Adaptive detection of a signal with angle uncertainty

This study 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, the authors devise a class of robust receivers accounting for the aforementioned uncertainty. To this end, the authors prove that the maximisation of the concentrated likelihood function over the phase parameter shares a hidden convexity property. Specifically, exploiting some recent results concerning trigonometric polynomials, the authors formulate the apparently non-convex maximisation over the phase as a semidefinite programming (SDP) convex optimisation problem. Then, the authors show that the receivers of the class (but for one) exhibit a bounded-constant false alarm rate (bounded-CFAR) behaviour and derive lower and upper bounds for both the false alarm and the detection performance. At the analysis stage, the authors assess the performance of the new receivers in comparison with some classic detectors available in open literature.