A robust adaptive detector for steering phase uncertainties

This paper deals with adaptive detection of a signal with unknown complex amplitude and whose steering vector presents angle uncertainties. The background environment is assumed homogeneous and Gaussian with unknown covariance matrix. At the design stage, we devise a robust receiver accounting for the aforementioned uncertainty. To this end, we prove that the maximization of the concentrated likelihood function over the phase parameter shares an hidden convexity property. Specifically, exploiting some recent results concerning trigonometric polynomials, we formulate the apparently non-convex maximization over the phase as a Semidefinite Programming (SDP) convex optimization problem. At the analysis stage, we assess the performance of the new receiver in comparison with some classic detectors available in open literature.