Adaptive Detection of Range-Spread Targets With Phase Uncertainty via Semidefinite Programming

Abstract

This article investigates the adaptive detection problem of range-spread targets in Gaussian clutter, where the target complex amplitudes, the steering vectors, and the clutter covariance matrix (CCM) are all unknown. Specifically, the steering vectors exhibit a complex exponential structure with uncertain phase components. Following the two-step generalized likelihood ratio test (GLRT) approach, two adaptive detectors are devised: one is designed to handle the scenarios where the phase is completely unknown, while the other is tailored to accommodate the situations where partial information about the phase is available. By exploiting the fundamental properties of trigonometric polynomials, we reformulate the original nonconvex optimization problem about phase into a computationally tractable semidefinite programming (SDP) framework, facilitating efficient convex optimization. Numerical results demonstrate that the two designed detectors maintain constant false alarm rate (CFAR) properties with respect to the unknown CCM. Compared to the existing one-step SDP-based GLRT detector, the proposed detectors demonstrate superior performance at high signal-to-clutter ratios (SCRs), albeit with some performance degradation in low SCR scenarios. However, as the number of training data increases, the performance advantages of both proposed detectors become increasingly pronounced relative to the existing detectors.