Radar Target Detection via Global Optimality Conditions for Binary Quadratic Programming

This article considers the problem of radar target detection in compound Gaussian clutter background. Different from the existing detector design criteria, we propose two new detection schemes for the detection problem from the optimization perspective. Specifically, in the first scheme, the detection problem is firstly studied by introducing an auxiliary variable and transforming it into a maximum likelihood estimation problem. Under this scheme, the maximum likelihood detector and its improved version with parameter estimation are developed by using maximum likelihood criterion. In the second scheme, the detection problem is recast into a binary quadratic programming (BQP) problem. Resorting to the global optimality conditions and solution for the BQP problem, we design four BQP detectors named BQPH, BQPS, BQPM and BQPW with the aid of hard decision fusion, data fusion based on summation and taking median, and whitening respectively. At the analysis stage, the statistical distributions of the BQP detectors are modelled using $t$ location-scale distribution, and the theoretical closed-form expressions of the false alarm probability, thresholds and detection probability of the four BQP detectors are further derived. Finally, simulation experiments on the simulated data and real sea clutter data are performed to highlight the effectiveness of the proposed detectors in comparison with several state-of-the-art detectors.