Theoretical Estimation of Target Detection Probability in Scanning Radar Systems

This paper addresses the problem of estimating target detection probabilities in surveillance radar systems operating with scanning antenna beams. Reliable evaluation of detection characteristics is a key task in radar engineering, since it determines the effectiveness of radar systems in monitoring airspace and detecting moving objects. Traditionally, such characteristics are obtained through large-scale experimental testing involving operational radar systems and numerous real targets. However, these experiments require substantial financial and time resources. Therefore, the development of theoretical and computational methods for estimating detection probabilities is of significant practical importance. The aim of this study is to develop a method for calculating unconditional probabilities of target detection for a surveillance radar system performing periodic scanning of a solid angle using a narrow beam. The research considers the detection of signals reflected from targets with random amplitude and initial phase, which corresponds to realistic radar observation conditions. The proposed methodology is based on radar detection theory and the Neyman – Pearson criterion. At the first stage, the radar energy potential is calculated using the radar equation in order to ensure a specified probability of correct detection under a fixed probability of false alarm. Based on these parameters, conditional detection probabilities are calculated for targets located at different distances within the radar operating range. In the second stage, a method is developed to determine unconditional detection probabilities that account for the cyclic scanning of the radar beam and the motion of the target toward the radar with constant velocity. The target trajectory is divided into small segments corresponding to radar scan cycles, and the cumulative probability of detection is calculated using an iterative probabilistic approach. The proposed method was implemented in computer programs that calculate conditional and unconditional detection probabilities for a wide range of radar parameters. Numerical experiments demonstrate the influence of target velocity and scanning time on detection probability and detection range boundaries. The results show that increasing the target velocity or the radar scanning period significantly reduces the effective detection range. The developed method provides a practical tool for evaluating radar detection performance without conducting expensive field experiments.