complex white Gaussian noise. The equivalent detection channel and the posterior probability distribution are derived based on the priori statistical characteristic of the noise, target scattering and existent state. The detection performance is measured by the false alarm and detection probabilities and the detection information that is defined as the mutual information between received signal and existent state. The false alarm theorem is proved that false alarm probability is equal to the prior probability of the target existence if the observation interval is large enough and the theorem is the basis for the performance comparison proposed detector with Neyman-Person detector. The sampling a posterior probability detector is proposed, and its performance is measured by the empirical detection information. The target detection theorem is proved that the detection information is the limit of the detection performance, that is, the detection information is achievable and the empirical detection information of any detector is no greater than the detection information. Simulation results verify the correctness of the false alarm and the target detection theorems, and show that the performance of the sampling a posterior probability detector is asymptotically optimal and outperforms other detectors. In addition, the detector is more favorable to detect the dim targets under the detection information than other detectors.